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

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.