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Full-Text Articles in Physics

Universal Off-Axis Light Transmission Properties Of The Bright State In Perfectly Compensated Liquid Crystal Devices, Yong-Kyu Jang, Philip J. Bos Oct 2013

Universal Off-Axis Light Transmission Properties Of The Bright State In Perfectly Compensated Liquid Crystal Devices, Yong-Kyu Jang, Philip J. Bos

Philip J. Bos

We studied the off-axis light transmission characteristics of the bright state of common liquid crystal device modes. The dark state of these device modes is optically compensated to have minimum light transmittance at all angles. Our research shows there is an unexpected universal shape of the off-axis light transmission value in its bright state, regardless of what liquid crystal mode is used. To understand this surprising fact, we consider simple dark and bright state models in terms of phase retardation and transmittance.


Monodomain Alignment Of The Smectic-A Liquid Crystalline Phase From The Isotropic Phase, Mitya Reznikov, Bentley Wall, Mark A. Handschy, Philip J. Bos Oct 2013

Monodomain Alignment Of The Smectic-A Liquid Crystalline Phase From The Isotropic Phase, Mitya Reznikov, Bentley Wall, Mark A. Handschy, Philip J. Bos

Philip J. Bos

The liquid crystal alignment method described here provides uniform orientation of otherwise difficult-to-align smectic-A liquid crystal materials lacking a nematic phase. The smectic-A phase is grown in the presence of a 10–20 K/mm temperature gradient from an air bubble located within a cell by a photolithographically defined channel in the cell substrates. We obtain uniform layer alignment in millimeter-wide smectic regions at growth rates below about 0.05 μm/s even though there is a tendency for spontaneous nucleation of focal-conic defects at higher growth rates once the width of the smectic-A region exceeds the critical value of about 20 μm.


Modeling And Design Of An Optimized Liquid-Crystal Optical Phased Array, Xinghua Wang, Bin Wang, Philip J. Bos, Paul F. Mcmanamon, John J. Pouch, Felix A. Miranda, James E. Anderson Oct 2013

Modeling And Design Of An Optimized Liquid-Crystal Optical Phased Array, Xinghua Wang, Bin Wang, Philip J. Bos, Paul F. Mcmanamon, John J. Pouch, Felix A. Miranda, James E. Anderson

Philip J. Bos

In this paper, the physics that determines the performance limits of a diffractive optical element based on a liquid-crystal(LC) optical phased array(OPA) is investigated by numerical modeling. The influence of the fringing electric fields, the LC material properties, and the voltage optimization process is discussed. General design issues related to the LCOPA configuration, the diffraction angle, and the diffraction efficiency are discussed. A design for a wide-angle LCOPA is proposed for high-efficiency laser beam steering. This work provides fundamental understanding for a light beam deflected by a diffractiveliquid-crystal device.


Twist-Energy-Driven Helfrich Modulations In Cholesteric Liquid Crystals Illustrated In The Transient-Planar To Planar Transition, P. Watson, James E. Anderson, Philip J. Bos Oct 2013

Twist-Energy-Driven Helfrich Modulations In Cholesteric Liquid Crystals Illustrated In The Transient-Planar To Planar Transition, P. Watson, James E. Anderson, Philip J. Bos

Philip J. Bos

The complete time evolution of a Helfrich-type instability that is driven by twist energy in a cholesteric liquid crystal is presented. The modulation is investigated using an initially uniform planar director configuration of a cholesteric liquid crystal ~with helical axes uniformly aligned along the cell normal! whose pitch is substantially longer than the equilibrium value.


Four-Domain Twisted Nematic Liquid Crystal Display Fabricated By Reverse Rubbed Polyimide Process, J. Chen, Philip J. Bos, D. L. Johnson, Douglas R. Bryant, J. Li, S. H. Jamal, J. R. Kelly Oct 2013

Four-Domain Twisted Nematic Liquid Crystal Display Fabricated By Reverse Rubbed Polyimide Process, J. Chen, Philip J. Bos, D. L. Johnson, Douglas R. Bryant, J. Li, S. H. Jamal, J. R. Kelly

Philip J. Bos

In Appl. Phys. Lett. 67, 1990 (1995), we proposed a particularly simple four‐domain (4‐D) twisted nematic(TN) liquid crystal display(LCD) device, which is composed of two left‐handed and two right‐handed TN subpixels. The two members of each pair of same handedness subpixels are rotated 180° with respect to each other, resulting in four domains that spatially average one another optically to provide a wide angle of viewing with no gray scale inversion. The optical performance of the 4‐D TN LCD was confirmed by studies of a test cell fabricated by a two‐step SiO x oblique evaporation technique. In this article, …


Molecular And Relative Segmental Order In The Nematic And Smectic C-Phases - A Nuclear Magnetic-Resonance Study, Philip J. Bos, A. Shetty, J. William Doane, Mary E. Neubert Oct 2013

Molecular And Relative Segmental Order In The Nematic And Smectic C-Phases - A Nuclear Magnetic-Resonance Study, Philip J. Bos, A. Shetty, J. William Doane, Mary E. Neubert

Philip J. Bos

No abstract provided.


Mechanism Of Electric-Field-Induced Segregation Of Additives In A Liquid-Crystal Host, Lu Lu, Vassili Sergan, Philip J. Bos Oct 2013

Mechanism Of Electric-Field-Induced Segregation Of Additives In A Liquid-Crystal Host, Lu Lu, Vassili Sergan, Philip J. Bos

Philip J. Bos

The mechanism for electric-field-induced segregation of additives, containing a polar group, in a host liquid crystal is proposed. It is shown that the polarity of an applied dc electric field, or the frequency of an ac electric field, strongly influences the segregation of reactive monomers containing an ester group. An explanation of this result is offered based on the association of dissolved ions with polar groups of the reactive monomers. This association is considered to cause these types of additives to drift to the cell surface in the presence of an external electric field. The described mechanism can be applied …


Fast Q-Tensor Method For Modeling The Dynamics Of Defects In A Liquid Crystal Director Field, Philip J. Bos, Gi-Dong Lee, Seon Hong Ahn, Kyeong Hyeon Kim Oct 2013

Fast Q-Tensor Method For Modeling The Dynamics Of Defects In A Liquid Crystal Director Field, Philip J. Bos, Gi-Dong Lee, Seon Hong Ahn, Kyeong Hyeon Kim

Philip J. Bos

A fast Q-tensor method, which can model the defect dynamics in a liquid crystal director field, is presented. Conceptually based on the Oseen-Frank approach, we have added temperature energy density terms in addition to the strain energy terms, and an improved normalization method for fast calculations. The method is more compact and allows a larger time step than previous methods. The method is used to model the defect dynamics occurring during the topological state change from a splay to bend director field configuration.


Modeling And Performance Limits Of A Large Aperture High-Resolution Wavefront Control System Based On A Liquid Crystal Spatial Light Modulator, Xinghua Wang, Bin Wang, Philip J. Bos Oct 2013

Modeling And Performance Limits Of A Large Aperture High-Resolution Wavefront Control System Based On A Liquid Crystal Spatial Light Modulator, Xinghua Wang, Bin Wang, Philip J. Bos

Philip J. Bos

The aberration introduced by the primary optical element of a lightweight large aperture telescope can be corrected with a diffractive optical element called the liquid crystal spatial light modulator. Such aberration is usually very large, which makes the design and modeling of such a system difficult. A method to analyze the system is introduced, and the performance limitation of the system is studied through extensive modeling. An experimental system is demonstrated to validate the analysis. The connection between the modeling data and the experimental data is given.


The Effect Of Salt On Ion Adsorption On A Siox Alignment Film And Reduced Conductivity Of A Liquid Crystal Host, Yi Huang, Achintya Bhowmik, Philip J. Bos Oct 2013

The Effect Of Salt On Ion Adsorption On A Siox Alignment Film And Reduced Conductivity Of A Liquid Crystal Host, Yi Huang, Achintya Bhowmik, Philip J. Bos

Philip J. Bos

It is shown that the addition of salt to liquid crystal cells, using a SiOx alignment layer, can actually reduce the ion concentration. This seeming contradiction may be explained by the ability of salt to complex with water and to aid the drying of the liquid crystal material. The results show a pathway to purifying liquid crystal devices to the extent needed for low-power low-refresh rate displays for e-book applications.


Spatial And Orientational Control Of Liquid Crystal Alignment Using A Surface Localized Polymer Layer, Lu Lu, Tatiana Sergan, Vassili Sergan, Philip J. Bos Oct 2013

Spatial And Orientational Control Of Liquid Crystal Alignment Using A Surface Localized Polymer Layer, Lu Lu, Tatiana Sergan, Vassili Sergan, Philip J. Bos

Philip J. Bos

We present an alignment method for the surface contacting liquid crystal (LC) director. This method allows complete control of the polar pretilt angle as a function of position in a liquid crystal device, and has the potential of controlling the azimuthal orientation of LC. Important considerations of this method are to form a thin layer of reactive monomers at the LC cell interior surface, and to control the deleterious effects of flow due to polymerization induced concentration gradients. To achieve these, the voltage and frequency of the applied electric field and the UV intensity during the polymerization process are significant.


Efficient, Polarization-Independent, Reflective Liquid Crystal Phase Grating, C. M. Titus, Philip J. Bos Oct 2013

Efficient, Polarization-Independent, Reflective Liquid Crystal Phase Grating, C. M. Titus, Philip J. Bos

Philip J. Bos

A reflective liquid crystal diffraction grating is proposed which makes use of the maximum available surface area. The structure consists of alternating stripes, each a twisted-nematic domain with surface orientation perpendicular to that of its neighbors. All domains have the same twist sense. This device yields, in principle, 100% diffraction efficiency independent of incident polarization. (C) 1997 American Institute of Physics.


Broadband Optical Phased-Array Beam Steering, Paul F. Mcmanamon, Jianru Shi, Philip J. Bos Oct 2013

Broadband Optical Phased-Array Beam Steering, Paul F. Mcmanamon, Jianru Shi, Philip J. Bos

Philip J. Bos

An array of phase retarders can be used as an optical phased array (OPA) to steer light [McManamon et al., Proc. IEEE 84 (2), 268 298 (1996)]. The introduction of resets enables steering to larger angles without requiring an optical path difference (OPD) greater than one wavelength. These resets, however, are correct only at the design wavelength. The beam steerer is therefore very dispersive. It has been shown theoretically that resets of an integer multiple of the wavelength will make the beam steerer less dispersive [McManamon and Watson, Proc. SPIE 4369, 140-148 (2001)]. We offer the first experimental proof that …


The Effect Of Surface Alignment On Analog Control Of Director Rotation In Polarization Stiffened Smc* Devices, Mitya Reznikov, Lena M. Lopatina, Michael J. O'Callaghan, Philip J. Bos Oct 2013

The Effect Of Surface Alignment On Analog Control Of Director Rotation In Polarization Stiffened Smc* Devices, Mitya Reznikov, Lena M. Lopatina, Michael J. O'Callaghan, Philip J. Bos

Philip J. Bos

The effect of surface alignment on the achievement of analog ("V"-shaped) electric field control of director rotation in SmC* liquid crystal devices is investigated experimentally and through numerical modeling. Ferroelectric SmC* liquid crystals are intrinsically analog and thresholdless, i.e. the director can be rotated freely around the tilt cone. Whether or not a SmC* liquid crystal cell exhibits thresholdless switching depends strongly on the influence of the cell's alignment layers, on the magnitude of the liquid crystal's spontaneous polarization, and on whether smectic layers adopt a bookshelf or chevron configuration. To study the effect of the surface alignment layers, we …


Nmr In Spinning Samples Of Biaxial Liquid-Crystals, Demetri J. Photinos, Philip J. Bos, Paul Ukleja, J. William Doane Oct 2013

Nmr In Spinning Samples Of Biaxial Liquid-Crystals, Demetri J. Photinos, Philip J. Bos, Paul Ukleja, J. William Doane

Philip J. Bos

Magnetic resonance measurements on a spinning sample of deuterated n-heptyloxyazoxybenzene (HOAB dsp) are presented. The resulting spectral patterns for the deuterated terminal methyl groups display the biaxial character of the smectic-C phase. Values for those biaxial order parameters which survive under free molecular rotation are directly determined from the shape of the spectral patterns. Parameters expressing biased rotation are also present and contribute significantly to the biaxiality.


Optimizing The Nematic Liquid Crystal Relaxation Speed By Magnetic Field, Bin Wang, Xinghua Wang, Philip J. Bos Oct 2013

Optimizing The Nematic Liquid Crystal Relaxation Speed By Magnetic Field, Bin Wang, Xinghua Wang, Philip J. Bos

Philip J. Bos

Nematic liquid crystalline materials have been widely used in electro-optical control of visible light. However, when IR light is considered, the thickness of the liquid crystal layer must be increased which causes the relaxation time of the material to be slower than required for many applications. In this paper we use a magnetic field to increase the speed of thick nematic devices. We show that above a particular magnetic field strength, thicker cells relax more quickly than thinner ones. Also, we find that there exists an optimal voltage range for devices of a particular thickness and with a particular applied …


Surface Localized Polymer Aligned Liquid Crystal Lens, Lu Lu, Vassili Sergan, Tony Van Heugten, Dwight Duston, Achintya Bhowmik, Philip Bos Mar 2013

Surface Localized Polymer Aligned Liquid Crystal Lens, Lu Lu, Vassili Sergan, Tony Van Heugten, Dwight Duston, Achintya Bhowmik, Philip Bos

Philip J. Bos

The surface localized polymer alignment (SLPA) method allows complete control of the polar pretilt angle as a function of position in liquid crystal devices. In this work, a liquid crystal (LC) cylindrical lens is fabricated by the SLPA method. The focal length of the LC lens is set by the polymerization conditions, and can be varied by a non-segmented electrode. The LC lens does not require a shaped substrate, or complicated electrode patterns, to achieve a desired parabolic phase profile. Therefore, both fabrication and driving process are relatively simple.


Physical Limitations And Fundamental Factors Affecting Performance Of Liquid Crystal Tunable Lenses With Concentric Electrode Rings, Liewi Li, Doug Bryant, Tony Van Heugten, Philip Bos Mar 2013

Physical Limitations And Fundamental Factors Affecting Performance Of Liquid Crystal Tunable Lenses With Concentric Electrode Rings, Liewi Li, Doug Bryant, Tony Van Heugten, Philip Bos

Philip J. Bos

A comprehensive analysis of fundamental factors and their effects on the performance of liquid crystal (LC)-based lenses is given. The analysis adopts numerical LC director and electric field simulation, as well as scalar diffraction theory for calculating the lens performance considering different variable factors. A high-efficiency LC lens with concentric electrode rings is fabricated for verifying and enriching the analysis. The measurement results are in close agreement with the analysis, and a summary of key factors is given with their quantitative contributions to the efficiency.


Near-Diffraction-Limited Tunable Liquid Crystal Lens With Simplified Design, Liwei Li, Doug Bryant, Tony Van Heugten, Dwight Duston, Philip Bos Mar 2013

Near-Diffraction-Limited Tunable Liquid Crystal Lens With Simplified Design, Liwei Li, Doug Bryant, Tony Van Heugten, Dwight Duston, Philip Bos

Philip J. Bos

A high-efficiency tunable refractive lens based on liquid crystals with concentric electrode rings and a simple unique design of a resistor network is reported, and used to assess the performance of an optimized electrically tunable lens. It has a large number of phase control points to be able to accurately control the phase profile and produce high efficiency. The lens design uses resistors between neighboring electrodes to minimize external connections. The lens optical path difference is measured as a near perfect parabolic shape and the Strehl ratio of about 80% is obtained (comparing to a high-quality glass lens). Image evaluations …


Near-Diffraction-Limited And Low-Haze Electro-Optical Tunable Liquid Crystal Lens With Floating Electrodes, Liwei Li, Doug Bryant, Tony Van Heugten, Philip J. Bos Dec 2012

Near-Diffraction-Limited And Low-Haze Electro-Optical Tunable Liquid Crystal Lens With Floating Electrodes, Liwei Li, Doug Bryant, Tony Van Heugten, Philip J. Bos

Philip J. Bos

A near-diffraction-limited, low-haze and tunable liquid crystal (LC) lens is presented. Building on an understanding of the key factors that have limited the performance of lenses based on liquid crystals, we show a simple design whose optical quality is similar to a high quality glass lens. It uses 'floating' electrodes to provide a smooth, controllable applied potential profile across the aperture to manage the phase profile.


Dynamics Of A Liquid-Crystal Variable Optical Prism Based On Pancharatnam Phase, Lei Shi, Paul F. Mcmanamon, Douglas Bryant, Ke Zhang, Philip J. Bos Feb 2010

Dynamics Of A Liquid-Crystal Variable Optical Prism Based On Pancharatnam Phase, Lei Shi, Paul F. Mcmanamon, Douglas Bryant, Ke Zhang, Philip J. Bos

Philip J. Bos

We consider the dynamics of a variable optical prism based on Pancharatnam phase. The device basics, using liquid crystals (LCs) as the electro-optical material, have been previously proposed. In this paper, we study the dynamics of discrete changes in the phase profile, and also continuous changes in the phase profile through acquired data and numerical modeling. We show that a design based on LCs whose dielectric anisotropy can change sign (as a function of frequency) allows continuous tuning with reasonable response times.


Design Considerations For High Efficiency Liquid Crystal Decentered Microlens Arrays For Steering Light, Lei Shi, Jianru Shi, Paul F. Mcmanamon, Philip J. Bos Jan 2010

Design Considerations For High Efficiency Liquid Crystal Decentered Microlens Arrays For Steering Light, Lei Shi, Jianru Shi, Paul F. Mcmanamon, Philip J. Bos

Philip J. Bos

We have investigated the causes of low efficiency for optical beam steering devices based on liquid crystal decentered microlens arrays (DLAs). We show that the efficiency is effected by the relative phase of light exiting the individual lenses, the imperfect focusing of small lenses due to diffraction, the aberrations related to off-axis light going through a lens, and the diffraction spreading of light beams going through the DLA structure. A high steering efficiency of over 94.4% is demonstrated by modeling the transmitted light through the DLA with scalar diffraction theory. We also propose modified phase profiles for the lenses that …


Switchable Polarization-Independent Liquid-Crystal Fabry-Perot Filter, Enkh-Amgalan Dorjgotov, Achintya K. Bhowmik, Philip J. Bos Dec 2008

Switchable Polarization-Independent Liquid-Crystal Fabry-Perot Filter, Enkh-Amgalan Dorjgotov, Achintya K. Bhowmik, Philip J. Bos

Philip J. Bos

A new approach to a polarization-independent twisted liquid-crystal (LC) structure, where phase difference between orthogonal eigenmodes is tuned to be an integer multiple of 2 pi, is demonstrated with a numerical model. For select wavelengths, polarization-independent operation can be achieved by tuning the twist rate and thickness of the LC cavity Applications can be found in polarization-independent switches and field sequential wavelength selection devices.


Alignment Memory Of A Nematic Liquid Crystal And Thermal Isotropization Of The Surface Adsorbed Layer, A. B. Nych, D. Yu. Reznikov, O. P. Boiko, V. G. Nazarenko, V. M. Pergamenshchik, Philip Bos Dec 2007

Alignment Memory Of A Nematic Liquid Crystal And Thermal Isotropization Of The Surface Adsorbed Layer, A. B. Nych, D. Yu. Reznikov, O. P. Boiko, V. G. Nazarenko, V. M. Pergamenshchik, Philip Bos

Philip J. Bos

We use a digital image analysis of the schlieren textures to study the effect of memory of the surface anisotropy in a nematic-liquid-crystal cell and establish its relation to the surface adsorbed molecular layer. The anisotropy is induced on an isotropic glass surface by a flow of the nematic liquid. The proposed technique allows us to quantify the alignment and its changes under the effect of temperature. The temperature at which the memory of the alignment texture is lost is interpreted as the temperature of the full isotropization of the initial anisotropic surface layer adsorbed during the flow: the molecules …


Selective Light-Induced Desorption: The Mechanism Of Photoalignment Of Liquid Crystals At Adsorbing Solid Surfaces, V. G. Nazarenko, O. P. Boiko, A. B. Nych, Yu. A. Nastishin, V. M. Pergamenshchik, Philip J. Bos Jul 2006

Selective Light-Induced Desorption: The Mechanism Of Photoalignment Of Liquid Crystals At Adsorbing Solid Surfaces, V. G. Nazarenko, O. P. Boiko, A. B. Nych, Yu. A. Nastishin, V. M. Pergamenshchik, Philip J. Bos

Philip J. Bos

We demonstrate experimentally that bare solid surfaces with adsorbed organic molecules can orient liquid crystals after UV light irradiation. The detailed structure and behavior of the surface-adsorbed molecules are not important to the effect: just their UV light absorption should depend on their orientation. The only requirement to the solid substrates is their transparency to the UV light. The universal reason for the photoinduced anisotropy in such systems is that photons clean from the surface those molecules that absorb them most intensively. This is a kind of light rubbing resulting in the anisotropic ablation of the adsorbed material.


Stressed Liquid-Crystal Optical Phased Array For Fast Tip-Tilt Wavefront Correction, Bin Wang, Guoqiang Zhang, Anatoliy Glushchenko, John L. West, Philip Bos, Paul F. Mcmanamon Dec 2005

Stressed Liquid-Crystal Optical Phased Array For Fast Tip-Tilt Wavefront Correction, Bin Wang, Guoqiang Zhang, Anatoliy Glushchenko, John L. West, Philip Bos, Paul F. Mcmanamon

Philip J. Bos

A liquid-crystal optical phased-array technology that uses stressed liquid crystals provides a new type of tip-tilt wavefront corrector. It demonstrates a very fast time response (10 kHz) and high beam-steering efficiency (similar to 91%). The new technology presented here will allow for a nonmechanical, high-speed correction with simple device construction.


High-Efficiency, Liquid-Crystal-Based, Controllable Diffraction Grating, Yanli Zhang, Bin Wang, Philip J. Bos, Jennifer Colegrove, David B. Chung Oct 2005

High-Efficiency, Liquid-Crystal-Based, Controllable Diffraction Grating, Yanli Zhang, Bin Wang, Philip J. Bos, Jennifer Colegrove, David B. Chung

Philip J. Bos

We propose a new reflective liquid-crystal diffraction grating design attained by combining the use of a polymer wall to reduce the detrimental effect of the fringing electric field in a high-resolution grating and a quarterwave plate to make the device polarization independent. This design could offer significant performance advantages in a projection display system. Results of calculations are compared with experimental data. (c) 2005 Optical Society of America.


Finite-Difference Time-Domain Simulation Of A Liquid-Crystal Optical Phased Array, Xinghua Wang, Bin Wang, Philip Bos, James E. Anderson, John J. Pouch, Felix A. Miranda Jan 2005

Finite-Difference Time-Domain Simulation Of A Liquid-Crystal Optical Phased Array, Xinghua Wang, Bin Wang, Philip Bos, James E. Anderson, John J. Pouch, Felix A. Miranda

Philip J. Bos

Accurate modeling of a high-resolution, liquid-crystal-based, optical phased array (OPA) is demonstrated. The modeling method is extendable to cases where the array element size is close to the wavelength of light. This is accomplished through calculating an equilibrium liquid-crystal (LC) director field that takes into account the fringing electric fields in LC OPAs with small array elements and by calculating the light transmission with a finite-difference time-domain method that has been extended for use in birefringent materials. The diffraction efficiency for a test device is calculated and compared with the simulation.


Finite-Difference Time-Domain Calculations Of A Liquid-Crystal-Based Switchable Bragg Grating, Bin Wang, Xinghua Wang, Philip Bos Jun 2004

Finite-Difference Time-Domain Calculations Of A Liquid-Crystal-Based Switchable Bragg Grating, Bin Wang, Xinghua Wang, Philip Bos

Philip J. Bos

A polymer-wall-confined transmissive switchable liquid crystal grating is proposed and investigated by two-dimensional finite-difference time-domain optical calculation and liquid-crystal-director calculation, to our knowledge for the first time. The results show how to obtain optimized conditions for high diffraction efficiency by adjusting the liquid crystal parameters, grating geometric structure, and applied voltages. The light propagation direction and efficiency can be accurately calculated and visualized concurrently.


Light Propagation In Variable-Refractive-Index Materials With Liquid-Crystal-Infiltrated Microcavities, Bin Wang, Philip Bos, Charles D. Hoke Oct 2003

Light Propagation In Variable-Refractive-Index Materials With Liquid-Crystal-Infiltrated Microcavities, Bin Wang, Philip Bos, Charles D. Hoke

Philip J. Bos

A liquid-crystal-infiltrated microcavity structure is proposed as a variable-refractive-index material. It has the advantages over previously considered nanostructured materials of having a larger phase-angle change and lower driving voltage. Two-dimensional liquid-crystal director and finite-difference time-domain optical simulations are used to select liquid crystal material parameters and optimize the dimension of the microcavity structured material.