Layer-Mode Transparent Boundary Condition for the Hybrid Fd-Fd Method

Abstract

Abstract-We combine the analytic eigen mode expansion method with the finite-difference, frequency-domain (FD-FD) method to study two-dimensional (2-D) optical waveguide devices for both TE and TM polarizations. For this we develop a layer-mode based transparent boundary condition (LM-TBC) to assist launching of an arbitrary incident wave field and to direct the reflected and the transmitted scattered wave fields back and forward to the analytical regions. LM-TBC is capable of transmitting all modes including guiding modes, cladding modes and even evanescent waves leaving the FD domain. Both TE and TM results are compared and verified with exact free space Green's function and a semi-analytical solution.

Field Analysis of Dielectric Waveguide Devices Based on Coupled Transverse-Mode Integral Equation-Numerical Investigation

“…We could have used fewer terms by choosing other auxiliary functions like guiding modes from a largecore highindex slab waveguide [21]. When comparing the field images with those computed by the hybrid FD-FD method [8] with a N λ = 30 (not shown), we find that CTMIE images posses same features (resolution, smoothness, etc.) as those obtained by FD-FD method.…”

“…We pick t G as the quantity of interest since it is the dominate power coefficient. In Figure 4, we show fluctuating behavior of TE polarized, t G as function of W D. Each data point is computed twice to form an average using Equation (8). We also set F SM = 25, F AF = 5 to keep the mode density sufficiently high.…”

“…We will discuss how to tune of CTMIE modeling parameters to obtain the solutions with minimum computational effort. We verify the convergence of the solutions with results computed by our hybrid FD-FD method [8] or by running separate CTMIE calculations with or without considering the problem symmetry. All cases are checked and verified for both TE and TM polarizations.…”

“…The two cases are decoupled and can each be treated as a scalar wave problem [3,4]. For complex but compact optical devices, full wave methods such as the finite-difference time-domain methods (FD-TD) [5], frequencydomain finite-difference methods (FD-FD) [6][7][8] and the finite element method [9] can be quite effective. For very large waveguides the beam propagation method (BPM) and its variations, FFT-BPM [1], FD-BPM [11] are used for studying field evolutions in a slowly varying waveguide and for mode profile determination in a 3-D straight waveguide.…”

Theoretical Foundation for the Method of Connected Local Fields

“…From these FourierBessel coefficients we derived FD-like, compact nine-point stencils for the 2D Helmholtz equation. We show that CLF is capable of advancing existing FD-FD methods [5][6][7][8][9] by reducing the sampling density to just a little more than two points per wavelength, which is theoretical limit for spatial sampling.…”