  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.
