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IMA Journal of Applied Mathematics Advance Access originally published online on September 26, 2007
IMA Journal of Applied Mathematics 2007 72(5):659-679; doi:10.1093/imamat/hxm033
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Existence and stability of TE modes in a stratified non-linear dielectric

C. A. Stuart{dagger}

Station 8, Institut d'Analyse et Calcul Scientifique-Faculté de Sciences de Base, EPFL, CH-1015 Lausanne, Switzerland

{dagger} Email: charles.stuart{at}epfl.ch

Received on September 1, 2006; Accepted on January 29, 2007

Starting from Maxwell's equations for a stratified optical medium with a non-linear refractive index, we derive the equations for monochromatic planar TE modes. It is then shown that TE modes in which the electromagnetic fields are travelling waves correspond to solutions of these reduced equations in the form of standing waves. The equations of the paraxial approximation are then formulated and the stability of the travelling waves is investigated in that context.

Keywords: non-linear waveguide; TE modes; travelling waves; orbital stability.


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