中国物理B ›› 2006, Vol. 15 ›› Issue (8): 1824-1830.doi: 10.1088/1009-1963/15/8/033

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇    下一篇

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

肖金标, 孙小菡   

  1. Laboratory of Photonics and Optical Communications, Department of Electronic Engineering,Southeast University, Nanjing 210096, China
  • 收稿日期:2005-11-09 修回日期:2006-02-26 出版日期:2006-08-20 发布日期:2006-08-20

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

Xiao Jin-Biao(肖金标)† and Sun Xiao-Han(孙小菡)   

  1. Laboratory of Photonics and Optical Communications, Department of Electronic Engineering,Southeast University, Nanjing 210096, China
  • Received:2005-11-09 Revised:2006-02-26 Online:2006-08-20 Published:2006-08-20

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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.

Abstract: 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.

Key words: beam propagation method, alternating direction implicit algorithm, finite difference, optical waveguides, integrated optics

中图分类号:  (Optical waveguides and couplers)

  • 42.79.Gn
42.82.Et (Waveguides, couplers, and arrays) 02.70.Bf (Finite-difference methods)