Light–matter interaction in liquid crystal cells

Abstract

In this thesis we study the interactions between light and matter in photorefractive liquid crystal
cells. To model the liquid crystal alignment we develop a fast and accurate approximation of
the normally stiff equations which minimise the Landau-deGennes free energy of a nematic
liquid crystal. The resulting equations are suitable for all configurations in which defects are
not present, making them ideal for device simulation. Specifically, they offer an increase in
computational efficiency by a factor of 100 while maintaining an error of order (10?4) when
compared to the full stiff equations. As this approximation is based on aQ–tensor formalism, the
sign reversal symmetry of the liquid crystal is respected. We consider both the simplified case,
where the director is restricted to a plane, and the full three-dimensional case. An approximation
of the error is also given. We use the liquid crystal model to understand two different optical
effects. The first of these is optical coupling. This effect is observed in liquid crystals in both the
Bragg and Raman–Nath regimes. To account for this behaviour we develop an extension to the
coupled wave theory which is suitable for all regimes of coupling. The model assumes that the
refractive index grating, generated by the liquid crystal, has an arbitrary profile in one direction
and is periodic (but not necessarily sinusoidal) in the other. Higher order diffracted terms are
considered and appropriate mismatch terms dealt with. It is shown that this model is analytically
equivalent to both the Bragg and Raman–Nath regime coupling models under an appropriate set
of assumptions. This model is also verified through comparison to finite element simulations of
Maxwell’s equations. The second effect we model is the coupling of surface plasmon polaritons
at the interface between a metal layer and a photorefractive liquid crystal cell. We implement
existing numerical models to gain a thorough understanding of the system. These models are
qualitatively compared with experimental observations. Analytic approximations to describe
the coupling of surface plasmon polaritons at the surface of the liquid crystal cell are developed.
These expressions provide a great deal of insight into the coupling mechanisms and will be of
fundamental importance in optimising these systems.

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Identifiers

ORCID for Giampaolo D'Alessandro: orcid.org/0000-0001-9166-9356

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