Energy minimizers in a periodic phase transition model of light-matter interaction in nematic liquid crystals

TL;DR

This paper analyzes global energy minimizers in a one-dimensional, periodic phase transition model for light-matter interaction in nematic liquid crystals, revealing complex kink structures influenced by forcing strength.

Contribution

It extends previous work by characterizing new complex minimizer configurations with multiple zeros under periodic forcing in a nematic liquid crystal model.

Findings

Existence of at most three-zero kinks depending on forcing strength.

Identification of two thresholds influencing minimizer structure.

Consistency of minimizer behavior with the original matter-light interaction model.

Abstract

In this paper we complete the study of global minimizers of a forced, non autonomous, one dimensional, phase transition model, initiated in [8]. Motivated by the recent findings in [9], revealing new configurations of topological structures in light, we consider a forcing term having two periods. We show that depending on the strength of the forcing, at most two thresholds that determine the structure of the minimizers (kinks) are attained. These kinks are now a combination of the previous types encountered in [8], and they may have at most three zeros. The existence of these complex types of phase transition follows from a periodic one dimensional model of matter-light interaction in nematic liquid crystal based on a thin sample limit of the Oseen-Frank energy. We show that the qualitative behaviour of global minimizers is consistent with the original model.