14.Characterization of T-ray binary lenses

July1,2002/Vol.27,No.13/OPTICS LETTERS1183 Characterization of T-ray binary lensesS.Wang and T.YuanDepartment of Physics,Rensselaer Polytechnic Institute,Troy,New York12180-3590E.D.Walsby,R.J.Blaikie,and S.M.DurbinDepartment of Electrical and Electronic Engineering,University of Canterbury,Private Bag4800,Christchurch,New ZealandD.R.S.CummingDepartment of Electronics and Electrical Engineering,University of Glasgow,Glasgow G128LT,Scotland,UKJ.Xu and X.-C.ZhangDepartment of Physics,Rensselaer Polytechnic Institute,Troy,New York12180-3590Received February13,2002Multilevel phase-shift Fresnel diffractive zone plates fabricated on silicon wafers have been used as T-rayimaging lenses.The imaging results,including spatial and temporal distribution of T-rays measured at thefocal planes in the frequency range from0.5to1.5THz,indicate that the performance of the diffractiveterahertz(THz)lens is comparable with or better than that of conventional refractive THz lenses.Theunique properties of the T-ray binary lens make it possible to fabricate excellent optics for narrow-band THzapplications.©2002Optical Society of AmericaOCIS codes:320.7080,320.7100,320.7160,320.7110,320.7150,190.7110.Lenses are basic elements in an optical imaging sys-tem.In imaging and terahertz(THz)time-domain spectroscopy technologies,T-ray focusing and colli-mating has relied mainly on parabolic mirrors,silicon lenses,and polyethylene lenses.However,for a THz beam,it is impossible to fabricate lenses with short focal lengths and large numerical apertures by using silicon or polyethylene.For two-dimensional CCD THz imaging,it is very difficult to obtain a high-quality THz image on a ZnTe sensor by using parabolic mirrors because of their aberration and the difficulty of alignment.However,fabricating a large-numerical-aperture T-ray binary lens with a short focal length is possible by using modern planar microfabrication technology,which makes such lenses attractive for THz applications.To our knowledge, binary lenses1–4have not yet been used as THz diffraction optics for maneuvering THz wave fronts. Binary lenses are much lighter and more compact than conventional THz optics and lend themselves to unique beam forming,and so they may see increasing application in the future.Furthermore,the investi-gation of T-ray binary lenses can provide a bridge to the study of microwave binary lenses.To acquire as much information as possible in THz imaging and THz time-domain spectroscopy applica-tions,researchers have used THz space and time prop-erties to extract characteristic data from objects under study.5,6Therefore,in this Letter,we investigate the performance of T-ray binary lenses by studying temporal and spatial THz distributions.We apply an electro-optic(EO)T-ray imaging technique7to acquire the two-dimensional amplitude,frequency,and phase properties of T-rays after they pass through binary lenses.Figure1shows a plot of the phase profile versus the square of the radius of a binary lens with phase level L,where L෇2M,M෇1,2,3,....The diffracted wave amplitude,u͑z͒,along the z axis with the binary lens can be written as3u͑z͒෇XnA nZsZexp∑i2pµnr p2112l z∂͑x21y2͒∏d x d y,(1)Fig.1.Schematic illustration of a circular multiphase-shift binary lens.L is the level number of the lens,and the origin is at the lens center point.The phase shift, F͑r2͒,is a function of r2෇x21y2.The phase shift for each step is2p͞L,which corresponds to an etch depth of l͓͞L͑n THz21͔͒.For an eight-level silicon lens at1THz, the etching depth step is15.5m m.N is the total number of zones.0146-9592/02/131183-03$15.00/0©2002Optical Society of America1184OPTICS LETTERS/Vol.27,No.13/July1,2002 Table1.Calculated and Measured Diffraction Eff iciency(%)of T-ray Binary LensesPhase Level Lh248Al Zone Plate Theory41819541Exp.11759038 where A n෇sinc͑n͞L͒,n is an integer,r p2is the Fresnel zone period with the area dimension,s is the area of the binary lens,and l is the wavelength.If n͞r p211͑͞2l z n͒෇0,a maximum diffraction in-tensity can be obtained at focal point z n:z n෇2r p22l n,n෇61,62, (2)The diffraction efficiency h is defined ash෇j A21j2෇sinc2͑1͞L͒.(3) The first-order focus is defined as the main focal point, with focal length f෇z21෇r p2͞2l.As can be seenfrom Eq.(3),the diffraction efficiency increases rapidly with the number of phase levels L,and the calcu-lated diffraction efficiency,h theory,verus L is shown in Table1.For a binary lens with L෇8,the diffraction efficiency reaches95%,in contrast with an Al zone plate or a two-level lens,which has41%efficiency. Two-,four-level,and eight-level lenses,each with a30-mm diameter consisting of a total of14zones, were fabricated on silicon wafers by means of ion etching.9Silicon has a refractive index of3.42in the far-infrared region from0.5to1.5THz,and therefore the required etch depth,l͓͞L͑n THz21͔͒,is small, and thin binary lenses can be fabricated.The lenses are designed for a1-THz T-ray with a focal length of 25mm.An Al zone plate of identical dimensions was fabricated on the same silicon substrate material for comparison.Figure2schematically illustrates an EO imaging setup with a CCD camera used to characterize the focal properties of these lenses.The laser is a1-kHz repeti-tion rate amplified Ti:sapphire laser,capable of gener-ating100-fs pulses with energy of700m J.The laser beam was split into a pump beam and a probe beam, and both beams were expanded to2.5cm͑1͞e͒and col-limated.Through a3-mm-thick͗110͘ZnTe emitter, the pump beam generated THz pulses via optical recti-fication.The two-dimensional THz image formed on the EO crystal was encoded onto the probe beam via the EO effect,8and a4-mm-thick͗110͘ZnTe with an effective aperture of2cm was used as an EO sensor. The image carried by the probe beam was focused onto a CCD camera.In this experiment we defined the lab-oratory coordinate system as follows:The axis of bi-nary lenses was selected as the z axis,the x axis was parallel to the optical table,and the y axis was per-pendicular to the optical table.By scanning the time delay between the THz and probe beam and moving the binary lenses along the z axis,we were able to obtain the spatial and temporal THz distribution for each lens.Figure3shows the binary lenses under study and their focal plane THz intensity -paring the THz distributions on the focal plane of the three binary lenses,we find that the focused THz intensity increases with the level number of T-ray binary lenses.As the level number of the binary lens increases,a smaller focal area and a more sharply focused THz peak are observed.These results cor-respond to enhanced diffraction efficiency,which increases dramatically with the level number of binary lenses.Table1lists the calculated and measured diffraction efficiencies of binary lenses at1THz.For convenience of testing,an Al T-ray Fresnel zoneplate Fig.2.Schematic of the experimental setup of the THz CCD imaging system.The probe beam reflected from the ZnTe sensor was focused to CCD via a pellicle and a polar-izer,P2.The polarization directions of polarizers P1and P2are perpendicular to eachother.Fig.3.(left)Photographs of T-ray binary lenses and (right)their THz wave intensity distribution on the x y plane at a distance of25mm(designed focal plane at1THz)between the lenses and the ZnTe sensor.The diameter of each lens is30mm.July 1,2002/Vol.27,No.13/OPTICS LETTERS1185Fig.4.V ariation of THz focal length with THz frequency for an eight-level T-ray binary lens.The line is the calcu-lated result,and the filled circles are the measured experi-mentaldata.Fig.5.Field distribution of a THz wave on the z y plane at peak amplitude.was also measured,and its efficiency was quite close to the theoretical value of 41%,which indicates the correct Fresnel zone structure for the binary lenses.In our experiment,as the level number of the binary lens increased,the measured diffraction efficiency approached the theoretical value.This result is in accordance with the rule of thumb that,as the binary level increases,the binary lens is more tolerant of fabrication errors.10We performed a Fourier transform of the mea-sured THz pulses to allow the frequency-dependent response of the binary lenses to be studied.For each frequency,we determined the focal length by finding the lens –detector separation that resulted in the maximum THz intensity.Figure 4shows the focal-length increases with the THz frequency for an eight-level T-ray binary lens;the experimental result is well fitted by a theoretical curve derived from Eq.(2).The T-ray binary lens has a focal length of25mm at 1THz as designed.We also observed less spherical aberration on the binary lens than with the polyethylene lens.The THz wave distributions in the z y plane for the eight-level binary lens are shown in Fig.5.The THz wave forms a number of rings after propagating through the T-ray binary lens,and the rings converge to a focal point.The convergence becomes tighter as the level number of the lens increases.If we consider the phase change near the focal point,as the level num-ber of the binary lens increases the phase variation also becomes more and more similar to that of a con-ventional THz lens.As Fig.5shows,a Guoy phase shift 11is clearly demonstrated for the eight-level lens.In summary,we have measured the temporal and spatial THz distribution of T-ray binary lenses.As the level number of the T-ray binary lens increases,not only does the diffraction efficiency increase from 10%to 90%,but also the THz spatial distribution is more and more similar to that of conventional refrac-tive THz lenses.Therefore,diffractive binary lenses can be used for THz applications.Because the binary lens has many unique properties,such as f lexibility in design,capacity for integration,and more freedom of choice of substrate,it is possible to fabricate excellent optics for narrow-band THz wave imaging and sens-ing applications.The potential applications of T-ray binary lenses warrant further exploration.This work was supported by the U.S.Army Research Office,the National Science Foundation,the Marsden Fund of the Royal Society of New Zealand,and the New Economy Research Fund (New Zealand).The authors are grateful to Brad Ferguson and Samuel Mickan for useful discussions.X.-C.Zhang ’s e-mail address is zhangxc@.References1.S.Noach,A.Lewis,Y.Arieli,and N.Eisenberg,Appl.Opt.35,3635(1996).2.J.W.Goodman,Introduction to Fourier Optics (McGraw-Hill,New Y ork,1996).3.G.B.Jin,Y.B.Yang,and M.X.Wu,Binary Optics ,1st ed.(China Defense Industry,Beijing,1998).4.J.Jahns and S.J.Walker,Appl.Opt.35,931(1990).5.B.Ferguson,S.H.Wang,and X.-C.Zhang,in Pro-ceedings of the 2001IEEE/LEOS Annual Meeting (Institute of Electrical and Electronics 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