Leaky waves in a nonlinear metamaterial rod

Abstract

We consider propagation of leaky TE waves in a rod filled with nonlinear metamaterial medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.

Keywords:

• Leaky TE waves
• metamaterial rod
• nonlinear permittivity
• nonlinear eigenvalue problem
• numerical method

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The reported study was funded by RFBR, project number 19-31-51004.

Notes on contributors

Eugene Smolkin

Eugene Smolkin is a Researcher working at the Departmentof Mathematics and Supercomputing, Penza State University, Penza, Russia. He received a PhD degree in applied mathematics from the Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS), Russia, in 2015. He is the co-author of more than fifty papers. His research interests are in the analysis of wave propagation in dielectric waveguides.

Yury Smirnov

Smirnov Yury is a Doctor of Physical and Mathematical Sciences, Professor. He is a Head of the Department of  “Mathematics and Supercomputer Simulation”. The research interests are following: partial differential equations, mathematical physics, integral and pseudo-differential equations, spectral problems, numerical methods, electrodynamics, hydrodynamics, aerodynamics, acoustics, theory of elasticity.

Maxim Snegur

Maxim Snegur is a PhD student of the Penza State University. He is the co-author of twelve conference papers. His research interests are in the analysis of wave propagation in metaldielectric waveguides.