Optical Bragg reflection from the TGBA phase

Abstract

We have studied theoretically the reflection band properties of the twist grain boundary A phase (TGBA). A 4 x 4 matrix approach for the electromagnetic wave propagation is used. At normal incidence, simple analytical expressions are found, while at oblique incidence numerical methods have to be used since no analytical solution is available. The chart of stability of the propagating waves and the reflection spectra are given and discussed. No evidence of the incommensurability properties of the TGBA phases can be found optically. However, the analysis of the output polarization within the Bragg reflection band, on thick enough samples, allows us to determine the physical parameters characterizing the TGBA phase. In particular conditions, we can get the rotation Delta Theta between two homogeneous slabs and the total optical phase phi of one slab. When Delta Theta and phi go to zero, the optical properties of the TGBA phase become identical to those of the cholesteric phase. The essential difference appears when Delta Theta and phi are increased; an infinite number of reflection bands forms each Bragg reflection order, due to the periodicity of the TGBA parameters.