Optical gratings induced by field-free alignment of molecules
光纤光学英文文献3
All-optical dynamic grating generation based on Brillouin scattering in polarization-maintainingfiberKwang Yong Song,1,*Weiwen Zou,2Zuyuan He,2and Kazuo Hotate21Department of Physics,Chung-Ang University,Seoul,Korea2Department of Electronic Engineering,The University of Tokyo,Tokyo,Japan*Corresponding author:songky@cau.ac.krReceived January30,2008;revised March20,2008;accepted March20,2008;posted March25,2008(Doc.ID92171);published April22,2008We report a novel kind of all-optical dynamic grating based on Brillouin scattering in a polarization main-tainingfiber(PMF).A moving acoustic grating is generated by stimulated Brillouin scattering between writ-ing beams in one polarization and used to reflect an orthogonally polarized reading beam at different wave-lengths.The center wavelength of the grating is controllable by detuning the writing beams,and the3dBbandwidth ofϳ80MHz is observed with the tunable reflectance of up to4%in a30m PMF.©2008OpticalSociety of AmericaOCIS codes:050.2770,060.2310,190.4370,290.5900.A high-speed and reconfigurable dynamic grating canbe used as a powerful tool in communication or sen-sor applications as a tunable opticalfilter,an opticalswitch,and a distributed sensor[1–4].The currentlyavailable scheme is to build up a gain or absorptiongrating in an Er-dopedfiber(EDF)by counterpropa-gating optical waves with the same optical frequency.However,such an EDF-based dynamic grating suf-fers a couple of significant problems,such as diffi-culty in separating the writing and reading beams[1,2]or an amplified spontaneous emission(ASE)noise due to optical pumping[3,4],which can givedisadvantages in practical applications.In this Letter,we demonstrate a novel kind of dy-namic grating based on stimulated Brillouin scatter-ing(SBS)in a polarization-maintainingfiber(PMF).An acoustic phonon generated by SBS between twocounterpropagating writing beams of one polariza-tion is used as a tunable and dynamic grating for theorthogonally polarized reading beam at differentwavelengths satisfying the phase-matching condi-tion.The reflected probe wave experiences an ordi-nary Brillouin shift by the Doppler effect,and the op-tical frequency difference between the writing andthe reading beams is determined by the birefringenceof the PMF.The basic theory,the operation principle,and the experimental configuration are described,and the results are explained using a simplifiedtheory of Brillouin scattering.SBS is generally modeled as a three-wave interac-tion between the pump͑1͒,Stokes͑2͒,and acousticwaves.When a phase-matching condition is satisfied(1−2=B,B being the Brillouin frequency),strongenergy transfer from the pump to the counterpropa-gating Stokes wave takes place generating acousticwaves,which stimulates the process.TheB is givenby following equation[5]:B=2nV a,͑1͒where n,V a,andare the refractive index,the veloc-ity of the acoustic wave,and the optical wavelength,respectively.In a PMF(or any medium with birefrin-gence),optical waves with two principal polarizations(i.e.,x and y polarization)experience differentB’sowing to their different refractive indexes.Consider-ing that the acoustic wave generated by SBS is a lon-gitudinal one that is free of the transversal polariza-tion[6],an interesting condition can be reached thatthe x-and the y-polarized optical waves in a PMFshow the sameB at different wavelengths.When thedispersion of the acoustic wave is ignored,the condi-tion is expressed by following equations:2n x V ax=2n y V ay,͑2͒n xx=n yy,͑3͒where n x,y andx,y(if n xϾn y,yϾx)are the refrac-tive indexes and the optical frequencies in x and y po-larizations,respectively.With⌬n=͑n x−n y͒ 1and⌬=y−x (x ory),Eq.(3)is simplified to⌬=⌬nn.͑4͒Since the SBS-induced acoustic waves can beviewed as moving gratings for the reflection of thepump wave without polarization dependence,it is ex-pected that acoustic waves generated by SBS be-tween the x-polarized pump and Stokes waves at theoptical frequencyx will show strong reflectance tothe y-polarized pump wave at the frequency ofx+⌬.Considering that the intensity and the wave-length of the acoustic waves are easily tuned by con-trolling the x-polarized“writing”beams,one may ex-pect the SBS in a PMF to play a role of a tunabledynamic grating.We composed an experimental setup,as shown inFig.1.For the writing of the dynamic grating,a926OPTICS LETTERS/Vol.33,No.9/May1,20080146-9592/08/090926-3/$15.00©2008Optical Society of America1550nm laser diode was used as a light source,and the output power was divided by a 50/50coupler.A single-sideband modulator (SSBM)and a microwave synthesizer were used to generate the Stokes wave (pump2)of the writing beams,and the output was amplified and polarized by an EDF amplifier (EDFA)and an x polarizer.The Brillouin pump wave (pump1)of the writing beams was prepared by amplifying the original wave with the same polarization as that of pump2.Pump1and the pump2were launched into a PMF in opposite direction to each other through po-larization beam combiners (PBC1,PBC2).The PMF was a PANDA fiber manufactured by Fujikura with a 30m length and a nominal ⌬n ϳ6.2ϫ10−4at the wavelength of 1300nm.For a reading beam (probe),a tunable laser with an operating wavelength near 1550nm was used as a light source after being polar-ized in the y axis.The output was launched into the PMF in the direction of the pump1through a polarization-maintaining circulator and PBC1.The transmitted power of the probe was measured using a power meter,and the backreflected spectrum was monitored using an optical spectrum analyzer (OSA)through a y polarizer.At first,we measured the Brillouin gain spectra of the PMF in the x and y axes.The B in the x axis was measured to be 10.502GHz,and the difference of the B ’s of two polarizations was ϳ3.6MHz,as depicted in the inset of Fig.1,which corresponds to ⌬n ϳ5.0ϫ10−4by Eq.(1).To induce the SBS in the x axis,we launched pump1and the pump2in the x axis with the output powers of 630and 10mW,respectively,setting their frequency offset ͑⌬f ͒to 10.502GHz.For the detection of the dynamic grating,the fre-quency of the probe was tuned at the higher fre-quency region while monitoring the spectrum with the OSA,and the result is shown in Fig.2.When ⌬(the frequency difference between pump1and the probe)was ϳ72.6GHz,a large reflection of the probe was observed (black curve)as a result of the dynamic grating at the frequency detuned from the probe by the same amount as that between pump1and pump2.When one of the pumps (pump1)was turned off,the dynamic grating disappeared as depicted by the gray curve although the probe was still propa-gated as confirmed by the Rayleigh scattering seen at the probe frequency.In both cases,the x -polarizedpumps were observed in spite of the use of the y po-larizer in front of the OSA,which originated from the finite extinction ratio ͑ϳ20dB ͒of the polarizing com-ponents.The small peaks near pump1correspond to the first-and second-order anti-Stokes waves that were suppressed in the SSBM used for the genera-tion of pump2.Figure 3(a)shows the reflectance of the dynamic grating with respect to ⌬,calculated from the ratio of the input and the reflected powers of the probe,while the pump powers were maintained to the same as the first measurement.The maximum reflectance was ϳ4%,and the 3dB width was ϳ80MHz.The overall shape looks asymmetric,which could be at-tributed to the irregularity of the local birefringence in the PMF.We fixed ⌬to 72.6GHz and swept ⌬f ,the fre-quency offset between pump1and pump2.The result is depicted in Fig.3(b),which fits well with a Lorent-zian curve with a 3dB width of 28MHz,similar to the ordinary Brillouin gain spectrum of the fiber.The dependence of the grating reflectance on the pump powers was measured by varying one of the pump powers with the other fixed,while ⌬was kept at 72.6GHz.Figures 4(a)and 4(b)show the reflec-tance of the grating as a function of the power of pump1and pump2,respectively.It is remarkable that the reflectance grows in an exponential form to some definite value with the power of pump1asFig. 1.Experimental setup:LD,laser diode;SSBM,single-sideband modulator;EDFA,Er-doped fiber ampli-fier;PBC,polarization beam combiner;OSA,optical spec-trum analyzer.The inset is the Brillouin gain spectra of the fiber under test in x and ypolarizations.Fig.2.Optical spectra monitored by an OSA in the gen-eration of dynamic grating.The gray curve corresponds to the case that one (pump1)of the writing beams is turned off,and the black curve with both writing beams turnedon.Fig.3.(Color online)(a)Reflectance of the dynamic grat-ing as a function of ⌬,the frequency difference between the pump1and the probe.(b)Reflectance of the dynamic grating at a fixed ⌬͑72.6GHz ͒as a function of the ⌬f ,the frequency offset between pump1and pump2.The curve shows the result of a Lorentzian fit.May 1,2008/Vol.33,No.9/OPTICS LETTERS 927shown in Fig.4(a),while it is linearly dependent on the power of pump2as depicted in Fig.4(b),where the result matches well with a linear fit with the slope of 3.8ϫ10−4͑/mW ͒.The slight inconsistency in the reflectance values of Figs.4(a)and 4(b)came from long-term drift of the optical frequencies of the pump and the probe lasers,whose effect was negli-gible in each measurement.The difference in dependence of the grating reflec-tance on the pump powers can be explained by the re-lation of the Brillouin gain and the reflectance.In the generation of the dynamic grating,the increased power of pump2through the gain of the SBS can be viewed as the reflection of pump1.Additionally,we may assume that pump1and the probe experience al-most the same reflectance,since they share the same acoustic grating.Therefore,if the pump depletion is ignored (i.e.,small reflection of pump1),the reflec-tance of the dynamic grating R can be estimated from the gain of the SBS [5]as follows:R =P probe out P probein Ϸ⌬P 2P 1=P 2͑e ͑g B P 1L eff /A eff ͒−1͒P 1,͑5͒where g B ,L eff ,A eff ,P 1,and P 2are the Brillouin gain coefficient,the effective length of the fiber,the mode effective area,the power of pump1,and the power of pump2,respectively.In Eq.(5),one can see that the reflectance of the grating linearly depends on P 2,and the reflectance will grow in an exponential form ac-cording to P 1if the gain is large enough.The final point in Fig.4(a)with pump1of 800mW looks devi-ated from the form of the exponential growth,which could be attributed to the gain saturation with the pump depletion due to too large amplification of pump2.The reflectance offset appearing in the lin-early fitted graph of Fig.4(b)can be attributed to the amplification of the SBS noise induced by the strong pump1.We think detailed properties of the grating can be explained by coupled wave equations (by five-wave mixing instead of the three-wave one in the ordinary case of the SBS),and there could be more factors that have an effect on the grating reflectance such as the probe power.Further research is needed on this point.The relation between the optical frequencies of pump1and the probe under the condition of the dy-namic grating generation is depicted in Fig.5,which shows good linearity as expected from Eq.(3).In the measurement,the powers of the pumps and the probe were kept constant,and the variation of B was negligible ͑Ͻ1MHz ͒.In conclusion,we have demonstrated a novel all-optical dynamic grating based on stimulated Bril-louin scattering in a polarization-maintaining fiber.The center frequency of the grating was ϳ72.6GHz detuned from the writing beam frequency,and the re-flectance as well as the peak frequency could be tuned by controlling the power and the frequency of the writing beam.Considering the high sensitivity of the dynamic grating to local birefringence [see Eq.(4)]as well as the high on–off extinction ratio ͑Ͼ60dB ͒,the spectral flexibility [7],and the short re-sponse time ͑ϳ10ns ͒[5]of the SBS,we believe the SBS-based dynamic grating has large potential for practical applications such as an all-optical switch and a highly sensitive fiber sensor.The authors are grateful to Luc Thévenaz from EPFL in Lausanne,Switzerland,for his contribution to the development of the idea.This work was sup-ported by the “Grant-in-Aid for Creative Scientific Research”and the “Global Center of Excellence Pro-gram”from the Ministry of Education,Culture,Sports,Science and Technology,Japan.K.Y.Song was supported by the Korea Research Foundation Grant funded by the Korean Government (MOE-HRD)(KRF-2007-331-C00116).References1.S.J.Frisken,Opt.Lett.17,1776(1992).2.B.Fischer,J.L.Zyskind,J.W.Sulhoff,and D.J.DiGiovanni,Opt.Lett.18,2108(1993).3.X.Fan,Z.He,Y.Mizuno,and K.Hotate,Opt.Express 13,5756(2005).4.X.Fan,Z.He,and K.Hotate,Opt.Express 14,556(2006).5.G.P .Agrawal,Nonlinear Fiber Optics ,2nd ed.(Academic,1995).6.W.Zou,Z.He,and K.Hotate,IEEE Photon.Technol.Lett.18,2487(2006).7.M.González Herráez,K.Y.Song,and L.Thávenaz,Opt.Express 14,1395(2006).Fig.5.(Color online)Optical frequency of the probe as a function of the frequency of pump1under the condition of the dynamic grating generation.The line is the result of a linearfit.Fig.4.(Color online)Reflectance of the dynamic grating as a function of pump power in the case of (a)pump1varied and pump2fixed to 10mW,and (b)pump2varied and pump1fixed to 200mW.The line is the result of a linear fit.928OPTICS LETTERS /Vol.33,No.9/May 1,2008。
分布式布拉格反射镜结构
分布式布拉格反射镜结构简介分布式布拉格反射镜结构（Distributed Bragg Reflector, DBR）是一种用于光学器件中的重要结构。
它由多个周期性层组成，具有优异的光学性能，广泛应用于激光器、光纤通信和光电子器件等领域。
本文将详细介绍分布式布拉格反射镜结构的原理、制备方法和应用。
原理分布式布拉格反射镜结构借助布拉格散射原理实现高反射率和波长选择性。
布拉格散射是当电磁波（光波）与周期性介质相互作用时，由于介质的周期性结构会对电磁波产生散射，从而形成反射现象。
该现象是由于波长等于介质周期的倍数时，散射波的相位受到干涉增强而形成明显的峰值。
基于这个原理，分布式布拉格反射镜结构通过设计周期性层和层间折射率来实现特定波长的反射。
制备方法光子晶体法光子晶体法是一种制备分布式布拉格反射镜结构的常见方法。
该方法利用介电材料或金属导体的周期性结构，通过光子晶体的光学带隙原理实现波长的选择性反射。
制备过程包括以下步骤：1.设计布拉格反射光子晶体的周期性层和层间折射率。
2.选择适当的材料，并通过溶液法、电镀法或物理气相沉积法（PECVD）等制备周期性层。
3.利用自组装技术或纳米制备技术，在基底上形成周期性结构。
4.通过检测反射光谱，对制备的分布式布拉格反射镜结构进行表征和优化。
分子束外延法分子束外延法是另一种常用的制备分布式布拉格反射镜结构的方法。
该方法通过分子束外延技术在单晶基底上逐层生长材料，制备周期性层。
制备过程包括以下步骤：1.准备适当的基底和衬底。
2.设置分子束外延设备，并控制扩散源的温度和功率。
3.通过打开和关闭单层或多层源，逐层生长材料，形成周期性结构。
4.利用光谱仪等工具对制备的样品进行表征和优化。
应用分布式布拉格反射镜结构在光学器件中有着广泛的应用。
激光器分布式布拉格反射镜结构在激光器中作为输出镜，能够实现高反射率和波长选择性。
通过调整周期性层的厚度和折射率，可以实现对特定波长的高度选择性反射，从而提高激光器的效率和性能。
透射光栅和反射光栅对比-英文
Comparison of a transmission grating spectrometer to a reflective grating spectrometer for standoff laser-induced breakdown spectroscopymeasurementsArel Weisberg,1,*Joseph Craparo,1Robert De Saro,1and Romuald Pawluczyk2 1Energy Research Company,2571-A Arthur Kill Road,Staten Island,New York10309,USA 2P&P Optica,330Gage Avenue,Suite11,Kitchener,Ontario N2M5C6,Canada*Corresponding author:aweisberg@er‑Received7October2009;revised3March2010;accepted12March2010;posted15March2010(Doc.ID118281);published30March2010We evaluate a new transmission grating spectrometer for standoff laser-induced breakdown spectroscopy(LIBS)measurements.LIBS spectra collected from standoff distances are often weak,with smaller peaksblending into the background and noise.Scattered light inside the spectrometer can also contribute topoor signal-to-background and signal-to-noise ratios for smaller emission peaks.Further,collectingstandoff spectra can be difficult because most spectrometers are designed for laboratory environmentsand not for measurements in the field.To address these issues,a custom-designed small,lightweighttransmission grating spectrometer with no moving parts was built that is well suited for standoff LIBSfield measurements.The performance of the spectrometer was quantified through10m standoff LIBSmeasurements collected from aluminum alloy samples and measurements from spectra of a Hg–Ar lamp.The measurements were compared to those collected using a Czerny–Turner reflective grating spec-trometer that covered a similar spectral range and used the same ICCD camera.Measurements usingthe transmission grating spectrometer had a363%improved signal-to-noise ratio when measuredusing the669nm aluminum emission peak.©2010Optical Society of AmericaOCIS codes:050.0050,120.6200,230.1950,280.3420,300.6365.1.IntroductionLaser-induced breakdown spectroscopy(LIBS)has a set of unique strengths that make it well suited for standoff measurement applications,where the sens-ing device is some distance removed from the target material.This is because LIBS measurements re-quire no sample preparation,and the laser pulses and plasma emissions are readily delivered and col-lected via telescopic optics.A number of standoff LIBS instruments have been built,as described in a recent review[1].Applications in the scientific literature for standoff LIBS include material inspection in the metals industries[2],measurements of radioactive materials in the nuclear power industry[3],detection of residues of explosive compounds[4],and cleaning of sculpture and other cultural objects[5].Many of the described applications would benefit from improved throughput and sensitivity of the in-strument.Improved throughput and sensitivity can result in detection of an increased number of ele-ments,lower limits of detection,greater standoff range,and improved precision.For example,in the area of explosive residue detection,the value of a standoff LIBS instrument is directly tied to the smal-lest trace residues it can detect at a given standoff distance,as this will afford the user the greatest mar-gin of safety in the field.Operating LIBS instruments in the field also pre-sents its own unique challenges.Many of the lasers,0003-6935/10/13C200-11$15.00/0spectrometers,optics,and optomechanical compo-nents used in laboratory LIBS instruments are ill suited to field operation due to several factors.First, environmental conditions of temperature,humidity, vibrations,and dust can swing to extremes in the field.Second,robustness is of primary importance because making adjustments and repairs to equip-ment in the field is impractical.Also,the instrument will likely need to be shipped to the location where it will operate,so it must be rugged enough to survive the trip intact.Third,packaging constraints,such as the size and weight of individual components,may dictate limitations on the instrument design.This would be especially true for a standoff LIBS instru-ment that must be transported manually for some distance.In particular,a great deal of potential exists for im-proving the spectrometer systems used in standoff LIBS instruments.This is because most of the spec-trometers described in the applications in[1]are simply laboratory models taken out to the field. Generally,these spectrometers do not adequately meet the operational challenges listed above,which limits the LIBS systems’overall usability and perfor-mance envelope.Furthermore,inherent limitations in optical de-signs of these spectrometers limit their performance. LIBS spectrometer systems are generally of either the Czerny–Turner or echelle configuration[6],as well as some reported Paschen–Runge designs[7].All these configurations generate diffraction patterns by re-flecting light off ruled or etched holographic gratings. These gratings have certain general characteristics that limit the overall system performance.First,their efficiency is usually a strong function of wavelength, diminishing with wavelengths departing from the blaze wavelength.This directly impacts the through-put of the spectrometer,reducing the overall sensitiv-ity and precision and raising the limits of detection for some elements.Second,light throughput generally varies inversely with resolution.Therefore,achieving high-resolution LIBS spectra generally involves the trade-off of diminished throughput.Third,because the reflecting gratings diffract light back along the op-tical path,the potential for stray light to reach the de-tector is increased.Higher levels of stray light reduce signal-to-background levels in LIBS spectra,which results in lower sensitivity and higher limits of detection.We describe here a new LIBS spectrometer that has significant performance advantages over typical spectrometers used for standoff LIBS,both in terms of analytical performance and performance in the field.This spectrometer is based on a transmission grating rather than the more typical reflective grat-ing.Further,rather than a ruled grating,the grating is a volume phase holographic design that further re-duces stray light because it has no ruled ing this type of grating allows for a spectrometer that achieves greater light throughput,higher resolution,package with no moving parts.While other compar-isons between spectrometers[8]and detectors[9–11] for LIBS applications have been reported,there have not been,to our knowledge,any studies on the merits of spectrometer designs based on different grating technologies while using the same detector with both spectrometer systems.This important equalizing factor allows for a more straightforward comparison between the systems.2.Volume Phase Holographic GratingsThe heart of the P&P Optica spectrometers is a vo-lume phase holographic(VPH)diffraction gel grating. Gel gratings work on a different principle from tradi-tional relief reflecting gratings.The manufacturing process of a gel grating begins when a layer of gel or polymer that is able to change refractive index un-der the influence of light is exposed to an optical beam whose intensity periodically changes.After proces-sing,the exposed layer is sandwiched between two transparent plates.The entire assembly then acts as a diffraction grating.For comparison,traditional gratings are usually produced as a result of a highly disruptive mechanical or chemical process,which produces periodic grooves with microscopic cracks on the surface.Efficiency of the grating depends on the profile of the grooves, while microcracks are responsible for severe light scattering.Transmission gel gratings do not have pro-blems with light scattering microcracks.Further-more,the diffracted light propagates at an angle in relation to the transmitted beam;hence,they can be used in optimal working conditions.The result is a more efficient use of available light and dramati-cally lowered scattered light levels.Figure1provides a comparison of efficiency values for a typicalspectral Fig.1.Absolute and average diffraction efficiency(AE)of P&P Optica’s600l=mm gel VPH grating at9°of incidence in compar-ison with holographic relief reflection grating(HRG)and diamond ruled reflective grating(RRG).The AE of the gel grating is mea-sured for a dispersive nonscanning configuration used in all P&P Optica Inc.spectrometers,while the efficiency of the other two gratings is measured under impractical Littrow conditions,as re-ported in the manufacturer’s catalog,corrected to representrange covering a full octave for VPH and ruled gratings.There is a great misunderstanding regarding the measurement of grating performance,including effi-ciency.First,the grating efficiencies of traditional re-flecting gratings provided in catalogs are measured in relation to the intensity of the beam reflected from a mirror coated with the same material used for coat-ing the grating(typically an aluminum layer with a reflectivity of about90%);hence,the absolute diffrac-tion efficiency is about8%–12%lower than that provided in catalogs.Second,for a given grating fre-quency,the efficiency depends on both the angle of incidence of the incoming beam and the groove pro-file of the grating.It is well known that the highest efficiency can be achieved for grating grooves is with a sawtooth profile with a90°angle at the top of the tooth.The efficiency of such gratings is optimized at a particular“blaze”wavelength when the incident beam intersects the grating at a particular“blaze an-gle”such that the diffracted beam propagates in a direction opposite to the incident beam.The efficien-cies at wavelengths other than the blaze wavelength are lower,but can be slightly increased by rotating the grating such that the diffracted beam is back in the direction of the incident beam[12–14].The reported efficiencies for reflective gratings are measured at this optimum incoming beam angle for each individual wavelength(i.e.,the grating is physically rotated between each measurement to op-timize performance).This is commonly referred to as the“Littrow”configuration.While this configuration is optimal from an efficiency point of view,it is im-practical because it can lead to interferences between the delivery and the collection optics.For this reason, typical reflective grating spectrometers(such as the Czerny–Turner system)normally use a single detec-tor and a rotating grating to register one spectral component under the best possible conditions for the chosen geometry.In most LIBS applications,it is impractical to scan every wavelength across a fixed detector.Instead,for a single LIBS measurement,the grating is held in a fixed position and the light is dispersed over an array of detectors(typically the pixels of an ICCD camera). In this case,the efficiency of a reflective grating sys-tem is significantly reduced at those wavelengths that are oriented away from their optimal angle with respect to the incoming light.In some cases,the aver-age absolute efficiency of gratings in spectrometers operating under real conditions can be as low as 10%–20%even though the reported efficiencies are high as measured in the Littrow configuration. Many of the deficiencies of reflective grating spec-trometers can be eliminated by replacing the reflec-tive grating with a transmission VPH diffraction grating and using lenses,rather than focusing mir-rors,to form both the incident and the diffracted beams.In contrast to reflective gratings,VPH grat-ings are most efficient when the diffracted beam pro-in line with,the nondiffracted part of the beam trans-mitted through the grating.This eliminates interfer-ence between the optical systems forming the incident and diffracted beams,allowing VPH grat-ings to be practically implemented in the orientation of maximum efficiency.An additional advantage is that there is less nondiffracted light,which normally contributes to the scattered light background.Appli-cation of lenses in place of mirrors,while potentially reducing the usable spectral range,allows for the construction of more compact spectrometers with better optical performance over larger detector areas,better f-numbers,and higher-quality imaging for longer slits.The increase in grating efficiency has a twofold ef-fect on the performance of a spectrometer system. First,a larger percentage of the incoming light reaches the detector,resulting in an increase in re-corded signal.Second,the number of photons enter-ing the system that do not directly impinge on the detector is reduced.This is important because these stray photons can reach the detector indirectly through multiple reflections resulting in scattered light noise.Typically,the ratio of signal to stray light is of the order of15times greater for a VPH grating than for a similar reflective grating,as shown in Fig.2. The result is a significant increase in photometric dy-namic range.3.ApparatusA.SpectrometersThe spectrometer system used to compare to the P&P Optica Inc.transmission grating spectrometer is an Acton300i Czerny–Turner system(Princeton Instru-ments,Trenton,New Jersey)with a150grooves=mm Fig.2.(Color online)Discharge from a He–Ne laser measured using Czerny–Turner and VPH spectrometers under identical con-ditions with dark signal subtracted.Background levels are propor-tional to stray light,seen here to be approximately150times lower for the VPH system.The graphs are not offset from their actualgrating blazed at 500nm and coupled to a Princeton Instruments PI-Max intensified CCD camera (1024×256pixel CCD array,25mm Gen II intensifier).The grating was mounted to a rotating turret that enables scanning across multiple wavelength ranges.The po-sition of the grating was fixed in this work such that the measured wavelength range was centered at 550nm.A photograph of the system is seen in Fig.3.This system is typical of many described in the LIBS literature,being a fairly compact and flexible design with a fiber optic cable attached to the input slit.The P&P Optica VPH transmission grating spec-trometer system coupled to the same PI-Max ICCD camera is shown in Fig.4.The compact form factor of the spectrometer is evident.A comparison of the spe-cifications of the two systems is seen in Table 1.The laser used for the LIBS experiments was a Quantel USA (Bozeman,Montana,formerly Big Sky Laser)CFR-400Nd:YAG Q -switched laser oper-ating at 1064nm.The laser outputs 330mJ =pulse in ∼7ns pulses,and it was operated in single-shot mode.The laser pulses were delivered to the aluminum alloy targets via a straightforward beam expansion and collimating optical arrangement followed by a Galilean telescope,with a ϕ25mm plano –concave lens and a ϕ50mm plano –convex lens,which,when combined,resulted in a 10m focal length for the telescope.The lenses were antireflection coated for 1064nm.The light from the LIBS plasma was collected with a ϕ200mm,f =4:9,f ¼1000mm,Newtonian tele-scope (SkyView Pro 8)from Orion Telescopes (Watsonville,California)that was modified by repla-cing the viewing eyepiece with a fiber optic cable SMA-905connector.A photograph of the modified telescope is seen in Fig.5,and a view down the barrel of the telescope toward the target samples placed 10m away is shown in Fig.6.A 2m long,600μm core,fiber optic cable was attached to the telescope.The mercury lamp used in some of the experiments was an Ocean Optics (Dunedin,Florida)CAL-2000mercury –argon wavelength calibration source with an SMA-905fiber optic cable connector.The input ends of the fiber optic cables attached to the spectro-meter systems are also fitted with SMA-905connectors.4.SamplesSix different Standard Reference Material (SRM)aluminum alloy samples were used as targets in this study.These SRMs were obtained from Brammer Standard (Houston,Texas).They are in theshapeFig.3.Acton Research 300i Czerny –Turner spectrometer system with PI-Max ICCD Camera and f -number matching fiber optic cable adapter attached.A 30cm ruler is also shown forscale.Fig. 4.P&P Optica transmission grating spectrometer and PI-Max ICCD camera.A 30cm ruler is also shown for scale.Table 1.Comparison of Specifications of Transmission Grating and Czerny –Turner Spectrometer Systems when Coupled to the PI-Max ICCDCamera Used in the ExperimentsP&P Optica Transmission GratingSpectrometerActon 300i Czerny –Turner Spectrometer Spectral range 366–796nm (Δλtotal ¼430nm)266–831nm (Δλtotal ¼565nm)f =#34Entrance slitNone —uses fiber optic bundle for 37μm ×6:6mm effective slit52μm ×1mmOptical fiber cross-section specifications68×50μm fibers arranged in a ϕ600μm circular bundle at the input end and in a vertical line at the spectrometer end 19×200μm fibers arranged in a ϕ1mm circular bundle at the input side and in a vertical line at the spectrometer end Optical fiber length1:5m 3:0m Fiber optic cable f -number matching moduleNoYesof approximately ϕ25–50mm disks.The concentra-tions of the elements examined in the tests reported below are given in Table 2.These alloys were selected to achieve a range of concentration values for each of these elements.5.Experimental Procedure A.Mercury Lamp TestsA mercury –argon line source,described in Section 3,was attached to each spectrometer via a simple col-limating and focusing optical design shown schema-tically in Fig.7.The positions of the fibers relative to the lenses were optimized for maximum throughput.The neutral density filter was needed to avoid satur-ating the ICCD detector.A procedure was also devel-oped that minimized the effects of attaching and removing the fiber optic cables from the optical assembly .Fifty mercury lamp spectra were collected with each spectrometer system using a temporal window of 5ms and an intensifier gain setting of zero.Dark spectra were also collected and automatically subtracted from the mercury lamp spectra by the software supplied by Princeton Instruments (Win-Spec).The resulting corrected spectra were averaged together.Repeatability was checked by collecting 25accu-mulations of 25spectra each,detaching the fibers from the optical assembly between each ing the 435and 579nm Hg emission lines,we measured a relative standard deviation (RSD)of 0.61%in the amplitudes of these lines in the set of spectral accumulations using the transmission grating spectrometer.B.Laser-Induced Breakdown Spectroscopy TestsThe SRM alloy samples were cleaned with acetone,followed by methyl alcohol,followed by isopropanol,prior to testing.The samples were then placed 10m from the telescope (Fig.6)and oriented vertically so that their surface was normal to the laser pulses.Fifty LIBS spectra were collected from each sam-ple by first applying 50laser shots (i.e.,“cleaning shots ”)to the same spot on the sample,followed by an analysis shot when the LIBS spectrum was re-corded.The sample was then rotated slightly for collecting the next spectrum from a new spot.The temporal settings for the ICCD camera relative to the laser shot were a delay of 3μs and a width of 1μs.The gain setting on the camera was 120(out of 255)for the transmission spectrometer and 160for the reflective grating spectrometer so that the peaks would be of roughly the same amplitude.The different gain setting amounts to an increase in absolute intensities (i.e.,counts)by a factor of 3.2and an increase in the RSD of the intensities by a factor of 1.3.These factors were taken into ac-count in the reported data.A PrincetonInstrumentsFig.5.Telescope used to collect the LIBS plasmalight.Fig.6.View from the Newtonian telescope used to collect the LIBS plasma light looking toward the target samples.Table 2.Concentrations of Elements in the Aluminum Alloy Standards Used in TestingStandard Cu (wt.%)Fe (wt.%)Mg (wt.%)Mn (wt.%)HG-40.0950.120.310.39HP-10.480.7220.11HP-2 1.50.5 1.250.25HP-33.520.220.790.42NCSHS53703-40.0330.350.040.055NCSHS53703-50.0791.310.1030.112programmable delay generator,Model ST133A,was used to control the laser –camera timing via the system ’s software package.Dark spectra were also collected with the same camera settings and automa-tically subtracted from the LIBS spectra.The fiber optic cable attached to the LIBS tele-scope (Fig.5)was connected to the fiber optic cables on the spectrometers via a simple SMA-905mating sleeve.This sleeve positions the ends of the two fiber optic cables up against each other to maximize the transmission of light from one fiber to the other.C.Data ComparisonThe procedure for the comparison between the two spectrometer systems was designed to compensate for the different system specifications that are unre-lated to the fundamental strengths and weaknesses of each system.The foremost example of this was the use of the same intensified CCD camera with both spectrometer systems.We also compensated for the difference in wavelength range between the grat-ings (Table 1).This is obviously a function of the par-ticular gratings and is unrelated to any benefits or drawbacks of the respective system optical config-urations.Therefore,the analysis presented below accounts for this difference.For the purpose of comparing the two systems,we did not attempt to compensate for the differences in how the optical fibers couple to their respective spec-trometer units.Each system ’s design has advantages and disadvantages in their fiber coupling method.The advantages of the P&P unit are the lack of an entrance slit and the low f -number of the unit (f =3).The advantages of the Acton unit are its fiber optic f -number matcher and the higher fill factor of its fiber optic cable bundle (the ratio of the total cross-sectional area of all the optical fibers in the bundle to the area of the front face of the fiber tip)as compared to the P&P unit (76%versus 47%).Given the difficulty in modeling and accounting for these differences accurately ,and the fact that the re-spectrometer units during the tests,the comparison presented here will consider the fiber optic cable as an integral part of the spectrometer unit.To compensate for the different spectral ranges of the spectrometers,the intensities of the spectra col-lected by the two units were normalized into counts/nanometer units.The spectral resolutions of the systems are reported in camera pixels rather than nanometers for this reason as well.6.ResultsA.Mercury Lamp TestsA comparison of the measured 435:8nm mercury emission peak for the reflective and transmissive grating spectrometers is presented in Fig.8and on a logarithmic scale in Fig.9.This clearly shows the throughput enhancement achieved by the transmis-sion grating spectrometer.The noise level for the re-flective spectrometer is approximately 13counts =nm ,while for the transmission spectrometer it is approxi-mately 20counts =nm .The peak areas by comparison are 5016and 11,091counts,resulting in signal-to-noise ratios of 394and 568for the reflective and transmission spectrometers,respectively .This is one example of the superior throughput and stray light minimization of the transmission grating spectrometer.Thesuperiorresolutionofthetransmissiondesignis demonstrated by the comparison of peak-normalized signals from the Hg 435:8nm emission line seen in Fig.10.The full width at half-maximum (FWHM)of the peak from the transmission spectrometer is mea-sured to be 2.37pixels,while the FWHM of the peak from the reflection spectrometer is 3.33pixels,or al-most 1pixel wider.The corresponding values for the 546:1nm Hg emission line are 2.67and 3.34pixels for the transmission and reflection grating spectro-meters,respectively .This indicates that theresolutionFig.7.(Color online)Schematic diagram of optical coupling arrangement for the mercurylamp.Fig.8.(Color online)Comparison of signals from the Hg 435:8nm emission line.Solid curve,transmission grating spectrometer;advantage of the transmission grating spectrometer persists across the wavelength range.The peak amplitudes,baseline,and noise levels of a number of Hg emission peaks were measured in all 50of the Hg spectra collected with each spectro-meter.The baseline was calculated as the average in-tensity of two 10nm wide regions on either side of the respective emission peak,and the noise level was calculated as the standard deviation of the intensity values in these two regions.The results are summar-ized in Table 3.In the table,throughput is measured as the peak area (baseline subtracted),the signal-to-background ratio is the peak area divided by the baseline value,and the signal-to-noise ratio is the peak area divided by the noise level.The repeatabil-ity was measured as the standard deviation of the peak heights over the 50Hg spectra divided by the mean amplitude value of the peak.The values in Table 3demonstrate how the perfor-mance advantage of the transmission grating spec-trometer as compared to the reflective grating spectrometer increases across the wavelength range.The signal-to-noise ratio improvement increasing from 6%to 130%highlights this trend especiallywell.This finding is in line with the general charac-teristic of reflection gratings that their efficiency is a strong function of wavelength.B.Laser-Induced Breakdown Spectroscopy TestsThe LIBS experiments were designed to highlight as-pects of spectrometer performance that are of most importance to standoff LIBS applications:through-put and limits of detection.Limits of detection are not only dependent upon how many of the incoming photons reach the detector (i.e.,efficiency),but are also dependent upon the level of scattered light.Since we used the same ICCD camera with both spec-trometers in these experiments,scattered light will be the dominant source of differences in the back-ground intensity levels.Spectral resolution was not evaluated using the LIBS spectra because,typically ,only a fraction of a LIBS spectral line ’s width is due to instrument broadening.LIBS spectral lines are often modeled as Voigt profiles,which are a convolution of a Lorent-zian profile primarily due to the Stark effect,and a Gaussian profile,which is due to a combination of instrument broadening and DopplerbroadeningFig.9.(Color online)Comparison of signals from the Hg 435:8nm emission line on a logarithmic scale.Solid curve,transmission grating spectrometer;dotted curve,reflective grating spectro-meter.Fig.10.(Color online)Comparison of normalized emissions from the Hg 435:8nm line.Solid circles,transmission spectrometer;open squares,reflective spectrometer.Table 3.Improvement of Transmission Spectrometer over Reflection Spectrometer as Measured by Three Hg Emission LinesHg 404:7nmHg 435:8nmHg 546:1nm Refl.Trans.Adv .a Refl.Trans.Adv .Refl.Trans.Adv .Throughput b1817307269%501611091121%350315377339%Signal/background c 647212%1781802%161374133%Signal/noise d 1351436%39456844%296679130%Repeatability e0.0730.04340%f0.0420.02639%0.0570.02066%a Adv .,transmission system advantage ¼ðtransmission value-reflection value)/reflection value.bIntegrated peak area in counts.cPeak area/mean background as described in text.dPeak area/mean noise as described in text.eRelative standard deviation (σ=μ)of peak amplitude over the 50collected spectra.[15].Therefore,quantitatively determining the in-strument broadening from a LIBS spectral line would require deconvolving the Voigt line shape and subtracting the Doppler broadening,which is de-pendent on the plasma temperature,from the total Gaussian width.Because of the potential inaccura-cies in this procedure,we chose to measure the reso-lution advantage of the transmission grating spectrometer using the Hg lamp spectra,as de-scribed in Subsection 6.A and shown in Fig.10,as they are not impacted by the LIBS plasma broaden-ing mechanisms [16].Sample 10m standoff LIBS spectra from the HP-3aluminum alloy is shown in Fig.11,taken at the same ICCD gain setting (120)with both spectro-meters.The figure demonstrates that the raw inten-sities vary from being 1order of magnitude greater in the transmission-grating spectrum to approaching 2orders of magnitude at the longer wavelengths.This is a clear indication that much more light is reaching the ICCD camera when the transmission grating spectrometer is used.While the increase in signal in-tensity is accompanied by an increase in background level,the signal levels of the LIBS peaks are enhanced by a greater amount,as evidenced by the improvements in the signal-to-background levels (see below).Consequently ,the increase in lightthroughput allows us to measure the smaller LIBS peaks in the spectrum without saturating the larger peaks.A comparison of the intensities from single laser shot LIBS spectra taken from the HG-4SRM is shown in Fig.12in the region of the Al I 669nm emis-sion line.This figure also shows the region over which baseline and noise statistics were gathered.As expected,the LIBS results verified the findings of the Hg lamp tests with regard to throughput,back-ground,and noise ing the Al I 669nm emis-sion line,the signal-to-noise ratio and repeatability of each spectrometer was quantified based upon all the single-shot LIBS spectra collected from the six alloys.This aluminum emission line is a nonreso-nance line that is also not self-absorbed.The results are summarized in Table 4.The relatively poor per-formance of the reflective grating system in this wavelength range illustrates one of the drawbacks of such systems for LIBS applications where the grating is fixed and one or more of the measured atomic emission lines is far from the angle at which the grating isoptimized.Fig.11.(Color online)Comparison of single laser shot LIBS spec-tra from the HP-3alloy .The plots are not offset from their actualvalues.Fig.12.(Color online)Comparison of Al 669nm peak from an HG-4alloy spectrum also showing the spectral region over which the baseline and noise statistics were computed.The curves are not artificially offset from each other.Top curve,transmission spec-trometer ICCD gain ¼120;middle curve,reflection spectrometer ICCD gain ¼160;bottom curve,reflection spectrometer ICCD gain ¼120.Table 4.Summary of Spectrometer System Performance as Measured by the Al I 669nm Emission Line StatisticsThroughputaAverage Signal/Background Ratio cAverage Signal/Noise Ratio dRepeatability eTransmission grating spectrometer 10953 3.1037.713%Reflection grating spectrometer 709b 2.888.15f 15%Transmission grating improvement1445%7.5%363%13%a Integrated area under the peak in counts.bCorrected for the 3.2times factor due to the increased gain setting (see text).cPeak area/mean background as described in text.dPeak area/mean noise as described in text.eRelative standard deviation (σ=μ)of peak amplitude over the 50collected spectra from each sample.。
新视图TM600s白光光学干涉三维扫描仪说明书
NewView TM 600s SpecificationsZYGO CORPORATIONLAUREL BROOK ROAD • MIDDLEFIELD, CT 06455VOICE: 860 347-8506 • FAX: 860 346-4188•EMAIL:****************SS-0036 06/09 © 2009 Zygo Corporation SYSTEMMeasurementTechniqueNon-contact, three-dimensional, scanningwhite light interferometryScanner Closed-loop piezo-based, with highlylinear capacitive sensorsField of View 0.05 to 3.5 mm (0.002 to 0.138 in.);objective dependentIlluminator Integrated long-life white-light LED withcomputer-controlled light levelObjectiveMountingQuick mount single objective dovetailControls Optical Filter Tray and Focus AidMeasurementArray640x480; user-selectablePart Viewing On-screen live display standard;second LCD monitor optionalFine FocusStageMedium and fine manual control, with 1.2in. (30 mm) of travelCoarse Z-StageCoarse, large range manual control, with10 in. (250 mm) of travel; actual travel isconfiguration dependentDimensions(HWD)27.6 x 12 x 16.5 in.(702 x 300 x 420 mm) NewView onlyWeight ~70 lb (32 kg), including part stageInput Voltage 100/120/220/240 VAC, 50/60 HzComputer High-performance Pentium-based Dell PCwith LCD monitorSoftware ZYGO MetroPro software running underMicrosoft Windows XPA CCESSORIES (O PTIONS)Objectives Infiniteconjugateinterferometricobjectives; 2X, 2.5X, 5X, 10X, 20X, 50X,100X.Refer to the NewView Objective Chart forobjective specifications.Turrets • Manual 6-position turret• Motorized 6-position turretPart Stage • Manual Tip/Tilt/X/Y, with±6° tip/tilt, 4 in. (100 mm) x/y travelVibrationIsolationSystem• Table, 31 x 24 x 24 in. (HWD)(787 x 610 x 610 mm); weight ~600 lb(272 kg); requires compressed air at60 psi (4 bar) with 1/4 in. input hose• Platform, tabletop, 2.75 x 20 x 24 in.(HWD) (70 x 508 x 610 mm); includesair pumpWorktable • Wrap-around, 34 x 52 x 35 in. (HWD)(864 x 1321 x 889 mm); nests next tothe vibration isolation tableMeasurementStandards• Lateral Calibration Standard• Precision Lateral Calibration Standard• SiC Reference Flat• Step Height StandardsGREAT PHOTOGOES HEREP ERFORMANCEVertical ScanRange ≤ 150 µm (5906 µin)Vertical Res. < 0.1 nm (0.004 µin)Lateral Res. 0.36 to 5.18 µm (14.2 to 204 µin);objective dependentDataScan Rate ≤ 15 µm/sec (591 µin/sec)MaximumData Points307,200RMSRepeatability< 0.01 nm (0.0004 µin) RMSσStep Height Accuracy ≤ 0.75%Repeatability≤ 0.1% @ 1σT EST P ART C HARACTERISTICSMaterial Various surfaces: opaque, transparent,coated, uncoated, specular, andnonspecularReflectivity 1-100%ENVIRONMENTAL R EQUIREMENTSTemperature15 to 30°C (59 to 86°F)Rate ofTemp. Change<1.0°C (1.8°F) per 15 minHumidity 5 to 95% relative, noncondensingVibrationIsolationRequired for vibration frequencies in therange of 1 Hz to 120 Hz。
Synopsys VR AR 光学设计与模拟手册说明书
Designing Augmented/Virtual Reality Devices using Multi-Domain Optical SimulationsSimulation and Design Using RSoft Tools and LightToolsOptics is Key for VR/AR•“Optics remains the key challenge in developing the ultimate virtual experience”Bernard Kress, Microsoft's Hololens Division @ SPIE Photonics West 2018:•New types of optical and photonics technologies need to be implemented in next-generation VR/AR systems in order to provide greater visual comfort for prolonged usage, and to achieve a better sense of display immersion or the user.AR/VR Requirements•Main VR/AR requirements:–Low weight–Small Size–Insensitive to vibration–Comfortableness•Types of existing systems include:–Freeform optical prisms projection systems–Retina scanning–Reflective systems or hybrid reflective/refractive systems–Optical planar waveguides with diffractiongratings–This system type has the potential to meet these requirements, Synopsys tools can help!•Diffractive Gratings Functions:–Couple light into waveguide plate and couple light out of plate into eyes –Wavelength selection–Wavefront reshaping•Gratings must be designed properly so that the optical system produces good imagesNear-Eye-Display (NED) SystemsBasic Schematic of Optical Waveguide System-110TIRTIRRSoft and LightTools Co-Simulation•RSoft Component Tools–Based on physical optics –Maxwell’s equations, etc–Small photonics devices–Wave propagation and multi-physics –Diffraction, polarization, nonlinearity, electro-optical, thermo-optics, etc.•LightTools–Based on geometrical optics –Snell’s law, etc.–Large bulk optical system–Ray tracing and beam propagation –Reflection, refraction, diffractionFeature Size vs. WavelengthLarger (> ~10l )Smaller…BeamPROP FullWAVELaserMOD DiffractMODPhysical optics~10lGeometrical opticsRSoftLightTools CODE VSimulating the Grating with RSoft Device ToolsDiffractMOD: RSoft’s RCWA tool •DiffractMOD is a very efficient tool to rigorously calculate diffraction properties of transversely periodic devices•DiffractMOD outputs :–Reflection/Transmission power for each diffraction order–Total reflection/transmission–Amplitude/Phase/Angle for each diffraction order–Field distribution in simulation domain•RSoft BSDF files:–Automatically calculated using RSoft’s FullWAVE or DiffractMOD packages–Contains information about how a surface (thin film, patterns, etc) scatters light–Reflection/transmission data is stored for illumination from both sides of the surface –Scatter information is stored as a function of two incident angles, wavelength, and polarization•The RSoft BSDF file is then used in LightTools to define a surface property–Rays that hit the surface in LightTools are ‘diffracted’ according to the data in the RSoft BSDF fileRSoft/LightTools BSDF InterfacePeriodic Nano-structure Light incident on BSDF surfaceScattering from BSDF surfaceBSDF SurfaceDesign Case 1•AR systems are complex and involve not only illumination optics but also imaging optics as well as ergonomic considerationsUse LightTools to Design the Nominal System •It is usual to lay the system out in LightTools usingidealized gratings in order to explore the system more easily and to discover the required grating settings that can then be designed in Rsoft–Since the imaging properties of the system are criticalto a successful design, it may be necessary to designat least part of the system in an imaging package such as Synopsys’ CODE V•Here we see half of a simple system using an imaging system, a light guide plate and two idealized gratings to transfer the image to the left eye while creating a well defined eye box (exit pupil)Light Guide PlateGratingsEye Box Image DeviceEye Lens•For wearable optical systems, the designer must make accommodations for variances inhuman size and usage The Importance of the Eye Box Imaging System in CODE VLight Guide Plate (unfolded)Eye box(Exit Pupil)Image Device–Specifically, the inter-ocular distance can vary significantly with each user–The device may also be worn at a different height with respect to the eye from user to user–This, then, requires a defined eye box•Because of this, it is critical that an AR/VR system create a proper exit pupil so that variations in the position of the eye don’t cause parts of the projected image to drop out–With a properly constructed pupil rays from every part of the image device will be found in every part of the eye boxEye Box Results for Our Nominal System•Here we see a false color illuminance map of our eye box–The eye box shows some complex structure due to the multiple bouncesand extraction events on input and exit grids–However, the image rays are uniformly represented across the eye boxas we shall see later5mm Iris overlaidon eye box•The imaging system is designed to put thevirtual image at an infinite distance from theeye–Collimated light–The system can be designed for a differentvirtual image distance, something closer to theuser (diverging light), but care should be takento avoid converging light at the eye box as theeye cannot focus converging beams•The image quality seen here is good–The field of view is +-5 degrees horizontal andvertical–There is a small amount of pincushion distortion–The circle pattern has been added in order tovisualize the imaging performance Image Quality Notice a very slight slope in the illuminance across the fieldImaging Quality at Different Eye Positions•Here we show the imaging quality at different eye positions–What we are looking for is variations in illuminance for different parts of the image (e.g. some parts may disappear)–We have removed the dots and lowered the resolution3mm Left3mm RightNominalDesigning Gratings•Once the nominal system has been developed and the designer is satisfied with the performance the ideal gratings must be converted to actual gratings•For this we use the RSoft Device suite to design actual gratings as near to the nominal specifications as possible•Once designed, the grating performance can then be transferred back into the LightTools model using the BSDF utility–The nominal gratings are simply replaced with the imported BSDF data•Further optimization can then be done to adjust the performanceDesign Case 1: Structure OverviewT Levola et al, ”Replicated slanted gratings with a high refractive index material for in andoutcoupling of light”, Optics Express, 15 (2007)Left In-coupler Right In-coupler Reflection Type Out-coupling Transmission TypeOut-coupling•Diffractive slanted gratings aremanufactured onto a highrefractive index plastic waveguidewith simple UV replicationtechnology. Large quantitymanufacturing is possible •The slanted gratings can be optimized to have high 1st order transmission efficient for right in-coupler and high -1st order transmission efficient for left in-coupling (> 92%).•Two types of slanted gratings for out-coupler. The efficiency can be optimized as well.•Grating Properties:–Wavelength:0.52 µm–Period:0.405 µm–H:grating height–A:slant angle–L:Left slope anglefrom slant axis–R:right slope anglefrom slant axis–Fill:duty ratio–Index:1.716Using DiffractMOD for Grating Design P H A L RIndex Profile Diffraction vs wavelength for different ordersDiffraction angle of -1Tvs wavelength•The charts below show the spectral bandwidth of the designed grating for the -1 through +1 orders (Reflected) as well as the diffraction efficiency as a function of angle–The angular bandwidth will limit the field of view of the projected image Grating PerformanceSpectral BandwidthAngular BandwidthDiffraction Efficiency as a Function of Rib Height •The plot below shows that the rib lengthcan be used to vary the diffractionefficiency of the +1 order•Because this is an effective parameter,we will use this to optimize the gratings tocreate a uniform output across the eyeboxRSoft BSDF Calculation for Optimal Structure•Angular range of RSoft BSDF file:–Phi(from normal): Range of [0,90] with 1°spacing–Theta(around normal): Range of [0,360] since thestructure is anisotropic with 5°spacing•BSDF Utility runs DiffractMOD simulations and bothpolarizations are automatically calculatedParametric BSDF DatabaseRSoft BSDF Generation Utility with FullWAVE FDTD or DiffractMODRCWA•In BSDF Generation Utility,parametric BSDF data issupported–Any variables defined in RSoftCAD can be selected–Multi-variables parametricBSDF is supported as wellUsing the BSDF File in LightTools•Once the BSDF data has been generated in RSoft, it is a simple matter to integrate the data into the LightTools Model•Simply create an optical property foreach grating–Set the Type to User-Defined–Select the UDOP_RSoftBSDF.dll,installed with RSoft Design Tools–Select the imported BSDF data file•Then assign the new optical propertyin place of the existing nominalgrating optical property–You may need to rotate the zone 180degrees to get the proper orientationParametric BSDF Database •In the optical propertieswith RSoft UDOPinterface, the parameterscalculated in RSoft areshown as variables, whichcan be defined asvariables in optimizationInitial Results with RSoft Gratings •Here we show the initial results from our previous system but using an initial grating design from RSoft–There are some differences in the eye box, and the image field is slightly less uniform horizontally–Also notice that the image intensity has dropped from 0.006W/mm2to 0.004 W/mm2because of the actual rather thanperfect grating efficiencyEye boxilluminancemapExpanding the Eye BoxOptics Size•As you may have noticed in the previous example, the imaging optics are quite large with respect to the device as a whole–This is undesirable because of the bulky size and excess weight–Driven by the field size and the need for the exit pupil to be a considerable distance in front of the lens–Without expanding the pupil, there is no way around this limitation•We can use an extra grating to expand theeye box and therefor allow us to greatlyreduce the size and weight of the imagingoptics•In this figure, DOE2 and DOE3 are shown as continuous regions•You can see that the output from DOE3 is far from uniform•To address this, we will sub-divide DOE2 and DOE3 into multiple zones and then use LightTools optimization to obtain a uniform output•The beams emerging from the DOE3 would be diverging and would overlap each other at the eye position, creating a large and relatively uniform eye boxBeam Expander ExampleDOE2 -TurningDOE3 -OutputDOE1 -InputRay Trace in LightTools•Here we see the ray trace of the demonstration system •DOEs 2 and 3 have not yet been sub-divided into zonesNote the strong non-uniformity ofthe DOE3 output•DOE2 and DOE3 are now sub-divided into 5 zones each•Each zone has its own optical property •Each grating property can then be optimized separately•To maximize the efficiency of the optimization the DOE2 was optimized first with the subzone furthest from DOE1 fixed for maximum extraction•Then DOE3 was optimized independently in a similar mannerSub-divide the Grating ZonesDOE3DOE2DOE1Optimizing Grating Rib Height•The grating rib height was optimized in LightTools using the standard optimizer –Parameter appears in the UDOP UI and can be made an independent variable for each zone optical property–A 5 x 5 output grid was used to optimize for uniform outputReceiver grid used for optimizationOptimized Result•Here we see the emerging collimated spots at the eye box after optimization –Note the uniformity across the entire eye box•8o projected grid pattern •Backward ray trace to improve ray trace efficiency •Some non-uniformity and residual distortion can be seen•We will now add an actual source and collimating optics andlook at the eye box uniformity and image result•Here we have put in a source with a field of view of +-4degrees–This blurs out the individual segments so that they overlapEye Boxes with Non-Collimated SourceEye-box illuminanceThinning Down the Plate•The original DOE spacing and plate thickness was chosen to give one ray bundle transmission per grating zone on the output grating–For a total of 25 exiting ray bundles•By thinning the plate down from 1.667mm to 1mm and adjusting the DOE spacing and size parameters then re-optimizing we were able to improve eye-box uniformity as well as image qualityConclusionConclusion•Augmented Reality and Virtual Reality systems are complex devices requiring careful design of the imaging, illumination and photonics portions of the system •All of these aspects need to work together•Synopsys Optical Solutions Group along with Photonics Optical Solutions Group provides an integrated solution with CODE V, LightTools and RSoft Device Tools to meet this challenge not just in simulating performance but to optimize to the best solutionThank You。
超快光学超快光谱
Chopper
Chopped excite pulse train
The excite pulse periodically changes the sample absorption seen by the probe pulse.
Probe pulse train
Lock-in detector
What’s going on in spectroscopy measurements
The excite pulse(s) excite(s) molecules into excited states, which changes the medium’s absorption coefficient and refractive index.
DT(t) / T0 Da0 exp(–t /tex) L
0
Delay, t
Modeling excite-probe measurements
(cont’d)
3
Excite transition
2 Probe transition
1
0
More complex decays occur if intermediate states are populated or if the motion is complex. Imagine probing an intermediate transition, whose states temporarily fill with molecules on their way back down to the ground state:
Ultrafast laser spectroscopy: Why
Most events that occur in atoms and molecules occur on fs and ps time scales because the length scales are very small.
All_normal_dispersion_femtosecond_fiber_laser
See discussions, stats, and author profiles for this publication at: /publication/26294738 All-normal-dispersion femtosecond fiber laser. Opt. Express 14(21), 10095-10100ARTICLE in OPTICS EXPRESS · NOVEMBER 2006Impact Factor: 3.49 · DOI: 10.1364/OE.14.010095 · Source: PubMedCITATIONS 299READS 1644 AUTHORS, INCLUDING:Andy ChongUniversity of Dayton73 PUBLICATIONS 2,087 CITATIONSSEE PROFILE William H RenningerYale University69 PUBLICATIONS 1,894 CITATIONSSEE PROFILEFrank W WiseCornell University427 PUBLICATIONS 13,703 CITATIONSSEE PROFILEAvailable from: Andy ChongRetrieved on: 16 November 2015All-normal-dispersionfemtosecondfiber laserAndy Chong,Joel Buckley,Will Renninger and Frank WiseDepartment of Applied Physics,Cornell University,Ithaca,New York14853cyc26@Abstract:We demonstrate a modelocked ytterbium(Yb)-dopedfiber laserthat is designed to have strong pulse-shaping based on spectralfiltering of ahighly-chirped pulse in the cavity.This laser generates femtosecond pulseswithout a dispersive delay line or anomalous dispersion in the cavity.Pulsesas short as170fs,with pulse energy up to3nJ,are produced.©2006Optical Society of AmericaOCIS codes:(320.7090)Ultrafast lasers;(320.5540)Pulse shaping;(140.7090)Ultrafastlasers.References and links1.R.L.Fork,O.E.Martinez,and J.P.Gordon,“Negative dispersion using pairs of prisms,”Opt.Lett.9,150-152(1984).2. E.B.Treacy,“Optical pulse compression with diffraction gratings,”IEEE J.Quantum Electron.QE-5,454-458(1969).3.R.Szipocs,K.Ferencz,C.Spielmann,and F.Krausz,“Chirped multilayer coatings for broadband dispersioncontrol in femtosecond lasers,”Opt.Lett.19,201-203(1994).4.O.E.Martinez,R.L.Fork,and J.P.Gordon,“Theory of passively mode-locked laser including self-phasemodulation and group-velocity dispersion,”Opt.Lett.9,156-158(1984).5.H.A.Haus,J.G.Fujimoto,and E.P.Ippen,“Analytic theory of additive pulse and Kerr lens mode locking,”IEEE J.Quantum Electron.28,2086-2096(1992).6. B.Proctor,E.Westwig,and F.Wise,“Operation of a Kerr-lens mode-locked Ti:sapphire laser with positivegroup-velocity dispersion,”Opt.Lett.18,1654-1656(1993).7.S.M.J.Kelly,“Characteristic sideband instability of periodically amplified average soliton,”Electron.Lett.28,806-807(1992).8.K.Tamura,E.P.Ippen,H.A.Haus,and L.E.Nelson,“77-fs pulse generation from a stretched-pulse mode-lockedall-fiber ring laser,”Opt.Lett.18,1080-1082(1993).9. F.O.Ilday,J.R.Buckley,W.G.Clark,and F.W.Wise,“Self-similar evolution of parabolic pulses in a laser,”Phys.Rev.Lett.92,213902-1-213902-4(2004).10. F.O.Ilday,J.R.Buckley,H.Lim,F.W.Wise,and W.G.Clark,“Generation of50-fs,5-nJ pulses at1.03μmfrom a wave-breaking-freefiber laser,”Opt.Lett.28,1365-1367(2003).11.J.R.Buckley,F.W.Wise,F.O.Ilday,and T.Sosnowski,“Femtosecondfiber lasers with pulse energies above10nJ,”Opt.Lett.30,1888-1890(2005).12.H.Lim,F.O.Ilday,and F.W.Wise,“Femtosecond ytterbiumfiber laser with photonic crystalfiber for dispersioncontrol,”Opt.Express10,1497-1502(2002).13. A.V.Avdkhin,S.W.Popov,and J.R.Taylor,“Totallyfiber integrated,figure-of-eight,femtosecond source at1065nm,”Opt.Express11,265-269(2003).14.I.Hartl,G.Imeshev,L.Dong,G.C.Cho,and M.E.Fermann,“Ultra-compact dispersion compensated fem-tosecondfiber oscillators and amplifiers,”Conference on Lasers and Electro-Optics2005,Baltimore,MD,paper CThG1.15.J.R.Buckley,A.Chong,S.Zhou,W.H.Renninger,and F.W.Wise,unpublished.16.H.Lim,F.O.Ilday,and F.W.Wise,“Generation of2-nJ pulses from a femtosecond ytterbiumfiber laser,”Opt.Lett.28,660-662(2003).#72994 - $15.00 USD Received 14 July 2006; revised 12 August 2006; accepted 23 August 2006 (C) 2006 OSA16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 100951.IntroductionThe need to compensate group-velocity dispersion(GVD)is ubiquitous in femtosecond pulse generation and propagation.Prisms[1],diffraction gratings[2],and chirped mirrors[3]have all been used to compensate or control GVD.Reliable femtosecond lasers had to await the devel-opment of a low-loss means of introducing controllable GVD[1].Pulse formation in modern femtosecond lasers is dominated by the interplay between nonlinearity and dispersion[4,5].In all cases of practical interest,a positive(self-focusing)nonlinearity is balanced by anomalous GVD.The need to compensate normal GVD in the laser,along with the balance of nonlinearity in soliton-like pulse shaping,underlies the presence of anomalous GVD in femtosecond lasers. Most femtosecond lasers have segments of normal and anomalous GVD,so the cavity con-sists of a dispersion map,and the net or path-averaged cavity dispersion can be normal or anomalous.With large anomalous GVD,soliton-like pulse shaping produces short pulses with little chirp.Some amplitude modulation is required to stabilize the pulse against the periodic perturbations of the laser resonator.Pulse formation and pulse evolution become more complex as the cavity GVD approaches zero,and then becomes normal.The master-equation treatment of solid-state lasers,based on the assumption of small changes of the pulse as it traverses cavity elements,shows that stable pulses can be formed with net normal GVD[5].Nonlinear phase accumulation,coupled with normal GVD,chirps the pulse.The resulting spectral broadening is balanced by gain-narrowing.By cutting off the wings of the spectrum,gain dispersion shapes the temporal profile of the chirped pulse.Proctor et al showed that the resulting pulses are long and highly-chirped[6],as predicted by the analytic theory[5].Stable pulse trains can even be produced without dispersion compensation,but the output pulses are picoseconds in duration and deviate substantially from the Fourier-transform limited duration,even after dechirping with anomalous GVD external to the cavity.Fiber lasers can be constructed entirely offiber with anomalous GVD,to generate solitons as short as∼200fs in duration.However,the pulse energy is restricted by the soliton area theorem and spectral sidebands[7]to∼0.1nJ.Much higher energies are obtained when the laser has segments of normal and anomalous GVD.In general,the pulse breathes(i.e.,the pulse duration varies periodically)as it traverses the cavity.Dispersion-managed solitons are observed as the net GVD varies from small and anomalous to small and normal[8],and self-similar[9]and wave-breaking-free[10]pulses are observed with larger normal GVD.The large changes in the pulse as it traverses the laser preclude an accurate analytical treatment,so numerical simulations are employed to study these modes.Amongfiber lasers,Yb-based lasers have produced the highest femtosecond-pulse energies,recently reaching15-20nJ[11].The normal GVD of single-modefiber(SMF)around1μm wavelength has been compensated by diffraction gratings,which detract from the benefits of the waveguide medium.With the goal of building integratedfiber lasers,microstructurefibers[12,13]andfiber Bragg gratings[14]have been implemented to compensate dispersion at1μm.However,performance is sacrificed compared to lasers that employ diffraction gratings.From a practical point of view, it would be highly desirable to design femtosecond-pulsefiber lasers without compensation of the GVD of several meters offiber.However,to our knowledge there is no prior report of any laser that generates∼100-fs pulses without elements that provide anomalous GVD in the cavity.Recently,Buckley et al.showed that the introduction of a frequencyfilter stabilizes mod-elocked operation of a Yb-dopedfiber laser with normal cavity GVD(∼0.015ps2),which allows the routine generation of15-nJ pulses as short as55fs[15].The frequencyfilter pro-duces self-amplitude modulation,which allows nonlinear polarization evolution(NPE)to be biased for higher pulse energies.By altering the laser cavity to operate at large normal GVD (0.04-0.10ps2),the frequencyfilter was found to stabilize modelocked operation character-#72994 - $15.00 USD Received 14 July 2006; revised 12 August 2006; accepted 23 August 2006 (C) 2006 OSA16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 10096ized by highly chirped,nearly static pulses as predicted by the theory of self-similar lasers[9]. Although Buckley et al.succeeded in enhancing the stability of modelocking at large normal GVD,the laser still required some dispersion compensation with a grating pair.Here we describe a femtosecondfiber laser with a cavity consisting only of elements with normal GVD.By increasing the nonlinear phase shift accumulated by the pulse and insert-ing a spectralfilter in the cavity,self-amplitude modulation via spectralfiltering is enhanced. The laser generates chirped picosecond pulses,which are dechirped to170fs outside the laser. These results are remarkable considering that the cavity consists of∼10characteristic disper-sion lengths offiber with respect to the dechirped pulse,yet no dispersion control is provided. The pulse energy is1-3nJ,and the laser is stable and self-starting.The laser is thus afirst step in a new approach to modelocking.Systematic understanding of the pulse-shaping and evolution will be interesting scientifically,and the freedom from anomalous dispersion offers significant practical advantages.2.Design rationale and numerical simulationsThe design of a femtosecondfiber laser without dispersion control in the cavity exploits the understanding gained by the recent work of Buckley et al.[15].The master-equation analysis does not apply quantitatively tofiber lasers,but we are guided qualitatively and intuitively by its predictions.The key elements of such a laser(Fig.1(a))are a fairly long segment of SMF, a short segment of gainfiber,a segment of SMF after the gainfiber,and components that pro-duce self-amplitude modulation.A significant nonlinear phase shift is impressed on the pulseFig.1.Numerical simulation result:a)schematic diagram of the laser.A ring cavity isassumed,so the pulse enters thefirst SMF after the NPE.Results of numerical simulationsare shown on the bottom.Power spectrum(b)and temporal intensity profile(c)after thesecond SMF.#72994 - $15.00 USD Received 14 July 2006; revised 12 August 2006; accepted 23 August 2006 (C) 2006 OSA16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 10097in the SMF that follows the gain,and NPE converts the differential phase shift to amplitude modulation.Numerical simulations show that stable solutions do exist in such a laser,for a reasonable range of parameters.The gain bandwidth has a major influence on the pulse evo-lution.With large gain bandwidth (>∼30nm),approximately parabolic pulses evolve as in a self-similar laser [9].As the bandwidth is reduced to ∼10nm,the spectrum develops sharp peaks on its edges,and for narrower bandwidths the solutions do not converge.Results of simulations with 10-nm gain bandwidth and 2-nJ pulse energy are shown in Fig.1.The pulse duration increases monotonically in the SMF,and then decreases abruptly in the gain fiber.In the second segment of SMF the pulse duration increases slightly,before dropping again owing to the NPE.The spectrum (Fig.1(b))exhibits a characteristic shape,with sharp peaks near its steep edges.The pulse is highly-chirped throughout the cavity,with the duration varying from ∼10to ∼20times the transform limit (Fig.1(c)).The simulations show that spectral filtering of a strongly phase-modulated pulse can produce substantial amplitude modulation under realistic conditions.With additional amplitude modu-lation from NPE,stable solutions exist.The pulse is highly-chirped inside the cavity,but the phase is roughly parabolic near the peak of the pulse,so the pulse can be dechirped outside the laser.3.Experimental resultsThe numerical simulations offer a guide to the construction of a laser without anomalous disper-sion.The laser (shown schematically in Fig.2)is similar to the Yb fiber laser of Lim et al .[16],but without the grating pair that provides anomalous GVD in earlier designs.The fiber section consists of ∼3m of SMF and 20cm of highly-doped Yb gain fiber,followed by another ∼1m of SMF.Gain fiber with a 4-μm core diameter (which is smaller than the 6-μm core of SMF)was chosen to increase self-phase modulation (SPM)in the gain fiber.A 980-nm laser diode delivers ∼350mW into the core of the gain fiber.NPE is implemented with quarter-waveplates,a half-waveplate,and a polarizing beamsplitter.The output of laser is taken directly from the NPE ejection port.Fig.2.Schematic of all-normal-dispersion fiber laser:QWP:quarter-waveplate;HWP:half-waveplate;PBS:polarizing beam splitter;WDM:wavelength-division multiplexer.In contrast to the simulations,it is not possible to vary the gain bandwidth easily.An inter-ference filter centered at 1030nm,with 10nm bandwidth,is employed.The optimum location for the filter is not clear.Placing it after the gain or second SMFsegment would maximize the amplitude modulation from spectral filtering and correspond most closely to the simulations described above.However,we also want to output the broadest spectrum and the largest pulse energy,to achieve the shortest and most intense pulse.Considering these factors,we placed the #72994 - $15.00 USD Received 14 July 2006; revised 12 August 2006; accepted 23 August 2006(C) 2006 OSA 16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 10098filter after the beam splitter.This location also allows as much of the laser to be spliced together as possible.The total cavity dispersion is∼0.1ps2.The threshold pump power for modelocking is∼300mW.Self-starting modelocked opera-tion is achieved by adjustment of the waveplates.The laser produces a stable pulse train with 45MHz repetition rate.Although the continuous-wave output power can be as high as∼200 mW,in modelocked operation the power is limited to120mW,which corresponds to a pulse energy of∼3nJ.Stable single-pulsing is verified with a fast detector down to500ps,and by monitoring the interferometric autocorrelation out to delays of∼100ps.Also,the spectrum is carefully monitored for any modulation that would be consistent with multiple pulses in the cavity.Remarkably,there is no evidence of multi-pulsing at any available pump power.How-ever,with a single pump diode the pump power only exceeds the modelocking threshold by ∼20%.Fig.3.Output of the laser:a)spectrum,b)interferometric autocorrelation of the output,c)interferometric autocorrelation of dechirped pulse and the interferometric autocorrelationof zero-phase Fourier-transform of the spectrum(inset),d)intensity autocorrelation of thedechirped pulse.Typical results for the output of the laser are shown in Fig.3.The spectrum(Fig.3(a))is qualitatively similar to the simulated spectrum(Fig.1(b))and is consistent with significant SPM within the cavity.The laser generates∼1.4-ps chirped pulses(Fig.3(b)),which are dechirped to 170fs(Fig.3(c and d))with a pair of diffraction gratings outside the laser.The dechirped pulse duration is within∼16%of the Fourier-transform limit(Fig.3(c)inset).The interferometric autocorrelation shows noticeable side-lobes,which arise from the steep sides and structure of the spectrum.Nevertheless,these amount to only∼10%of the pulse energy.The output pulse energy is∼2.7nJ,and after dechirping with lossy gratings the pulse energy is∼1nJ.Pulse ener-#72994 - $15.00 USD Received 14 July 2006; revised 12 August 2006; accepted 23 August 2006 (C) 2006 OSA16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 10099gies of2nJ could be obtained by dechirping with high-efficiency gratings or photonic-bandgap fiber.The laser is stable and self-starting.In addition to verifying as carefully as possible that the laser is not multi-pulsing,we compared the pulse peak power to that of a fully-characterized femtosecond laser available in our lab.Within the experimental uncertainties,the two-photon photocurrent induced by the all-normal-dispersion laser scales correctly with the nominal peak power,which is∼5kW.Detailed understanding of pulse formation and evolution in this laser will require more ex-perimental work and theoretical analysis.Because the simulated laser is not identical to the ex-perimental version,it is not appropriate to compare the calculated and measured performance in detail.However,qualitative and even semi-quantitative observations of the laser properties are consistent with the intended pulse-shaping through spectralfiltering.The behavior of the laser depends critically on the spectralfilter:without it,stable pulse trains are not generated.By rotating the spectralfilter to vary the center wavelength,either of the sharp spectral features can be suppressed,which may slightly improve the pulse quality.When the spectrum changes,the magnitude of the chirp on the output pulse can change substantially:the pulse duration varies from approximately1to2ps.With standard femtosecond Yb-dopedfiber lasers,mechanical perturbation of thefiber extinguishes modelocking.In the laser described here,wefind that it is possible to touch and move thefiber without disrupting modelocking,which indicates that NPE plays a reduced role in pulse-shaping.The simulations(e.g.,Fig.1)show that the role of NPE is reduced compared to a laser with a dispersion map,but it is still crucial to the generation of stable pulses.4.ConclusionIn conclusion,we have demonstrated afiber laser that generates reasonably high-quality fem-tosecond pulses without the use of intracavity dispersion control.The behavior and perfor-mance of the laser agree qualitatively with numerical simulations that illustrate the intended pulse-shaping mechanism by enhanced spectralfiltering of chirped pulses in the cavity.Never-theless,our picture of this modelocking process is rudimentary,and more work will be required to obtain a systematic understanding.Improved performance should accompany better under-standing of this modelocking process.AcknowledgementThis work was supported by the National Science Foundation under grant ECS-0500956and by the National Institutes of Health under grant EB002019.#72994 - $15.00 USD Received 14 July 2006; revised 12 August 2006; accepted 23 August 2006 (C) 2006 OSA16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 10100。
光纤的色散与非线性效应
光纤的色散
随着脉冲在光纤中传输，脉冲的宽度被展宽
模间色散(Mode Dispersion) 色度色散(Cromatic Dispersion) 偏振色散(Polarization Mode Dispersion)
劣化的程度随数据速率的平方增大
决定了电中继器之间的距离
色散对传输的限制
结论: 不适用于10Gb/s以上速率传输，但可应用于 2.5Gb/s以下速率的DWDM。
G.653单模光纤（DSF）
低损耗 零色散 小有效面积 长距离、单信道超高速EDFA系统 四波混频（FWM）是主要的问题，不利于DWDM技术Fra bibliotek结论:
适用于 10Gb/s 以上速率单信道传输，但不适 用于 DWDM应用，处于被市场淘汰的现状。
Calculating Dispersion
• in a typical single-mode fibre using a laser with a spectral width of 6 nm over a distance of 10 km : Dispersion = 17ps/nm/km × 6 nm × 10 km = 1020 ps • At 1 Gbps a pulse is 1 ns long. So the system would not work. (20% is a good guideline for the acceptable limit.) But it would probably work quite well at a data rate of 155 Mbps (a pulse length of 6.5 ns). • A narrow spectral width laser might produce only one line with a linewidth of 300 MHz. Modulating it at 1 Gbps will add 2 GHz. 2,300 MHz is just less than .02 nm (at 1500 nm). So now: • Dispersion = 17ps/nm/km × .02 nm × 10 km = 3.4 ps
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After a general introduction and a summary of the basicrequirements, specific guidelines are given for all major manuscriptelements (such as abstract, headings, figures, tables, and references) toachieve optimal typographic quality. The use of complete and properlyformatted references is particularly important.2010 Optical Society of AmericaOCIS codes: (000.0000) General; (000.2700) General science.References and links1.P. J. Harshman, T. K. Gustafson, P. Kelley, “Title of paper,” J. Chem. Phys. 3, (to be published).2. C. van Trigt, “Visual system-response functions and estimating reflectance,” J. Opt. Soc. A m. A 14, 741-755 (1997).3.K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetricwaveguide,” J. Opt. Soc. B 16, 267-269 (1999).4. B. R. Masters, "Three-dimensional microscopic tomographic imagings of the cataract in a human lens invivo," Opt. Express 3, 332 (1998), /abstract.cfm?URI=OPEX-3-9-332.5. B. R. Masters, “Three-dimensional confocal microscopy of the human opt ic nerve in vivo,” Opt. Express 3,356 (1998), /abstract.cfm?URI=OPEX-3-10-356.1. IntroductionAdherence to the specifications listed in this style guide is essential for efficient review and publication of submissions. Since Optics Express paper are not routinely copyedited and typeset, use of the Optics Express macros and style guide is critical to providing a consistent appearance.Except for numbering and titling of sections, which may not be desirable for short articles, the Optics Express style and layout rules have been followed in this guide. Also note that there is a checklist available in Section 6 that summarizes the style specifications.2. Page layout and lengthPaper size should be U.S. Letter, 21.505 cm x 27.83 cm (8.5 in. x 11 in.). 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Please include the country at the end of the affiliation.Joseph Richardson,1,* Antoinette Wrighton,2and Jennifer Martin2,31Department of Peer Review, Optical Society of America, 2010 Massachusetts Avenue, NW, Washington, D.C. 20036,USA2Department of Editorial Services, Optical Society of America, 2010 Massachusetts Avenue, NW, Washington, D.C.20036, USA3Currently with the Department of Electronic Journals, Optical Society of America, 2010 Massachusetts Avenue, NW,Washington, D.C. 20036, USA************Affiliation line with two e-mail addresses (only one for the corresponding author)Joseph Richardson,1,* Antoinette Wrighton,2,4and Jennifer Martin2,31Department of Peer Review, Optical Society of America, 2010 Massachusetts Avenue, NW, Washington, D.C. 20036,USA2Department of Editorial Services, Optical Society of America, 2010 Massachusetts Avenue, NW, Washington, D.C.20036, USA3Currently with the Department of Electronic Journals, Optical Society of America, 2010 Massachusetts Avenue, NW,Washington, D.C. 20036, USA4***********************4.4 AbstractBegin the section with the word “Abstract:” in bold print followed by a colon. 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At the point of citation within the main text, designate the reference by typing the number in after the last corresponding word [1]. Reference numbers should proceed a comma or period [2]. Two references [3,4], should be included together, separated by a comma, while three or more consecutive references should be indicated by the bounding numbers and a dash [1-4].Optics Express follows the following citation style:Journal paperFor journal articles, authors are listed first, followed by the article’s full title in quotes, the journal’s title abbreviation, the volume number in bold, inclusive page numbers, and the year in parentheses. Journal titles are required.6. C. van Trigt, “Visual system -response functions and estimating reflectance,” J. Opt. Soc. Am. A 14, 741-755 (1997).BookFor monographs in books, authors are listed first, followed by ar ticle’s full title in quotes, the word “in,” followed by the book title in italics, the editors of the book in parenthesis, the publisher, city, year.7. David F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic, Orlando, Fla., 1985).Chapter in a bookFor citation of a book as a whole or book chapter, authors or editors are listed first, followed by title in italics, and publisher, city, and year in parenthesis. Chapter number may be added if applicable.8. F. Ladouceur and J. D. Love, Silica-Based Buried Channel Waveguides and Devices (Chapman & Hall,1995), Chap. 8.Electronic citationsInternet links may be included as references. Internet links should list the author, title (substitute file name, if needed), and the full URL (universal resource locator). Include the date of access, if relevant:9. C. Gerry, “Remarks on the use of group theory in quantum optics,” Opt. Express 8, 76-85 (2001)./abstract.cfm?URI=OPEX-8-2-76.10.Extreme Networks white paper, “Virtual metropolitan area networks” (Extreme Networks, 2001)./technology/whitepapers/vMAN.asp.Paper in a published conference proceedings11.R. E. Kalman, “Algebraic aspects of the generalized inverse of a rectangular matrix,” in Proceedings ofAdvanced Seminar on Genralized Inverse and Applications, M. Z. Nashed, ed. (Academic, San Diego,Calif., 1976), pp. 111-124.Paper in unpublished conference proceedings12. D. Steup and J. Weinzierl, “Resonant THz-meshes,” presented at the Fourth International Workshop onTHz Electronics, Erlangen-Tennenlohe, Germany, 5-6 Sept. 1996.For citation of proceedings, follow the individual format for SPIE, IEEE and OSA Proceedings:SPIE proceedings13.G. D. Love, C. N. Dunlop, S. Patrick, C.D. Saunter, “Horizontal turbulence measurements usingSLODAR,” Proc. SPIE 5891, 27–32 (2005).IEEE proceedings14.T. Darrel and K. Wohn, "Pyramid based depth from focus," in Proceedings of IEEE Conference onComputer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York,1988), pp. 504-509.OSA proceedings15.G. Kalogerakis, M. E. Marhic, L. G. Kazovsky, and K. K. -Y. Wong, "Transmission of OpticalCommunication Signals by Distributed Parametric Amplification," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies,Technical Digest (CD) (Optical Society of America, 2005), paper CTuT2./abstract.cfm?URI=CLEO-2005-CTuT2Paper accepted for publication16. D. Piao, "Cancelation of coherent artifacts in optical coherence tomography imaging," Appl. Opt. (to bepublished).Manuscript in preparation17.J. Q. Smith, Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester,N.Y. 14623, and K. Marshall are preparing a manuscript to be called "Optical effects in liquid crystals." Personal communication18.Barbara Williams, Editorial Department, Optical Society of America, 2010 Massachusetts Avenue, N.W.,Washington, D.C., 20036 (personal communication, 2001).4.10 AcknowledgmentsAcknowledgments should be included at the end of the document. The section title should read “Acknowledgments” in 10-pt. bold font. The section title should not follow the numbering scheme of the body of the paper. The body of the section should follow the font and layout of the body of the paper (see Subsection 4.7 above). Please identify all appropriate funding sources by name and contract number in the Acknowledgment section.5. Figures, multimedia and tables5.1 FiguresFigures should be included directly in the document. All photographs must be in digital form and placed appropriately in the electronic document. All illustrations must be numbered consecutively (i.e., not by section) with Arabic numbers. The size of a figure should be commensurate with the amount and value of the information conveyed by the figure.Authors must use one image file per figure. Figures must be inserted as objects that are fixed and move with the text, not as floating objects. Figures should never be placed in a table environment.All the figures should be centered, except for small figures no wider than 2.6 in.(6.6 cm), which may be placed side by side. Place figures as closely as possible to where they are mentioned in the text. No part of a figure should go beyond the typing area. The figure should not be embedded inside the text.All figure captions should be centered beneath the figure. Longer figure captions should be centered beneath the figure and alignment double (left and right) justified, but are not to exceed the left and right edge of the figure by more than 0.5 in. The abbreviation “Fig.” for figure should appear first followed by the figure number and a period. 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If it is essential to the scientific quality of the paper to have files that are larger than this, two different versions of such multimedia files (usually video files) must be made. One version, less than 4 MB in size, will serve as a low-resolution or truncated version for readers who have slower network connections and cannot download the larger file. The other version can be up to 15 MB in size. Multimedia files larger than 15 MB can be linked from the References section, but they will not be a reviewed part of the paper, they will not be kept at OSA, and they will not be part of the archival paper.Please refer to the online style guide for more detailed instructions on acceptable multimedia formats for audio and tabular data.5.3 TablesTables should be centered and numbered consecutively. Authors must use Word’s Table editor to insert tables. Authors must not import tables from Excel. All content for each table should be in a single Word table (do not split content for a single table across multiple Word tables). Tables should use horizontal lines to delimit the top and bottom of the table and column headings. Detailed explanations or table footnotes should be typed directly beneath the table. Position tables as closely as possible to where they are mentioned in the main text.Table 1. Optical Constants of Thin Films of Materials a83.4 nm 121.6 nmMaterial n K n kIr 1.182 0.865 1.450 1.040MgF2 1.584 0.487 1.682 0.0627Al 0.09874 0.1915 0.0424 1.137Mo 0.98 1.08 0.78 1.03C 1.16 1.29 1.85 1.10a From Appl. Opt. 40, 1128 (2001).6. Article Thumbnail UploadAuthors have the option to upload a thumbnail image that will appear next to the published article on the Forthcoming, Current Issue, and Abstract pages.Authors must submit a .JPG file. The image will be resized automatically to 100 x 100 pixels. 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Refractive index modulation in photonic crystal fibers
Refractive index modulation in photonic crystal fibers induced by mechanical stress relaxation based on CO2 laserirradiationYinian Zhu, Ping Shum, Hui-Wen Bay, Min Yan, Xia Yu, and Chao LuNetwork Technology Research Centre, School of Electrical and Electronic Engineering,Nanyang Technological University, 50 Nanyang Drive, Research TechnoPlaza, Singapore 637553Tel: +65-6790 4682; Fax: +65-6792 6894; E-mail: eynzhu@.sgAbstract: Refractive index modulation in endlessly-single-mode photonic crystal fiber by CO2laser irradiation without surface-deformation is experimentally confirmed with a value of1.68x10-3 for the first time, which is contributed by mechanical stress relaxation in fiber.2005 Optical Society of AmericaOCIS codes: (060.2330) Fiber optics communications; (230.3990) Microstructure devices; (350.5610) Radiation.1. IntroductionPhotonic crystal fiber (PCFs), also called microstructured optical fibers or holey fibers, have potential applications because of their unique optical performances that cannot be achieved by conventional fibers. The PCF consists of regularly spaced air holes running along the fiber cladding, and the core is formed through introducing a defect or missing a hole at the center of the fiber. It has been reported more recently that the attenuation of PCF at transmission windows has reached as low as that of single-mode fibers [1]. On the other research field, long-period gratings (LPGs) and phase-shifted long-period gratings (PS-LPGs) as one major building block for dense wavelength-division multiplexing (DWDM) optical fiber communication networks and sensing systems could play the most important function in selecting optical signal channels and adjusting their amplitudes. LPGs can be fabricated in the optical fiber doped with germanium by UV-light exposure through an amplitude mask. Due to the fact that the PCFs are mainly made up of pure silica, the refractive index modulation cannot be generated in such fiber through UV-exposing without the applied photosensitivity. However, post-processing of PCFs with non-UV irradiation is a very powerful and versatile procedure for fabricating compact PCF-based devices, such as long- period gratings [2], rocking filters [3], Mach-Zehnder interferometer [4], tunable fiber coupler [5], and torque sensor [6]. So far several techniques and methods for the fabrication of LPGs in PCFs have been recently reported, which include the arc discharge with or without the periodic collapse of the holes [7,8], the CO2 laser with physical deformation of the fiber [2], and the use of periodic mechanical pressure [9]. Although it was demonstrated that the LPGs have been written in conventional fiber as well as PCF based on the irradiation of CO2 laser, the investigation of refractive index change in PCF by CO2 laser exposure is limited. In this paper, we study the refractive index modulation induced by the use of a CO2 laser as the heat-treatment source, and present the fabrication of LPG in large-mode-area photonic crystal fiber (LMA-PCF) with fiber geometrical deformation, and LPG and PS-LPG in endlessly-single-mode photonic crystal fiber (ESM-PCF) without surface deformation of the fiber by the focused pluses of CO2 laser and point-by-point writing technique. It is also explained that mechanical stress relaxation is the possible mechanism and contributions to the change of refractive index in the PCF as well as the keeping of fiber’s appearance as original.2. Refractive index modulation by mechanical stress relaxation in PCFIt is well established that the residual stress can be accumulated in standard optical fiber during the drawing process, while the residual stress consists of thermal stress that results from the mismatching of the thermal expansion coefficients of doping components and silica in the fiber, and mechanical stress that is built up as a result of the radial variation of the viscoelastic properties (stress-effect) of the fiber. Since the first PCF was practically developed in 1996, most of the PCFs have been manufactured with stack-and-draw method, in which an array of silica capillaries for the cladding and a silica rod for the core were employed. In contrast to the conventional fibers, only mechanical stress can be taken up in PCF during the fiber drawing, and the thermal stress does not exist in the fiber, which is due to the pure-silica of the fiber. For analysis of mechanical stress in PCF formed during fiber drawing stage, a silica-air system should be considered in the cladding, and hence the cladding shows a much lower viscosity than that of the core. In this case, most of the drawing tension is concentrated in the core. When the PCFRefractive index (n )2laser2laserFigure 1. Diagram of refractive index modulation in PCF by mechanical stress relaxation: photomicrograph of cross-section of PCF preform and SEM images of cross-sections of PCFs before and after irradiation by CO 2 laser (no holes collapsed in the cladding).cladding behaves more and more elastically on cooling, it gives rise to the fixing of stress in the core material. Consequently, the tension is frozen in the core and the compression in the cladding after removal of the drawing force. In order to protect the holes from collapsing at drawing temperature of conventional fiber because of low fiber tension and viscosity under that condition, the PCF drawing is suitable at higher tension, and the drawing temperature should be lowered. On the other hand, there is a temperature gradient transversely in the drawing furnace, which causes the temperature near the furnace wall is higher that in the center of it. Meanwhile, the holes with positive pressure in cladding of the preform keep the heat from radiating into the core. Such temperature distribution in the PCF preform results in a core at lower temperature and higher viscosity, leading to a strong tension in it. The compression of the capillaries at drawing temperature also applies the tension on the core. For the pure silica material, such as PCF, the compressive stress gives rise to the increase of its refractive index, whereas the tension stress will result in a decrease of it. Therefore, mechanical stress in PCF can be relaxed as the temperature ofthe CO 2-laser-exposed area becomes higher than the transition temperature (T t ≈ 1300 0C in our high temperature experiment) of pure-silica, which gives rise to the difference in refractive indices before and after CO 2 laser irradiation. The index modulation is formed by the change of mechanical stress, which is given by()ms ai core ms bi core ms core C n )()(σσ−≈∆ms bi core )(σms ai core )(σ, where C is the stress-optic coefficient and its value is –4.2 x 10-12 Pa -1 for pure-silica glass, and and are the mechanical stresses before and after CO 2 laser irradiation, respectively. Fig. 1 shows the diagram of refractive index modulation in PCF, the photomicrograph of cross-section of PCF preform, and thescanning electron microscope (SEM) images of PCF’s cross-sections before and after CO 2 laser irradiation. It can be clearly seen that there are no any hole-collapses in the fiber after the gratings are inscribed by CO 2 laser, and the refractive index of the core exposed could be higher then the regions that are not exposed to the radiation. This is because the tension is released periodically and in such a way LPGs and PS-PCFs could be formed in the PCF.3. Experimental resultsThe experimental setup for the fabrication of LPG in LMA-PCF, and LPG and PS-LPG in ESM-PCF is the same as one reported in Ref. 3. The LMA-PCF and ESM-PCF used in our experiments were supplied from Crystal Fiber A/S and BlazePhotonics Ltd., and the scanning electron microscope (SEM) images of the fiber cross-section are shown in insets (above) of Fig. 2 (a) and (b), respectively. They are single-mode at all wavelengths for which fused silica is transparent, and the external fiber diameter of 125 µm. First, we use the physical deformation method to periodically collapse the holes by heat treatment of CO 2 laser for the formation of LPG in LMA-PCF. After 10 periods was written, a resonance of –29.4 dB at 1468.2 nm with high insertion loss of 7.6 dB and a 22.7% decrease of fiber diameter on every period were obtained, which are shown in Fig. 2 (a) and inset (below), respectively. Then we useΛ(a) (b)Figure 2. (a) Evolution (periods from 3 to 10) of transmission spectra of LPG in LMA-PCF. Insets: SEM image of LMA-PCF cross-section (above), and photomicrograph of the appearance of the fiber with physical deformation (below); (b) Evolution (periods from 3 to 14) of transmission spectra of LPG and PS-LPG with π-phase shift at the middle of the grating in ESM-PCF (LPG formed with 6 periods). Insets: SEM image of ESF-PCF cross-section (above), and photomicrograph of the appearance of the fiber without surface deformation (below).the mechanical stress relaxation method based on CO2 laser irradiation to inscribe LPG and π-PS-LPG in ESM-PCF. The resonance wavelength of the formed LPG with 6 periods is at 1330.1 nm with the insertion loss of 0.8 dB and a dip of –33.1 dB, which is achieved with mode overlap at the lowest mode of LP01 by stronger coupling mode and a higher coupling coefficient that is proportional to the refractive index change. By using the mode coupling of LP01-LP04 of LPG in ESM-PCF, the effective refractive index contrast of 1.68x10-3 can be reached, which is contributed to the mechanism of stress relaxation in the fiber. We have observed the evolution of transmission spectra of a π-PS-LPG in ESM-PCF shown in Fig. 2. By inserting a blankness of half period into the center of the grating causes the conversion of destructive mode-coupling into constructive mode-coupling at the phase-matching wavelength. The transmission spectrum of two notches in π-PS-LPG with pass-bandwidth is as wide as 86.5 nm at FWHM. It also can be seen, from the inset (below) of Fig. 2 (b), that there were no any holes collapsed in the cladding after the π-PS-LPG was induced in the fiber. Meanwhile, the glass structure of fiber is adjusted into the original state of the relaxation at T t provided by the heat from CO2 laser so that the gratings are thermal stable under T t.4. ConclusionIn conclusion, the fabrication of LPG and PS-LPG in ESM-PCF with CO2 laser and point-by-point writing technique was demonstrated for the first time of our knowledge, which has confirmed that the mechanical stress relaxation was contribution to the refractive index modulation in PCFs, and no geometrical deformation of the fiber surface and collapse of holes inside fiber occurred after the gratings were inscribed. Such fiber gratings can be applied at high temperature (below T t), and their good performances on fiber-reliability and anti-radiation make themselves to be a potential candidate for the application as sensors in harsh environment, such as space-aircraft and nuclear-power plant.5. References[1] K. Tajima, J. Zhou, K. Nakajima, and K. Sato, “Ultralow loss and long length photonic crystal fiber,” J. Lighteave Technol. 22, 7-10 (2004).[2] Y. Zhu, P. Shum, J. H. Chong, M. K. Rao, and C. Lu, “Deep-notch, ultracompact long-period grating in a large-mod-area photonic crystalfiber,” Opt.Lett. 28, 2467-2469 (2003).[3] G. Kakarantzas, A. Ortigosa-Blanch, T. A. Birks, P. St. J. Russell, L. Farr, F. Couny, and B. J. Mangan, “Structural rocking filters in highlybirefringent photonic crystal fiber,”Opt.Lett. 28, 158-160 (2003).[4] J. H. Lim, H. S. Jang, K. S. Lee, J. C. Kim, and B. H. Lee, “Mach-Zehnder interferometer formed in a photonic crystal fiber based on a pairof long-period fiber gratings,” Opt.Lett. 29, 346-348 (2004).[5] H. Kim, J. Kim, U-C Paek, B. H. Lee, and K. T. Kim, “Tunable photonic crystal fiber coupler based on a side-polishing technique,”Opt.Lett. 29, 1194-1196 (2004).[6] S. Oh, K. R. Lee, U-C Paek, and Y. Chung, “Fabrication of helical long-period fiber gratings by use of a CO2 laser,” Opt.Lett. 29, 1464-1466(2004).[7] G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric are-induced long-period gratings in Ge-free air-silica microstructurefibers,” Electron. Lett. 39, 349-350 (2003).[8] K. Morishita and Y. Miyake, “Fabrication and resonance wavelengths of long-period gratings written in a pure-silica photonic crystal fiberby the glass structure change,” J. Lighteave Technol. 22, 625-630 (2004).[9] J. H. Lim, K. S. Lee, J. C. Kim, and B. H. Lee, “Tunable fiber gratings fabricated in photonic crystal fiber by use of mechanical pressure,”Opt.Lett. 29, 331-333 (2004).。
衍射光栅的拼接方法
衍射光栅的拼接方法魏江【摘要】随着啁啾脉冲放大技术的发展,为用拼接的方法获得大尺寸衍射光栅已经成为一项急待解决的课题.本文从拼接的六种偏差出发,通过比较不同的消除方法,将拼接法分为:补偿拼接法、干涉拼接法、远场光斑拼接法和平移曝光法,为用拼接法获得大尺寸光栅提供了理论依据.【期刊名称】《常熟理工学院学报》【年(卷),期】2007(021)010【总页数】5页(P51-55)【关键词】拼接光栅;拼接参量;干涉仪;监控【作者】魏江【作者单位】常熟理工学院,物理与电子科学系,江苏,常熟,215500【正文语种】中文【中图分类】TH74近年来,随着啁啾脉冲放大(Chirped Pulse Amplification简称CPA)技术[1,2,3,4]的发展,更高强度的超短脉冲[5,6,7]已经成为研究光和物质相互作用以及惯性约束核聚变等领域的有效手段．用来进行脉冲压缩的衍射光栅是CPA系统的核心元件之一,该系统要求光栅具有高衍射效率、高损伤阈值和大尺寸,这是普通光栅远远不能满足的,目前性能最好的是多层介质膜光栅(MLD)[8,9]．CPA系统为了产生拍瓦级(1015W)功率输出,需要宽度达到米级的大尺寸高效衍射光栅．但是,大尺寸多层介质膜光栅的制造非常困难,迄今为止,只有美国的LLNL实验室有能力制造米级的光栅(此面积是目前我国所能刻制的最大光栅面积的7倍多),但是其造价昂贵,生产周期很长．有人认为用大光栅刻划机就会很容易刻划出大光栅,但是7倍于最大刻划尺寸的大光栅的刻划机目前尚未研制出,与此同时还要解决大面积镀膜均匀性的问题,由于刀具损坏还需实现高精度的自动换刀等问题,因此不可能用机械刻划的方法制作出适合要求的脉冲压缩光栅．为此,人们提出了用光栅拼接的方法[10,11]制作大口径的多层介质膜光栅,即由多块光栅拼接成一块大光栅,这就为获得米级多层介质膜光栅提供了新的思路．拼接光栅中的偏差(如图1所示)包括平移偏差:shift (dx)、piston(dz),旋转偏差:tip(绕x轴的角度偏差dθx)、tilt(绕y轴的角度偏差dθy)、twist(绕z轴的角度偏差dθz)和刻线宽度偏差Δd．由于沿光栅刻线方向的平移dy不会影响光栅的位相分布,因此不作讨论．理想的光栅拼接对于任意波长、入射角和衍射级都不会引入相位差,它完全可以代替单一的大尺寸光栅．理想的拼接应满足三方面的要求:光栅表面必须共面(dz=0,dθx=0,dθy=0);光栅刻槽必须彼此平行(dθz=0);横向平移偏差dx必须是光栅周期的整数倍(dz=nd,d是光栅周期)．基于光栅拼接的六种偏差,按照消除方法的不同,可将拼接法分为以下几种．2.1 补偿拼接法对单色光和特定的入射角的拼接光栅,存在三种类型的相位差[12]:相对X轴和Z轴的偏差dx、dz称位移相位差;相对X轴和Z轴的旋转偏差dθx、dθz产生竖直倾斜相位差;相对Y轴的旋转偏差dθy和刻线周期偏差Δd产生水平倾斜相位差．光栅拼接的六个偏差相互联系,这将大大降低拼接光栅的复杂性,因为一个偏差带来的相位差将在其它方面被补偿[12],下面以位移相位差为例说明(如图2所示)．对两块参数相同且无旋转偏差的光栅G1和G2,当入射角为α,衍射角为β时,1,2两束光之间存在的光程差(OPD)为:当光程差为波长λ的整数倍时(OPD=nλ,n为整数),相位差的影响减小为零．令n=0,则OPD=0,可推出:dz是比较容易调节的,通过调节dz产生的位相差来补偿dx引起的位相差．实验中通过探测位相差,合理调节dz就可使(2)式成立,即拼接光栅对单色入射光的某衍射级次实现同相位．2.2 干涉拼接法[13,14]两块相同参数的衍射光栅在拼接过程中(如图3所示),当使用的入射光不是单色光,拼接的关键是调节两光栅共面(dz=0)和调节二者的间距dx,使其调整为光栅周期的整数倍．干涉拼接法借助一个参考光栅很好地解决了这一问题．假设待拼接的两块光栅G1、G2间无旋转偏差,G3为参考光栅,G1、G2、G3具有相同的周期,假设三块光栅的平面、刻线均相互平行．将激光束λa,λb同轴混合(波长λab)、展宽后入射到两块光栅,在P、Q点第一次衍射光相位分别改变了第二次入射到参考光栅的A、B两点,在这两点衍射光相位分别改变光线射回P,Q两点,相位改变分别为φφ图中是在P、Q点反射光相对入射光改变的相位,则两束光在光栅G1上的相位差为φ在光栅G2上的相位差为φ其中φφ则其中整理后得到考虑到垂直于光栅平面的纵向平移偏差dz,可得相位差为由(5)式发现dz产生的相位差与波长有关,而dx产生的相位差与波长无关．实验中采用双波长外差式干涉仪将dx产生的相位差与dz产生的相位差分开．基本操作方法见文献[14],利用这种调节法能使Δx的误差小于1%d．2.3 远场光斑拼接法[15]同干涉拼接法一样,可用两种波长的衍射光来辨别dz与dx产生的相位差,利用激光束垂直入射光栅,通过观察-1级衍射光的远场衍射图案来调节两个平移偏差．图4是几种光斑的示意图．其中(a)图是理想的远场光斑,(b)图是位移相位差为π,无倾斜相位差时的光斑．通过(b)图是否在两种波长的衍射图案中同时出现来调节纵向平移偏差dz,使dz=0．依照(a)图来调节横向偏差dx,使其调整为光栅周期的整数倍．实验中[15]利用泰曼-格林干涉仪,通过观察零级干涉图来调节两光栅面的平行,即面内偏转角dθx=0,dθy=0．(c)图是位移相位差为零,有竖直倾斜相位差时的光斑,(d)图是位移相位差和竖直倾斜相位差同时存在时的光斑．依照特殊的远场光斑来调节偏转角dθz,使dθz=0．实验中对远场光斑的定量分析使得dθz、dz、dθx 的调节更精确．2.4 平移曝光法在一块干板上通过两次(或两次以上)曝光得到拼接光栅．原理如图5所示,首先遮挡位置2,对位置1曝光,然后平移干板,对位置2曝光．由于只在同一干板上平移、曝光,因此拼接中只存在两种偏差:两光栅的横向平移偏差dx,面内角度偏差dθz．通过测量两次干涉条纹的相位差,调节实验装置使每次记录的条纹彼此平行,当两条纹间距dx是光栅周期的整数倍时,可以得到光栅的理想拼接．实验中如何获得干涉条纹的相位是关键,以前[16]采取引入一块参考光栅与第一次曝光的干涉场形成莫尔条纹,用光电探测器记录这一信号,并以此为标准来确定下次曝光位置．在此介绍一种无需引入参考光栅的方法来制做大面积光栅[17]，实验装置如图6所示．其中BS0,BS1,BS2是分束器,S1,S2是观测屏,D是一小型光电探测器,G是全息记录材料．首先用记录光对AC区域曝光,在AC区域形成一个很微弱的光栅-潜像,由于它的衍射效率很低,肉眼很难辨别,但用光电探测器很容易观测到．用波长为632．8nm的检测波(光刻胶对此波长不敏感,不影响潜像)探测曝光边界两端的相位,当A端产生的干涉条纹的周期是潜像周期的整数倍,移动G探测C端的相位,调节使右边界的相位与潜像相位也相同,这就保证了dx=nd,其中d是潜像的周期．移动G到下一区域继续曝光,由于保证了两边界的相位相等,因此实现了光栅的理想拼接．具体方法如下:实验中用到一个锁相放大器,压电传感器PZT在函数信号发生器的作用下使分束器BS2在水平方向上做正弦振动,相应的探测器D上的光强也会产生正弦变化,用锁相器记录二者的相位差φ1,同样,移动G探测C端的相位差φ2,当调节G的位置到φ1=φ2时,满足了dx=nd,可以进行下一区域的继续曝光．对高效的多层介质膜光栅,由于尺寸很难做大,用光栅拼接的方法获得大尺寸光栅具有制作简便、衍射效率高、制造成本较低等优点．本文从研究拼接光栅的偏差参量出发,论述了拼接光栅的几种方法,其中补偿法、干涉拼接法、远场光斑拼接法属于机械拼接,平移曝光法属于光学拼接．补偿法操作相对简单,但它只适用于单色光和特定的入射角的拼接光栅,使用条件非常受限．干涉拼接法借助一个含参考光栅的双波长外差干涉仪,解决了光栅在拼接过程中调节共面和调节两光栅间距的问题,但它没有考虑旋转偏差的影响．远场光斑拼接法利用干涉图和远场光斑图完全解决了拼接光栅中的平移偏差和旋转偏差,但调节过程过于繁杂,而且只能用位移相位差为π时的光斑作为判定依据也略显单一．用光学拼接法获得大面积光栅近来也有了很大发展,平移曝光法原理简单,只需考虑两个偏差参量,但代价是制作过程繁杂,调节难度较大,而且由于平行光路系统存在像差,两曝光区域相邻边界处干涉条纹的相位有偏差．如何精确控制干板,简化操作过程将是今后研究的重点．致谢: 本文得到了苏州大学信息光学工程研究所吴建宏教授的大力帮助,在此表示衷心感谢!【相关文献】[1] 孟昭贤.高功率脉冲激光系统的原理和进展[J].物理学进展,1998,18(4):333-357.[2] Strichland D， Mouton G. Compression of amplified chirped optical pulses[J]. OptCommon,1985,56(3):219-221.[3] Xu Z Z, Yang X D, Leng Y X， et al. High-power output from a compact OPCPA laser system[J].Chin Opt Lett, 2003,1(I):24-27.[4] Maine P, Strick land D, Bado P, et al. Generation of ultrahigh peak power pulses by chirped pulse amplification[J]. IEEEJ Quantum Electron,1988, QE-24(2):398-403.[5] Hunt J T， Speck D R. Present and future performance of the Noval asers ystem[J]. Optical Engineering,1989,28 (4):461-468.[6] Perry M D, Mourou G. Terawatt to petawatt subpicosecond lasser[J].science,1994,264:917-924.[7] Shore B W, Perry M D, Briten J A, et al. Design of high-efficiency dielectric reflection gratings[J]. Opt Soc Am A, 1997,14(5):1124-1136.[8] Li L F， Hirsh J. All-dielectric high-efficiency reflection gratings made with multiplayer thin-film coatings[J]. Opt Lett,1995,20(11):1349-1351.[9] Li L, Hirsh J. All-dielectric high-efficiency reflection gratings made with multilayer thin-film coatings[J].Optics Letters, 1995,20(11):1349-1351.[10] ZhangT J. A narray-grating compressor for high-power chirped-pulse amplification lasers [J]. Opt Commun, 1998,14(5):367-376.[11] Hoose John,Lowen Erwin, Wiley Robert, Blasiak Thomas. A new generation of larger telescopes presents an un-precedented challenge to optics manufactures[J].Photonics Spectra,1995,(12):118-120.[12] Rushford M C, Molander W A,et al. Diffraction grating eigenvector for translational and rotational motion[J]. Opt Lett, 2006,31(2):155-167.[13] Yoneyoshi Kitagiwa, Hisanori Fujita, Ryosuke Kodama,et al. Prepulse-free petawatt laser for a fast ignitor [J]. IEEE J Quantum Electron,2004,40(3):281～293.[14] Lijiang Zeng, Lifeng Li. Method of making mosaic gratings by using a two-color heterodyne interferometer containing a reference grating[J]. Opt Lett, 2006,31(2):152-154.[15] Yao Hu, Lijiang Zeng, Lifeng Li.Method to mosaic gratings that relies on analysis of far-field intensity patterns in two wavelengths[J]. Opt Lett, 2007，269(2)：285～290. [16] Turukhano B G, Gorelik V P,Kovalenko S N, Turukhano N. Phase synthesis of a holographic metrological diffraction grating of unlimited Length[J]. Optics &Laser Technology,1996,28(4):263-268.[17] Lijiang Zeng,Lifeng Li. Optical mosaic gratings made by consecutive, phase-inter locked,holographic exposes using diffraction from latent fringes[J]. Optics Letters,2003，32(9):1081-1083.。
华中科技大学研究生先进光纤传感课程罗海鹏--OE(2015)多模微纳光纤测T、RI,基于菲涅尔反射-6
Lecture5 表面等离激元ppt课件
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Band-structure effects
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可以证明：s-polarized wave (TE mode) 在表面上不能存在！ 因此，我们只考虑 p-polarized wave (TM mode)：
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几种极限情况
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Z. Yuan and S. Gao, Phys. Rev. B 73, 155411 (2006)
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模型（Non-retarded regime）
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进行紫外曝光时，由于光栅区曝光部分B 参加反应的氢分子要比被遮挡部分A 参加反应 的氢分子多,在光栅制作完毕后B 区中残留的氢分子要比A区中的少,所以当经历退火后A 区由于氢分子逃逸导致折射率的减小量要比B 区大,这就导致纤芯折射率调制深度的增加， 引起谐振峰的较大的变化。为了解决这个问题,作者应用了均匀紫外曝光技术。
3 应力或温度传感器 长周期光纤光栅用作传感器不仅具有光纤传感器的一切优点: 如体积小、重量轻、可 重复性好等, 而且对温度、应力变化非常灵敏。因此, 它是一种比较理想的温度或应力 敏感元件。研究表明 ,长周期光纤光栅温度灵敏度是光纤B ragg 光栅的7 倍。长周期 光纤光栅的多个损耗峰可以同时进行多轴应力及温度测量, 也可以将级联的长周期光 纤光栅作为传感器阵列进行多参数分布式测量。随着研究逐渐深入, 长周期光纤光栅 应用越来越广。就目前所知, 在通信领域中的带通滤波、光上下路复用、光纤光源、 光纤耦合、偏振器件等方面都有相关的研究结果。在传感领域, 由于其谱特性对温度、 应力、微弯及外部折射率变化相当灵敏, 因此, 能够产生温度、应力、微弯及外部折射 率变化的物理量就间接导致其谱特性变化。目前研究结果包括长周期光纤光栅用作温 度传感、振动测量、磁场传感、载重传感器、液体气体传感器等。 4 带通滤波器 光纤B ragg 光栅带通滤波器一个潜在缺点是产生光反馈或不希望的光谐振。利用长周 期光纤光栅组合设计成光学带通滤波器件, 可以避免这一点。原理如图,在四端口的瞬 逝型(evanescen t) 单模光纤耦合器两纤芯中分别写入一对相位相反的长周期光纤光栅。 将光栅的周期与折射率调制深度设定为特定比率, 这样在耦合作用长度内, 特定波长的 光耦合得到抑制, 而其它波长能够进行光耦合, 从耦合器纤芯1 耦合进纤芯2。只有希望 的特定波长的光由于耦合极弱, 保
光纤布拉格光栅自致啁啾效应的研究
耦合系数 ,κ为交流耦合系数 。
传输矩阵法[11 ,12 ] 是分析光纤光栅的重要方法 ,
它将一个非均匀的光栅近似为 M 个均匀周期的小
光栅的串联 。M 不能无限大 ,一般 M > 50 即可得到
较为准确的结果 。整段光纤光栅的传输矩阵为
3 数值模拟和实验结果
采用传输矩阵法 ,首先对均匀光纤布拉格光栅 进行数值模拟 ,得到的反射谱存在左右对称的旁瓣 , 如图 2 所示 ;然后 ,以高斯函数作为切趾函数进行数 值模拟 ,得到的反射谱其旁瓣得到了很好的抑制 ,如 图 3 所示 。
摘要 根据耦合模理论 ,采用传输矩阵法分析了相位掩模法制作的光纤布拉格光栅的反射谱特性 。设计了一种新 的写制光纤光栅的光路 ,利用高斯激光光束写制出具有短波自致啁啾效应的切趾光栅 (栅长 0. 015 m) 。对具有短 波自致啁啾效应的光纤光栅进行了物理切割 (剩余光栅的长度分别取 0. 007 m 和 0. 0055 m) ,得到了一种新型的具 有长波自致啁啾效应的光纤光栅 ,原本的自致啁啾光栅反射谱中旁瓣分布在短波长方向 ,而得到的新型自致啁啾 光栅的反射谱中长波长方向的旁瓣更为明显 。基于对光纤布拉格光栅自致啁啾效应的分析 ,提出一种新型类高斯 切趾函数 ,以此函数对自致啁啾效应进行数值模拟 ,得到了与实验结果相一致的光谱图 。 关键词 光纤光学 ; 光纤布拉格光栅 ; 切趾光栅 ; 自致啁啾 ; 传输矩阵法 中图分类号 TN253 文献标识码 A doi : 10. 3788/ AOS20082809. 1671
E2mail : zhangwg @nankai. edu. cn
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Optics Express投稿模板
Attention Optics Express AuthorsOptics Express has made significant changes to its production process by creating archival-quality XML along with the PDF output. XML is the industry standard for producing and archiving scientific journal articles and is used in producing all other OSA journals. Having full-text XML will allow Optics Express to be indexed more accurately and completely in MEDLINE, PubMed Central, and other databases; it will also allow the journal to meet its archival obligations and to prepare for new services such as full-text semantic search and repurposing of content.In order to prevent delays in production, we ask that authors carefully adhere to the following new guidelines:•Word and LaTeX. OSA accepts Word and LaTeX submissions; however, we encourage authors to submit papers in MS Word. OSA will not publish the sameWord file that authors submit for their final revisions, so it is imperative that authorscarefully check the final version of their paper before paying the publication fee.OSA uses a Word plug-in called eXtyles to normalize, format, tag, and parse the fileinto full-text XML. eXtyles automatically reformats, checks, and updates thereferences against the CrossRef and PubMed databases. In addition to running otherauto-redact editing rules, eXtyles checks all reference, figure, table and equationcallouts in the text to ensure all items are cited. At this time full-text XML will begenerated from LaTeX papers after publication.•Author listing. All authors must be grouped together using superscripts to callout each affiliation. Hard returns (Enter key) must be used to separate each individualaffiliation. Soft-returns (Shift + Enter key) should be use for line breaks within asingle paragraph.•Main text. Authors must identify equations and figures in the text by inserting Fig.or Eq. before the number. All references, figures, and tables must be called out in the text.•Figures. Authors must use one image file per figure. Figures need to be inserted as objects that are fixed and move with the text, not as floating objects. Figures shouldnever be placed in a table environment.•Tables.Authors must use Word’s Table editor to insert tables. Authors must not import tables from Excel. All content for each table should be in a single Word table(do not split content for a single table across multiple Word tables).•Equations. OSA does not accept equations built using the Word 2007 Equation Builder. All equations should be created in MathType (or the Microsoft Equationeditor from Design Science). See Instructions for Users of Word 2007/DOCX fordetails. We strongly encourage authors to use MathType 6.5. Note that LaTeX userscan type LaTeX code directly into MathType for rendering in Word.Adherence to the above guidelines will significantly expedite the production of your paper.Instructions for the preparation of a manuscriptfor Optics ExpressJoseph Richardson,1,* Antoinette Wrighton,2and Jennifer Martin2,31Department of Peer Review, Optical Society of America, 2010 Massachusetts Avenue, NW, Washington, D.C. 20036,USA2Department of Editorial Services, Optical Society of America, 2010 Massachusetts Avenue, NW, Washington, D.C.20036, USA3Currently with the Department of Electronic Journals, Optical Society of America, 2010 Massachusetts Avenue, NW,Washington, D.C. 20036, USA************Abstract: Explicit and detailed rules are given for preparing a manuscriptfor Optics Express. After a general introduction and a summary of the basicrequirements, specific guidelines are given for all major manuscriptelements (such as abstract, headings, figures, tables, and references) toachieve optimal typographic quality. The use of complete and properlyformatted references is particularly important.2010 Optical Society of AmericaOCIS codes: (000.0000) General; (000.2700) General science.References and links1.P. J. Harshman, T. K. Gustafson, P. Kelley, “Title of paper,” J. Chem. Phys. 3, (to be published).2. C. van Trigt, “Visual system-response functions and estimating reflectance,” J. Opt. Soc. Am. A 14, 741-755 (1997).3.K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetricwaveguide,” J. Opt. Soc. B 16, 267-269 (1999).4. B. R. Masters, "Three-dimensional microscopic tomographic imagings of the cataract in a human lens invivo," Opt. Express 3, 332 (1998), /abstract.cfm?URI=OPEX-3-9-332.5. B. R. Masters, “Three-dimensional confocal microscopy of the human optic nerve in vivo,” Opt. Express 3,356 (1998), /abstract.cfm?URI=OPEX-3-10-356.1. IntroductionAdherence to the specifications listed in this style guide is essential for efficient review and publication of submissions. Since Optics Express paper are not routinely copyedited and typeset, use of the Optics Express macros and style guide is critical to providing a consistent appearance.Except for numbering and titling of sections, which may not be desirable for short articles, the Optics Express style and layout rules have been followed in this guide. Also note that there is a checklist available in Section 6 that summarizes the style specifications.2. Page layout and lengthPaper size should be U.S. Letter, 21.505 cm x 27.83 cm (8.5 in. x 11 in.). The printing area should be set to 13.28 cm x 21.54 cm (5.25 in. x 8.5 in.); margins should be set for a 2.54-cm (1 in.) top and 4.11-cm (1.625 in.) left, right, and bottom.To maintain a rapid publication cycle, the recommended page length for an Optics Express article is 6 pages. Higher publication fees apply to articles 7-15 pages in length. There is an additional fee for manuscripts longer than 15 pages.3. SoftwareOptics Express accepts Word and TeX files. OSA strongly encourages authors to submit papers in MS Word rather than in LaTeX.4. Typographical styleAll fonts for text should be some version of Times New Roman. Text should be 10-pt., the title should be 18-pt., and the affiliation and references should be 8-pt. Do not add hyphenation at the end of a line.4.1 TitleCenter the title. The title should be in 18-pt. bold font. Use initial cap for first word in title or for proper nouns. Use lowercase following colon. Title should not begin with an article or contain the words "first," "new" or "novel."4.2 Author nameCenter author names in 10-pt. bold font. Author names should appear as used for conventional publication, with first and middle names or initials followed by surname. Every effort should be made to keep author names consistent from one paper to the next as they appear within OSA publications.4.3 Author affiliationAll authors and affiliations should be styled in the following below. If all authors share one affiliation, superscript numbers are not needed. The corresponding author will have an asterisk indicating footnote. All authors must be grouped together using superscripts to callout each affiliation. Hard returns (Enter key) must be used to separate each individual affiliation. Soft-returns (Shift + Enter key) should be use for line breaks within a single paragraph. Abbreviations should not be used. Center the e-mail address of author(s) directly below the affiliation. Please include the country at the end of the affiliation.Joseph Richardson,1,* Antoinette Wrighton,2and Jennifer Martin2,31Department of Peer Review, Optical Society of America, 2010 Massachusetts Avenue, NW, Washington, D.C. 20036,USA2Department of Editorial Services, Optical Society of America, 2010 Massachusetts Avenue, NW, Washington, D.C.20036, USA3Currently with the Department of Electronic Journals, Optical Society of America, 2010 Massachusetts Avenue, NW,Washington, D.C. 20036, USA************Affiliation line with two e-mail addresses (only one for the corresponding author)Joseph Richardson,1,* Antoinette Wrighton,2,4and Jennifer Martin2,31Department of Peer Review, Optical Society of America, 2010 Massachusetts Avenue, NW, Washington, D.C. 20036,USA2Department of Editorial Services, Optical Society of America, 2010 Massachusetts Avenue, NW, Washington, D.C.20036, USA3Currently with the Department of Electronic Journals, Optical Society of America, 2010 Massachusetts Avenue, NW,Washington, D.C. 20036, USA4***********************4.4 AbstractBegin the section with the word “Abstract:” in bold print followed by a colon. Indent left and right margins 1.27 cm (0.5 in.). Font size should be 10-pt. and alignment double (left and right) justified.The abstract should be limited to approximately 100 words. It should be an explicit summary of the paper that states the problem, the methods used, and the major results and conclusions. It also should contain the relevant key words that would allow it to be found in a cursory computerized search. If the work of another author is cited in the abstract, a separate citation should be included in the body of the text. Do not include numbers, bullets, or lists inside the abstract.4.5. CopyrightThe line immediately following the abstract should be © 2007 Optical Society of Americain 9-pt. type. Indentation should match the abstract, i.e., 1.27 cm (0.5 in.). Insert a 4-pt. space above and below the copyright line. See the first page of these instructions.4.6 OCIS subject classificationOptics Classification and Indexing Scheme (OCIS) subject classifications should be included at the end of the abstract. List the OCIS code in parenthesis, followed by the term spelled out; separate OCIS terms with semicolons. Each paper must contain two to six OCIS codes. Use 8-pt. type for this line. For a complete list of OCIS codes, visit this site: /submit/ocis/OCIS codes: (260.1440) Birefringence; (050.1950) Diffraction gratings4.7 Main textThe first line of the first paragraph of a section or subsection should start flush left. The first line of subsequent paragraphs within the section or subsection should be indented 0.62 cm (0.2 in.). All main text should be alignment double (left and right) justified.Section headings may be numbered consecutively and consistently throughout the paper in Arabic numbers and typed in bold. Use an initial capital letter followed by lowercase, except for proper names, abbreviations, etc. Always start headings flush left. Do not include references to the literature, illustrations, or tables in headings. Insert a 6-pt. space above and below each section heading as shown in this paper.Subsection headings may be numbered consecutively in Arabic numbers to the right of the decimal point, with the section number to the left of the decimal point as shown in this paper. Subsection headings should be in italics, with an initial capital letter followed by lowercase, except for proper names, abbreviations, etc. Start subsection headings flush left. Do not include references to the literature, illustrations, or tables in headings. Create a 6-pt. space above and below each subsection heading as shown in this paper.Numbering of section headings and subsection headings is optional but must be used consistently throughout papers in which it is applied.4.8 EquationsOSA does not accept equations built using the Word 2007 Equation Builder. All equations should be created in MathType (or the Microsoft Equation editor from Design Science). See Instructions for Users of Word 2007/DOCX for details. We strongly encourage authors to use MathType 6.5. Note that LaTeX users can type LaTeX code directly into MathType for rendering in Word.Equations should be centered, unless they are so long that less than 1 cm will be left between the end of the equation and the equation number, in which case they may run on to the next line. Equations should have a 6-pt. space above and below the text. Equation numbers should appear at the right-hand margin, in parenthesis. For long equations, the equation number may appear on the next line. For very long equations, the right side of the equation should be broken into approximately equal parts and aligned to the right of the equal sign. The equation number should appear only at the right hand margin of the last line of the equation:(1)All equations should be numbered in the order in which they appear and should be referenced from within the main text as Eq. (1).In-line math of simple fractions should use parentheses when necessary to avoid ambiguity; for example, to distinguish between 1/(n - 1) and 1/n - 1. Exceptions to this are the proper fractions such as 12, which are better left in this form. Summations and integrals that appearwithin text such as 12n =1n =∞(n 2-2n )-1∑ should have limits placed to the right of the symbol to reduce white space. Use MS Word Equation Editor or MathType for in-text and display notation wherever possible.4.9 References and linksReferences should appear at the top of the article, below the abstract, in the order in which they are referenced in the body of the paper (see below). The font should be 8-pt. aligned left. Lines should be single-spaced. The words “References and links ” should head the section (no number) in bold print followed by one blank line, directly above the first reference. Insert a 6-pt. space above the “References and links ” line. All references should be indented 0.5 cm (0.2 in), with succeeding lines indented sufficiently to preserve alignment. The references section should be delimited by horizontal rules above and below the section, separated by at least 6-pts. of white space from the text.Optics Express uses numerical notation in brackets for bibliographic citations. At the point of citation within the main text, designate the reference by typing the number in after the last corresponding word [1]. Reference numbers should proceed a comma or period [2]. Two references [3,4], should be included together, separated by a comma, while three or more consecutive references should be indicated by the bounding numbers and a dash [1-4].Optics Express follows the following citation style:Journal paperFor journal articles, authors are listed first, followed by the article’s full title in quotes, the journal’s title abbrevia tion, the volume number in bold, inclusive page numbers, and the year in parentheses. Journal titles are required.6. C. van Trigt, “Visual system -response functions and estimating reflectance,” J. Opt. Soc. Am. A 14, 741-755 (1997).BookFor monographs in books, authors are listed first, followed by article’s full title in quotes, the word “in,” followed by the book title in italics, the editors of the book in parenthesis, the publisher, city, year.7. David F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic, Orlando, Fla., 1985).Chapter in a bookFor citation of a book as a whole or book chapter, authors or editors are listed first, followed by title in italics, and publisher, city, and year in parenthesis. Chapter number may be added if applicable.8. F. Ladouceur and J. D. Love, Silica-Based Buried Channel Waveguides and Devices (Chapman & Hall,1995), Chap. 8.Electronic citationsInternet links may be included as references. Internet links should list the author, title (substitute file name, if needed), and the full URL (universal resource locator). Include the date of access, if relevant:9. C. Gerry, “Remarks on the use of group theory in quantum optics,” Opt. Express 8, 76-85 (2001)./abstract.cfm?URI=OPEX-8-2-76.10.Extreme Networks white paper, “Virtual metropolitan area networks” (Extreme Networks, 2001)./technology/whitepapers/vMAN.asp.Paper in a published conference proceedings11.R. E. Kalman, “Algebraic aspects of the generalized inverse of a rectangular matrix,” in Proceedings ofAdvanced Seminar on Genralized Inverse and Applications, M. Z. Nashed, ed. (Academic, San Diego,Calif., 1976), pp. 111-124.Paper in unpublished conference proceedings12. D. Steup and J. Weinzierl, “Resonant THz-meshes,” presented at the Fourth International Worksh op onTHz Electronics, Erlangen-Tennenlohe, Germany, 5-6 Sept. 1996.For citation of proceedings, follow the individual format for SPIE, IEEE and OSA Proceedings:SPIE proceedings13.G. D. Love, C. N. Dunlop, S. Patrick, C.D. Saunter, “Horizontal turbulence m easurements usingSLODAR,” Proc. SPIE 5891, 27–32 (2005).IEEE proceedings14.T. Darrel and K. Wohn, "Pyramid based depth from focus," in Proceedings of IEEE Conference onComputer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York,1988), pp. 504-509.OSA proceedings15.G. Kalogerakis, M. E. Marhic, L. G. Kazovsky, and K. K. -Y. Wong, "Transmission of OpticalCommunication Signals by Distributed Parametric Amplification," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies,Technical Digest (CD) (Optical Society of America, 2005), paper CTuT2./abstract.cfm?URI=CLEO-2005-CTuT2Paper accepted for publication16. D. Piao, "Cancelation of coherent artifacts in optical coherence tomography imaging," Appl. Opt. (to bepublished).Manuscript in preparation17.J. Q. Smith, Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester,N.Y. 14623, and K. Marshall are preparing a manuscript to be called "Optical effects in liquid crystals." Personal communication18.Barbara Williams, Editorial Department, Optical Society of America, 2010 Massachusetts Avenue, N.W.,Washington, D.C., 20036 (personal communication, 2001).4.10 AcknowledgmentsAcknowledgments should be included at the end of the document. The section title should read “Acknowledgments” in 10-pt. bold font. The section title should not follow the numbering scheme of the body of the paper. The body of the section should follow the font and layout of the body of the paper (see Subsection 4.7 above). Please identify all appropriate funding sources by name and contract number in the Acknowledgment section.5. Figures, multimedia and tables5.1 FiguresFigures should be included directly in the document. All photographs must be in digital form and placed appropriately in the electronic document. All illustrations must be numbered consecutively (i.e., not by section) with Arabic numbers. The size of a figure should be commensurate with the amount and value of the information conveyed by the figure.Authors must use one image file per figure. Figures must be inserted as objects that are fixed and move with the text, not as floating objects. Figures should never be placed in a table environment.All the figures should be centered, except for small figures no wider than 2.6 in.(6.6 cm), which may be placed side by side. Place figures as closely as possible to where they are mentioned in the text. No part of a figure should go beyond the typing area. The figure should not be embedded inside the text.All figure captions should be centered beneath the figure. Longer figure captions should be centered beneath the figure and alignment double (left and right) justified, but are not to exceed the left and right edge of the figure by more than 0.5 in. The abbreviation “Fig.” for figure should appear first followed by the figure number and a period. Captions should be in 8- pt. font. At least one line of space should be left before the figure and after the caption.Fig. 1. Sample figure.5.2 MultimediaOSA accepts multimedia files—video, tabular data, static illustrations, and other types—as a part of the manuscript to be peer-reviewed and published. Multimedia files should be submitted only if they provide a more efficient or effective presentation of the information and should not be included as merely "supplemental" data.To ensure consistent presentation, broad accessibility, and long-term archiving, please follow these guidelines on presentation.Fig. 2. Single-frame excerpts from video recordings of metallic objects concealed by opaqueplastic tape. (a) Utility blade (Media 1). (b) Dentist's pick (Media 2). (c) Paper clip (Media 3).(d) Plastic/wire tie twisted into the shape of a loop (Media 4). [Sample figure adapted from Opt.Lett. 33, 440 (2008).]QuickTime Non-Streaming (.mov), AVI (.avi), and MPEG (.mpg) movies are accepted. There are a variety of software applications to aid in creating this file format. OSA accepts the following QuickTime compressor types: Video, Graphics, Animation, Motion JPEG, Cinepak, and Uncompressed/None. OSA does not accept the Indeo 5 compressor.The following multimedia guidelines will help with the submission process:• 4 MB is the recommended maximum multimedia file size.•Use one of the accepted compression codecs to minimize file sizes.•720 x 480 pixels (width by height) is the recommended screen size.•Insert a representative frame from each movie in the manuscript as a figure.•Videos must be playable using the free version of QuickTime on the Mac and PC.•Animations must be formatted into a standard video file.Authors are advised that, in general, multimedia files should be kept to a size of 4 MB or smaller. If it is essential to the scientific quality of the paper to have files that are larger than this, two different versions of such multimedia files (usually video files) must be made. One version, less than 4 MB in size, will serve as a low-resolution or truncated version for readers who have slower network connections and cannot download the larger file. The other version can be up to 15 MB in size. Multimedia files larger than 15 MB can be linked from the References section, but they will not be a reviewed part of the paper, they will not be kept at OSA, and they will not be part of the archival paper.Please refer to the online style guide for more detailed instructions on acceptable multimedia formats for audio and tabular data.5.3 TablesTables should be centered and numbered consecutively. Authors must use Word’s Table editor to insert tables. Authors must not import tables from Excel. All content for each table should be in a single Word table (do not split content for a single table across multiple Word tables). Tables should use horizontal lines to delimit the top and bottom of the table and column headings. Detailed explanations or table footnotes should be typed directly beneath the table. Position tables as closely as possible to where they are mentioned in the main text.Table 1. Optical Constants of Thin Films of Materials a83.4 nm 121.6 nmMaterial n K n kIr 1.182 0.865 1.450 1.040MgF2 1.584 0.487 1.682 0.0627Al 0.09874 0.1915 0.0424 1.137Mo 0.98 1.08 0.78 1.03C 1.16 1.29 1.85 1.10a From Appl. Opt. 40, 1128 (2001).6. Article Thumbnail UploadAuthors have the option to upload a thumbnail image that will appear next to the published article on the Forthcoming, Current Issue, and Abstract pages.Authors must submit a .JPG file. The image will be resized automatically to 100 x 100 pixels. For best results, authors should upload an image this size or an image with square dimensions.The 100 x 100 pixel image will be displayed on the article abstract page and a 50 x 50 pixel image will be displayed on the Table of Contents page.Fig. 3. Preview of thumbnail image display on the author submission page.7. SummaryConforming to the specifications listed above is of critical importance to the speedy publication of a manuscript. Authors should use the following style guide checklist before submitting an article.Table 2. Optics Express style guide checklistStandard Page Text Area: 5.25 x 8.5 in.; Margins: 1 in. top, 1.625 in. left, right & bottomIndent Alignment NotesType of Text Font Size(Points)Title 18 Center BoldAuthor Name 10 Center8 Center ItalicAuthor Affiliation &Email addressAbstract 10 0.5 in. left/right Justified Bold “Abstract:”Copyright 9 0.5 in.OCIS Codes 8 0.5 in. Bold “OCIS codes:”Main TextFirst paragraph Subsequent paragraphs 10None0.2 in.Justified The first paragraph of asection or subsection is notindented. The first line ofsubsequent paragraphs isindented 0.2 in.Section & Subsection Headings 10 None Left Insert 6-pt. space above andbelow each heading. Sectionheaders: BoldSubsection headers: ItalicEquations 10 None Center Eq. Number: right tab to endof last line of Eq., inparentheses.References and Links 8 0.2 in. Left Bold “References andlinks”. Delimit withhorizontal rules. Acknowledgments 10 None Justified Bold “Acknowledgments”Figures CenterFigure Captions 8 0.5 in left/right Justified Bold font. Long captions:indent 0.5 in. left/right. Tables 8 None CenterTable Heads 8 None Center Long heads follow tablemargins.7. ConclusionAfter proofreading, the final step in submitting a manuscript to Optics Express is to go online at /submission, type in the requested information into the Optics Express online submission system, and then upload the Word file. For further instructions, please see the Optics Express Author Information pages.。
长周期光栅
长周期光纤光栅最典型用于三个方面:EDFA 增益平坦、带阻滤波器、光纤传感。 1 EDFA 增益平坦 通信系统中, 如果掺铒光纤放大器(EDFA )增益谱分布不平坦, 则各个信道增益不同, 一 方面限制了无中继跨接距离, 另一方面也造成接收端误码率的增大。可以用B lazed 光 栅进行增益平坦, 此法的缺陷在于总存有一定程度的反射光, 长周期光纤光栅可以克服 这一缺点。将两个具有不同工作波长的长周期光纤光栅组合进行EDFA 增益平坦, 在 25nm～ 30nm 带宽内EDFA 增益谱的起伏小于0.2dB。将之应用于20×5Gb/s 的WDM 通信系统中, 通信信道以0. 6nm 的间隔分布于1550.4nm～ 1561. 8nm 的带宽内, 增益平 坦带宽提高了3 倍。 2 带阻滤波器 长周期光纤光栅的耦合机理决定了它对特定的波长具有损耗的能力, 在谱特性曲线上 表现为一个损耗波峰。特殊设计长周期光纤光栅的周期及长度, 可以使谐振波长强烈 衰减, 而其余波长基本没有损耗的通过, 从而实现了基于光纤的光学带阻滤波。其中光 栅周期与调制深度决定谐振波长, 而光栅长度决定阻带带宽。
9
均匀紫外曝光技术：在制作光栅的时候去掉振幅掩模板,让紫外光均匀地照射到光栅区
上一段时间。在利用掩摸板制作光栅之后引入均匀紫外曝光技术,使整个光栅区都接收紫 外曝光,让整个光栅区残留下来氢分子都有机会参与反应。由于A区残留氢气的浓度比B 区 大,在同时接受紫外曝光的时候,A 区所参与反应的氢分子要比B 区多,这样可减小A 区和B 区在退火前的氢气浓度差,在一定程度上减少了退火前后折射率调制深度的变化。但是对 光栅进行均匀紫外曝光同时会改变光纤光栅的耦合特性。图2 为实验中测得的长周期光纤 光栅第四个谐振峰在均匀紫外曝光过程中的变化情况。图2(a) 中谐振峰的波长随脉冲的 增加而增加,而损耗则相反。这是由于均匀紫外曝光能同时使A 区和B 区的折射率有很大 的提高,引起谐振波长的增加。但是由于A 区的氢气浓度比B 区大,所以它的光敏性也比B 区要好。当同时接受紫外光幅照的时候,A 区的折射率增长速度要比B 区快。这样也就导 致了光栅折射率调制深度的减小,谐振峰的损耗也就相应地发生变化。图2 (b) 为均匀紫外 曝光前后光纤光栅的透射谱,通过它我们可以更直观地看到均匀紫外曝光对长周期光纤光 栅耦合特性的影响。
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a r X i v :q u a n t -p h /0609155v 1 20 S e p 2006Optical gratings induced by field-free alignment of moleculesA.Rouz´e e,V.Renard,S.Gu´e rin,O.Faucher,andvorelLaboratoire de Physique de l’Universit´e de Bourgogne,UMR CNRS 5027,BP 47870,21078Dijon Cedex,France(Dated:February 1,2008)We analyze the alignment of molecules generated by a pair of crossed ultra-short pump pulses of different polarizations by a technique based on the induced time-dependent gratings.Parallel polarizations yield an intensity grating,while perpendicular polarizations induce a polarization grating.We show that both configurations can be interpreted at moderate intensity as an alignment induced by a single polarized pump pulse.The advantage of the perpendicular polarizations is to give a signal of alignment that is free from the plasma contribution.Experiments on femtosecond transient gratings with aligned molecules were performed in CO 2at room temperature in a static cell and at 30K in a molecular expansion jet.PACS numbers:33.80.b,32.80.Lg,42.50.Hz,42.50.MdI.INTRODUCTIONExcitation with non-resonant high power laser pulses has become a powerful technique for preparing aligned molecules [1].With ultra-short laser pulses,typically of less than 100fs pulse duration,molecules periodically re-align after the pump extinction,showing revivals in the observed signal.Various methods are employed to mea-sure such post-pulse molecular alignment.They make use either of ionization-fragmentation combined with an imaging technique [1,2]or of non-linear optical prop-erties [3,4].In the methods of the latter category,the depolarization or the spatial deformation of a probe pulse is measured as a function of time elapsed after the align-ing pulse.The effect is based on the time-dependent non-linear contribution of alignment to the refractive in-dex [3,4].Transient grating experiments have been also performed to explore alignment of molecules [5,6].In these experiments,a transient grating was produced by two synchronized pump pulses,and the amount of light diffracted from a third probe pulse was recorded at differ-ent delays.It appeared that the recorded signal exhibited the same time behavior than other alignment signals,i.e.confirming the detection of post-pulse molecular align-ment.As in Refs.[3,4]a deformation of the measured signal with increasing intensity has been noted.Whereas in Ref.[5],the change in the shape of the revivals has been attributed to molecular changes and the apparition of a constant background due to ionization and plasma formation,a more likely explanation for this modifica-tion of DFWM transient shapes has been suggested [7]:the background is due to permanent alignment and the alteration of revivals is a consequence of heterodyning with this background.In fact,this had been already pointed out for all experiments with homodyne detec-tion [3].Stavros et al.[6]corroborated this explanation in the case of DFWM for O 2molecules.At the highest intensity investigated in Ref.[6],the possible contribu-tion of an ion grating has also been suggested.The aim of the present work is to investigate the mech-anisms involved in high intensity DFWM experiments byusing two types of gratings (intensity or polarization grat-ing)produced by two crossed beams.Furthermore,it will be shown that quantitative measurement of alignment with both configurations is possible with this technique.II.EXPERIMENTAL SETUPThe experimental setup uses the well known femtosec-ond degenerate four-wave mixing technique (DFWM)also called femtosecond transient grating spectroscopy [8].It consists of exciting the molecular sample by two synchronized pump pulses at 800nm (pulse duration of 90fs)focused and crossed at a given angle Θ(Fig.1).They are both derived from a chirped pulse amplified Ti:Sapphire system working at 20Hz.The energy and the polarization direction of the two pump pulses are controlled by means of a half-wave plate and a polar-izer.A third probe pulse,time delayed with respect to the pumps,is mixed with the others.The probe beam sees a transient grating and is diffracted.The amount of diffracted light is monitored as a function of the time delay with a photomultiplier.The sample is a CO 2gas,either at room temperature in a static cell,or in a molec-ular supersonic jet for lower rotational temperatures.Both beams are focused and collimated with f =300mm lenses.It is noticed that,like in other all-optical methods,DFWM gives the opportunity to work with a good sensitivity in a wide pressure range (typically from 1mbar to a few bars).The role of the two pump pulses is to excite the rotational coherence of the molecules.Two different experiments have been performed which corre-spond to parallel and perpendicular polarizations of the pump pulses.The two cases are treated separately in the next sections.2III.THEORYA.Parallel polarizations:linear total polarization,intensity gratingWe consider a simplified model for thethe grating.We assume two plane waves,with length λ,propagating in the (x,z )plane with tors (−k x ,0,k z )and (k x ,0,k z )(see Fig.1).The cross-angle between the two pump beams is sin(Θ/2)=k x λ/2π≈Θ/2.With two pump pulses ized along the y -axis (of vector unit e y ),an ing is formed with a total electric field periodically lated along the x -axis: E pump =2E p (t )cos(k x x )k z z ) e y ,where E p (t )is the pump field envelope same for both fields).We are facing therefore the molecules interacting with a non resonant linearly ized laser field,which has been extensively Ref.[1]and references therein).The additional dient is the spatial modulation of the total we consider a weak probe pulse polarized parallel pumps (y -axis)and which propagates with the tor (−k x ,0,k z ),the only component of the induced at a position r =(x,y,z )whose expectation not average out is the y -component :µind r ,t =¯α+∆α cos 2θy r ,t−1/3×E probe (t )cos(ωt +k x x −k z z ) e y ,(1)where ¯αis the mean polarizability,∆α=α −α⊥is the difference of polarizability parallel and perpendicular to the molecular axis,E probe (t )is the probe envelope,and θy is the angle between the molecular axis and the common polarization direction (y -axis).The expectation value cos 2θy r ,t is a measure of alignment and is a func-tion of the total pump intensity at the position r .Conse-quently,it has the same spatial period as the total inten-sity.It also depends on the time delay between the pump and probe pulses.The signal electric field measured by the photo-detector is then obtained by summation over the interaction volume of spherical waves radiated by the dipole.The first term of the right hand side of Eq.(1)describes the effect of the linear index of refraction on the probe beam and is not interesting for our purpose.The second term is periodic and leads to constructive interference along symmetric phase-matching directions x/z =(2n −1)k x /k z ,with n the diffraction order.Only the order 1is considered experimentally (see Fig.1).The experimental signal measured at a position r 0,pro-portional to the modulus squared of the total electric field,is interpreted as the diffraction of the probe beam by the transient grating produced by the pumpsI sig ( r 0,t )∝| E sig ( r 0,t )|2∝|Vdr R [ Erad ( R,t )]|2,(2)with Erad the spherical electric field radiated by the dipole momentE rad ( R,t )=k 2R(3)cos 2θy r ,t −1/3is approximately proportional to the total pump intensity 4I 0cos 2(k x x )=2I 0(1+cos 2k x x ),where I 0is the peak intensity of a single pump (see Ap-pendix A 1).The constant term 2I 0corresponds to the zeroth order of diffraction and is responsible for nonlinear variation of the refractive index seen by the probe pulse.The second term 2I 0cos 2k x x leads to diffraction orders n =±1.It is shown in Appendix A 1that :cos 2θy r ,t −1/3≈ cos 2θy t −1/3 (1+cos 2k x x ),(4)withcos 2θy t −1/3≈2ξ0[δ+κf (t )],(5)andξ0=∆α/4dtE 2p (t ),(6)the intensity area of a single pump. cos 2θy t corre-sponds to the alignment that would be induced by asingle linearly polarized pulse of intensity 2I 0.For a given molecule and temperature,δand κare constant (δand κ→0at low intensity),and f (t )is a specific func-tion independent of ξ0.The summation over the volume (Eq.(2))gives a signal of intensity :I sig (t )∝ cos 2θy t −1/3 2,(7)where the spatial dependence has now disappeared.Themeasured signal (order 1)can thus be calculated for any pump-probe time delay,solving the time-dependent3Schr¨o dinger equation [3]usingasinglelinearly polarizedpump beam of intensity 2I 0.This takes into account the fact that the spatial distribution of the total intensity is modulated between 0and 4I 0.In other words,the sample of aligned molecules presents a nonlinear index of refraction,which depends on the pump intensity.As the intensity along the grating is modulated by optical interferences,a spatial modula-tion of refractive index is formed.This gives a refractive index grating and a signal directly related to the post-pulse alignment,as shown by Eq.(7).B.Perpendicular polarizations:elliptic total polarization,polarization gratingFor perpendicular polarizations,with one pump aligned at −45◦and the other at +45◦with respect to the y -axis,the resulting field is in general elliptically polar-ized.The state of polarization of the total pump electric field depends on the spatial position and alternates be-tween linear and circular,forming a polarization grating.In a grating period,the total electric field varies from lin-ear (along the y -axis),circular (right),linear (along the x -axis),to circular (left),with intermediate elliptic polar-izations.Furthermore,its magnitude varies periodically along the x -coordinate and is maximum for the linear polarization and minimum for the circular one.Since Θis a small angle,the total pump field is indeed polarized in the (x,y )plane asE pump =√2E 2p (t )∆αsin 2θz × A 2(x )−B 2(x ) cos 2φz +B 2(x )(9a)=−12∆αE probe (t )cos(ωt +k x x −k z z )×( cos 2θx r ,t − cos 2θy r ,t ).(10)It is shown in Appendix (A 2)that the preceding equationcan be approximated by :µind r ,t ≈∆αE probe (t )cos(ωt +k x x −k z z )×32((1−cos 2k x x )−(1+cos 2k x x )).Itfollows that the induced dipole can be considered as cre-ated by two out of phase intensity gratings with a spatial modulation (1±cos 2k x x ).This has been initially demon-strated at low intensities when the perturbation theory applies [12]:a polarization grating can be decomposed in two out of phase intensity gratings with perpendicular polarizations.One result of the present work is to show that this simple decomposition can be extended beyond the perturbation regime at moderate intensities.As in Section III A,the calculation of the observable requires the summation of the radiated spherical electric fields over the interaction volume.We consider the signal pro-duced along the phase-matching direction x/z =k x /k z (order 1)and find that the associated signal can be ob-tained by calculating numerically cos 2θ t −1/3using a linearly polarized field at an intensity I 0since the induced dipole moment (11)is modulated between 0(circular po-larization,A =B )and a maximum value corresponding to a pump linear polarization with an intensity 2I 0.IV.RESULTSA.Parallel polarizationsFor parallel polarizations,optical interferences be-tween the two pumps lead to an intensity grating.The in-teraction Hamiltonian can thus be directly derived from earlier studies of alignment with a linear polarization.The molecular alignment reflects the total intensity and follows the fringe pattern.An example is shown in Fig.2for pump intensities I 0=19TW/cm 2.As in the po-larization technique,the modification of the experimen-tal signal with respect to the weak field signal,is inter-preted as alignment revivals heterodyned by the perma-nent alignment.The simulations (Eq.(7))should be per-formed at an intensity taking into account the transverse profile of the two pump beams (gaussian distribution)which was not considered in the theoretical section.This effect can be roughly accounted for by a factor 1/2in the experimental intensity,i.e.by comparing the theoretical4intensity (about 20TW/cm 2for the best fit)to the peak intensity I 0of only onepump beam (19TW/cm 2).It is noted that,unlike in Ref.[5],here no molecular de-formation is put forward to interpret the experimental signal.FIG.2:Recorded DFWM signal (dots)as a function of pump-probe time delay in a static cell of CO 2at room temperature for parallel polarizations.Pressure is 0.1bar and the peak intensity of each pump is 19TW/cm 2.Simulated signal [full line,Eq.(7)]is calculated at 20TW/cm 2.At higher intensity,a strong background is observed which heterodynes and distorts the alignment signal.This phenomenon is attributed to the contribution of a refractive index grating due to a spatial distribution of electron density.Indeed,the electronic density pro-duced by ionization follows the spatial intensity distri-bution of the pump with a lifetime of several nanosec-onds [13].As a consequence,the refractive index seen by the probe is modified and a grating is formed.The effect becomes very strong as the peak intensity of the bright fringes approaches the ionization saturation inten-sity (200TW/cm 2for CO 2).Some applications of this effect,which limits the range of intensity for the present study of alignment,is discussed in Ref.[14].B.Perpendicular polarizationsTo overcome the intensity limitation discussed above,the polarizations of the two pump beams have been crossed.In that case,no optical interferences occur,and the intensity is constant over the interaction volume,ex-cept for the overall Gaussian distribution.A polarization grating is formed as discussed in the previous sections.Nevertheless,the instantaneous total intensity for the lin-ear polarization is twice that of the circular one.As the ionization process is a function of the instantaneous in-tensity,the ionization rate and the electron density reflect the periodic distribution of this quantity.A refractive in-dex grating due to the electrons is formed as in the linear case.But as the ionization rate is the same for the two linear (along the x and y -axis)and for the two circular polarizations (left and right),the grating has a periodic-ity twice that of the parallel polarizations case (A).Theangle of diffraction is doubled and the probe diffracted by this grating can be spatially resolved from the one diffracted by the alignment-induced grating.The exper-iment is therefore not sensitive to the electron density grating.The Hamiltonian describing the interaction of the molecules with an elliptic electric field as well as the induced dipole moment have been given in the theo-retical section.It has been shown that the observed signal can be approximated by using the dipole mo-ment (11)at low and moderate intensities.To simu-late the experimental data,we thus used the same rou-tine as for parallel polarizations.Some results are shown in Fig. 3.Again the transverse spatial profile of the pump pulses should be taken into account through a factor 1/2,i.e.the simulated intensity has to be com-pared to 1/2times the maximum intensity of one pump beam.The degree of alignment,quantified by cos 2θ t ,is directly deduced from simulations.Even though the higher experimental intensities correspond to saturation of cos 2θ r,t −1/3,the calculated intensity approaches the expected value (see Fig.3).The volume averaging of the signal tends to smooth out the saturation pro-cess of alignment.For much higher intensities,discrep-ancies between calculated and experimental (I 0/2)inten-sity should appear,as shown in Ref.[10].This effect is due to the strong saturation of alignment at the center of the pumped volume.In that case,Eq.(11)can not be used and the observed signal is no more accurately sim-ulated by Eq.(A9).Nevertheless,it would be possible,even though it would be time consuming,to reproduce the experimental data by numerical simulation of Eqs.(9,10).One of the goals of the present work was to align cold molecules in order to increase the efficiency of the pro-cess.To obtain low temperatures,we used a pulsed su-personic jet in which the pressure is only a few mbar,de-pending on the distance from the nozzle.Before attempt-ing an experiment,some preliminary studies at low static pressure and room temperature have been performed.The sensitivity was high enough to record signals at a pressure around 6mbar of CO 2,with an excellent sig-nal to noise ratio.The supersonic jet has allowed us to decrease the temperature down to 30K (Fig.4).The alignment that can be achieved at this temperature with an experimental intensity of 47TW/cm 2corresponds to cos 2θ =0.65.This value is comparable to the one achieved at higher intensity in our previous study using a polarization technique at 60K.But in the present case the experiment is free from heterodyne contribution due to spurious birefringence from optics.The polarization grating (case B)can be discussed in terms of alignment distribution,as for the intensity grat-ing (case A).For example at a delay close to zero (modulo T R ),the molecules are aligned along the linear polarized field (x and y -axis)and delocalized in the plane of polar-ization xy (circular right and left).At time delay T R /4(modulo T R ),the molecules are delocalized in the planes5FIG.3:Experimental DFWM signal recorded as a function of the pump-probe time delay in CO 2at room temperature for perpendicular polarizations.The pressure is 0.03bar and pump peak intensity is (a)37TW/cm 2,(b)78TW/cm 2,and (c)135TW/cm 2.The numerical simulations [Eq.(7)]are shown inverted for (a)15TW/cm 2,(b)30TW/cm 2,(c)and 55TW/cm 2.These theoretical values compare well with I 0/2(see text).xOz or yOz ,or aligned along the z -axis (circular right and left).Intermediate elliptic polarization leads to in-termediate state of alignment.V.CONCLUSIONThe main conclusions of this work are the follow-ing.DFWM experiments with two synchronized spa-tially crossed femtosecond pulses allow to produce tran-sient gratings reflecting alignment of molecules.A contri-bution due to ionization and plasma formation appears at high intensities that heterodynes and therefore dis-turbs the experimental signal.With perpendicular po-larizations,the alignment signal can be isolated from the plasma contribution.The experiments can thus be per-formed at higher intensity keeping a good signal to noise ratio.DFWM experiments prove to be very sensitive for probing low density and low temperature samples suchas those obtained with a supersonic jet.Furthermore,it is shown that quantitative measurements of alignment are obtained through simulations by using a simplified model,even in the case of perpendicular polarizations which was a priori non-trivial.Using different polarization schemes would permit toFIG.4:Recorded DFWM signal (lower panel,dots)as a func-tion of pump-probe time delay in CO 2at 30K in the super-sonic jet for perpendicular polarizations.Measured peak in-tensity of one pump is 47TW/cm 2.Simulated signal [lower panel,full line,Eq.(7)]is calculated at 25TW/cm 2.The calculated time dependence of cos 2θ is shown in the upper panel.create interesting patterns of aligned molecules that could be used as a large frequency bandwidth spatial modulator.AcknowledgmentsThis work was supported by the Conseil R´e gional de Bourgogne,the ACI photonique ,the CNRS,and a Marie Curie European Reintegration Grant within the 6th Eu-ropean Community RTD Framework Programme.The authors thank H.R.Jauslin for helpful discussions.[1]H.Stapelfeldt and T.Seideman,Rev.Mod.Phys.75(2),543(2003).[2]H.Sakai,C.P.Safvan,rsen,K.M.Hilligsøe,K.Hald,and H.Stapelfeldt,J.Chem.Phys.110(21),102356(1999); F.Rosca-Pruna and M.J.J.Vrakking,Phys.Rev.Lett.87(15),153902/1(2001);P.W.Dooley,I.V.Litvinyuk,K.F.Lee,D.M.Rayner,M.Spanner,D.M.Villeneuve,and P.B.Corkum,Phys.Rev.A68(2), 23406(2003).[3]V.Renard,M.Renard,S.Gu´e rin,Y.T.Pashayan,B.Lavorel,O.Faucher,and H.R.Jauslin,Phys.Rev.Lett.90(15),153601(2003).[4]V.Renard,O.Faucher,and vorel,Opt.Lett.30,70(2005).[5]stock,V.Senekerimyan,and M.Dantus,J.Phys.Chem.A107,8271(2003).[6]V.G.Stavros,E.Harel,and S.R.Leone,J.Chem.Phys.122(6),64301(2005).[7]vorel,H.Tran,E.Hertz,O.Faucher,P.Joubert,M.Motzkus,T.Buckup,ng,S.H.,G.Knopp,P.Beaud,and H.M.Frey,C.R.Physique5,215(2004).[8]E.J.Brown,Qingguo-Zhang,and M.Dantus,J.Chem.Phys.110(12),5772(1999).[9]M.Renard,E.Hertz,S.Gu´e rin,H.R.Jauslin,-vorel,and O.Faucher,Phys.Rev.A72,025401(2005).[10]V.Renard,M.Renard, A.Rouz´e e,S.Gu´e rin,H.R.Jauslin,vorel,and O.Faucher,Phys.Rev.A70, 033420(2004).[11]D.Daems,S.Gu´e rin,E.Hertz,H.R.Jauslin,vorel,and O.Faucher,Phys.Rev.Lett.95,063005(2005). [12]J.T.Fourkas,R.Trebino,and M.D.Fayer,J.Chem.Phys.97(1),69(1992).[13]C.W.Siders,G.Rodriguez,J.L.W.Siders, F.G.Omenetto,and A.J.Taylor,Phys.Rev.Lett.87(26), 2630021(2001).[14]V.Loriot,E.Hertz,A.Rouze,B.Sinardet,vorel,and O.Faucher,Opt.Lett.31(19),2897(2006).APPENDIX A:POSTPULSE ALIGNMENT FOR LOW AND MODERATE INTENSITIESWe analyse in this appendix the dependence of the postpulse alignment of linear molecules on the pump field intensities below the intrinsic saturation regime.We show in particular that(i)for a linearly polarized pulse the baseline of cos2θ obeys the following law:quadratic and next linear,(ii)its shape is linear and(iii)the align-ment induced by an elliptically polarizedfield can be ana-lyzed in term of the decomposition into linearly polarized fields.1.Linearly polarizedfieldA linearly polarizedfield leads to a postpulse alignment characterized by cos2θ t,withθthe angle between the molecular axis and thefield polarization axis,which can be generally characterized bycos2θ t−1/3=C+ J|a J|cos(ωJ t+φJ),(A1)where C is a constant value corresponding to the per-manent alignment,and the second term,describing the rotational wave packet revivals,is written in terms of Fourier components of the amplitude|a J|,the phaseφJ, and the frequencyωJ(Raman frequency of rotational transitions).In the present experimental conditions,the phases are roughly constant:φJ≈−π/2[9].Within the sudden impulsive regime(i.e.forτ≪h/B withτthe duration of the pulse and B the rotational constant of the molecule in Joule),where the pulse can be considered as aδ-function,the coefficients C and|a J|depend on the effective areaξ=∆α/4 dtE2,(A2)which is proportional to the peakfield intensity I.For CO2molecules interacting with a Gaussian pulse of a full-width at half maximumτFWHM=0.1ps,we have ξ≈0.444×I[TW/cm2].Figure5shows the dependence of the law(A1)on the pump intensity(centrifugal distorsion has not been con-sidered in this study.)This allows us to define three regimes of intensity:(i)low intensity associated to a quadratic dependence of C(here up to I=30TW/cm2), (ii)moderate intensity associated to a linear dependence of C,and(iii)high intensity associated to the satu-ration of max t cos2θ −1/3−C.Below the satura-tion,one can consider with a good approximation that max t cos2θ −1/3−C is approximately linear with the field intensity.This leads for low intensities tocos2θ t−1/3≈βξ2+κξf(t)≈κξf(t),(A3) where,for a given molecule and temperature,κandβare constant and f(t)is a specific function independent ofξ.7as a function of the peak pump intensity ofτFWHM=0.1ps in CO2at T=293K(dotted lines).The former is quadratic (fullfitting line)approximately up to I=30TW/cm2and linear for higher intensities.The latter is linear(fullfitting line)for moderate intensities.Similar dependencies can be found for other linear molecules and temperatures.We can notice that the regime of low intensities extendsthe result of the perturbative regime,even if it is not itself a perturbative regime(usually defined as a smallpopulation transfer),since it can exhibit a non negligible alignment(max t cos2θ t≈0.45for I=30TW/cm2). We also haveβξ2≪κξ,which shows that the permanent alignment is negligible for low intensities.For moderateintensity,Fig.5shows that the permanent alignment is linear with respect to the peakfield intensity,which leads tocos2θ t−1/3≈[δ+κf(t)]ξ.(A4) We can thus conclude that at low and moderate intensi-ties(i.e.below the saturation of alignment), cos2θ t−1/3is approximately proportional toξ,i.e.to the pump intensity I.2.Elliptically polarizedfieldWe consider here the postpulse alignment induced by an elliptically polarizedfield E(t)=E(t)(A cos(ωt) e x+ B sin(ωt) e y),A2+B2=1.The associated interaction readsH int=−∆α4E2(t) A2cos2θx+B2cos2θy (A5b)with the particular cases of linear polarizations along x for A=1,along y for B=1,and of circular polarization in the(x,y)plane for A=B=1/√2B2ξ(δ+κf(t)),using again A4.The summa-tion in(A7)gives cos2θx t−1/3≈ξ(A2−B2/2)(δ+κf(t)).Performing the same calculation for i=y,z,we finallyfind that in the intermediatefield regime,cos2θx t−1/3≈ξ(A2−B2/2)(δ+κf(t)),(A8a) cos2θy t−1/3≈ξ(B2−A2/2)(δ+κf(t)),(A8b) cos2θz t−1/3≈−ξ(δ+κf(t))/2.(A8c) We have in particular that cos2θx t−1/3is well approx-imated by the quantityξ(δ+κf(t))obtained from the interaction with a linearly polarizedfield of peak inten-sity I times the scale factor(A2−B2/2).We remark that cos2θz t−1/3does not depend on the ellipticity.We also notice that cos2θy t−1/3≈0when B2=A2/2,i.e. B2=1/3,A2=2/3.This particular ellipticity allows the directionsθx andθz to play a symmetric role in(A5a). This property has been used in Ref.[11]to demonstrate the optimal alternation of postpulse alignment.For perpendicular polarizations,the observable cos2θx t− cos2θy t is required.We obtaincos2θx t− cos2θy t≈38We can conclude that a good approximation for cos2θx t− cos2θy t can be obtained in the interme-diate regime by calculating numerically cos2θi t−1/3with a singlefield linearly polarized along i of intensity I and by applying the scale factor3。