Optimization of electromagnetic wave propagation through a liquid crystal layer

Eric P. Choate; Hong Zhou

doi:10.3934/dcdss.2015.8.303

Article Contents

2015, Volume 8, Issue 2: 303-312. Doi: 10.3934/dcdss.2015.8.303

This issue Previous Article A Landau--de Gennes theory of liquid crystal elastomers Next Article Conley's theorem for dispersive systems

Optimization of electromagnetic wave propagation through a liquid crystal layer

Eric P. Choate^1, and
Hong Zhou^2,

1.
Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943
2.
Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943-5216

Received: April 2013

Revised: October 2013

Published: April 2015

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Abstract

We study the propagation of electromagnetic plane waves through a liquid crystal layer paying particular attention to the problem of optimizing the transmitted intensity. The controllable anisotropy of a liquid crystal layer, either through anchoring conditions on supporting glass plates sandwiching the layer or by the imposition of an external electromagnetic field, allows us to tune the orientation of the layer to maximize or minimize the transmitted intensity of a given wavelength through the layer. For a homogeneous liquid crystal orientation field, we find analytical formulas for the orientation that maximizes the transmission and discuss the circumstances under which we can make the layer effectively transparent for a given wavelength and the possibility of multiple maximizing orientations. The minimizing orientation is unique for a given wavelength, and we can define its value implicitly.

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Mathematics Subject Classification: Primary: 74E15, 78A40; Secondary: 78M50.

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