Reflectivity of cholesteric liquid crystals with spatially varying pitch

TL;DR

This paper numerically investigates how spatial variation in the pitch of cholesteric liquid crystals affects their reflectivity, revealing complex reflection mechanisms beyond simple local Bragg conditions.

Contribution

It introduces a numerical approach to analyze reflectivity in cholesteric liquid crystals with linearly varying pitch, challenging traditional local Bragg assumptions.

Findings

Reflection occurs in evanescent regions, not just where Bragg condition is met.

Variation rate of structure influences wave decay and reflection efficiency.

Analytical estimates for transmission coefficients are provided.

Abstract

Solids with spatially varying photonic structure offer gaps to light of a wider range of frequencies than do simple photonic systems. We solve numerically the field distribution in a solid cholesteric with a linearly varying inverse pitch (helical wavevector) using equations we derive for the general case. The simple idea that the position where the Bragg condition is locally satisfied is where reflection takes place is only true in part. Here, reflection is due to a region where the waves are forced to become evanescent, and the rate of variation of structure determines over which distance the waves decay and therefore how complete reflection is. The approximate local Bragg-de Vries schemes are shown to break down in detail at the edges of the gap, and an analytical estimate is given for the transmission coefficient.