# American Institute of Mathematical Sciences

April  2015, 8(2): 303-312. doi: 10.3934/dcdss.2015.8.303

## Optimization of electromagnetic wave propagation through a liquid crystal layer

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

Received  April 2013 Revised  October 2013 Published  July 2014

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.
Citation: Eric P. Choate, Hong Zhou. Optimization of electromagnetic wave propagation through a liquid crystal layer. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 303-312. doi: 10.3934/dcdss.2015.8.303
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