Parameter Estimation of an Inhomogeneous Medium by Scattered Electromagnetic Fields Using Nonlinear Optics and Wavelets

Abstract

The aim of this work is to study the parameter estimation of a nonlinear medium in terms of scattered electromagnetic fields. The surface parameters are defined in terms of linear and nonlinear components of susceptibility and permeability. A set of Maxwell's equations are derived for an inhomogeneous medium using Green's function and the scattered Electromagnetic fields solving integrodifferential equations. Mathematical formulas are simplified using wavelet based method. Susceptibility and permeability is assumed as a function of wavelet basis. For parameter estimation, least square method and inner product methods are used with wavelets as a basis function, which gives solutions for nonlinear integrodifferential equation. Both time and spatial domain analysis is done using wavelets, and parameter coefficients are obtained. It is found that in both the parameter estimation methods, least square estimation gives better results. At the end of the paper statistical analysis of the scattered signals is included by calculating the mean and covariance of the signals.

Simulation of a plasmonic sensor using kinetic theory of plasma with the Vlasov equation in MATLAB

“…In discrete analysis, if a basis function is φ (x) = K h k φ (2x − k), where n = 1, then φ is a scale function of MRA. Here, the 2 n factor gives the graph of contraction and expansion [2,5] Thus, {{ ψ n,k } n,k∈Z is a wavelet system, and then every function f 1 is written as [53] f = (a.24)…”