It is shown that the Maxwell's equations for surface electromagnetic TM waves, propagating along the plane boundary between two nonlinear dielectrics with arbitrary diagonal tensor of dielectric permittivity, depending on | (E) over right arrow |(2), can be integrated in quadratures. For the TM plane wave the magnetic intensity has only the transverse component, but the electric intensity has both transverse and longitudinal ones. This fact permits one to find the first integral of the Maxwell's equations and eliminate the magnetic intensity. The resulting equations for the electric intensity can be simplified and integrated, if one uses the transverse permittivity as the independent variable. Finally, we consider the Kerr dielectrics, with the permittivity being a quadratic function of the electric intensity. In this case the quadratures can be reduced to the elliptical integrals.

Authors

Publisher

INST MECHANICS CONTINUA & MATHEMATICAL SCIENCES

Language

English

Pages

429-437

Status

Published

Year

2019

Organizations

^{1}RUDN Univ, Inst Phys Res & Technol, Moscow, Russia^{2}Joint Inst Nucl Res, Dubna, Moscow Region, Russia

Keywords

Maxwell's Equations; Surface Waves; Dielectric Permittivity; Kerr; Dielectrics

Date of creation

24.12.2019

Date of change

24.12.2019

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JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES.
INST MECHANICS CONTINUA & MATHEMATICAL SCIENCES.
2019.
P. 420-428

JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES.
INST MECHANICS CONTINUA & MATHEMATICAL SCIENCES.
2019.
P. 438-446