Ray tracing and reflectivity measurements in nematic hybrid cells

Abstract

We propose an experimental procedure to show that an optical beam may propagate in a planar-homeotropic hybrid nematic crystal cell for incidence angles i larger than the critical one. Its effect on the reflectance coefficient R as a function of i is accounted for by using total internal reflection techniques. We model the propagation of a linearly polarized Gaussian beam of finite diameter through the cell and the reflectance curves R vs. i are calculated theoretically in the total internal reflection regime by using an analytical description. The experimental procedure, cell assembling and methodology are designed so that there is reasonable consistency with the model assumptions. In the optical limit approximation this model allows us to calculate analytically the phase shift, the trajectory and the reflectivity curves of a beam traveling with an extraordinary polarization (P-polarization) inside the cell. Since only some parts of the reflected beams will interfere, Berreman’s method is not suitable for the physical situation considered. The possibility of leakage through the tunneling effect across the cell is also considered and estimated quantitatively. The comparison between the theoretical results and the experimental data shows good agreement between our experimental results and the theoretical curves R vs. i. We compare our results with other measurements reported in the literature and find that the behavior of the reflectance curve is highly affected by the cell thickness-beam waist ratio. The values of this parameter can produce different behaviors of the reflectivity measurements. The analysis of the model predictions and experimental results suggest a possible interpretation of the physical origin of the reflectivity curves and give a qualitative insight into the phenomena behind the total internal reflection regime. Finally, we emphasize the limitations and advantages of the model and of the experimental results presented.