Study of optical properties of DM–DM planar interface by incorporating non-linearity and NID space

Abstract

Study of the optical characteristics of materials, objects and geometries has wider role and applications in science and engineering. Reflection and transmission coefficients are used to study the optical properties of planar geometries. Primary aim of the presented work is to study the reflection and transmission of second harmonic generation in non-integer dimensional environment. Nonlinear medium in our considered geometry is of second harmonic generation type hence we only studied the second order reflection and transmission characteristics. Solution of the nonlinear wave equation is obtained by using slowly varying amplitude approximation and method of separation of variables in NID space is used to study how the presence of NID medium alter the electromagnetic waves. As a special case of the original geometry we also studied the changes in the behavior of the coefficients when an epsilon negative and a mu negative NID mediums are used as a reflected half space. In all the cases impact of the non-linearity and the noninteger dimensions on the unknown coefficients are studied separately. It is studied that higher amplitude of the reflection coefficient can be achieved by using a dielectric magnetic NID medium compared to epsilon negative NID medium. On the other hand it is also noted that for epsilon near zero medium, amplitude of the reflection coefficient reaches zero for specific values of the nonlinear permeability and incident angle whereas, for mu negative NID medium amplitude of both the coefficients increases (decreases) by increasing the values of ϵic(ϵrc). It is also noted that dimensions of the NID mediums can be used as a controlling factor for the amplitude of the coefficients by keeping the same shape. For the verification of the analytical results nonlinear power law is used.