Impact of non-linearity and non-integer dimension on the reflection and transmission coefficients

Abstract

Presented manuscript is devoted to the study of reflection and transmission coefficients of a second-order nonlinear dielectric and linear dielectric NID interface excited by a P-polarized electromagnetic wave. Impact of the non-linearity of the NL medium and non-integer dimension of the NID medium are studied separately. The method of separation of variables is used to model the propagation of waves in NID medium and the solution of the non-linear wave equation is obtained by following the procedure of slowly varying amplitude approximation. We extend our analysis for special cases of the original geometry, i.e. epsilon negative non-linear, mu negative non-linear and epsilon negative NID mediums are considered in this regard. We also calculated the specific values of the permittivities, permeability and dimension of the NID medium for which maximum amplitude of the reflection and transmission coefficients can be achieved.