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Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner.

Siu Lit Chui1, Ya Yan Lu

  • 1Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|March 10, 2004
PubMed
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This study introduces an efficient solver for wide-angle beam propagation methods (BPMs), crucial for simulating light in 3D structures. The new method enhances accuracy and computational speed for optical waveguide analysis.

Area of Science:

  • Computational Electromagnetics
  • Wave Optics
  • Numerical Analysis

Background:

  • Wide-angle beam propagation methods (BPMs) are essential for simulating wave propagation in complex 3D structures.
  • Existing BPMs face challenges in efficiently solving the large linear systems arising from wide-angle approximations.
  • The alternating direction implicit (ADI) method efficiently solves simpler BPM variants but is less effective for wide-angle cases.

Purpose of the Study:

  • To develop an efficient numerical solver for wide-angle full-vector beam propagation methods (BPMs).
  • To address the computational challenges associated with solving linear systems in advanced BPM formulations.
  • To enable accurate simulation of wave propagation in intricate three-dimensional wave-guiding structures.

Main Methods:

Related Experiment Videos

  • Derivation of wide-angle full-vector BPMs using rational approximants of the square root operator.
  • Implementation of a Krylov subspace method for solving the complex linear systems.
  • Application of an alternating direction implicit (ADI) preconditioner to accelerate the Krylov subspace solver.

Main Results:

  • An efficient and accurate solver for wide-angle full-vector BPMs has been successfully developed.
  • The proposed solver demonstrates improved performance in handling the linear systems characteristic of wide-angle propagation.
  • Successful simulation of wave field propagation in representative structures like Y branches and tapers.

Conclusions:

  • The presented Krylov subspace method with an ADI preconditioner offers an efficient solution for wide-angle full-vector BPMs.
  • This advancement facilitates more accurate and computationally feasible simulations of optical waveguides.
  • The method is validated through successful simulations of wave propagation in key photonic device geometries.