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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 3 — Mar. 1, 2004
  • pp: 420–425

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

Siu Lit Chui and Ya Yan Lu  »View Author Affiliations

JOSA A, Vol. 21, Issue 3, pp. 420-425 (2004)

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Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

© 2004 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(130.2790) Integrated optics : Guided waves
(350.5500) Other areas of optics : Propagation

Original Manuscript: October 7, 2003
Manuscript Accepted: November 4, 2003
Published: March 1, 2004

Siu Lit Chui and Ya Yan Lu, "Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner," J. Opt. Soc. Am. A 21, 420-425 (2004)

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  1. M. D. Feit, J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3997 (1978). [CrossRef] [PubMed]
  2. G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17, 1426–1428 (1992). [CrossRef]
  3. D. Yevick, “A guide to electric-field propagation techniques for guided-wave optics,” Opt. Quantum Electron. 26 (Suppl.), S185–S197 (1994). [CrossRef]
  4. H. J. W. M. Hoekstra, “On beam propagation methods for modelling in integrated optics,” Opt. Quantum Electron. 29, 157–171 (1997). [CrossRef]
  5. R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000). [CrossRef]
  6. D. Yevick, J. Yu, W. Bardyszewski, M. Glasner, “Stability issues in vector electric-field propagation,” IEEE Photon. Technol. Lett. 7, 658–660 (1995). [CrossRef]
  7. D. Yevick, “The application of complex Padé approximants to vector field propagation,” IEEE Photon. Technol. Lett. 12, 1636–1638 (2000). [CrossRef]
  8. W. P. Huang, C. L. Xu, “Simulation of three-dimensional optical waveguides by a full-vector beam-propagation method,” IEEE J. Quantum Electron. 29, 2639–2649 (1993). [CrossRef]
  9. I. Mansour, A. D. Capobianco, C. Rosa, “Noniterative vectorial beam propagation method with a smoothing digital filter,” J. Lightwave Technol. 14, 908–913 (1996). [CrossRef]
  10. E. E. Kriezis, A. G. Papagiannakis, “A three-dimensional full vectorial beam propagation method for z-dependent structures,” IEEE J. Quantum Electron. 33, 883–890 (1997). [CrossRef]
  11. E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three-dimensional z-varying optical waveguides,” J. Lightwave Technol. 16, 703–714 (1998). [CrossRef]
  12. J. Yamauchi, G. Takahashi, H. Nakano, “Full-vectorial beam-propagation method based on the McKee-Mitchell scheme with improved finite-difference formulas,” J. Lightwave Technol. 16, 2458–2464 (1998). [CrossRef]
  13. Y.-L. Hsueh, M.-C. Yang, H.-C. Chang, “Three-dimensional noniterative full-vectorial beam propagation method based on the alternating direction implicit method,” J. Lightwave Technol. 17, 2389–2397 (1999). [CrossRef]
  14. R. Barrett, M. W. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1994).
  15. R. P. Ratowsky, J. A. Fleck, “Accurate numerical solution of the Helmholtz equation by iterative Lanczos reduction,” Opt. Lett. 16, 787–789 (1991). [CrossRef] [PubMed]
  16. Q. Luo, C. T. Law, “Propagation of nonparaxial beams with a modified Arnoldi method,” Opt. Lett. 27, 1708–1710 (2001). [CrossRef]
  17. Y. Y. Lu, P. L. Ho, “Beam propagation method using a [(p-1)/p] Padé approximant of the propagator,” Opt. Lett. 27, 683–685 (2002). [CrossRef]
  18. H. Van der Vorst, “Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Statist. Comput. 13, 631–644 (1992). [CrossRef]

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