Simple derivative-free method of zero extraction by phase-based enclosure for determination of complex propagation constants in planar multilayer waveguides.

A rigorous and simple way to implement a numerical method for extracting the propagation constants and modal characteristics of lossless, lossy, and active planar multilayer waveguides is presented. The method can accurately determine the complex propagation constants of both guided and leaky modes. The method does not utilize the derivative of the dispersion function nor any integrals of it.

Review and accuracy comparison of various permittivity-averaging schemes for material discontinuities in the two-dimensional FDFD method: implementation using efficient computer graphics techniques.

Several known and widely used averaging techniques aiming to improve the accuracy of the two-dimensional finite-difference frequency-domain (FDFD) method, in the presence of material discontinuities, are reviewed, numerically tested, and compared with respect to their accuracies. Furthermore, all averaging techniques are rigorously and efficiently implemented using the Supercover Digital Differential Analyzer algorithm and a modified Liang-Barsky algorithm suitably adapted from computer graphics applications. The FDFD with Gaussian blurring; the FDFD with volume-polarized effective permittivity; the FDFD with volume-polarized effective permittivity on shifted cells; and the FDFD with anisotropic smoothing [FDFD (AS)] are compared with respect to their accuracies (for both TE and TM polarization), in the case of scattering by an infinite homogeneous cylinder (for which analytical solution exists) comprising a lossless dielectric, a high-index, low-loss dielectric, or a metal.

Performance analysis of waveguide-mode resonant optical filters with stochastic design parameters.

The performance of optical filters with resonant waveguide gratings is investigated numerically in a stochastic context, assuming random fluctuations of various design variables. Specifically, we derive stochastic models based on polynomial chaos expansions, whose involved coefficients are obtained by computing spectral projections via sparse-grid quadrature. The latter exploits purely deterministic results from a rigorous coupled-wave analysis solver and requires less simulation data than standard Monte Carlo (MC) techniques.

Preferential input-waveguide grating couplers: rigorous analysis using the pseudospectral time-domain method.

Preferential input-waveguide grating couplers are rigorously analyzed using the pseudospectral time-domain method in the total field/scattered field formulation for TE and TM polarizations in conjunction with the convolutional perfect matching layer approach. Four kinds of preferential input-waveguide grating couplers are studied: the volume holographic grating coupler, the slanted parallelogrammic surface-relief grating coupler, the double-corrugated surface-relief grating coupler, and the reflecting-stack surface-relief grating coupler. Coupler's input coupling efficiencies to various waveguide modes are calculated.

Preferential-order waveguide grating couplers: a comparative rigorous analysis using the finite-difference time-domain method.

We rigorously analyze and compare preferential-order waveguide grating output couplers using the finite-difference time-domain method in the total-field/scattered-field formulation for TE and TM polarizations. Four kinds of preferential-order grating couplers are studied: volume holographic grating couplers, slanted parallelogrammic surface-relief grating couplers, double-corrugated surface-relief grating couplers, and reflecting-stack surface-relief grating couplers. The outcoupling efficiencies and branching ratios of the couplers, revealing their preferentiality, are calculated and compared with the rigorous coupled-wave analysis leaky-mode method.

Optical waveguide grating couplers: 2nd-order and 4th-order finite-difference time-domain analysis.

Output optical waveguide grating couplers are rigorously analyzed using the 2-order and the 4-order finite-difference time-domain (FDTD) method in conjunction with the total field/scattered field (TF-SF) approach and special averaging and regularization techniques for the mitigation of permittivity discontinuities. Volume-holographic and surface-relief grating couplers are analyzed for both TE and TM polarizations. The 2- and 4-order FDTD results are compared in terms of computational efficiency and accuracy.

Finite-difference-time-domain analysis of finite-number-of-periods holographic and surface-relief gratings.

The total-field-scattered-field formulation of the finite-difference time-domain method (FDTD) is used to analyze the diffraction of finite incident beams by finite-number-of-periods holographic and surface-relief gratings. Both second-order and fourth-order FDTD formulations are used with various averaging schemes to treat permittivity discontinuities and a comparative study is made with alternative numerical methods. The diffraction efficiencies for gratings of several periods and various beam sizes, for both TE and TM polarization cases, are calculated and the FDTD results are compared with the finite-difference frequency-domain (FDFD) method results in the case of holographic gratings, and with the boundary element method results in the case of surface-relief gratings.

Optimization of sawtooth surface-relief gratings: effects of substrate refractive index and polarization.

The effect of the refractive index of the substrate together with the incident polarization on the optimization of sawtooth surface-relief gratings (SRGs) is investigated. The global optimum diffraction efficiencies of the -1st forward-diffracted order of sawtooth SRGs are 63.3% occurring at n2=1.

Optimization of anisotropically etched silicon surface-relief gratings for substrate-mode optical interconnects.

The optimum profiles of right-angle-face anisotropically etched silicon surface-relief gratings illuminated at normal incidence for substrate-mode optical interconnects are determined for TE, TM, and random linear (RL) polarizations. A simulated annealing algorithm in conjunction with the rigorous coupled-wave analysis is used. The optimum diffraction efficiencies of the -1 forward-diffracted order are 37.

Three-dimensional converging-diverging Gaussian beam diffraction by a volume grating.

The diffraction characteristics of a volume grating (VG) illuminated by a three-dimensional (3-D) converging-diverging Gaussian beam at conical incidence are investigated by applying 3-D finite-beam (FB) rigorous coupled-wave analysis (RCWA) based on the conventional 3-D RCWA in conjunction with two-dimensional plane-wave decomposition. The Gaussian beam is assumed to have an arbitrary incidence angle, an arbitrary azimuthal angle, and any linear polarization. The two cases with linear polarizations of the central beam of the Gaussian (E perpendicular K and H perpendicular K) are investigated.

Angular sensitivities of volume gratings for substrate-mode optical interconnects.

The angular sensitivities of slanted volume gratings (VGs) illuminated by three-dimensional (3-D) converging-diverging spherical Gaussian beams for substrate-mode optical interconnects in microelectronics are analyzed by application of 3-D finite-beam rigorous coupled-wave analysis. Angular misalignments about the z, y, and x axes that correspond to yaw, pitch, and roll misalignments resulting from manufacturing tolerances of chips are investigated. Two cases of linear polarization of the central beam of the Gaussian are considered: E perpendicular K and H perpendicular K, where K is the grating vector.

Optimization of finite-length input volume holographic grating couplers illuminated by finite-width incident beams.

A finite volume holographic grating coupler (VHGC) normally illuminated with various incident-beam profiles (such as a Gaussian beam, a flat cosine-squared beam, and an exponential-decay beam) with finite beam widths for input coupling is rigorously analyzed by use of the finite-difference frequency-domain method. The effects of the incident-beam width, the incident-beam position, the incident-beam profile, and the incident-beam angle of incidence on the input coupling efficiency are investigated. The optimum conditions for input coupling are determined.

Wavelength response of waveguide volume grating couplers for optical interconnects.

The wavelength response of a waveguide volume grating coupler (WVGC) is analyzed for coupling light from a slab waveguide into the superstrate. A leaky-mode approach is used in conjunction with rigorous coupled-wave analysis. A quantitative theoretical study of the effect of index modulation, waveguide index, and grating thickness on the wavelength bandpass of a WVGC is also presented.

Volume holographic grating couplers: rigorous analysis by use of the finite-difference frequency-domain method.

Two configurations of volume holographic grating couplers are rigorously analyzed by means of the finite-difference frequency-domain method (FDFD) for both TE and TM polarizations and for 0- and 45-deg output coupling. The two configurations depend on the position of the grating coupler, which can be placed either in the film or in the cover waveguide region. The FDFD results are compared with those obtained by the rigorous coupled-wave analysis in conjunction with the leaky-mode approach (RCWA-LM).

Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method.

The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations.

Colorimetry-based retardation measurement method with white-light interference.

A colorimetry-based retardation measurement (CBRM) method is presented. The specimen, between crossed polarizers, is illuminated with a white-light source. The retardation that is due to the birefringence of the specimen produces a white-light interference color.

Volume grating couplers: polarization and loss effects.

We analyze the polarization-dependent performance and the loss performance of volume grating couplers using a leaky-mode approach in conjunction with rigorous coupled-wave analysis for two configurations: the volume grating in the cover layer and the volume grating in the waveguide. The angular dependence of TE and TM polarization coupling efficiency is studied, and designs for polarization-dependent and polarization-independent couplers are presented for both configurations. Polarization-dependent couplers are obtained with an outcoupling angle close to normal.

Two-dimensionally-periodic diffractive optical elements: limitations of scalar analysis.

The range of validity of the scalar diffraction analysis is quantified for the case of two-dimensionally-periodic diffractive optical elements (crossed gratings). Three canonical classes of two-dimensionally-periodic grating structures are analyzed by using the rigorous coupled-wave analysis as well as the scalar diffraction analysis. In all cases the scalar-analysis diffraction efficiencies are compared with the exact diffraction efficiencies.