集成光学课程第八章-1

Electro-Optic Modulators⏹8.1 Basic Operating Characteristics of Switches andModulators⏹8.2 The Electro-Optic Effect⏹8.3 Single-Waveguide Electro-Optic Modulators⏹8.4 Dual-Channel Waveguide Electro-optic Modulators ⏹8.5 Mach-Zehnder Type Electro-Optic Modulators⏹8.6 Electro-Optic Modulators Employing Reflection orDiffraction⏹8.7 Comparison of Waveguide Modulators to BulkElectro-Optic Modulators在本章将学到⏹单波导电光调制器的工作原理⏹双沟道波导电光调制器的工作原理⏹波导调制器比“体”调制器更为优越⏹如何设计波导电光调制器重点掌握单波导电光调制器和双沟道波导电光调制器的工作原理⏹modulator：调制器⏹switch：开关⏹modulation depth：调制深度⏹bandwidth：带宽⏹insertion loss：插入损耗⏹power consumption：功率损耗⏹isolation：隔离度⏹Pockels effect：普克尔效应⏹Kerr effect：克尔效应⏹indicatrix：指标线；光率体⏹index ellipsoid：折射率椭球⏹centrosymmetric：中心对称的⏹single-waveguide electro-optic modulators：单波导电光调制器⏹phase modulator：相位调制器⏹polarizer：起偏器⏹polarization–selective filter(usually called an analyzer)：检偏器⏹intensity modulator：强度调制器⏹electro-absorption modulator：电致吸收调制器⏹Franz-Keldysh effect：弗兰茨－凯第希效应（当一半导体材料中存在强电场时，材料的吸收光谱向长波方向移动）⏹direct bandgap material：直接带隙材料⏹depletion layer：耗尽层⏹Mach-Zehnder interferometer：马赫---泽德干涉仪⏹Permittivity：介电常数This chapter begins the discussion of optical-signal modulation and switching. In many cases, the same device can function as either a modulator or a switch, depending on the strength of the interaction between the optical waves and the controlling electrical signal, as well as on the arrangement of input and output ports. The device is considered to be a modulator if its primary function is to impress information on a light wave by temporarily varying one of its properties. A switch, on the other hand, changes the spatial position of the light, or else turns it off and on.8.1 Basic Operating Characteristicsof Switches and ModulatorsOne important characteristic of modulators and switches is the modulation depth, or modulation index, η. In the case of an intensity modulator in which the applied electrical signal acts to decrease of thetransmitted light, ηis given by00)(I I I -=η(8.1.1)where I is the transmitted intensity and I 0is the value of I with no electrical signal applied.8.1.1 Modulation Depthm I I I )(0-=η(8.1.2)where I m is the transmitted intensity when maximum signal is applied. The maximum modulation depth, or extinction ratio, is given by00m ax )(I I I m -=ηforI I m ≤(8.1.3)or by m o m I I I )(m ax -=ηfor 0I I m ≥(8.1.4)It is also possible to define the modulation depth for phase modulators, as long as the phase change can be functionally related to an equivalent intensity change.If the applied electrical signal acts to increase the transmitted light intensity, ηis given byFor the case of interference modulators, it can be shown that the modulation depth is given by)2(sin 2ϕη∆=(8.1.5)where ∆ϕis the phase change.Modulation depth has been defined for intensitymodulators (and indirectly for phase modulators); however, an analogous figure of merit, the maximum deviation of a frequency modulator, is given by00m ax f f f D m -=(8.1.6)where f 0is the optical carrier frequency, and f m is the shifted optical frequency when the maximum electrical signal is applied.8.1.2 BandwidthAnother important characteristic of modulators and switches is the bandwidth, or range of modulation frequencies over which the device can be operated. By convention, that bandwidth of a modulator is usually taken as the difference between the upper and lower frequencies at which the modulation depth falls to 50% of its maximum value. In the case of a switch, frequency response is usually given in terms of the switching speed, or switching time. The switching time T is related to the bandwidth ∆f by the expression=π2(8.1.7)fT∆Minimizing switching time is most important when large-scale arrays of switches are used to route optical waves over desired paths. Similarly, modulation bandwidth is a critical factor when information channels are to be multiplexed onto the same optical beam. Thus, the unusually fast switching speed and wide bandwidth of waveguide switches and modulators, which will be discussed later in this chapter, make them particularly useful in large telecommunications system.8.1.3 Insertion LossInsertion loss is another important characteristic of optical switches and modulators that must be known for system design. Insertion loss is generally stated in decibels, and for the case in which the modulating signal acts to decrease in the intensity, it is given by)log(100I I L t i (8.1.8)where I t is the optical intensity that would betransmitted by the waveguide if the modulator were absent, and I 0is the intensity transmitted with the modulator in place, but with no applied signal.For a modulator in which the applied signal acts to increase the transmitted intensity, the insertion loss is given by)log(10m t i I I L (8.1.9)where I m is the transmitted intensity whenmaximum signal is applied. Insertion loss is, of course, an optical power loss. However, it ultimately increases the amount of electrical power that must be supplied to the system, since higher power optical sources must be used.8.1.4 Power ConsumptionElectrical power must also be supplied to drive the modulator or switch. In the case of modulators, the required drive power increase with modulation frequency. Hence, a useful figure of merit is the drive power per unit bandwidth, P/∆f, usually expressed in milliwatts per megahertz. As is discussed in more detail in Sect.8.7, a key advantage of channel-waveguide modulators is that they have a significantly lower P/∆f than that required for bulk modulators.8.1.5 IsolationThe degree of isolation between variousinputs and outputs of a switch or modulator is a major design consideration. In a modulator, the isolation between input and output is merely the maximum modulation index, as defined previously. However, it is usually expressed in decibels when used to specify isolation. In the case of a switch, the isolation between two ports (either input or output) is given by21[]10log()isolation dB I I =-(8.1.10)where I1is the optical intensity in the driving port, and I2is the intensity at the driven port when the switch is in the off state with respect to port 1 and 2. Thus, a switch with a signal leakage, or crosstalk, of 1% with respect to two ports would have 20dB isolation.8.2 The Electro-Optic EffectThe fundamental phenomenon that accounts for the operation of most electro-optic modulators and switches is the change in index of refraction produced by the application of an electric field. In the most general case, this effect is non-isotropic, and contains both linear (Pockels effect)and nonlinear (Kerr effect)components. In crystalline solids, the change in index produced by the linear electro-optic effect, can be most conveniently characterized by the change in the components of the optical indicatrix matrix.The equation of the index ellipsoid in the presence of an electric field is1121212111625242232222212=⎪⎭⎫ ⎝⎛+⎪⎭⎫ ⎝⎛+⎪⎭⎫ ⎝⎛+⎪⎭⎫ ⎝⎛+⎪⎭⎫ ⎝⎛+⎪⎭⎫ ⎝⎛xy n xz n yz n z n y n x n (8.2.1)If x ,y , and z are chosen to be parallel to the principal dielectric axes of the crystal, the linear change in the coefficients due to an electric field E is given by∑==⎪⎭⎫ ⎝⎛∆3121j j ij i E r n (8.2.2)where i =1,2,3,4,5,6, and where j =1,2,3 are associated with x ,y ,z , respectively.If (8.2.2) is written in matrix form, the 6x3[r ij] matrix is called the electro-optic tensor. It can be shown that the linear electro-optic effect exists only in crystals that do not possess inversion symmetry. Even in the case of these non-centrosymmetric crystals, for most symmetry classes, only a few elements of the electro-optic tensor are nonzero. Hence, in the design of an electro-optic modulator or switch, both the waveguide material and its orientation with respect to the applied electric field must be chosen carefully. Nevertheless, many materials that can be used to make low loss waveguides, such as GaAs, GaP, LiNbO3, LiTaO3and quartz, also have significantly large Pockels coefficients, for certain orientation. Thus, the linear eletro-optic effect is widely used in integrated optic applications.The nonlinear (quadratic) Kerr electro-optic coefficient is relatively weak in commonly used waveguide materials. Also, a nonlinear dependence in electric field introduces unwanted modulation crossproducts (distortion) into the modulated signal. Consequently, it is not particularly useful in most integrated optic applications.8.3 Single-Waveguide Electro-OpticModulatorsThere are several different types of electro-optic modulators and switches that can be fabricated in a single-waveguide structure. The waveguide may be either a planar, or a channel guide. For example, the relatively simple planar waveguide shown in Fig.8.1 can function as either a phase modulator, an amplitude (intensity) modulator, or as an optical switch.Fig.8.1 Basic electro-optic modulator structureThe waveguide shown in Fig.8.1 is formed in Ga(1-x)Al x As using the hetero-epitaxial growth technique described in Chap 4. However, any electro-optic semiconductor such as GaAs x P(1-x), GaAs, or GaP could be used, and also the waveguide could alternatively be formed by the carrier-concentration-reduced method.8.3.1 Phase ModulationThe waveguide of Fig.8.1 is asymmetric, since the indices of the air and the metal at the top surface are both much less than n 2, while n 3is relatively close to n 2. The total change in index between the guide and the substrate is given by EO CCR chemical n n n n n ∆+∆+∆=-=∆3223(8.3.1)where ∆n chemical is the index change due to the differing aluminium concentrations a and b , ∆n CCR is the change resulting from decreased carrierconcentration (if any) in the guide, and ∆n EO is the index change caused by the electro-optic effect.To make a phase modulator, the dimensions and doping of the waveguide are chosen so that it is above cutoff for the m=0 mode at the wavelength desired, but is below cutoff for the m=1 mode. Thus, from (3.1.12)202202329321⎪⎪⎭⎫ ⎝⎛<∆+∆<⎪⎪⎭⎫ ⎝⎛g CCR chemical g t n n n t n λλ(8.3.2)When a voltage V is applied with reverse bias polarity to the Schottky barrier diode, as shown in Fig.8.1, the waveguide becomes part of the depletion layer of the diode, and the electric field causes a change in the phase of light waves traveling along the guide that is proportional to V .For the crystal orientation shown, the change in index of refraction caused by the field for a TE wave (polarized along the y axis) is given byg EO t V r n n 24132=∆(8.3.3)while there is no field-induced index change for TM waves (polarized in the x direction). Bydefinition of terms,πβλβ2)(0∆=∆=∆k n (8.3.4)g EO t VL r n L 41320λπβϕ=∆=∆Hence, if (8.3.4) is substituted into (8.3.3), the phase change produced by the electric field is given by(8.3.5)where L is the length of the modulator in the z direction. Many variations of the basic single-waveguide phase modulator structure have been demonstrated.8.3.2 Polarization Modulation Phase modulators are limited in their usefulness by the fact that a phase coherent detection system must be used. To avoid this complication, the simple modulator structure of Fig.8.1 can be used in a slightly different fashion by introducing the linearly polarized optical beam at 45 to the x and y axes. Because the phase change occurs only for waves polarized in the y direction and not for those polarized in the x direction, a rotation of the polarization vector will result as the waves propagate in the z direction.This change of polarization can be detected with a polarization –selective filter (usually called an analyzer) ahead of the detector. In the case of a discrete waveguide modulator, used for an air beam, a conventional wire-grid polarizer or an absorptive polarizing filter can be used as the analyzer. An analogous system can be implemented for the optical integrated circuit. For example, both grating and prism couplers are polarization sensitive and, hence, can be used as analyzers. However, the difficulty of fabricating an effective analyzer monolithically has limited the use of polarization modulators in OIC’s, and has led to a preference for intensity modulation.8.3.3 Intensity ModulationSince polarization and phase modulation are difficult to detect compared to intensity modulation, the device of Fig.8.1 is most often used in an intensity modulation mode. To make an intensity modulator, the difference in index of refraction at the waveguide-substrate interface must be carefully tailored to make the waveguide be just at the threshold for guiding the lowest order mode with no electric field present. Then, when an electric field is created by applying a voltage to the electrodes, it produces a slight additional change in index which causes the waveguide to become transmissive. The total change of index is given by (8.3.1).Hence, the zero field threshold condition for an intensity modulator of this type is given by20223321⎪⎪⎭⎫ ⎝⎛=∆+∆=∆g CCR chemical t n n n n λ(8.3.5)where (3.1.12) has been used for the cutoff condition of an asymmetric guide. An intensity modulator of this type was first implemented by Hall et al. , in a GaAs carrier-concentration-reduction planarwaveguide, for light of 1.15 μm wavelength. A voltage of 130 V was required to bring the guide above cutoff for the TE 0mode.Obviously, intensity modulators such as have been described in this section, can alsofunction as effective optical switches, as long as the magnitude of (∆n chemical + ∆n CCR ) is chosen to place the waveguide just below threshold and the applied field V /t g is large enough to bring the guide well above cutoff at the desired wavelength.202202329321⎪⎪⎭⎫ ⎝⎛<∆+∆<⎪⎪⎭⎫ ⎝⎛g CCR chemical g t n n n t n λλ20223321⎪⎪⎭⎫ ⎝⎛=∆+∆=∆g CCR chemical t n n n n λ20223321⎪⎪⎭⎫ ⎝⎛<∆+∆=∆g CCR chemical t n n n n λWithout an electric field (m=0)With an electric field Phasemodulator Intensitymodulator above cutoffOpticalswitch well above cutoffchange in the phase8.3.4 Electro-Absorption Modulation There is another type of modulator, the electro-absorption modulator, which uses an electric field to produce intensity modulation, yet it does not employ the Pockels effect. In the presence of a strong electric field, the absorption edge of a semiconductor is shifted to longer wavelength, as shown in Fig.8.2 for the case of GaAs in a field of 1.3x105V/cm. Because of the steepness of the absorption edge in a direct bandgap material such as GaAs, very large changes in absorption of wavelength near the band edge can be produced by application of an electric field.Fig.8.2 Franz-Keldysh shift of the absorption edge of GaAs. Curve A is the zero field absorption curve for GaAs.(Circular dots represent experimental data points for n-type material with carrier concentrationn=3x1016cm-3. For the square dotsn=5.3x1016cm-3) Curv e B shows the shifted absorption edge for a field of 1.3x105V/cmThe mechanism responsible for the Franz-Keldysh effect can be described straightforwardly with reference to the semiconductor energy band diagramin Fig.8.3. In the presence of a strong electric field, the band edges bend. The left-hand limit of the diagram represents the surface of the semiconductor, at which a Schottky barrier contact or shallow p-n junction has been formed. Application of a reverse-bias voltage to this rectifying junction causes a charge depletion layer to form, extending to depth x within the semiconductor.A nonuniform electric field is present within the depletion layer, with the largest amplitude existing at the surface.Fig.8.3 Energy band diagram of a semiconductor exhibiting the Franz-Keldysh effect in the presence of a strong electric field. The parameter x represents the distance from the surface of the semiconductor, and E is the electron energy. E c and E v are the conduction and valence bandedges, respectively.Outside of the depletion layer where the field exists, the bands are flat, as at the right side of Fig.8.3. In this region, a photon can be absorbed only if it has enough energy to lift an electron across the bandgap, as in transition (a). Closer to the surface, where the bands have been bent by the field, a transition (b) can occur in which photon energy is sufficient only to lift the electron partway across the gap. Ordinarily such a transition could not occur because there would be no allowed state within the bandgap. However, the electric field effectively broadens the states of the conduction band so that there is a finite probability of finding the electron in the gap.This , of course, reduces the effective bandgap andthereby shifts the absorption edge to longer wavelength. It can be shown that the effective change in bandgap energy ∆E is given by3231)(*)(23ε q m E -=∆(8.3.6)where m * is the effective mass of the carrier, q is the magnitude of the electrical charge of a carrier, is Planck’s constant divided by 2π, and εis the electric field strength.Since ∆E depends on the electric field strength, and since αis a very strong function of ∆E, as shown in Fig.8.2, a very effective electro-absorption modulator can be made for light of slightly less than bandgap wavelength. A basic structure is shown in Fig.8.4. Aluminum concentration b in the waveguide should be chosen so that the absorption edge wavelength is just slightly shorter than the guided wavelength, i.e., the guide is transparent with V=0. Carrier concentrations should be chosen so that N3>>N2, thus, a relatively large electric field is produced in the guide when V is applied.Fig.8.4 Basic electro-absorption modulator structure.The surface electrode can be either a Schottky barrier contact or shallow p-n junction. In either case the electric field is produced in the depletion layer. Ideally the dopant concentration in the waveguide N2should be small enough that the depletion layer extends all the way through the guide in the x direction. The length of the modulator, and the applied voltage are chosen by using absorption curves such as those of Fig.8.2 in order to establish a desired minimum insertion loss and maximum modulation depth for a given wavelength.Although any type of waveguide can be used, the waveguide modulator structure can be improved by using a GaAlAs heterostructure guide, as shown in Fig.8.4. In that case, the aluminum concentration in the guide can be adjusted to produce optimum performance at a given wavelength. For example, Reinhart has produced such structure for use at 900nm which exhibit a change in transmission by a factor of 100 for -8V applied bias. The power necessary for 90% modulation was on the order of 0.1mW/MHz.In sect.8.3, electro-optic modulators employing a single waveguide have been discussed.。