Numerical simulation of an arbitrarily ended asymmetrical slab waveguide by guided-mode extracted integral equations

The scattering phenomenon from an arbitrary-shaped end of a asymmetrical slab waveguide for the cases of TE and TM guided modes is simulated by means of boundary integral equations that are called guided-mode extracted integral equations. The integral equations that we derive can be solved by the conventional boundary-element method. Numerical results are presented for problems of three-layer asymmetrical waveguides with tilted ends. The reflection coefficient, reflected and scattered powers, and radiation patterns are calculated numerically for the cases of incident TE and TM guided modes.     

Satellite peaks in the scattering of p-polarized light from a randomly rough film on a perfectly conducting substrate

Abstract

The diffuse scattering of p-polarized light from a one-dimensional, randomly rough dielectric film deposited on a planar, perfectly conducting surface is studied by means of small-amplitude perturbation theory. The dielectric constant ε_d and the thickness d of the dielectric film are chosen in such a way that in the absence of roughness the scattering system supports N (≥ 2) guided modes whose wavenumbers are q ₁ (ω), …,q _N(ω) at the frequency ω of the light incident at an angle θ_o. We investigate the occurrence of satellite peaks, in addition to the enhanced back-scattering peak, in the angular distribution of the intensity of the diffusely scattered light, at angles θ_s(n, m) given by sin θ_s(n, m)= ? sin θ₀± (c/ω) [Q_n(ω) ? q_m(ω)] for n, m=1, …, N(n ≠ m). These satellite peaks are multiple-scattering effects due to degenerate timereversal symmetry.     

Reflectivity properties of an anisotropic slab waveguide with isolated substrate

The scattering properties for both TE and TM modes of an abruptly ended two-layered slab waveguide with anisotropic core and isolated substrate are examined by an improved iteration technique, which is based on the integral equation method with accelerating parameters. The relative dielectric constants of the core for the three Cartesian directions are considered to be different, but cases with isotropic core are also considered. The electric field distribution on the terminal plane and the reflection coefficients of the dominant TE and TM guided modes, as well as the near-field distribution and the far-field radiation pattern, are computed, while numerical results are presented for several cases of the core anisotropy.     

Reflectivity of buried slab waveguides

The scattering properties of an abruptly ended buried slab waveguide for both TE and TM modes are examined by an improved iteration technique that is based on the integral equation method with "accelerating" parameters. The waveguide is considered a symmetrical slab, for which the weakly guiding conditions are invalid, and it is embedded in a different dielectric material. The tangential electric field distribution on the terminal plane, the reflection coefficient of the first TE and TM guided modes, and the far-field radiation pattern are computed. Numerical results are presented for several ended waveguides, while special attention is given to the far-field radiation pattern rotation and the terminal field distributions.     

Air bubble-induced light-scattering effect on image quality in 193 nm immersion lithography

As an emerging technique, water immersion lithography, offers the capability of reducing critical dimensions by increasing the numerical aperture that is due to the higher refractive indices of immersion liquids than that of air. However, in the process of forming a water fluid layer between the resist and the lens surfaces, air bubbles are often created because of the high surface tension of water. The presence of air bubbles in the immersion layer will degrade the image quality because of the inhomogeneity-induced light scattering in the optical path. Analysis by geometrical optics indicates that the total reflection of light causes the enhancement of scattering in the region in which the scattering angle is less than the critical scattering angle, which is 92 deg at 193 nm. Based on Mie theory, numerical evaluation of scattering that is due to air bubbles, polystyrene spheres, and poly(methyl methacrylate) spheres was conducted for TE, TM, or unpolarized incident light. Comparison of the scattering patterns shows that the polystyrene spheres and air bubbles resemble each other with respect to scattering properties. In this paper, polystyrene spheres are used to mimic air bubbles in studies of lithographic imaging of bubbles in immersion water. In an interferometric lithography system, the distance beyond which bubbles will not print can be estimated by direct counting of defect sites.     

Quarter-wave layers with 50% reflectance for obliquely incident unpolarized light

The conditions under which light interference in a transparent quarter-wave layer of refractive index n1 on a transparent substrate of refractive index n2 leads to 50% reflectance for incident unpolarized light at an angle phi are determined. Two distinct solution branches are obtained that correspond to light reflection above and below the polarizing angle, phi(p), of zero reflection for p polarization. The real p and s amplitude reflection coefficients have the same (negative) sign for the solution branch phi>phi(p) and have opposite signs for the solution branch phior=(square root 2+1)square root n2. A monochromatic design that uses a high-index TiO2 thin film on a low-index MgF2 substrate at 488 nm wavelength is presented as an example.     

Focusing concave lens using photonic crystals with magnetic materials

The guided modes lying in the upper gap-edge band in the photonic band structure of photonic crystals have negative values of refractive index. This feature generates many interesting optical phenomena, and some spectacular photonic devices such as focusing slabs have been developed. We report the design of a photonic-crystal, planoconcave lens for focusing incident parallel light, and theoretically analyze the chromatic aberrations for TM and TE modes. In addition to dielectric photonic crystals, the chromatic aberration of a magnetic photonic-crystal planoconcave lens was investigated because the magnetic permeability may also contribute to the periodic index contrast in photonic crystals, especially at long wavelengths. A significant difference was found in the chromatic aberration for a TM mode propagating in a dielectric than in a magnetic photonic-crystal planoconcave lens.     

Design of retrodiffraction gratings for polarization-insensitive and polarization-sensitive characteristics by using the Taguchi method

We present the design of retrodiffraction gratings that utilize total internal reflection (TIR) in a lamellar configuration to achieve high performance for both TE and TM polarized light and polarization-sensitive performance for gratings behaving as polarizer filters; the design was based on rigorous coupled wave analysis (RCWA) and the Taguchi method. The components can thus be fabricated from a single dielectric material and do not have to be coated with a metallic or dielectric film layer to enhance the reflectance. The effects of the structural and optical parameters of lamellar gratings were investigated, and the TIR gratings in a lamellar configuration were structurally and optically optimized in terms of the signal-to-noise ratio (S/N) and a statistical analysis of variance (ANOVA) of the refractive index, grating period, filling factor, and grating depth as control factors and the estimated efficiency by RCWA as a noise factor. For more accurate robustness, a two-step optimization process was used for each purpose. For TIR gratings designed to perform similarly for TE and TM incident polarization, the -1st-order efficiencies were estimated to be up to 92.0% and 88.5% for TE and TM polarization, respectively. Also, for the TIR gratings designed to achieve polarization-sensitive performance when behaving as a polarizer filters, the -1st-order diffraction efficiencies for TE and TM polarization were estimated to be up to 95.5% and 2.7%, respectively. From these analysis results, it was confirmed that the Taguchi method shows feasibility for an optimization approach to a technique for designing optical devices.     

Analysis of the focal characteristics of cylindrical lenses made of anisotropically dielectric material based on rigorous electromagnetic theory

Abstract

The focal characteristics of refractive cylindrical lenses made of anisotropically dielectric material (uniaxial crystal) are analysed based on rigorous electromagnetic theory and the boundary element method. The performances of the lenses with different f numbers are appraised for both incident waves of the TE (transverse electric) and TM (transverse magnetic) polarizations. Numerical results show that the focal performance of this kind of lens for the TE polarization and the TM polarization of incident light wave is a difference, in particular, different focal lengths, owing to the anisotropy of the material. However, for the conventional isotropic lens, the focal features for both the TE and TM polarizations are the same. It is anticipated that this new kind of lens proposed for the first time may serve as a light switching device with high speed used in the micro-optical communication.     

TM Wave Resonant Peaks in Defect-Free Multilayer Structures Containing Nano-Scale Y123 Superconductors

In the ultraviolet region and by using transfer matrix method, the transmission spectra of electromagnetic waves through one-dimensional quasiperiodic photonic structures consisting of high-temperature yttrium barium copper oxide (Y123) superconductor and strontium titanate (STO) dielectric layers are studied theoretically. It is shown that for TE polarization at oblique incidence two band gaps are created, while for TM polarization three band gaps are produced. The edges of both polarizations shift to higher wavelengths by increasing incident angles. Also, for angles of incidence greater than 78^°, the second gap for TM-polarized light is eliminated. It is also found that in the supposed structure the number of PBGs can be modulated by the thickness of dielectric layer, while it is nearly insensitive to the thickness of superconductor layer. Interestingly, for the incidence angles other than normal incidence the structure can exhibit some narrow resonant peaks near wavelengths where the electric permittivity of the superconductor layer changes sign. These resonant peaks are only for TM polarization and not present for TE polarization. This structure can act as a very compact polarization sensitive splitters and defect-free multichannel narrowband tunable filters.     

Analysis of Reflectance Properties in 1D Photonic Crystal Containing Metamaterial and High-Temperature Superconductor

In the present work, reflectance properties of one-dimensional photonic crystal (1D PC) containing a metamaterial and high-temperature superconductor have been investigated theoretically and analyzed. The reflectance/transmittance spectrum of the proposed structure is obtained by using the characteristic or transfer-matrix method (TMM). The results show that by increasing the thickness of the metamaterial layer, the width of the second reflection band decreases while the width of the first reflection band remains almost the same though it shifts towards the higher frequency side. In addition to this, a new band gap arises in the lower side of frequency. But, when the thickness of the superconductor layer is increased, the width of both the bands increases and no additional band arises in this case. Moreover, the reflection band is also affected by varying the operating temperature of the superconducting layer and the results show that bands get narrower by increasing the operating temperature. Finally, the effect of incident angle on the reflection band has been discussed for both transverse electric (TE) and transverse magnetic (TM) polarizations.     

Critical Angles for Reflectivity at an Isotropic-anisotropic Boundary

Abstract

The angular dependent reflectivities, and in particular sharp, critical, edges in these have been analysed for the boundary between an isotropic and a uniaxial medium. For the general uniaxial case, it is shown that for measured reflectivities of the type transverse magnetic (TM) incident to TM reflected or transverse electric (TE) incident to TE reflected there is only one sharp critical angle, the other being rounded due to TM to TE conversion. On the other hand if the TM to TE conversion reflectivity is measured (or TE to TM) then a sharp cusp occurs at the otherwise rounded critical edge. This thereby allows, from some very simple reflectivity measurements the determination of the optical tensor for the anisotropic medium. A full analytic treatment of this behaviour is presented together with numerical evaluations of the electromagnetic field distributions which illustrate how this cusp arises. The possible application of the use of this TE to TM conversion cusp measurement in the case of obliquely oriented liquid crystals is also discussed.     

Microwave absorbers of two-layer composites laminate for wide oblique incidence angles

Advanced microwave absorbers for wide oblique incidence angles are required in many applications including wireless communication or vehicle identification in Intelligent Transport System (ITS) where 5.8 GHz Dedicated Short Range Communication (DSRC) system is applied. In this study, two-layer microwave absorbers are designed for the achievement of low reflection coefficient over wide incidence angles at 5.8 GHz. The absorbing layer of rubber composite containing magnetic iron flake particles and the surface layer of low dielectric constant (carbon black composite and glass fiber composite) have been used in the absorber design. On the basis of transmission line theory, the reflection loss has been calculated with variation of incident angles for both Transverse Electric (TE) and Transverse Magnetic (TM) polarization. At the optimum thickness of the composite layers, a low value of reflection loss (less than −10 dB) has been predicted for wide incidence angles up to 60° for both TE and TM polarization, which is well consistent with the reflected power measured by free-space arch test. The two-layer composite laminate consisted of magnetic absorbing layer with high magnetic and dielectric loss and surface impedance-matching layer of a controlled dielectric constant can be proposed for high potential microwave absorbers in ITS.     

Polarization dependent solar cell conversion efficiency at oblique incident angles and the corresponding improvement using surface nanoparticle coating

Despite tremendous efforts on improving the solar cell conversion efficiency at normal incidence, improvement at oblique angles has not been widely addressed, not to mention the corresponding light absorption behaviors at different polarizations. Here we report the characterization of the solar cell conversion efficiency and the spectra of photoresponsivity at various tilted angles. The results show that TM (transverse magnetic) polarized light possesses higher photoresponsivity than TE (transverse electric) polarized light and the difference becomes larger with the incidence angle. To address the issue, a monolayer of silica nanoparticles on the solar cell surface was employed to improve the light absorption. Even though both TE and TM waves show a decrease in the surface reflectivity with the presence of nanoparticles, the interaction between the silica particles and the TE wave is more significant. The improvement of the conversion efficiency for obliquely incident light is explained from the refractive index difference of the nanoparticles for the TE and TM polarizations.     

板状粘接结构中对称和反对称纵波与界面的相互作用

为了激发粘接结构中的导波或界面波,通常需要将声波从两半无限介质同相位或反相位地同时入射多层系统。针对此问题,基于矩阵方法,推导了界面处于理想连接的情况下,对称或反对称纵波从上下半无限空间入射时,三层板状粘接结构中纵、横波的反射与透射系数表达式。分析了入射角度、粘接层厚度以及基体材料等对声波反射(或透射)特性的影响。结果表明,对称或反对称纵波垂直入射时不发生波型转换。粘接结构中声波的反射(或透射)特性与入射角度、频率以及粘接层厚度等参数密切相关。在相同的粘接层厚度(或频率)范围内,随着声波频率(或粘接层厚度)的增加,谐振频率曲线向低频漂移。该方法可作为粘接结构中体波或导波传播特性研究的重要理论基础。     

Bragg reflection from space charge waves in a semiconductor waveguide

A dispersion relation for the space charge waves (SCWs) in a thin semiconductor layer with symmetric dielectric surrounding is obtained. The collinear waveguide SCW-optic interaction is analyzed for the zero-order (homogeneous) and first-order SCW modes. It is shown that effective Bragg reflection is possible on the SCW-optic TE and TM modes of various orders.     

Dispersion relation of guided-mode resonances in multimode grating waveguide structures

It is well known that the location of guided-mode resonance (GMR) in grating waveguide structures closely tracks the leaky mode dispersion curves. In this paper, taking Bragg reflection due to periodicity and interaction between different modes into account, we first present a schematic diagram of the dispersion relations of leaky modes in multimode grating waveguide structures, both for s-polarized (TE mode) and p-polarized (TM mode) incident waves. Due to the perturbation of the grating layer, the interaction between different resonance modes (transverse standing waves) is inevitable. This transverse interference will result in the non-Bragg nature resonance band gaps in the dispersion curves. Exploiting the characteristics of leaky mode dispersions over the full range of the first Brillouin zone, we hoped we could gain some insight into the relationship among the mode interactions, band gaps, and their benefits to optical elements utilizing the GMR effect in grating waveguide structures. Finally, a specific structure is analyzed.     

The syncang method for simultaneous measurement of film refractive index and thickness

The synchronous angle method (SYNCANG) for the simultaneous determination of the refractive index and film thickness of thin dielectric films is especially useful for researchers involved in integrated optics.The method involves the measurement of the synchronous angles θ_5E and θ_5M (see Fig. 1) required to couple transverse electric (TE) and transverse magnetic (TM) modes into light guides, and the solution of the resulting pair of simultaneous transcendental eigenvalue equations yields n₁ and W.The sensitivity of the method has been studied, and it is shown that n₁ may easily be resolved within 0.002 per minute of arc, considering θ_5E and θ_5M as having equal errors. W may be resolved within 0.02 μ (200 Å) per minute of arc, depending primarily on the proximity of the synchronous guide angle θ₁ to 90°. The method does not require a step in the film, and may be easily reduced to measuring n₁ knowing either the TE or the TM synchronous angle and W.     

Excitation of waveguide modes in organic light-emitting diode structures by classical dipole oscillators

Analytical techniques known in the literature are used to (i) identify all the planar waveguide modes in four top-emitting organic light-emitting diode (OLED) structures over the visible spectrum, and (ii) compute both TM and TE power spectra for classically radiating dipoles in the emissive layers of these OLED structures. Peaks in the computed power spectra are identified with the waveguide modes in the OLED devices, and areas associated with these peaks are used to estimate the excitation probability of the waveguide modes. In cases where ambiguities arise because of overlapping peaks, it is shown that computed power spectra can be approximated as sums of Lorentzian line shapes. It is found that for all four structures, the dipoles couple almost 80% of their radiant energy into TM modes with only about 20% going into TE modes. Furthermore, except for a narrow spectral band, the excited TM modes are primarily short-range surface plasmon polaritons. Excitations in the narrow spectral band correspond to TM and TE Fabry-Perot microcavity modes. Finally, the analysis shows that, in the absence of grating couplers, only light in the microcavity modes escapes into the air cover.     

Scattering by a dense layer of infinite cylinders at normal incidence

The solution for scattering by a layer of densely distributed infinite cylinders is presented. The layer is irradiated by an arbitrarily polarized plane wave that propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilized the effective field and quasi-crystalline approximation to treat the multiple scattering interactions in the dense finite medium. Governing equations for the propagation constants and amplitudes of the effective fields are derived for TM and TE mode incident waves, from which the scattered intensity distribution and scattering cross section for arbitrary polarization are obtained. The dense medium gives rise to coherent and incoherent scattered radiation that propagates in the plane normal to the axes of the cylinders. The coherent scattered radiation includes the forward component in the direction of the incident wave and the backward component in the direction of specular reflection. The incoherent scattered intensity distribution shows a pronounced forward peak that coincides with the angle of refraction of the effective waves inside the medium. Numerical results are presented to illustrate the scattering characteristics of a dense layer of cylinders as a function of layer thickness for a given solid volume fraction.