Chin. Phys., 2006, Vol. 15(8): 1824-1830    DOI: 10.1088/1009-1963/15/8/033
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# Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

Xiao Jin-Biao, Sun Xiao-Han
Laboratory of Photonics and Optical Communications, Department of Electronic Engineering,Southeast University, Nanjing 210096, China
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.
Received:  09 November 2005      Published:  20 August 2006
 PACS: 42.79.Gn (Optical waveguides and couplers) 42.82.Et (Waveguides, couplers, and arrays) 02.70.Bf (Finite-difference methods)