Semivector Finite-Difference Formula for the Analysis of a Step-Index Waveguide With a Tilted Interface

Abstract

Abstract-A three-point finite-difference formula is derived for the analysis of a step-index waveguide with a tilted interface. The formula is suitable for the use of the alternating-direction implicit method. Through the analysis of a rib waveguide with a sloped side wall and a hollow triangular waveguide, improvement in accuracy and stability is demonstrated.Index Terms-Alternating-direction implicit method (ADIM), beam-propagation method (BPM), finite-difference (FD) formula.

Topology optimization of nonlinear optical waveguide devices considering output signal phase

“…The finite element method (FEM) [6][7][8][9][10][11], the finite difference time domain (FDTD) method [12,13], or the beam propagation method (BPM) [14][15][16] has been utilized as a numerical simulation method in these topology optimization method. Among them, BPM [17][18][19] is a quite useful technique in the analysis of long-length waveguide devices in which backward reflection hardly occurs. BPM can treat the large-scale problem which is difficult to be analyzed by FEM or FDTD due to the lack of computational resources.…”