American Institute of Mathematical Sciences

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

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, 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.
Keywords: Electromagnetic wave, anchoring conditions., liquid crystal layer.
Mathematics Subject Classification: Primary: 74E15, 78A40; Secondary: 78M5.
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
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.  doi: 10.1088/1464-4258/1/5/311.  Google Scholar

[2]

D. W. Berreman, Optics in stratified and anisotropic media: 4x4 matrix formulation,, J. Opt. Soc. Am., 62 (1972), 502.   Google Scholar

[3]

M. Born and E. Wolf, Principles of Optics,, Cambridge University Press, (1999).  doi: 10.1017/CBO9781139644181.  Google Scholar

[4]

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals,, Oxford University Press, (1993).   Google Scholar

[5]

J. A. Fleck, Jr and M. D. Feit, Beam propagation in uniaxial anisotropic media,, J. Opt. Soc. Am, 73 (1983), 920.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.  doi: 10.1016/j.jnnfm.2006.11.006.  Google Scholar

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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.  doi: 10.1016/S0030-4018(99)00219-9.  Google Scholar

[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.  doi: 10.1016/S0030-4018(00)00595-2.  Google Scholar

[11]

P. Yeh, Optical Waves in Layered Media,, Wiley, (2005).  doi: 10.1063/1.2810419.  Google Scholar

[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.  doi: 10.1007/s11082-008-9261-2.  Google Scholar

show all references

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.  doi: 10.1088/1464-4258/1/5/311.  Google Scholar

[2]

D. W. Berreman, Optics in stratified and anisotropic media: 4x4 matrix formulation,, J. Opt. Soc. Am., 62 (1972), 502.   Google Scholar

[3]

M. Born and E. Wolf, Principles of Optics,, Cambridge University Press, (1999).  doi: 10.1017/CBO9781139644181.  Google Scholar

[4]

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals,, Oxford University Press, (1993).   Google Scholar

[5]

J. A. Fleck, Jr and M. D. Feit, Beam propagation in uniaxial anisotropic media,, J. Opt. Soc. Am, 73 (1983), 920.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.  doi: 10.1016/j.jnnfm.2006.11.006.  Google Scholar

[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.  doi: 10.1016/S0030-4018(99)00219-9.  Google Scholar

[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.  doi: 10.1016/S0030-4018(00)00595-2.  Google Scholar

[11]

P. Yeh, Optical Waves in Layered Media,, Wiley, (2005).  doi: 10.1063/1.2810419.  Google Scholar

[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.  doi: 10.1007/s11082-008-9261-2.  Google Scholar

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