Thermal effects on nonlinear optical beam propagation in nematic liquid crystals
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Date
27/11/2021Author
Khan, Cassandra Chaya
Metadata
Abstract
This thesis examines in detail the study of nonlinear wave phenomena arising
in different contexts in applied nonlinear optics. In particular, it explores the
intricate nonlinear interplay between light and matter using tools from nonlinear
PDEs—from the modulation solution for the nonlinear Schr¨odinger equation to
classical approaches, such as Newton’s method, to numerical techniques from
nonlinear dynamical systems.
A framework is presented to study the dynamics of nonlinear optical beams
propagating in nematic liquid crystals (NLCs), a substance similar in its fluidity
to ordinary (isotropic) liquids, but whose refractive index and other properties
change in the presence of optical beams. NLCs are unique in that they exist
in a state between a crystal and an isotropic liquid. This intermediate state
gives rise to molecular long-range orientational order, which in turn can be
controlled by weak electromagnetic fields. Thermo-optical solitary waves
form as a result of the NLC’s response to the light beam, consisting of a
combination of focussing electric field-induced molecular rotation and defocussing
temperature effects due to optical absorption by the medium. This nonlinear
medium can support an optical solitary wave, termed a ’nematicon’, which can
travel through this self-focusing medium as a diffractionless beam, able to both
direct itself and guide other optical signals, rendering these waves useful
for all optically reconfigurable integrated circuits and light-controlled switching.
Modulation theory and an averaged Lagrangian analysis is used to model light
beam evolution in NLCs. With modulation theory, a (2 + 1)-dimensional model
is developed, based on approximations of the full nonlinear system, to describe
the interplay between light beams and the thermo-optical and reorientational
responses they induce in NLCs. This model describes the trajectories that
spatial optical solitary waves (nematicons) follow in the anisotropic (strongly
directional) NLC environment. Introducing several approximations based on the
nonlocal physics of the material enables the prediction of the effect of temperature
on nematicon trajectories and their angular steering, which establishes the
analytical structure of the energy exchange between the input beam and the
medium through one-photon absorption. The theoretical results are compared
with existing experimental data, showing excellent agreement. In an NLC,
nematicons exhibit competing nonlinear responses: extraordinarily polarized light
waves are self-focusing due to reorientation and self-defocusing due to thermal
effects. ithhen the beam power is strong enough, these opposing effects can
lead to the formation of two-humped and ring-shaped solitary waves possessing
a cross-sectional volcano profile. The formation of two-humped nematicons in
(1 + 1) dimensions and volcano shaped nematicons in (2 + 1) dimensions are
analysed and numerically modelled by calculating numerical solutions of their
full governing equations and variational approximations. These full equations
governing nonlinear optical beam propagation in NLC consist of an NLS-type
equation for the light beam and elliptic equations for both the reorientational and
thermal responses, in contrast to the simplified molecular and thermal responses
of previous work. The simplified variational solutions for these localized ring
waves are in remarkably good agreement with numerical results.