The temporal evolution of the steady-sate holographic performance and the response time were investigated in a low glass-transition temperature photorefractive polymer composite. With a constant poling field applied and under continuous illumination during seven days, 100 writing cycles of one hour duration were performed. We found a slight increase of the steady-state performance over time, while the response time decreased by a factor of three, clearly indicating an aging process. The device did not show phase separation or optical damage after this extended measurement period, but the exact nature of the aging process remains currently unclear. This study shows that holographic long-term measurements are important for an accurate characterization of photorefractive materials which are taken into consideration for applications. Especially changes of the response time during long-term usage have to be taken into account.

We describe new high T_g multi-functional polymers. In order to develop a photorefractive system with stable phase behavior at elevated temperatures we synthesized a series of maleimide/methyl vinyl isocyanate copolymers with carbazole as charge transporting moieties. We chose carbazole substituents attached with different spacer groups to adjust Tg of the polymers between 60 degrees C and 194 degrees C. As NLO chromophores we used hydroxyl alkyl functionalized 2- (N-ethyl-4-(4-nitrogen-phenylazo)-anilino)-ethanol and 2- (2,5-dimethyl-4-(4-nitro-phenylazo)-ethanol and 1-(4- ethylhydroxyphenyl)-3-methyl-4-(4-diethylaminophenyl)imino- pyrazole-5-on. Chromophore contents up to 44 mol percent have been attached under mild conditions by polymer analogous reactions. The materials are amorphous and posses excellent solubility in common solvents, e.g. chloroform and THF. Holographic four-wave mixing experiments was performed on a device made from a polymer elasticized such that the glass-transition temperature was T_g equals 80 degrees C. For the grating formation two exponential response times were found wit (tau) ₁ equals 100 ms and (tau) ₂ equals 1,5 s and a logarithmically weighted average response time of 200 ms.

The photorefractive effect of liquid crystalline polymers doped with photoconductive compound was investigated and compared to those of amorphous polymers. The photorefractive diffraction efficiency of the isotopic phase of liquid crystalline polymers was found to be larger than those of amorphous polymers with similar molecular structures. The diffraction efficiency of the isotropic phase of liquid crystalline polymers do not come from the pretransitional effect.

In this report, we introduce new organic photorefractive composites consisting of charge transporting den-drimers highly doped with a stilbene nonlinear optic chromophore, The purpose of making these composites is to improve charge transport, by reducing inhomogeneity when compared to ordinary polymer-based systems. Because the structure of this material gives us freedom to control the orientation of charge transport agents synthetically, we can study the charge transport mechanism more systematically than in polymers. We discuss this point and present the characterization results for this material.

We present an organic photorefractive material based on a low molar mass glass with both photoconductive and nonlinear optical properties. By implementing a novel plasticizer and doping with the well known sensitizer C₆₀ we obtained a composite material, which shows extremely fast initial response times of 2.5 ms at writing beam intensities of I_write equals 1 W/cm² and 450 microsecond(s) at I_write equals 10.8 W/cm². Combined with high refractive index modulations of up to (Delta) n equals 6 X 10^-3 and sample lifetimes of over 6 months this material exhibits an excellent overall performance.

One challenge for photorefractive organic materials is to overcome the problem of their relatively low speed. The latter may be caused by either the photoelectric properties of the material or by the reorientation of nonlinear optical chromophores in a space-charge field. This contribution focuses on the first aspect. Using holographic and pulsed experiments, we determine the charge carrier mobility in a bifunctional glass. A comparison of both techniques shows the critical influence of several parameters, such as the concentration of the photoconductor and the sample thickness, on the photoelectric properties of the material.

We consider application of the in situ poling optical polarimetry method to guest-host systems consisting of a Corona-poled, sol-gel, porous silicate film matrix doped with Disperse Red 1 (DR1) chromophores. Refractive indices, and physical thicknesses are consistently determined by ex situ null ellipsometry, atomic force microscopy and Abeles- Hacskaylo characterization. Due to the pronounced poling- induced birefringence we found in the composite films, in opposition to previous approaches, we could not disregard it with respect to refractive index values. Even for the case of strong birefringence, this procedure and associated modeling allow estimation of electro-optic coefficients and second-order susceptibilities of poled dielectric films doped with DR1, or with other high hyperpolarizability chromophores.

A new easy method for obtaining a drift mobility and a diffusion coefficient from a nondispersive time-of-flight transient has been developed. Nondispersive transients are described well in the theoretical photocurrent equation (PTE) based on the fact that a carrier packet drifts at a constant velocity and is spread by diffusion, the top electrode acts as a reflecting and partially absorbing wall, and the counter electrode acts as an absorbing wall. The fitting of the PTE to photocurrent transients gives the mobility and the diffusion coefficient (D) simultaneously. These are suitable characteristic values for descriptions of carriers transport because they do not show the thickness dependence and the negative field dependence in a low electric field. The mobility that sometimes shows the thickness dependence and the negative field dependence in a low electric field, however, has usually been measured from the time of the intersection of the asymptotes to the plateau and trailing edge of the transients. In order to obtain (mu) _a from photocurrent transients by a simple method, we have tried to describe t₀ and tail-broadening parameter W as functions of (mu) _a and D, where W is defined as (t_1/2 - t₀)/t_1/2 and t_1/2 is the time at which the current is a half of that in the plateau region. The dependences of calculated (mu) _k and W on the electric field and the sample thickness agreed well with those of the experimental data. These results verify the PTE and suggest that (mu) _a and D can be calculated from t₀ and W. We also report that the diffusion coefficient is proportional to the power of 2 of the mobility. This result agrees with a theory based on the Langevin equation which describes motions of carriers in a fluctuated field.

The non-steady-state photo-ElectroMotive Force (photo-EMF) effect has been observed in photoreflective (PR) polymer films based on poly(N-vinylcarbazole) (PVK). It was investigated in the typical tilted transmission configuration without and with application of moderate external DC electric fields. The dependencies of the photo- EMF signals on the frequency and the amplitude of the phase modulation, the tilt angle, and the externally applied DC field are qualitatively explained using a simple model of the effect, developed earlier for unipolar photoconductive inorganic crystals without saturation of the trapping centers. Quantitatively, however, the experimental data turned out to be interpreted considering the presence of additional space-charge gratings appearing due to light reflection from the rear interfaces of the thin-film device, as could be proven by numerical simulation. The photo-EMF technique is a powerful experimental tool for the characterization of PR polymers without or at low external DC fields, where conventional holographic techniques give insufficient signal. It can be extended for the evaluation of organic xerographic photoconductors in general.

MBB-PPV/C₆₀ and MB-PPV/C₆₀ composite films were fabricated by physical jet deposition technique and the effect of the film structure and the polymer on the photoconductivity of composite film were studied. Both composite films show the enhancement of the photoconductivity over the pure PPV and C₆₀ while the enhancement of the photoconductivity of MBB-PPV/C₆₀ film was found better than that of MB-PPV/C₆₀ due to more efficient excitation transfer and charge transfer properties in MBB-PPV/C₆₀ multilayer film. The result of time- resolved photoluminescence further confirms the high efficiency of charge transfer process occurring at the interface between MBB-PPV and C₆₀ layers in the composite film.

A long standing issue for transport in molecularly doped polymers is the compatibility of the small polaron hopping rate. It has been recently shown that the Poole-Frenkle field dependence of the mobility of injected charges in molecularly doped polymers arises as a natural consequence of the charge-dipole interaction. In this paper we address the extent to which the Poole-Frenkle behavior is compatible with the dependent upon the size of the polaron binding energy.

We present results of computer simulations of the charge carrier mobility dependence on the electric field and trap concentration in disordered polar organic materials. Recently an unusual dependence of the charge carrier drift mobility in molecularly doped polymers on the concentration of traps has been reported. This dependence differs from the expected inverse proportionality that should be valid for trap-controlled transport. Using our results we argue that this dependence is caused by the existence of different regimes of charge carrier transport for layers with different trap concentrations, i.e. dispersive transport for small trap concentrations and nondispersive transport for high trap concentrations. Our results also show that the mobility, estimated from the time of intersection of the asymptotes to plateaus and trailing edge of photocurrent transient, is very sensitive to variation of transient shape and, in some case, effectively masquerades real concentration and field dependence of the true mobility. Change of the shape with the change of electric field in trap-containing matrices distorts significantly the field dependence of the mobility, calculated by the intersection procedure, and even transforms the usual Poole-Frenkel dependence to the linear one.

Random variables for the position, energy, and orientation of donors are used to simulate hole transport in polymers with donor fraction p < 10 percent and clusters. Marcus hopping rates yield decreasing drift velocity with increasing bias field E. In contrast to energetic disorder emphasized in models at p approximately 50 percent, the mean dwell time (tau) (E) increases as positional or orientational disorder restricts hopping. Competition between energetic and positional disorder suggests a compensation temperature. Simulations of dilute systems are analyzed in terms of transient random walks, ensemble averages, and order statistics.

The proportionality of the logarithm of the mobility to the square root of the electric field is most likely caused by the broadening of the density of states according to both the Gaussian disorder model and the 3D correlated disorder model (CDM). Using these models, the relation between the slope of the mobility against the electric field and the dipolar component of the width of the density of states ((sigma) _d) is analyzed. The (sigma) _d for the donor and the host polymer are calculated using the dipolar disorder model in which a random distribution of permanent dipoles generates fluctuation in electric potential. A successful interpretation of the relation between (beta) and (sigma) _d has been achieved using the formula based on the CDM. Assuming that all components of the density of states are described using Gaussian statistics, the van der Waals component is evaluated to be negligibly small from analyses of temperature dependence of the relation between (beta) and (sigma) _d. The experimental results also shows that the value of the DOS width that is derived from the analysis of the temperature dependence of the zero-field mobility is different for the value of the DOS width that is derived from the analysis of the electric field dependence.

Charge carrier generation and charge carrier transport in binary mixtures of the electron acceptor 4H-1,1-dioxo-4- dicyanomehtylidene-2-p-tolyl-6-phenylthiopyran (PTS) and the electron donor N,N'-bis(3-methylphenyl)-(1,1'-bi-phenyl)- 4,4'-diamine (TPD) have been studied. It is found that charge generation in TPD:PTS is sensitized by the formation of exciplexes and charge-transfer complexes. Moreover, TPD:PTS displays hole transport as well as electron transport. Charge carrier mobilities have been measured for different TPD:PTS ratios and are discussed within the framework of the disorder model of Baessler and coworkers. TPD:PTS displays trap-free electron transport over a wide range of electric fields, temperatures, and mixture ratios. The results demonstrate that the presence of the donor molecules has no influence on the electron transport properties. In contrast to this, the hole transport is apparently affected by dipolar interactions between TPD and PTS molecules. THus the width of DOS increases from 0.08 eV in TPD to 0.12 eV upon adding PTS. Agreement with experiment requires that the van der Waals component is dependent on the concentration of the transport molecules, increasing with increasing dilution. Surprisingly the highest non- diagonal disorder for hole transport of about (Sigma) equals 5 is found in mixtures of similar TPD and PTS ratio indicating that the formation of charge-transfer complexes causes additional disorder.

Addition of an electron or hole to a conducting polymer chain has been shown to cause the chain to distort, creating a large polaron. We show, by numerical solution of the coupled equations for the electron wavefunctions and the lattice displacements on a polyacetylene chain with an extra electron, that the polaron does not form in electric fields >= V/cm an already formed polaron will be dissociated. Implications for the current-voltage characteristic will be discussed.

For devices based on the use of electronic polymers there is practical interest in exploring the variations in contact behavior that might result under realistic manufacturing conditions like multilayer device assembly based on solution coating technology. Small molecule doped polymers (MDPs) developed principally as large area coatings for electrophotographic use are now finding wider device applications. These polymers are insulators capable of transporting excess injected charge with a unipolar drift mobility which can be tuned over a wide range by varying the concentration of transport active species. Most significant in the present context, MDPs can be rendered trap free by molecular design. These unique characteristics of MDPs make it possible to analyze the relative injection efficiencies of their interfaces with various contacts simply by a direct comparison of current voltage characteristics with time of flight drift mobility measurements carried out on the same film coatings. Measurements were carried out by measuring dark hole injection into the MDP film TPD/polycarbonate and a polymeric analog, PTPB, from various preformed metal substrates as well as evaporated top contacts. For preformed metal substrates under fully relaxed conditions, it was found that while injection efficiency nominally scaled with the estimated interfacial energy step there was significant variance that in some cases could be clearly associated with the specific details of interfacial chemistry. Time and temperature dependent phenomenon were also delineated and analyzed. Here contact injection efficiencies were observed to increase monotonically, following initial formation, from an emission limited to final steady state which could be ohmic.

We studied photoconductivity in particle dispersions and vacuum evaporated films of benzimidazole perylene (BZP) pigment in contact with a tetraphenyldiamine (TPD) hole transport layer. Xerographic photoreceptors based on evaporated BZP photogenerator layers showed about two times higher carried generation efficiency than photoreceptors containing generator layer in the form of a particle dispersion. Time resolved fluorescence measurements were performed on these two types of structures. Fluorescence time evolution was compared in samples with and without TPD in a polycarbonate overcoat layer. Significantly larger decrease in average fluorescence lifetime was observed in structures containing thin evaporated films compared to the structures with the pigment in the form of particle dispersion. This indicates that reduced carrier generation efficiency in particle dispersion sin a consequence od exciton bulk trapping which significantly reduces the number of excitons reaching BZP/TPD interface. As carrier generation in BZP/TPD system is a result of exciton dissociation at the interface to produce electron-hole pairs. Thus a smaller number of excitons reaching the interface leads to reduction of carrier generation efficiency.

Photogeneration of charge carriers in a methyl-substituted ladder-poly(para-phenylene) (LPPP), which possesses a high intrachain order, has been studied by xerographic experiments. The time-of-flight technique was used to study charge carrier transport in LPPP. The quantum efficiency of charge carrier generation was calculated by evaluating the photoinduced-discharge curves and found to be independent of both excitation wavelength and temperature. The results can be described by a modified Braun theory with a simple exponential distribution of radii of thermalized electrons. LPPP shows a high charge carrier mobility up to 10^-3 cm²/V s, a high primary quantum efficiency of 80 percent, a low residual potential and a small dark decay. THus, LPPP represents a promising material to build single component single-layer photoreceptors. For a comparison, another polymer ladder-type poly(para-phenylene thienylene) (LPPPT), which possesses low intrachain order, is also studied. The quantum efficiency of free charge generation in LPPPT is about one order of magnitude smaller as compared to that in LPPP.

The photo-hole generation process in the smectic phases of a liquid crystalline photoconductor, 2-(4'-octylpheny)-6- dodecyoxylnaphthalene (8-PNP-012) was investigated by using steady-state and transient photocurrent measurements. It was revealed that the photo-generation of holes was governed by two different processes: Onsager type of photo-carrier generation in the bulk and electrode-enhanced hole injection induced by the charge transfer from photo-excited 8-PNP-012 molecules to the electrode interface. In the former process, for fairly high light intensity, the collected photo- generation charge was found to be approximately proportional to the square of the light intensity irrespective of the phase, suggesting the contribution of exciton-exciton interactions. And in the latter process, the photogeneration quantum yield can be one order of magnitude larger than that in the bulk generation process. We will discuss totally the photo-carrier generation process in mesophases of 8-PNP-012, in terms of exciton-exciton and exciton-electrode interactions including the effect of electrode materials and the disorder of molecular arrangement.

Some kinds of bisazo pigments and single-crystal hydrazone derivatives have been synthesized and three types of experimental organic photoconductors for advanced electrophotography were prepared and tested. The result shows that under visible light the photoconductor of ortho- chloride bisazo pigment is far more sensitive than p- chloride and non-chloride bisazo pigments. Its sensitivity reaches 0.71 Lx.s and is appropriate for advanced xerography.

A physical description of the qualitatively different stages in the kinetics of the development of symmetric rosette-type formations is given. It is shown experimentally that these formations possess a hexagonal symmetry at low supercriticality and are characterized by a severe mode of excitation. Under high fields a square lattice form occurs to have lower energy.

Hole drift mobilities (mu) were measured in a series of triphenylamine (TPA) molecules and oligomers dispersed into bisphenol-A polycarbonate (PC) by conventional time-of- flight techniques. The transport molecules were oligomeric triphenylamine (OTPA) containing 8-10 TPA units TPD and TPA. In PC doped with 50 wt percent OTPA, TPD, and TPA, (mu) values were of 1 X 10^-7, 1 X 10^-5, and 7 X 10^-6 cm²/(V S) accordingly, at the electric field of F equals 5 $ MUL 10⁵V/cm and room temperature. In order to elucidate the relationship between structure of transport site and mobility, the molecular orbital calculations were made for the TPA, TPD and OTPA molecules. For the calculations, the PM3 method was chosen because it gave better agreement between calculated and experimentally parameters than the AM1 method for the molecules studied. The result obtained from the hole mobility measurements and the quantum chemistry calculations demonstrate that the N-Ph-Ph-N fragment is a transporting center for both TPD and OTPA molecules. For OTPA, the end fragments of the molecule appear as transport sites.

This paper summarizes the work currently in progress at CRC Canada on wavelength multiplexing components based on polymer waveguide devices for operation at 1550 nm. Planar arrayed waveguide gratings (AWGs) of various bandwidths were designed, fabricated and tested using acrylate polymer materials developed by Allied Signal Inc. Eight channel polymer demultiplexers fabricated by standard lithography show on-chip losses of 8 dB and a crosstalk of -25 dB between channels spaced 1.6 nm part. Owing to the thermo- optic properties of these polymers, the spectral response of the device scan be tuned by more than 7 nm without changes in optical crosstalk or on-chip loss. Very compact AWGs made with Allied Signal polymers are being designed and tested to address the need for cost effective, high bandwidth optical components in the telecom and datacom industries.

For all optical path networks there is a need for optical crossconnect systems and switching matrices. Using polymer materials and technologies, not only low cost components but low power consumption devices can be fabricated. We optimize ORMOCER's, a new class of polymer materials, which combine the specific advantages of organic polymers and inorganic glasses, with respect to the need of photonic applications. They exhibit a high thermal stability of up to 250 degrees C and a low optical attenuation of 0.2 dB/cm at 1.3 micrometers and 0.4 dB/cm at 1.55 micrometers .

In microsystem technology the fabrication of either passive or active micro optical components made from polymers becomes more and more evident with respect to the intense expanding application possibilities e.g. in telecommunication. Actually, the LIGA process developed at the FZK, Germany allows the direct fabrication of microcomponents with lateral dimensions in the micrometer range, structural details in the submicrometer range, high aspect ratios of up to several hundreds and a final average surface roughness of less than 50 nm in small up to large scales. The molding of polymer components for microoptical applications, especially in the singlemode range, is determined by the achievable maximum accuracy of the molding technique itself and of the acceptable tolerances for low damping and coupling losses. Following the LIGA and related technique e.g. mechanical microengineering we want to present in this work the fabrication of polymer singlemode waveguides using a combination of micromolding and light- curing steps.

A multifunctional polymeric deice capable of performing functions such as electro-optic modulation, optical amplification, and electro-optic switching simultaneously is described. All three modules can be built on a single substrate. A novel polymeric modulator with structure based on 1 X 2 Y-fed directional coupler is demonstrated. The results of preliminary investigations on optical amplifiers are presented.

The advantages of polymeric thermo-optic space switches based on modal evolution effects in X- and Y-junctions are now well established for telecommunications applications. An alternative device structure based on tapered directional couplers, in which the guide effective index is tapered in opposite directions in each arm of a distributed coupling device has been suggested theoretically, but fabrication of these devices with existing mask based technologies has proved extremely difficult. In this paper we demonstrate that laser direct writing of refractive index tapered structures in the photosensitive polymer material system BDK:PMA with a TEM₀₁ 'doughnut' laser beam allows high performance mode evolution couplers to be delineated with crosstalk values < -40 dB and excess losses of approximately 0.3 dB. It is demonstrated that complete switching can be obtained through thermo-optic detuning of the device.

Polyimides are widely used in electronics as heat-resistant organic materials and are now being studied for possible use in optical components. The fluorinated polyimides developed by NTT have high transparency at telecommunication wavelengths, a controllable index of refraction, and high thermal stability, making them suitable for use in optical communication systems. Here, optical components developed using fluorinated polyimides are reviewed, and the relationships between the material characteristics and the device parameters are discussed.

There is growing interest in the use of planar waveguide devices in telecommunications. Polymeric planar waveguide devices are of special interest in thermo-optic devices because of their high values for dn/dT. This paper details the possible choices in different photolithographic system that could be used in making such devices. This paper explains the benefits of using fluorinated acrylates in achieving low-loss waveguides with low birefringence. It also explains the unique benefits of fluorinated acrylates in making Bragg gratings.

Published work on organic materials for photonic device applications has tended to emphasize enhancements in nonlinear optical properties. Yet the linear properties of these materials are just as critical for determination of whether working devices are feasible. Simple calculations are presented to demonstrate the interplay between index of refraction, optical loss, and nonlinearity in device design. The implications of the result are discussed.

Recent status of the polymer optical fiber (POF) for high speed data communication and telecommunication is reviewed. The GI POF was proposed for the first time at Keio University, and several methodologies to fabricate GI POF have been currently proposed. In this paper, we clarify the great advantage of perfluorinated (PF) polymer can decrease the intrinsic absorption loss compared with poly methyl methacrylate (PMMA), which is the conventional material of POF. Furthermore, it was found that low material dispersion of the PF polymer is another advantage to obtain the high bandwidth GI POF. It was clarified for the first time that the power distribution of modes formed by the mode dependent attenuation was the dominant factors of the higher bandwidth of the GI POF than theoretically predicted bandwidth, while the effect of the mode coupling was small.

For the design of polymeric electrooptic devices, the indices of refraction of each layer are needed. There are a number of experimental techniques that can be used to determine these values for available polymers. Methods for the estimation are also possible for many proposed systems. We will explain these approximate methods for single systems, dispersion to the currently useful wavelengths in the IR, and the estimation of indices of refraction for composite system of either two polymers or a polymer and a nonlinear optically active chromophore. By these methods the design of new optoelectronic devices can be accelerated.

The weak absorption of waveguide materials can be measured by Photothermal Deflection Spectroscopy (PDS) with two orders of magnitude or higher sensitivity than conventional UV-VIS absorption spectroscopy. While it is easy to obtain relative absorption spectra for thin polymer films with PDS, extracting absolute absorption coefficients is more involved. The PDS measured signals depend on both thermal and optical absorption properties of materials. Knowledge of thermal properties is necessary to extract absorption coefficients. We report a methodology to obtain from PDS independently the thermal properties and absolute absorption coefficients.

We apply the side-illumination fluorescence (SIF) technique to study the excited states of ISQ molecules in polymer optical fibers (POFs). Fluorescence from ISQ-doped POFs is used as a broad wavelength light source to characterize aggregate electronic states of the ISQ dye. We show that a model which accounts for inhomogeneous broadening characterizes the J-aggregate like excited sate in highly concentrated ISQ-doped poly(methyl methacrylate) multimode fibers. These aggregate states are undetectable using standard transmission spectroscopy technique due to the large absorbance on resonance and are typically red-shifted 100-150 nm from the dominant excited state. The classification of the formation of aggregate states off- resonance is important for both linear and nonlinear optical device applications.

An optical directional waveguide coupler with polymer cover has been studied with silicon-on-insulator (SOI) structure consisting of a 1.5 micrometers thick silicon surface layer, a 0.4 micrometers buried-oxide layer, and a 1 micrometers polymer cover layer. The characteristics of rib waveguide, radial curvature of S- shaped waveguide, coupling length an gap distance of SOI directional waveguide coupler have been studied at wavelength 1.55 micrometers . Simulation with beam-propagation- method, we demonstrate that using polymer cover on SOI direcitonal waveguide coupler will reduce the coupling length, relax the gap distance constraint, even increase output optical field intensity efficiently. The optimal result of propagation loss of the straight waveguide and the S-shaped waveguide can be designed to be 0.1dB/cm, respectively. The maximum bending angle of S-shaped SOI waveguide with polymer cover can be designed up to 0.63 degrees. The simulation of optical SOI directional waveguide coupler with polymer cover shows promising result for achieving optical interconnections on Si optical electronic high speed devices.

Thermally stable polymer waveguide was fabricated using polycarbonate as the core material. Polycarbonate is thermally stable up to 190 degrees C, has small birefringence of 0.003 and good otpical transparency at 1.3 micrometers . We used Cyclotene 3022 as the cladding material. The material has 0.45 percent lower refractive index than the core material, resulting in a good mode matching waveguide with a single mode silica fiber. Buried channel waveguides were fabricated by conventional photolithography and dry etching technique. The thickness of the guiding layer was 5.3 micrometers and the width of the waveguides varied form 3 to 8 micrometers . They showed an optical loss of less than 0.8 and 1.4 dB/cm at the wavelength of 1.3 micrometers for TE and TM polarizations, respectively.