The effect of the width of the incident pulse to the dielectric transition layer in the scattering of an electromagnetic pulse -- a quantum lattice algorithm simulation

TL;DR

This paper investigates how the thickness of the dielectric boundary layer affects electromagnetic pulse scattering, revealing deviations from classical Fresnel predictions and observing a persistent dip in transmitted pulses, using a quantum lattice algorithm simulation.

Contribution

It introduces a quantum lattice algorithm simulation to study the impact of dielectric boundary layer thickness on electromagnetic pulse scattering, extending analysis beyond classical Fresnel and WKB approximations.

Findings

Thin boundary layer mimics Fresnel conditions with augmented transmission.

Thicker boundary layers cause deviations from Fresnel and approach WKB propagation.

A persistent small dip in the transmitted pulse is observed.

Abstract

The effect of the thickness of the dielectric boundary layer that connects a material of refractive index $n_1$ to another of index $n_2$ is considered for the propagation of an electromagnetic pulse. For very thin boundary layer the scattering properties of the pulse mimics that found from the Fresnel jump conditions for a plane wave - except that the transmission to incident amplitudes are augmented by a factor of $\sqrt{n_2/n_1}$. As the boundary layer becomes thicker one finds deviations away from the Fresnel conditions and eventually one approaches WKB propagation. However there is found a small but unusual dip in part of the transmitted pulse that persists in time. The quantum lattice algorithm (QLA) used recovers the Maxwell equations to second order in a small parameter -- but QLA still recovers Maxwell equations when this parameter is unity. The expansion parameter is the speed of the pulse in medium $n_1$.