Goos-H\"anchen shifts in frustrated total internal reflection studied with wave packet propagation

TL;DR

This study investigates the Goos-H"anchen shifts in frustrated total internal reflection using wave packet propagation, revealing how second-order effects and beam width influence the shift at various angles.

Contribution

It provides a detailed analysis of GH shifts in FTIR considering second-order corrections and beam width effects, enhancing understanding of tunneling delay times.

Findings

GH shift saturates asymptotically at first order

Second-order correction makes GH shift depend on beam width

GH shift behavior varies with incidence angle and beam width

Abstract

We have investigated that the Goos-H\"anchen (GH) shifts in frustrated total internal reflection (FTIR) studied with wave packet propagation. In the first-order approximation of the transmission coefficient, the GH shift is exactly the expression given by stationary phase method, thus saturates an asymptotic constant in two different ways depending on the angle of incidence. Taking account into the second-order approximation, the GH shift always depends on the width of the air gap due to the modification of the beam width. It is further shown that the GH shift with second-order correction increases with decreasing the beam width at the small incidence angles, while for the large incidence angles it reveals a strong decrease with decreasing the beam width. These phenomena offers the better understanding of the tunneling delay time in FTIR.