Goos-Hanchen shift for higher order Hermite-Gaussian beams

TL;DR

This paper investigates the reflection properties of higher order Hermite-Gaussian beams, revealing that they experience a Goos-Hänchen shift near the critical angle without significant distortion, contrasting with Laguerre-Gaussian beams.

Contribution

It provides the first detailed analysis of the Goos-Hänchen shift for higher order Hermite-Gaussian beams near the critical angle, highlighting differences from Laguerre-Gaussian beams.

Findings

Hermite-Gaussian beams show no significant distortion upon reflection.

Goos-Hänchen shift occurs near the critical angle for all spots of the beam.

Shift is negligible away from the critical angle.

Abstract

We study the reflection of a Hermite-Gaussian beam at an interface between two dielectric media. We show that unlike Laguerre-Gaussian beams, Hermite-Gaussian beams undergo no significant distortion upon reflection. We report Goos-H\"anchen shift for all the spots of a higher order Hermite Gaussian beam near the critical angle. The shift is shown to be insignificant away from the critical angle. The calculations are carried out neglecting the longitudinal component along the direction of propagation for a spatially finite, s-polarized, full 3-d vector beam. We briefly discuss the difficulties associated with the paraxial approximation pertaining to a vector Gaussian beam.