Nonlinear waves In nematic liquid crystals

Abstract

In the last few decades, nonlinear, nonlocal optical media have emerged as an ideal setting for experimentally observing and studying nonlinear optical phenomena such as modulation instability, random lasing, spatial solitons and shock waves. In particular, liquid crystals in the nematic mesophase (NLC) support self-confined optical spatial solitons, named in this context as nematicons, i.e. stable and robust self-confined beams which can propagate without diffraction within the self-induced channel waveguide. They have become the focus of several studies following their demonstration in planar nematic liquid crystal cells and hold special interest due to their potential use in the design of all-optical devices such as diodes, isolators and optical switches. From a theoretical perspective, nematicon propagation is described by a system of nonlinear dispersive-wave equations constituted by a nonlinear Schrödinger-like equation for the optical beam and an elliptic Poisson equation for the response of the liquid crystal. This system of equations has no exact solutions, therefore most effort is devoted to improving numerical methods, although modulation theories can also give insight into the mechanisms behind the optical beam evolution.

In this thesis, we investigate self-induced waveguides which, by launching nematicons from the opposite ends of a sample cell, establish signal pipelines with distinguishable paths, resulting in a diode-like transmission. We specifically examine the generation and path of extraordinary-wave nematicons in planar cells of nematic liquid crystals (NLC) when launching identical beams from the opposite ends of samples with linearly modulated angle distributions of the optic axis, i.e. a varying molecular background orientation across the transverse and propagation coordinates.