Goos-Hänchen effect on a one transverse dimensional Hermite-Gaussian Beam

Abstract

We study the lateral displacement (Goos-H\"{a}nchen effect) of a Hermite-Gaussian beam incident on a dielectric interface of lower index of refraction than the incident media. Unlike previous results on the same subject, the present result can be applied to an infinite family of higher order solutions (or modes) of the Huygens-Fresnel integral. The final theoretical expression is valid for values that are close to the critical angle $\theta_{c}$. Discussion is made for the behavior of the lateral displacement for different modes of the Hermite-Gaussian beam.