Sparse polynomial chaos algorithm with a variance-adaptive design domain for the uncertainty quantification and optimization of grating structures.

In this work, an algorithm is introduced based on polynomial chaos expansions (PCEs) to tackle uncertainty quantification problems related to grating filters. Our approach adaptively constructs anisotropic PC models for the quantities of interest, accommodating varying polynomial orders. It exploits the sparsity of the PCE coefficients, which are computed using the least angles regression (LARS) sparse solver, leading to a highly efficient process.

Statistical Analysis of Plasma Dynamics in Gyrokinetic Simulations of Stellarator Turbulence.

A geometrical method for assessing stochastic processes in plasma turbulence is investigated in this study. The thermodynamic length methodology allows using a Riemannian metric on the phase space; thus, distances between thermodynamic states can be computed. It constitutes a geometric methodology to understand stochastic processes involved in, e.

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.

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.