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Determining reflections for beam propagation algorithms

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Abstract

Reflections occur whenever different waveguide sections are concatenated. In this paper, we will give approximate formulas for determining the reflection coefficient. Starting with generalized transmission line equations we will derive general formulas where suitable approximations are introduced. These approximations allow the determination of the reflections with low numerical effort. The expressions were implemented in an FD-BPM algorithm to determine the field distribution in waveguide devices. For an application in CAD systems the reflection coefficient of the fundamental mode was computed with the approximate formulas. Numerical results were obtained for various concatenations of different waveguide sections. A comparison with the method of lines, a semi-analytic algorithm, shows a good agreement.

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References

  • Chiou, Y.-P. and H.-C. Chang. IEEE Photon. Technol. Lett. 9 964, 1997.

    Google Scholar 

  • El-Refaei, H., I. Betty and D. Yevick. IEEE Photon. Technol. Lett. 12 158, 2000a.

    Google Scholar 

  • El-Refaei, H., D. Yevick and I. Betty. In: Integr. Photo. Resear. Technic. Digest. Santa Barbara, USA, p. 104, 1999.

  • El-Refaei, H., D. Yevick and I. Betty. IEEE Photon. Technol. Lett. 12 389, 2000b.

    Google Scholar 

  • Felsen, L.B. and N. Marcuvitz (eds.). Radiation and Scattering of Waves, IEEE Press, New York, USA, 1996.

    Google Scholar 

  • Glingener, C., J.-P. Elbers and E. Voges. AEÜ 51 20, 1997.

    Google Scholar 

  • Helfert, S.F. and R. Pregla. Opt. Quantum Electron. 32 681, 2000. (Special Issue on Optical Waveguide Theory and Numerical Modelling.)

    Google Scholar 

  • Leijtens, X., L. Spiekman, C. van Dam, L. de Vreede, M. Smit and J. Tauritz. European Conference on Integrated Optics and Technical Exhibit, Delft, The Netherlands, p. 463, 1995.

  • Pregla, R. In: Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices (PIER 11), ed. W.P. Huang, Progress in Electromagnetic Research. EMW Publishing, Cambridge, Massachusetts, USA, p. 51, 1995.

    Google Scholar 

  • Pregla, R. Integr. Photo. Resear. Technic. Digest. Santa Barbara, USA, p. 40, 1999a.

  • Pregla, R. International Conference on Transparent Optical Networks. Kielce, Polen, p. 49, 1999b.

  • Pregla, R. European Conference on Integrated Optics and Technical Exhibit. Torino, Italy, p. 55, 1999c.

  • Pregla, R. and W. Pascher. In: Numerical Techniques for Microwave and Millimeter Wave Passive Structures, ed. T. Itoh, Wiley, New York, USA, p. 381, 1989.

    Google Scholar 

  • Tripathi, V.K. IEEE Trans. Microw. Theory Tech. MTT-25 726, 1977.

    Google Scholar 

  • Xu, C., K. Li, W.P. Huang, W. Lui and K. Yokoyama. Integr. Photo. Resear. Technic. Digest, Vol. 4, p. 20. Victoria, Canada, 1998.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Allgemeine und Theoretische Elektrotechnik, FernUniversität, 58084, Hagen, Germany

    S.F. Helfert & R. Pregla

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  1. S.F. Helfert
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  2. R. Pregla
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Correspondence to S.F. Helfert.

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Helfert, S., Pregla, R. Determining reflections for beam propagation algorithms. Optical and Quantum Electronics 33, 343–358 (2001). https://doi.org/10.1023/A:1010834615308

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