Propagation of TM waves in a layer with arbitrary nonlinearity Authors
First Online: 18 September 2011 Received: 02 September 2010 Accepted: 01 November 2010 DOI:
10.1134/S096554251109017X Cite this article as: Valovik, D.V. Comput. Math. and Math. Phys. (2011) 51: 1622. doi:10.1134/S096554251109017X Abstract
A boundary value problem for Maxwell’s equations describing propagation of TM waves in a nonlinear dielectric layer with arbitrary nonlinearity is considered. The layer is located between two linear semi-infinite media. The problem is reduced to a nonlinear boundary eigenvalue problem for a system of second-order nonlinear ordinary differential equations. A dispersion equation for the eigenvalues of the problem (propagation constants) is derived. For a given nonlinearity function, the dispersion equation can be studied both analytically and numerically. A sufficient condition for the existence of at least one eigenvalue is formulated.
Keywords nonlinear boundary eigenvalue problem for Maxwell’s equations nonlinear layer dispersion equation numerical-analytical solution method
Original Russian Text © D.V. Valovik, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 9, pp. 1729–1739.
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