Coupled electromagnetic TE-TE wave propagation in nonlinear layer with saturated nonlinearity

ABSTRACT

We present an analysis of propagation of coupled electromagnetic TE-TE waves in a nonlinear plane waveguide located between two half-spaces with constant permittivities in which the permittivity of the guiding layer is described by a saturated nonlinearity. The physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of nonlinear ordinary differential equations on a segment. Existence and uniqueness of solution to two-parameter eigenvalue problem is proved. Iteration method for solving given problem is presented. Convergence theorem of the iteration method is proved. Numerical results are presented.

KEYWORDS:

• Nonlinear two-parameter eigenvalue problem
• Maxwell's equations
• nonlinear guided wave
• dispersion equation
• iteration method

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

V. Yu. Martynova http://orcid.org/0000-0002-9098-8600

Yu. G. Smirnov  http://orcid.org/0000-0001-9040-628X

Additional information

Funding

This study is supported by the Ministry of Education and Science of the Russian Federation [project number 1.894.2017/4.6] and by the Russian Foundation for Basic Research [project number 18-31-00109].