Investigation of phase matching conditions for helielectric structures by numerical simulation of SHG using Berreman’s 4×4 matrix method

Abstract

The numerical simulation of second harmonic generation (SHG) based on the Berreman 4×4 matrix method was performed for a polar helical liquid crystal phase, dubbed helielectric, where the spontaneous polarization rotates helically. We investigated the phase matching conditions for helielectric structures at equilibrium and under electric field. We show the simulation results are consistent with the experiments. The generalized theory enables simulating various SHG properties for arbitrary polar structures.