Analytical method of optical wave behavior studying in nonlinear medium with periodically arranged conducting nanofilms

Abstract

The purpose of this work is to build the analytical model of the behavior of a harmonic wave in a nonlinear optical medium with periodically arranged nanofilms. Methods. The modernized method is presented of non-smooth transformation of the argument to eliminate the Dirac functions on the right side of the non-linear inhomogeneous differential equation describing linear polarized wave behavior within a non-linear optical medium with periodically arranged conducting nanofilms. Small parameter methods, in particular, the averaging method, is also used to find an approximate analytical solution. Results. The fully analytical model of the behavior of a linear polarized harmonic wave within a nonlinear optical medium with periodically arranged conducting nanofilms is constructed. Conclusion. For the case of propagation of a linearly polarized harmonic wave in a nonlinear optical medium with periodically arranged conducting nanofilms, the mathematical model based on the non-smooth argument transformation method is constructed. The model is fully analytical, all expressions are obtained directly from Maxwell’s equations by identical transformations. The limits of its applicability are determined by the limits of application of the wave theory of light. 

Keywords

• nonlinear optical medium
• periodic structure
• dirac function
• non-smooth argument transformation
• solution stability