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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 2 — Jan. 22, 2007
  • pp: 402–407

A three-dimensional wide-angle BPM for optical waveguide structures

Changbao Ma and Edward Van Keuren  »View Author Affiliations

Optics Express, Vol. 15, Issue 2, pp. 402-407 (2007)

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Algorithms for effective modeling of optical propagation in three- dimensional waveguide structures are critical for the design of photonic devices. We present a three-dimensional (3-D) wide-angle beam propagation method (WA-BPM) using Hoekstra’s scheme. A sparse matrix algebraic equation is formed and solved using iterative methods. The applicability, accuracy and effectiveness of our method are demonstrated by applying it to simulations of wide-angle beam propagation, along with a technique for shifting the simulation window to reduce the dimension of the numerical equation and a threshold technique to further ensure its convergence. These techniques can ensure the implementation of iterative methods for waveguide structures by relaxing the convergence problem, which will further enable us to develop higher-order 3-D WA-BPMs based on Padé approximant operators.

© 2007 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(130.2790) Integrated optics : Guided waves

ToC Category:

Original Manuscript: December 8, 2006
Revised Manuscript: January 11, 2007
Manuscript Accepted: January 16, 2007
Published: January 22, 2007

Changbao Ma and Edward Van Keuren, "A three-dimensional wide-angle BPM for optical waveguide structures," Opt. Express 15, 402-407 (2007)

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  1. M. D. Feit and J. A. FleckJr., "Light propagation in graded-index optical fibers," Appl. Opt. 17, 3990-3998 (1978). [CrossRef] [PubMed]
  2. D. Yevick, "A guide to electric field propagation techniques for guided-wave optics," Opt. Quantum. Electron. 26, S185-S197 (1994). [CrossRef]
  3. J. Van Roey, J. van der Donk, and P. E. Lagasse, "Beam-propagation method: analysis and assessment," J. Opt. Soc. Am. 71, 803-810 (1981). [CrossRef]
  4. R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques for modeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-161 (2000). [CrossRef]
  5. Y. Chung and N. Dagli, "An assessment of finite difference beam propagation," J. Quantum. Electron. 26, 1335-1339 (1990). [CrossRef]
  6. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, Numerical recipes: The art of scientific computing, (Cambridge University Press, New York, 1986).
  7. G. R. Hadley, "Transparent boundary condition for beam propagation," Opt. Lett. 16, 624-626 (1991). [CrossRef] [PubMed]
  8. M. D. Feit and J. A. FleckJr., "Analysis of rib waveguides and couplers by the propagation method," J. Opt. Soc. Am A 7, 73-79 (1990). [CrossRef]
  9. C. Vassallo, "Reformulation for the beam-propagation method," J.Opt. Soc. Am. A 10, 2208-2216 (1993). [CrossRef]
  10. J. Gerdes and R. Pregla, "Beam-propagation algorithm based on the method of lines," J. Opt. Soc. Amer. A 8, 389-394 (1991). [CrossRef]
  11. R. P. Ratowsky and J. A. FleckJr., "Accurate numerical solution of the Helmholtz equation by iterative Lanczos reduction," Opt. Lett. 16, 787-789 (1991). [CrossRef] [PubMed]
  12. P. -C. Lee, D. Schulz, and E. Voges, "Three-dimensional finite difference beam propagation algorithms for photonic devices," J. Lightwave Technol. 10, 1832-1838 (1992). [CrossRef]
  13. P. -C. Lee and E. Voges, "Three-dimensional semi-vectorial wave-angle beam propagation method," J. Lightwave Technol. 12, 215-225 (1994). [CrossRef]
  14. A. Sharma and A. Agrawal, "New method for nonparaxial beam propagation," J. Opt. Soc. Am. A 21, 1082-1087 (2004). [CrossRef]
  15. S. L. Chui and Y. Y. Lu, "Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner," J. Opt. Soc. Am. A 21, 420-425 (2004). [CrossRef]
  16. G. R. Hadley, "Wide-angle beam propagation using Padé approximant operators," Opt. Lett. 17, 1426-1428 (1992). [CrossRef] [PubMed]
  17. G. R. Hadley, "Multistep method for wide-angle beam propagation," Opt. Lett. 17, 1743-1745 (1992). [CrossRef] [PubMed]
  18. H. J. W. M. Hoekstra, G. J. M. Krijnen and P. V. Lambeck, "On the accuracy of the finite difference method for applications in beam propagating techniques," Opt. Commun. 94, 506-508 (1992). [CrossRef]
  19. Z. Ju, J. Fu and E. Feng, "A simple wide-angle beam-propagation method for integrated optics," Microwave Opt. Technol. Lett. 14, 345-347 (1997). [CrossRef]
  20. C. Ma and E. V. Keuren, "A simple three dimensional wide-angle beam propagation method," Opt. Express 14, 4668-4674 (2006). [CrossRef] [PubMed]
  21. W. P. Huang and C. L. Xu, "A wide-angle vector beam propagation method," IEEE Photon. Technol. Lett. 4, 1118-1120 (1992). [CrossRef]

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