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: March 31, 2013

Revised: September 30, 2013

Published: March 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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References

[1]	I. Abdulhalim, Analytic propagation matrix method for linear optics of arbitrary biaxial layered media, J. Opt. A: Pure Appl. opt., 1 (1999), 646-653.doi: 10.1088/1464-4258/1/5/311.
[2]	D. W. Berreman, Optics in stratified and anisotropic media: 4x4 matrix formulation, J. Opt. Soc. Am., 62 (1972) , 502-510.
[3]	M. Born and E. Wolf, Principles of Optics, Cambridge University Press, Cambridge, 1999.doi: 10.1017/CBO9781139644181.
[4]	P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, Oxford University Press, Oxford, 1993.
[5]	J. A. Fleck, Jr and M. D. Feit, Beam propagation in uniaxial anisotropic media, J. Opt. Soc. Am, 73 (1983), 920-926.
[6]	D. K. Hwang and A. D. Rey, Computational modeling of the propagation of light through liquid crystals containing twist disclinations based on the finite-difference time-domain (FDTD) method, Appl. Opt., 44 (2005), 4513-4522.
[7]	D. K. Hwang and A. D. Rey, Computational modeling of light propagation in textured liquid crystals based on the finite-difference time-domain (FDTD) method, Liquid Crystals, 32 (2005), 483-497.
[8]	D. K. Hwang, W. H. Han and A. D. Rey, Computational rheooptics of liquid crystal polymers, J. Non-Newtonian Fluid Mech., 143 (2007), 10-21.doi: 10.1016/j.jnnfm.2006.11.006.
[9]	E. E. Kriezis and S. J. Elston, Finite-difference time domain method for light wave propagation within liquid crystal devices, Optics Communications, 165 (1999), 99-105.doi: 10.1016/S0030-4018(99)00219-9.
[10]	E. E. Kriezis and S. J. Elston, Light wave propagation in liquid crystal displays by the 2-D finite-difference time-domain method, Optics Communications, 177 (2000), 69-77.doi: 10.1016/S0030-4018(00)00595-2.
[11]	P. Yeh, Optical Waves in Layered Media, Wiley, Hoboken, New Jersey, 2005.doi: 10.1063/1.2810419.
[12]	G. D. Ziogos and E. E. Kriezis, Modeling light propagation in liquid crystal devices with a 3-D full-vector finite-element beam propagation method, Opt Quant Electron, 40 (2008), 733-748.doi: 10.1007/s11082-008-9261-2.