Nonlinear propagation of coupled electromagnetic waves in a circular cylindrical waveguide

D. V. Valovik   ; E. Yu. Smol'kin

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1304-1320

Résumé

The problem of the propagation of coupled surface electromagnetic waves in a two-layer cylindrical circular waveguide filled with an inhomogeneous nonlinear medium is considered. A nonlinear coupled TE-TM wave is characterized by two (independent) frequencies $\omega_e$ and $\omega_m$ and two propagation constants $\widehat\gamma_e$ and $\widehat\gamma_m$. The physical problem reduces to a nonlinear two-parameter eigenvalue problem for a system of nonlinear ordinary differential equations. The existence of eigenvalues $(\widehat\gamma_e, \widehat\gamma_m)$ in proven and intervals of their localization are determined.

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