AFRL-ML-WP-TP-2007-551 LIQUID CRYSTAL BRAGG GRATINGS: DYNAMIC OPTICAL ELEMENTS FOR SPATIAL LIGHT MODULATORS (POSTPRINT) J.M. Wofford, D.R. Evans, and T.J. Bunning Hardened Materials Branch Survivability and Sensor Materials Division JANUARY 2007 Approved for public release; distribution unlimited. See additional restrictions described on inside pages STINFO COPY AIR FORCE RESEARCH LABORATORY MATERIALS AND MANUFACTURING DIRECTORATE WRIGHT-PATTERSON AIR FORCE BASE, OH 45433-7750 AIR FORCE MATERIEL COMMAND UNITED STATES AIR FORCE NOTICE AND SIGNATURE PAGE Using Government drawings, specifications, or other data included in this document for any purpose other than Government procurement does not in any way obligate the U.S. Government. 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Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YY) 2. REPORT TYPE 3. DATES COVERED (From - To) January 2007 Journal Article Postprint 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER LIQUID CRYSTAL BRAGG GRATINGS: DYNAMIC OPTICAL ELEMENTS In-house FOR SPATIAL LIGHT MODULATORS (POSTPRINT) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62102F 6. AUTHOR(S) 5d. PROJECT NUMBER R.L. Sutherland, V.P. Tondiglia, L.V. Natarajan, and S.A. Siwecki (Science 4348 Applications International Corporation) 5e. TASK NUMBER J.M. Wofford, D.R. Evans, and T.J. Bunning (AFRL/MLPJ) RG G. Cook (Universal Technology Corporation) 5f. WORK UNIT NUMBER P.F. Lloyd (UES, Inc.) M08R1000 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Science Applications International Corporation Universal Technology Corporation AFRL-ML-WP-TP-2007-551 Dayton, OH 45431 Dayton, OH 45432 ------------------------------------------------------------------ --------------------------------------------------- Hardened Materials Branch (AFRL/MLPJ) UES, Inc. Survivability and Sensor Materials Division Dayton, OH 45432 Materials and Manufacturing Directorate Wright-Patterson Air Force Base, OH 45433-7750 Air Force Materiel Command, United States Air Force 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING Air Force Research Laboratory AGENCY ACRONYM(S) Materials and Manufacturing Directorate AFRL/MLPJ Wright-Patterson Air Force Base, OH 45433-7750 11. SPONSORING/MONITORING Air Force Materiel Command AGENCY REPORT NUMBER(S) United States Air Force AFRL-ML-WP-TP-2007-551 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited. 13. SUPPLEMENTARY NOTES Journal article published in Proceedings of SPIE, Vol. 6487, 2007. The U.S. Government is joint author of this work and has the right to use, modify, reproduce, release, perform, display, or disclose the work. PAO Case Number: AFRL/WS 07-0163, 25 Jan 2007. Paper contains color. 14. ABSTRACT Bragg gratings yield a single diffracted order when irradiated by a coherent beam at the appropriate Bragg angle. In many cases, nearly all of the energy of the incident beam can be coupled to the diffracted beam. Hence these gratings can form many useful optical elements, and this has been realized in 1-D, 2-D, and 3-D photonic crystals. Bragg gratings made with liquid crystals offer the added dimension of dynamic properties through the large electro-optical effect in liquid crystals. Applications for spatial light modulators are numerous, including optical switches, modulators, active optical elements (e.g., lenses), laser sources, and tunable filters. We have been exploring a number of approaches for making liquid crystal Bragg gratings, including holographic polymer-dispersed liquid crystals, cholesteric liquid crystals, and homogenous nematic liquid crystals in hybrid devices. We have studied the dynamic properties of these Bragg gratings by electrical, thermal, and optical stimulation. Modification and control of optical and dynamic properties have been obtained through combinations of liquid crystals with polymers, combinations of various dopant materials, and interactions of liquid crystals with organic and inorganic interfaces. We discuss the materials, fabrication, characterization, and physics of liquid crystal Bragg gratings and present the results of various devices we have studied in our lab. We will also discuss potential applications. 15. SUBJECT TERMS spatial light modulators, Bragg gratings, liquid crystals 16. SECURITY CLASSIFICATION OF: 17. LIMITATION 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON (Monitor) a. REPORT b. ABSTRACT c. THIS PAGE OF ABSTRACT: OF PAGES Dean R. Evans Unclassified Unclassified Unclassified SAR 20 19b. TELEPHONE NUMBER (Include Area Code) N/A Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. Z39-18 i Invited Paper Liquid crystal Bragg gratings: Dynamic optical elements for spatial light modulators R. L. Sutherland*a,b, V. P. Tondigliaa,b, L. V. Natarajana,b, J. M. Wofforda, S. A. Siweckia,b, G. Cooka,c, D. R. Evansa, P. F. Lloyda,d and T. J. Bunninga aAir Force Research Laboratory (AFRL/MLPJ), Wright-Patterson Air Force Base, OH, USA 45433 bScience Applications International Corporation, Dayton, OH, USA 45431 cUniversal Technology Corporation, Dayton, OH, USA 45432 dUES, Inc., Dayton, OH, USA 45432 ABSTRACT Bragg gratings yield a single diffracted order when irradiated by a coherent beam at the appropriate Bragg angle. In many cases, nearly all of the energy of the incident beam can be coupled to the diffracted beam. Hence these gratings can form many useful optical elements, and this has been realized in 1-D, 2-D, and 3-D photonic crystals. Bragg grat- ings made with liquid crystals offer the added dimension of dynamic properties through the large electro-optical effect in liquid crystals. Applications for spatial light modulators are numerous, including optical switches, modulators, active optical elements (e.g., lenses), laser sources, and tunable filters. We have been exploring a number of approaches for making liquid crystal Bragg gratings, including holographic polymer-dispersed liquid crystals, cholesteric liquid crys- tals, and homogenous nematic liquid crystals in hybrid devices. We have studied the dynamic properties of these Bragg gratings by electrical, thermal, and optical stimulation. Modification and control of optical and dynamic properties have been obtained through combinations of liquid crystals with polymers, combinations of various dopant materials, and interactions of liquid crystals with organic and inorganic interfaces. We discuss the materials, fabrication, characteriza- tion, and physics of liquid crystal Bragg gratings and present the results of various devices we have studied in our lab. We will also discuss potential applications. Keywords: spatial light modulators, Bragg gratings, liquid crystals 1. INTRODUCTION A spatial light modulator (SLM) typically consists of a two-dimensional array of optical elements, or pixels, each of which can independently modulate the intensity, phase, or both of an incident optical beam. This produces a spatially varying modulation of the entire beam with control at the pixel level. Such devices are useful for delivering an image to a screen, for example in projection displays, or to a printer. However, the spatially modulated beam does not have to represent a visual image, but can also contain generic data. Thus, SLMs have also been proposed for use in direct-write lithography systems, holographic data storage, and optical computing. Two types of SLM that have been extensively studied are the electrically addressed (EA-SLMs) and optically addressed (OA-SLMs) spatial light modulators. These are illustrated in Figure 1. To address an SLM implies that a signal is sent to modify the SLM properties at the pixel level. For the EA-SLM, a signal voltage is typically applied to a pixel elec- trode which results in a modification of the material’s optical properties proportional to the applied voltage. A “read” beam of light incident on the material is thus spatially modulated in its intensity, phase, or both. The EA-SLM can be either transmissive or reflective. In an OA-SLM a spatially modulated beam, called the “write” beam, spatially modifies the material’s optical properties, either directly or indirectly, in proportion to the write beam’s intensity. A read beam, not necessarily of the same wavelength, interrogates the modulated material, resulting in a spatially modulated beam (usually reflected) that carries the same information as the write beam. Bragg gratings have been proposed for use in SLMs1 in situations where one can take advantage of their strong wave- length selectivity and highly efficient coupling of light into a single diffraction order. These gratings consist of a peri- odic modulation of the index of refraction in a material. If the index of refraction can be strongly modulated on a pixel *[email protected] Emerging Liquid Crystal Technologies II, edited by Liang-Chy Chien, Proc. of SPIE Vol. 6487, 64870V, (2007) · 0277-786X/07/$15 · doi: 10.1117/12.710829 1 Proc. of SPIE Vol. 6487 64870V-1 level, then a Bragg grating can form an efficient EA-SLM or OA-SLM. Liquid crystals are often the material of choice for such a device because of their large birefringence which can be easily modulated. We have extensively investigated such liquid crystal based Bragg gratings in our laboratories. We have studied the dynamic properties of these gratings by electrical, thermal, and optical stimulation. Modification and control of optical and dynamic properties have been obtained through combinations of liquid crystals with polymers, combinations of various dopant materials, and interac- tions of liquid crystals with organic and inorganic interfaces. In this paper we present recent results on three types of Bragg gratings that we have studied: electrically switchable liquid crystal-polymer composites, thermally tunable cho- lesteric liquid crystals, and hybrid nematic liquid crystal-photorefractive crystal devices. We discuss the materials, fab- rication, characterization, and physics of liquid crystal Bragg gratings and present some potential applications. EEEllleeeccctttrrrooodddeeesss ““““RRRReeeeaaaadddd”””” “““RRReeeaaaddd””” “““WWWrrriiittteee””” LLLLiiiigggghhhhtttt LLLiiiggghhhttt LLLiiiggghhhttt ((aa)) ((bb)) Figure 1. Schematic diagram of spatial light modulators. (a) EA-SLM. (b) OA-SLM. 2. SWITCHABLE COMPOSITE LIQUID CRYSTAL-POLYMER BRAGG GRATINGS 2.1. Holographic Polymer-Dispersed Liquid Crystals For several years we have been studying holographic polymer-dispersed liquid crystals (HPDLCs) for switchable Bragg grating applications. These materials consist initially of a homogeneous mixture of monomer, liquid crystal (LC), and photointiator dye (and, in some cases, additional materials). The mixture is sandwiched between two transparent elec- trodes, and a hologram is written in the material. Monomer is preferentially polymerized in the bright regions of the optical interference pattern, while liquid crystal diffuses to the dark regions. When the miscibility gap is breached, liq- uid crystal phase separates into domains. The index contrast between the polymer and liquid crystal provides the modu- lation to create a Bragg grating. These domains can be reoriented by an applied electric field. At some field value the index of the liquid crystal matches that of the surrounding polymer, and the grating is switched off. An advantage of using HPDLCs for switchable Bragg gratings is that complex holograms can be recorded in these ma- terials, in addition to simple sinusoidal gratings, and hence many additional applications are possible, such as switchable flat, diffractive lenses with built-in aberration corrections. We will focus here on reflection gratings. Thiol-ene-based reflective HPDLCs have recently been demonstrated to have substantial diffraction efficiency and good switching properties.2 This is a simple three (or four3) component material system, consisting primarily of thiol-ene monomer and liquid crystal, with a small amount of initiator (and possibly a co-initiator3) which is consumed in the photochemical reaction, and hence the grating should be environmentally robust. The phase-separated liquid crystal domains (droplets) in this material are highly spherical and distinct. Hence the morphology of this material leads to in- coherent or diffuse scattering as well as Bragg diffraction. Scattering can be a major issue in some applications. 2 Proc. of SPIE Vol. 6487 64870V-2 We have studied the coherent diffraction and random scattering in thiol-ene-based HPDLC reflection gratings using a 2 × 2 matrix method and an effective medium theory.4 The model incorporates realistic interfacial roughness and index inhomogeneities present in liquid crystal monolayer-droplet type gratings. Key parameters in the model are identified with morphological and optical properties of the grating. These include directly measurable parameters such as average droplet diameter, droplet diameter standard deviation, optical period, sample thickness, and refractive indices of the liquid crystal and polymer as functions of wavelength. Indirect or fitting parameters include volume fractions of drop- lets in high index regions and liquid crystal remaining in solution within the low index regions. Agreement of the model with experimentally measured transmission spectra of gratings at different Bragg wavelengths is excellent. The major impact of scattering is a reduction in the baseline transmittance, especially in the blue region of the spectrum, but it pro- duces only a minor reduction in the diffraction efficiency at the Bragg wavelength. The predominant contribution to scattering loss is index inhomogeneity, and the inclusion of index dispersion for all material constituents is crucial to obtain agreement with data in the blue end of the spectrum. Some key findings from this study are that the diffraction efficiency and scattering loss can be simultaneously improved by shaping the LC droplets and increasing the volume fraction of phase-separated LC. The index inhomogeneity in this system has two contributions: 1) droplet separation by polymer material, and 2) random orientation of droplet symmetry axes. The first contribution can be minimized by increasing the volume fraction of droplets, while the second is mini- mized by ordering the droplet symmetry axes in the grating plane. These effects will also increase the index modulation of the grating, at lease for one polarization of light, and hence increase the diffraction efficiency. The key is to stretch the droplets, i.e., to deform and coalesce them into LC “needles”. Our approach to achieving this is to shear the holograms in a direction perpendicular to the grating vector. Although this approach has been tried before,5 our technique is different in that we incorporate an in situ shear during the optical re- cording.6 We thus take advantage of some of the properties of the thiol-ene system. Since LC droplets are formed in this system by liquid-liquid instead of liquid-gel demixing, the system is fluid and allows significant deformation of the LC droplets. However, the system is also sufficiently viscous that the shear is easily transmitted from the boundary win- dows to the middle of the developing film. The key is timing the shear to occur during the optimal phase of the material during the photocure. When fully cured, the film locks in the droplet deformation. 2.2. Experiment The liquid crystal BL037 was mixed in Norland NOA65 at an LC concentration of 35.5% by weight with a 2.0 wt-% concentration of the UV initiator Irgacure 4265. The mixture was then sandwiched between two indium-tin-oxide- coated glass slides using various spacers. Reflection gratings were recorded using a prism geometry.2 The angle of inci- dence of 364-nm radiation from an Ar-ion laser was varied to control the Bragg wavelength of the hologram. Intensity incident on the sample was ~ 120-140 mW/cm2, and the exposure time was varied. Figure 2 shows the device and optical setup for shearing experiments. A linear shear deformation is produced in an HPDLC sample by sliding the glass sides of a sample cell past each other in a parallel direction. Since the formation of an HPDLC filter is a dynamic process, the timing of the shear during the grating formation is studied. The computer controlled motor allows the shear to be accomplished anytime during the formation process, while the shutter controls stops the exposure during the shear. A white light probe and a fiber spectrometer capture the notch formation and shear effects during the whole process of writing, shearing, writing, and releasing. Samples cured without shearing were also studied while applying a post-cure shear. Spectra were taken as the shear was applied. Transmittance spectra of the sheared (either in situ or post-cured) HPDLC gratings were obtained by directing an unpo- larized white-light source at the sample at normal incidence and collecting the transmitted light with an optical fiber connected to an Ocean Optics spectrometer. Each spectrum was normalized to the transmittance of a bare piece of glass to factor out air-glass Fresnel reflection losses. A linear polarizer allows for collection of transmission spectra of light polarized parallel to and perpendicular to the shear direction. For TEM studies, cured holographic films were embedded in flat molds using Epo-fix resin and cured overnight in a 60 °C oven. The blocks were trimmed and ultramicrotomed at room temperature using an RMC Ultramicrotome. Sections of 50-60 nm thickness were cut with a 35° Diatome diamond knife, picked up onto 400-mesh hex Cu grids and vapor 3 Proc. of SPIE Vol. 6487 64870V-3 stained with RuO . The sections were then imaged using bright-field TEM in an FEI CM200 transmission electron mi- 4 croscope. Images were obtained of varying magnifications between 5,000× and 50,000×. Shutter Beam Expander Mirror Laser Polarized (in shear direction) White Light Neutral Density Filter Fiber Spectrometer Prism DC Motor Spring To computer Slide Sample Shear Direction Figure 2. Schematic diagram of holographic recording apparatus incorporating in situ sample shear. 2.3. Results and Discussion The response of HPDLC samples with varying cell thickness of 5, 8, 15, and 20 µm subjected to shear deformation only after curing was studied. Shear stress was applied to the samples while monitoring the transmission spectrum for light polarized in both the parallel and perpendicular directions to the shear. The electric field required for switching was measured for some samples while the films were under shear deformation. Also examined were the effects of applying a thin film of the thiol-ene (cured, uncured and gelled) to the glass surfaces before cell construction. As the shear stress increases, the notch minimum decreases for polarization parallel to the shear deformation (i.e., higher diffraction efficiency) while the notch minimum for light polarization perpendicular to the shear increases. At higher shear, the perpendicular curve approaches zero and the parallel curve continues to increase approximately line- arly. This is in agreement with previous similar work on this type of dependence of HPDLC reflection gratings.5 No permanent deformation is apparent when releasing the shear force. The slides actually seem to slip across the film with- out losing optical contact. Thin films of thiol-ene were spin-coated onto glass slides used for cell construction in an attempt to increase the bond strength between the film and the slides, thus reducing slippage and increasing the maximum shear. Films were treated in one of three ways before cell construction. Gelled samples were not exposed to UV light prior to filling. Oligomer- ized samples were exposed to UV light for 5 seconds (partially cured), and the polymerized samples were exposed to UV light for 45 seconds (fully cured). Coated cells yield a larger decrease in notch transmission for a given shear than the uncoated cell and result in lower attainable minimum notch depth (higher diffraction efficiency). Samples coated with a gelled thiol-ene performed the best with no lag between shear displacement and observed transmission notch decrease. Of the coated samples, polymerized coatings did the worst with similar results for the uncoated sample. Sample thickness can also affect the shearing characteristics of the film. As sample thickness increases, diffraction effi- ciency goes up as usual, as well as the threshold value for notch deformation and the shear required for the notch to dis- appear in the perpendicular polarization. This might be explained by a non-uniform shear within the film from slide to slide, with thicker films showing a larger variation throughout the thickness. The in situ shearing apparatus was modified to eliminate slippage of the driving actuator and an external dial microme- ter was used to verify the shearing displacement. We show in Figure 3a the results of a sample subject to shear deforma- tion in situ. Note the polarization dependence. For polarization perpendicular to the shear the diffraction efficiency is zero. On the other hand, the diffraction efficiency for light polarized parallel to the shear is nearly 99%. This is the highest diffraction efficiency we have observed in an HPDLC reflection grating. The baseline transmittance is also im- 4 Proc. of SPIE Vol. 6487 64870V-4 proved. For comparison, we show in Figure 3b a sample recorded without shear.4 A clear improvement in coherent dif- fraction and random scattering can be seen. For the plot in Figure 3b, the spectra for both polarization directions are nearly identical. This suggests that the in situ applied shear has indeed elongated the LC droplets. We emphasize that this and similar samples are under no externally applied shear during these measurements; the polarization dependence is permanent. 100 100 80 (a) 80 (b) %) %) e ( 60 e ( 60 nc nc mitta PPaerraplelenldicular mitta Trans 40 Trans 40 20 20 0 0 400 450 500 550 600 650 700 400 450 500 550 600 650 700 Wavelegth (nm) Wavelength (nm) Figure 3. Transmittance spectra of thiol-ene HPDLC reflection gratings. (a) Sheared in situ. (b) Unsheared. In Figure 4 we compare TEM images of sheared and unsheared samples. Figure 4b corresponds to the data in Figure 3a. The unsheared sample in Figure 4a displays the typical morphology for thiol-ene HPDLC reflection gratings.4 Notice the spherical shape of the droplets. The sample in Figure 4b displayed some inhomogeneity and was heat-treated at ~ 70-80 ºC prior to the measurement of the spectrum in Figure 3a. The sample in Figure 4c has not been heat-treated. No- tice that in this sample the droplets have been severely elongated along the shear direction (i.e., perpendicular to the grating vector). This sample also has some inhomogeneities, but in certain areas it displays a similar spectrum as that shown in Figure 3a. It is interesting that the droplet axes in Figure 4b do not align with the shear direction. Although we do not have enough data at this time to be certain, we speculate that this may be related to the heat treatment. Neverthe- less, the droplets are still distinctly elongated compared to those in Figure 4a. Hence we believe that this confirms a realignment of the director orientation as expected, which yields the polarization dependence seen in the spectra of Fig- ure 3a. 555000000 nnnmmm 555000000 nnnmmm 555000000 nnnmmm S - I - ((aa)) ((bb)) ((cc)) Figure 4. TEM micrographs of thiol-ene HPDLC Bragg gratings. (a) Unsheared. (b) Sheared and heat-treated. (c) Sheared but not heat-treated. 5 Proc. of SPIE Vol. 6487 64870V-5 We have performed some preliminary studies of the electric fields required for switching these films. The required switching field decreases for light polarized perpendicular to the shear direction and increases for light polarization in the shear direction. The larger the shear, the greater the difference in switching field. However, the critical field for switching has not increased dramatically. We are continuing these studies. 3. TUNABLE CHOLESTERIC LIQUID CRYSTAL BRAGG GRATINGS 3.1. Cholesteric Liquid Crystal (CLC) Bragg Gratings The cholesteric LC (CLC) in these studies consists of a nematic LC doped with a chiral agent. In any given plane, the mole- cules exhibit nematic orientational order. However, steric hindrances prohibit molecules in contiguous planes from achieving the same average orientation. Hence, the average orientation direction is slightly rotated from layer to layer. The sense of rotation is the same in each layer, resulting in a periodic twist of the average nematic orientation through the bulk of the liq- uid. The sense of the rotation depends on the chiral agent, and both right-handed and left-handed twists are possible. The twist is linearly proportional to z, and the natural twist rate is q . This rate is determined by the concentration of the 0 chiral dopant. A wide range of q is possible. The distance along z over which the twist angle goes through a 360° rota- 0 tion is called the pitch p , where p =2π/q . The total twist angle Φ in a cell with these chiral-doped LCs depends on the 0 0 0 natural twist rate, the cell thickness, and boundary conditions at the confining substrates. The actual twist rate q and pitch p may differ slightly from the natural values. When the pitch is such that p ~ λ, where λ is an optical wavelength, a single domain CLC will exhibit selective Bragg reflection over the wavelength range n p < λ < np. Light polarized along the local director sees a refractive index n, o e e while light polarized perpendicular to this direction sees n . For light propagating along the z axis, the normal modes of o propagation in this inhomogeneous medium can be computed exactly in terms of Bloch waves.7 The normal modes are elliptically polarized, in general. In the Bragg regime (n p <λ < np), the wavevector of one mode is purely imaginary, o e which corresponds to an evanescent wave. This mode cannot propagate in the medium. The other normal mode is al- most circularly polarized with the opposite handedness of the CLC helix. Hence the CLC is a Bragg grating, for the proper handedness of incident polarized light, and in the Bragg regime it acts as a reflection filter. The incident light is not necessarily one of the normal modes. If the birefringence is not too large, so that (n)2 − (n )2 << (n)2 + (n )2, then the wave propagation can be analyzed using coupled-wave theory.7 The field e o e o inside the CLC is taken to be a superposition of incident and reflected waves with wavevectors ±k given by 2π n2 +n2 k = e o (1) λ 2 If a left-hand circularly polarized wave is incident on a CLC with a left-handed twist (or, conversely, a right-hand circu- larly polarized wave incident on a right-handed CLC), then the wave is reflected with an efficiency R given by κ2sinh2sL R= , (2) s2cosh2sL+(∆k 2)2sinh2sL where s2 =κ2 −(k−q)2, (3) ∆k =2(k−q), (4) ( ) 1 πn2 −n2 e o κ= 2 . (5) λ n2 +n2 e o The filter efficiency has the same form for the HPDLC Bragg reflection grating. However, for unpolarized incident light, the CLC filter has a peak reflection efficiency of 6 Proc. of SPIE Vol. 6487 64870V-6 Rpeak = 1tanh2κL. (6) unpolarized 2 Thus, to obtain high rejection efficiency for unpolarized light, two CLC filters of opposite handedness in tandem are required. 3.2. Tunable CLC Filters The Bragg wavelength of the CLC filter is given by λ =np, where n is the average refractive index. Hence to tune B the filter, one can change the average refractive index or the pitch. A convenient way to do both is to apply an electric field. However, this results in reorientation of the molecular axis along the direction of the field, which reduces the amount of extraordinary index seen by the optical wave. From Eq. (5), we can see that this reduces the coupling coeffi- cient and hence the diffraction efficiency. At some voltage the CLC will abruptly untwist and exist in a homeoptropic nematic state. This is sometimes referred to as a cholesteric-nematic transition. In the homeotropic state the selective Bragg reflection is destroyed. When the voltage is turned off, the cell attempts to return to the twisted CLC condition. Typically, though, this transition proceeds through an intermediate state, what is known as the focal conic state. In this state there are multiple domains of CLC with helical axes approximately parallel to the substrates. At domain bounda- ries the azimuth angle of the helix changes abruptly. This produces strong light scattering. The return to the single do- main CLC state usually takes a very long time (minutes to hours or days). The above effects are undesirable for SLM applications. Some techniques have been developed to alleviate these ef- fects, such as adding a small amount of polymer to the CLC to stabilize the cholesteric state. Patterning the polymer holographically has been demonstrated to offer sufficient elastic memory to the grating to return the electrically per- turbed molecules to their original orientation while lowering the switching voltage and improving the baseline scatter- ing.8 However, the problem of a reduction in coupling efficiency with applied field is still evident. A more desirable approach would be to gently unwind the CLC helix without reorienting the molecules. The pitch depends on the concentration of chiral dopant. This concentration can be controlled thermally, which allows a simple tuning of the Bragg wavelength. Work demonstrating this has been reported using a left-handed CLC twist in medium with a positive dielectric anisotropy.9 We have discovered an analogous effect in a left-handed medium with a negative dielectric anisotropy. We describe next our experiments with this type of Bragg grating. 3.3. Experiment Cholesteric cells were made by mixing the chiral dopant S811 with nematic liquid crystals having negative dielectric anisotropy. Nematic LCs ZLI 2806 and ZLI 4788 were chosen for this study. The chiral dopant concentration was var- ied from 20% to as high as 60% in the mixture. Windows of the CLC cells were pretreated with an alignment layer formed by mechanical rubbing. The alignment is such that the helical axis is perpendicular to the rubbing direction. Cell thickness was set by using 10 or 15-µm spacers. For some studies, one of the cell windows was coated with a thin layer of pre-cured NOA65 doped with 1 wt-% of the broadband absorber nigrosin. The spectrum of the CLC cell was measured using an unpolarized white light source in conjunction with an Ocean Op- tics spectrometer. Two types of experiment were performed. In one, the cell was housed in a hot stage and the tempera- ture of the cell was varied. In the second, the nigrosin cell was irradiated with a Kr-ion laser at 647 nm. Nigrosin is well known as a heat transfer dye and has absorption from 420 nm to 700 nm. 3.4. Results and Discussion A blue shift of the Bragg grating is expected as the chiral dopant concentration in the mixture is increased due to a tightening of the helical structure. We show in Figure 5 a plot of the Bragg wavelength as a function of chiral dopant concentration for a cell at 55 °C (35 wt-% S811 in ZLI 2806). At room temperature, however, the Bragg wavelength was in the red end of the spectrum for all concentrations of chiral dopant and, depending on the concentration of the dopant, a red shift was observed. Interestingly, the Bragg wavelength did not correlate with the chiral dopant concentra- tion at room temperature, and no such systematic trend was evident. 7 Proc. of SPIE Vol. 6487 64870V-7