Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method |
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Authors: | Xiao Jin-Biao and Sun Xiao-Han |
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Institution: | Laboratory of Photonics and Optical Communications, Department of Electronic Engineering,Southeast University, Nanjing 210096, China |
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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. |
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Keywords: | beam propagation method alternating direction implicit algorithm finite difference optical waveguides integrated optics |
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