Optical and Quantum Electronics

, Volume 38, Issue 1–3, pp 45–62 | Cite as

A Simple Bi-directional Mode Expansion Propagation Algorithm Based on Modes of a Parallel-plate Waveguide

Article

Abstract

The bi-directional mode expansion propagation algorithm (BEP) is known to be an accurate and efficient method for modelling field distribution in high-index contrast waveguide structures with strong back-reflections like Bragg gratings and photonic crystals. The main difficulty of this method is that for lossy structures, the propagation constants of modes are to be searched in the complex plane. To speed-up this procedure, a two-step algorithm for eigenmode calculation based on the expansion into the modes of an empty metallic waveguide has recently been proposed. Proper truncation rules possessing good convergence of the expansion method for both TE and TM modes have also been recently published. In this contribution, both these approaches are combined in the development of an extremely simple version of the two-dimensional BEP method that makes use of the field expansion into the eigenmodes of a parallel-plate waveguide. The method is strictly reciprocal and appeared to be computationally reliable also for strongly lossy structures. High numerical stability is ensured using the scattering matrix formalism, and an efficient method of calculating Bloch modes for symmetric as well as asymmetric periodic waveguide structures is adopted. A wide range of applicability of the method is demonstrated by a few examples.

Keywords

bi-directional mode expansion Bloch modes optical waveguide theory periodic structures photonic crystals waveguide gratings 

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References

  1. Berends, H. DBR grating spectral filters for optical waveguide sensors. PhD thesis, TU Twente, 1997.Google Scholar
  2. Bienstman, P. www.sourceforge.net/CAMFR, 2003.Google Scholar
  3. Bienstman, P. 2004Opt. Quant Electron.365CrossRefGoogle Scholar
  4. Bienstman, P., Derudder, H., Baets, R., Olyslager, F., Zutter, D. 2001IEEE T. Microw. Theory MTT49349Google Scholar
  5. Collin, R.E. 1991Field theory of guided waves2IEEE PressNew YorkGoogle Scholar
  6. Čtyroký, J., Helfert, S., Pregla, R. 1998Opt Quant Electron.30343Google Scholar
  7. Čtyroký, J., Helfert, S., Pregla, R., Bienstman, P., Baets, R., Ridder, R., Stoffer, R., Klaasse, G., Petráček, J., Lalanne, P., Hugonin, J.-P., Rue, R.M. 2002Opt. Quant. Electron.34455Google Scholar
  8. Helfert, S.F. and R. Pregla. 12th International Workshop on Optical Waveguide Theory and Numerical Modelling, Ghent, Belgium, 21–23 March 2004, 31, 2004Google Scholar
  9. Huang, K.C., Lidorikis, E., Jiang, X., Joannopoulos, J.D., Nelson, K.A., Bienstman, P., Fan, S. 2004Phys. Rev.691Google Scholar
  10. Hugonin, J.P., Lalanne, P., Villar, I.d., Matias, I.R. 2005Opt. Quant. Electron.37107CrossRefGoogle Scholar
  11. Chew, W.C., Jin, J.M., Michielsen, E. 1997Microw Opti. Techn. Let.15383Google Scholar
  12. Petráček, J. Modelling of optical waveguide structures by mode matching method. PhD thesis, Brno University of Technology, 2004Google Scholar
  13. Sauvan, C., Lalanne, P., Hugonin, J.-P. 2004Opt. Quant. Electron.36271CrossRefGoogle Scholar
  14. Schelkunoff, S.A. 1952Bell Syst. Technol. J.31784MathSciNetGoogle Scholar
  15. Sztefka, G., Nolting, H.-P. 1993IEEE Photonic. Tech. L.5554Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Institute of Radio Engineering and Electronics AS CRPraha 8

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