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TE Mode Mixing Dynamics in Curved Multimode Optical Waveguides

Published online by Cambridge University Press:  20 August 2015

Emmanuel Perrey-Debain*
Affiliation:
Laboratoire Roberval, Université de Technologie de Compiègne 60205 Compiègne BP 20529, France
I. David Abrahams*
Affiliation:
School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, England, U.K
*
*Corresponding author.Email:[email protected]
*Corresponding author.Email:[email protected]
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Abstract

Propagation of light through curved graded index optical waveguides supporting an arbitrary high number of modes is investigated. The discussion is restricted to optical wave fields which are well confined within the core region and losses through radiation are neglected. Using coupled mode theory formalism, two new forms for the propagation kernel for the transverse electric (TE) wave as it travels along a curved two-dimensional waveguide are presented. One form, involving the notion of “bend” modes, is shown to be attractive from a computational point of view as it allows an efficient numerical evaluation of the optical field for sharply bent waveguides.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Skorobogatiy, M., Anastassiou, C., Johnson, S. G., Weisberg, O., Engeness, T. D., Jacobs, S. A., Ahmad, R. U. and Fink, Y., Quantitative characterization of higher-order mode converters in weakly multimoded fibers, Opt. Exp., 11(22) (2003), 28382847.CrossRefGoogle ScholarPubMed
[2]Lu, Y. Y. and Ho, P. L., Beam propagation modeling of arbitrarily bent waveguides, IEEE Photon. Tech. Lett., 14(12) (2002), 16981700.Google Scholar
[3]Snyder, A. W. and Love, J. D., Optical Waveguide Theory, London, Chapman and Hall, 1983.Google Scholar
[4]Bornatici, M., Egorchenkov, R. A., Kravtsov, Y. A., Maj, O. and Poli, E., Exact beam tracing and complex geometrical optics solutions for the propagation of gaussian electromagnetic beams, Proc. 28th EPS Conference on Controlled Fusion and Plasma Physics, Vol. 25A, (2001).Google Scholar
[5]Skorobogatiy, M., Johnson, S. G., Jacobs, S. A. and Fink, Y., Geometric variations in high indexcontrast waveguides, coupled mode theory in curvilinear coordinates, Opt. Exp., 10(21) (2002), 12271243.Google ScholarPubMed
[6]Feynman, R. P. and Hibbs, A. R., Quantum Mechanics and Path Integrals, McGrawHill New York, 1965.Google Scholar
[7]Lopez, R. M. and Suslov, S. K., The Cauchy problem for a forced harmonic oscillator, arXiv:0707.1902v6 [mathph], preprint.Google Scholar
[8]Longhi, S., Janner, D., Marano, M. and Laporta, P., Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: dynamic-mode stabilization and radiation-loss suppression, Phys. Rev. E, 67 (2003), 036601.Google Scholar
[9]Marcuse, D., Theory of Dielectric Optical Waveguides, 2nd edn, New York, Academic Press, 1991.Google Scholar
[10]Lim, T. K., Garside, B. K. and Marton, J. P., Guided modes in fibres with parabolic-index core and homogeneous cladding, Opt. Quant. Electron., 11 (1979), 329344.CrossRefGoogle Scholar
[11]Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, Vol. 55 of Appl. Math. Ser. 10th edition National Bureau of Standards U.S. Governement Printing Office Washington, D.C., 1972.Google Scholar
[12]Basdevant, J.-L. and Dalibard, J., Quantum Mechanics, Springer-Verlag, Berlin Heidelberg, 2002.Google Scholar
[13]Moler, C. and Van Loan, C., Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev., 45(1) (2003), 146.Google Scholar
[14]Perrey-Debain, E. and Abrahams, I. D., A band factorization technique for transition matrix element asymptotics, Comput. Phys. Commun., 175 (2006), 315322.Google Scholar
[15]Sharma, A. and Meunier, J.-P., On the scalar modal analysis of optical waveguides using approximate methods, Opt. Commun., 281 (2008), 592599.Google Scholar