Effective dielectric tensor of deformed-helix ferroelectric liquid crystals with subwavelength pitch and large tilt angle

TL;DR

This paper derives accurate analytical formulas for the effective dielectric tensor of short pitch deformed helix ferroelectric liquid crystals, outperforming traditional approximations especially at large tilt angles, with implications for optical device applications.

Contribution

It introduces new analytical formulas for the dielectric tensor that are accurate beyond the space average approximation, including for large tilt angles, and compares two approaches for calculating effective properties.

Findings

Formulas accurately predict optical properties in practical situations.

Both dielectric tensor expansion and transfer matrix methods are effective with two-photon scattering.

The methods outperform the space average approximation, especially at large tilt angles.

Abstract

Short pitch deformed helix ferroelectric liquid crystals have numerous applications as active materials in displays, optical telemetry and biomedical devices. In this paper, we derive convenient analytical formulas to calculate the effective dielectric tensor of these materials beyond the space average approximation. By comparison with exact numerical calculations, we show that our formulas are remarkably accurate in predicting optical properties in virtually all practical situations, including the important case of large tilt angles, where the space average approximation breaks down. We also present a comparison between the two complementary approaches of expanding the mesoscopic dielectric tensor vs. the mesoscopic transfer matrix, by deriving an expression for the effective transfer matrix as an infinite expansion and explicitly calculating the corresponding effective dielectric tensor for the first time. Our results demonstrate that both methods give accurate predictions when two-photon scattering terms are taken into account.