Paper detail

Maximal breaking of symmetry at critical angle and closed form expression for angular deviations of the Snell law

A detailed analysis of the propagation of laser gaussian beams at critical angles shows in which conditions it is possible to maximize the breaking of symmetry in the angular distribution and for which values of the laser wavelength and beam waist is possible to find an analytic formula for angular deviations of the Snell law. For propagation throughout $N$ dielectric blocks and for a full breaking of symmetry, overcoming the well known problem of the infinity at critical angle, a closed expression for the Goos-Haenchen shift is obtained. The multiple peaks phenomenon clearly represents an additional evidence of the breaking of symmetry in the angular distribution of optical beams. Finally, laser wavelength and beam waist conditions to produce focal effects in the outgoing beam are also briefly discussed.