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Truncation rules for modelling discontinuities with Galerkin method in electromagnetic theory

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Abstract

It is well known that apparently similar discretization schemes of Maxwell's equations in Fourier series may provide very different convergence performances because of truncation. We argue that this work performed in grating theory can be applied to other electromagnetic theories relying on expansions over series different from Fourier series. This generalization is supported by an intuitive argument and by a simple numerical example with Hermite–Gauss functions.

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References

  • Abramowitz, M. and I.A. Stegun. Handbook of Mathematical Functions, Dover Publications, New York, Chapter 22, 1972.

    Google Scholar 

  • Bérenger, J.P. J. Comput. Phys. 114 185, 1994.

    Google Scholar 

  • Booton, R.C. Computational Methods for Electromagnetics and Microwaves, p. 113. John Wiley, New York, 1992.

    Google Scholar 

  • Chandezon, J., D. Maystre and G. Raoult. J. Opt. (Paris) 11 235, 1980.

    Google Scholar 

  • Ctyroky, J., S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. de Ridder, R. Stoffer, G. Klaasse, J. Petracek, Ph. Lalanne, J.P. Hugonin and R.M. De La Rue. Opt. Quantum Electron. 34 455, 2002.

    Google Scholar 

  • Enoch, S., E. Popov and M. Nevière. Proc. SPIE 4438 183, 2001.

  • Gallawa, R.L., I.C. Goyal, Y. Tu and K. Ghatak. IEEE J. Quantum. Electron. 27 518, 1991.

    Google Scholar 

  • Gaylord, T.K. and M.G. Moharam. Proc. IEEE 73 894, 1985.

    Google Scholar 

  • Granet G. and B. Guizal. J. Opt. Soc. Am. A 13 1019, 1996.

    Google Scholar 

  • Helfert, S.F. and R. Pregla. J. Lightwave Technol. 14 2414, 1996.

    Google Scholar 

  • Ho, K.M., C.T. Chan and C.M. Soukoulis. Phys. Rev. Lett. 65 3152, 1990.

    Google Scholar 

  • Hoekstra, H.J.W.M., G.J.M. Krijnen and P.V. Lambeck. J. Lightwave Technol. 10 1352, 1992.

    Google Scholar 

  • Knop, K. J. Opt. Soc. Am. A 68 1206, 1978.

    Google Scholar 

  • Lalanne, Ph. Phys. Rev. B 58 9801, 1998.

    Google Scholar 

  • Lalanne, Ph. IEEE J. Quantum. Electron. 38 800, 2002.

    Google Scholar 

  • Lalanne, Ph. and J.P. Hugonin. J. Opt. Soc. Am. A 17 1033, 2000.

    Google Scholar 

  • Lalanne, Ph. and G.M. Morris. J. Opt. Soc. Am. A 13 779, 1996.

    Google Scholar 

  • Lalanne, Ph. and E. Silberstein. Opt. Lett. 25 1092, 2000.

    Google Scholar 

  • Li, L. J. Opt. Soc. Am. A 13 1870, 1996.

    Google Scholar 

  • Li, L. J. Opt. Soc. Am. A 14 2758, 1997.

    Google Scholar 

  • Li, L. In: Mathematical Modeling in Optical Science, Frontiers in Applied Mathematics, eds. G. Bao, L. Cowsar and W. Masters, p. 111. Society for Industrial and Applied Mathematics, Philadelphia, 2001.

  • Li, L. and J. Chandezon, J. Opt. Soc. Am. A 13 2247, 1996.

    Google Scholar 

  • Li, L. and C.W. Haggans, J. Opt. Soc. Am. A 10 1184, 1993.

    Google Scholar 

  • Marcuse, D. IEEE J. Quantum. Electron. 28 459, 1992.

    Google Scholar 

  • Mogilevtsev, D., T.A. Birks and P.S. Russell. Opt. Lett. 23 1662, 1998.

    Google Scholar 

  • Monro, T.M., D.J. Richardson, N.G.R. Broderick and P.J. Bennett. IEEE J. Lightwave Technol. 17 1093, 1999.

    Google Scholar 

  • Nevière, M., P. Vincent, R. Petit and M. Cadilhac. Opt. Commun. 9 48, 1973.

    Google Scholar 

  • Ortega-Monux, A., J.G. Wanguemert-Perez and I. Molina-Fernandez. J. Opt. Soc. Am. A 20 557, 2003.

    Google Scholar 

  • Palamaru, M. and Ph. Lalanne. Appl. Phys. Lett. 78 1466, 2001.

    Google Scholar 

  • Popov, E. and M. Nevière. J. Opt. Soc. Am. A 17 1773, 2000.

    Google Scholar 

  • Rasmussen, T., J.H. Povslen, A. Bjarklev, O. Lumholt, B. Pedersen and K. Rottwitt. IEEE J. Lightwave Technol. 11 429, 1993.

    Google Scholar 

  • Sauvan, C., Ph. Lalanne, J.C. Rodier, J.P. Hugonin and A. Talneau. IEEE Photon. Technol. Lett. 15 1243, 2003.

    Google Scholar 

  • Silberstein, E., Ph. Lalanne, J.P. Hugonin and Q. Cao. J. Opt. Soc. Am. A 18 2865, 2001.

    Google Scholar 

  • Snyder, A.W. and J.D. Love. Optical Waveguide Theory, Chapman & Hall, London, 1983.

    Google Scholar 

  • Tervo, J., M. Kuittinen, P. Vahimaa, J. Turunen, T. Aalto, P. Heimala and M. Leppihalme. Opt. Comm. 198 265, 2001.

    Google Scholar 

  • Villeneuve, P.R. and M. Piché. J. Mod. Opt. 41 241, 1994.

    Google Scholar 

  • Welsshar, A., J. Li, R.L. Gallawa, I.C. Goyal, Y. Tu and K. Ghatak. IEEE J. Lightwave Technol. 13 1795, 1995.

    Google Scholar 

  • Yeh, P. Optical Waves in Layered Media, John Wiley, New York, Chapter 11, 1998.

    Google Scholar 

  • Zhang, Z. and S. Satpathy. Phys. Rev. Lett. 65 2650, 1990.

    Google Scholar 

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Authors and Affiliations

  1. Laboratoire Charles Fabry de l'Institut d'Optique, Centre National de la Recherche Scientifique, Université Paris Sud Bât. 503, F-91403, Orsay Cedex, France

    CH. Sauvan, P. Lalanne & J.P. Hugonin

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  1. CH. Sauvan
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  2. P. Lalanne
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  3. J.P. Hugonin
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Correspondence to CH. Sauvan.

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Sauvan, C., Lalanne, P. & Hugonin, J. Truncation rules for modelling discontinuities with Galerkin method in electromagnetic theory. Optical and Quantum Electronics 36, 271–284 (2004). https://doi.org/10.1023/B:OQEL.0000015645.39040.0e

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  • DOI: https://doi.org/10.1023/B:OQEL.0000015645.39040.0e

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