Born-Pad\'e approach to electromagnetic scattering in complex one-dimensional inhomogeneous slabs

TL;DR

This paper introduces a generalized Born-Padé method for accurately analyzing electromagnetic scattering in complex one-dimensional inhomogeneous slabs, accommodating oblique incidence and both Hermitian and non-Hermitian structures.

Contribution

The paper develops a versatile analytical approach combining perturbation theory and Padé approximants for precise scattering analysis in complex inhomogeneous slabs.

Findings

High-accuracy analytical expressions for transmission and reflection amplitudes

Applicable to Hermitian and non-Hermitian structures

Handles oblique incidence effectively

Abstract

Perturbation theory is applied to one-dimensional scattering systems consisting of a general class of inhomogeneous and isotropic slabs having size $L$ described by the relative permittivity $\varepsilon(z) = 1 + \alpha \chi(z)$, where $\chi(z)$ is the electric susceptibility and $\alpha$ the perturbation parameter. The transmitted and reflected amplitudes are shown to be written as Born series in powers of $\alpha$ and Pad\'e approximants are used to obtain analytical results with a high and arbitrary degree of accuracy. The approach is very general and can handle oblique incidence. Examples are given for the transmission and reflection amplitudes of plane waves interacting with Hermitian and non-Hermitian structures with known and unknown exact solutions.