Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

• 来源期刊: 中国物理（英文版）
• 关键词: beam propagation method alternating direction implicit algorithm finite difference optical waveguides integrated optics
• 年，卷（期）: 2006,（8）
• 页码范围: 1824-1830
• 页数: 7页
• 语种: 英文

摘要

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.