# The effect of the geometrical optical phase on the propagation of Hermite-Gaussian beams through transversal and parallel dielectric blocks

## TL;DR

This paper investigates how the second order geometrical optical phase affects Hermite-Gaussian beam propagation through dielectric blocks, revealing conditions for symmetry breaking and recovery, and discussing axial spreading delays.

## Contribution

It introduces an analysis of second order geometrical phase effects on Hermite-Gaussian beams, highlighting symmetry breaking and recovery in dielectric block configurations.

## Key findings

- Second order phase causes transverse symmetry breaking.
- Symmetry can be maximized or recovered depending on configuration.
- Axial spreading delay is also affected.

## Abstract

When an optical beam propagates through dielectric blocks, its optical phase is responsible for the path of the beam. In particular, the first order Taylor expansion of the geometrical part reproduces the path predicted by the Snell and reflection laws whereas the first order expansion of the Fresnel phase leads to the Goos-Haenchen shift. In this paper, we analyze the effects of the second order Taylor expansion of the geometrical phase on the shape of the optical beam and show how it affects the transversal symmetry of Hermite-Gaussian beams. From the analytical expression of the transmitted beam, it is possible to determine in which transversal and parallel dielectric blocks configuration the transversal symmetry breaking is maximized or when the symmetry is recovered. We also discuss the axial spreading delay.