Waveguiding in a Nematic Hybrid Slab

Abstract

We develop an analytical approach to study the propagation of optical fields through a nematic slab model with hybrid boundary conditions studied numerically by Lin et al. [I]. For a low intensity beam we first derive the eikonal equation and from it we then calculate the ray trajectories in the limit of geometrical optics. We show that there may exist caustics within the slab. Then we consider the WKB limit and calculate the field transverse magnetic modes, their number and their cutoff frequencies. We show that for both limits the agreement between the analytical and numerical results for the propagation constants is excellent, when caustics are not present; however, their presence introduces larger differences in the values of the calculated field amplitudes but the comparison is still quite good. We show that these discrepancies have their origin in the fact that the chosen parameter values in the exact numerical calculations, do not lie within the limits of validity of our WKB approximation. Thus, a more precise comparison between these approaches requires different sets of values of the relevant parameters. Finally, we discuss the scope and limitations of our method.

Total Internal Reflection in a Hybrid Nematic Cell Submitted to Weak Boundary Conditions

“…The usual method to solve Maxwell's equations has been carried out in detail for a hybrid cell similar to the one considered here [37], and it is found that there is a regime for the incidence angle where the ray trajectory presents a caustic, that is, a geometrical place where the beam bends and remains inside the cell until it returns back towards the incidence substrate (see Figure 1). This trajectory is given by [37]…”