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Photostimulated control of laser transmission through photoresponsive cholesteric liquid crystals

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Abstract

Cholesteric liquid crystals (CLCs) are selectively reflective optical materials, the color of which can be tuned via electrical, thermal, mechanical, or optical stimuli. In this work, we show that self-regulation of the transmission of a circularly polarized incident beam can occur upon phototuning of the selective reflection peak of a photosensitive CLC mixture towards the pump wavelength. The autonomous behavior occurs as the red-shifting selective reflection peak approaches the wavelength of the incident laser light. Once the red-edge of the CLC bandgap and incident laser wavelength overlap, the rate of tuning dramatically slows. The dwell time (i.e., duration of the overlap of stimulus wavelength with CLC bandgap) is shown to depend on the radiation wavelength, polarization, and intensity. Necessary conditions for substantial dwell time of the CLC reflection peak at the pump beam wavelength include irradiation with low intensity light (~1mW/cm2) and the utilization of circularly polarized light of the same handedness as the helical structure within the CLC. Monitoring the optical properties in both reflection and transmission geometries elucidates differences associated with attenuation of the light through the thickness of the CLC film.

©2013 Optical Society of America

1. Introduction

Cholesteric liquid crystals (CLCs) self-organize into a periodic helical structure that reflects circularly polarized light of the same handedness. The CLC phase occurs naturally in some materials, but is often studied through the use of mixtures of an achiral nematic liquid crystal (NLC) host and a chiral dopant (added to induce twist). A transmission notch/reflection peak (i.e., 1-D photonic bandgap) is formed by selective reflection of light from the periodic structure. The center of the bandgap position (λB) is determined by the average of the extraordinary and ordinary refractive indices (<n>) of the LC and by the magnitude of the helical pitch (P = one full rotation of the director orientation) — λB = P<n>. For a given CLC mixture, the color of the selective reflection can thus be controlled by influencing the pitch length. Increasing the chiral dopant concentration decreases the pitch and blue-shifts the bandgap. The bandgap position can be estimated via Eq. (1), where c is either the molar fraction or the weight percent of chiral dopant and HTP is the helical twisting power of the chiral dopant. A larger HTP value indicates a shorter induced pitch (more twisted helix) for the same concentration of chiral dopant.

λB=<n>/(HTP*c)

CLC mixtures/cells have a number of components that may be substituted with (or functionalized to be) photosensitive materials to promote unique responses to light, some of which have been investigated for over 40 years [1,2]. Photoresponsive liquid crystal mixtures have been featured in several recent reviews [3-5]. Photosensitive command surfaces, or so-called photoalignment layers, have been utilized to pattern areas of enhanced reflectivity or to switch between reflective and scattering states [6,7]. Photosensitive LC mixtures have been shown to exhibit phase change behavior upon exposure to light (NLC → isotropic [8], CLC → isotropic [9,10], and isotropic → NLC [11]). Phototuning (i.e., changing the spectral position of the bandgap with light exposure) of CLCs is typically achieved through utilization of photosensitive chiral dopants [12-15] or photosensitive NLC molecules [4,10]. Such phototuning may be reversible [16], has been demonstrated over large (2000 nm) wavelength range [17], can be either blue- or red- shifting [18], and has been shown to cause optically induced helical inversion [19,20]. Additionally, doping CLC mixtures with photosensitive guest dyes has enabled fast, reversible, all-optical switching between reflective CLC and transparent isotropic states [21].

In this work, the bandgap of a CLC mixture doped with photosensitive chiral dopant is initially located in the UV/blue end of the visible spectrum. The bandgap undergoes red-shifting upon exposure to circularly polarized blue/green light and exhibits a dramatic reduction in rate of change of spectral position at the wavelength of the incident radiation. The polarization of the helical structure must match that of the pump beam. If linearly polarized or opposite handedness circularly polarized light is utilized, continuous tuning of the bandgap position through and past the incident laser wavelength occurs. With careful selection of laser intensity, radiation polarization, and concentration of photosensitive chiral dopant, self-regulation of laser transmission through a CLC cell was demonstrated. Such self-regulation is an example of the utilization of light to control light, a concept which has potential in a number of applications including passive optical elements in lasing, filtering, and displays. The autonomous nature of this process provides unique opportunities for photoaddressing. For example, rather than using carefully controlled intensity or exposure times for creating images, color images may be simultaneously, or serially, written with data/pixel color autonomously tuning to the color of the low power writing beam.

2. Results and discussion

The CLC mixtures in this study were formulated by mixing two left-handed (LH) chiral dopants (QL76 and MSB-10 — structures shown in Fig. 1 ) with the NLC host (MDA-00-1444). Both MSB-10 [22] and QL76 [17,23] are based on a binaphthyl core and exhibit exceptionally large (>40 µm−1) HTPs. The pitch of this mixture can be modulated with light due to the isomerization of the two azobenzene units within QL76 which subsequently reduces the magnitude of the HTP of the mixture. MSB-10 was employed here to allow the impact of the concentration of QL76 to be examined in formulations in which the initial reflection peak position remained constant. Ultimately, the solubility of QL76 in cyanobiphenyl hosts such as MDA-00-1444 is limited, and thus the maximum concentration of QL76 was ~6 wt% in order to avoid phase separation over time. In contrast to a prior report [24], this study uses low concentrations of the photosensitive chiral dopants rather than azobenzene-containing nematics in order to reduce absorbance and avoid any possibility of the formation of a photoinduced isotropic state.

 figure: Fig. 1

Fig. 1 Skeletal formulas of (a) the bis(azobenzene) chiral dopant (QL76) and (b) the non-photosensitive chiral dopant (MSB-10). (c) Schematic illustration of experimental set-up utilized to simultaneously collect transmission and reflection spectra from CLC cells irradiated with either RHCP light or LHCP laser light.

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The CLC mixtures were drawn into self-prepared alignment cells. Reflection and transmission spectra (see schematic of experimental set-up Fig. 1(c)) of the cells composed from the LH CLC mixtures were collected simultaneously before, during, and after irradiation with either left-handed or right-handed circularly polarized (LHCP or RHCP) light from an Argon-ion laser (457, 488, or 514 nm). Spectra were collected from within the laser-irradiated area every 0.27 sec with a spectral resolution of 3 nm. As recently documented by Li et al. [25], irradiation with blue/green light builds up a photostationary state concentration of cis isomer that strongly depends on the color of the incident light (magnitude of decrease in HTP increases with blue shift in radiation wavelength). A prior examination from our group has reported the HTP of QL76 decreases from ~43 µm−1 (nearly 100% trans/trans conformation) to 12 µm−1 (majority cis/cis conformation) upon irradiation with UV light in a 1444 NLC host [26].

Within Fig. 2 are reflection spectra from a LH CLC cell irradiated with either RHCP (Fig. 2(a)) or LHCP (Fig. 2(b)) 514 nm radiation of 1.0 mW/cm2 intensity. These spectra illustrate the red-shifting of the reflection notch induced by irradiation with 514 nm light. As expected, the reflection peak of the CLC cell irradiated with RHCP light quickly red-shifted through and past 514 nm ultimately reaching approximately 580 nm (photostationary state for this wavelength and intensity). Conversely, irradiation of the LH CLC cell with LHCP light resulted in increased dwell time (i.e., duration of the overlap of the pump wavelength with the CLC bandgap). Evident in Fig. 2(b) is the appearance and increase in intensity of the reflected laser line at 514 nm, which confirms that the handedness of the CLC and laser line match. The differences in the temporal dependence of the red-shifting between RHCP and LHCP light is contrasted in the plot of reflection peak central wavelength position as a function of irradiation time shown in Fig. 2(c). From Fig. 2(c) it is apparent that phototuning induced with RHCP is nearly linear for the first three minutes of exposure, slowing as the reflection notch approaches the photostationary state. RHCP light, which is transmitted through the cell independent of bandgap position shows the effective tuning range of the QL76 upon irradiation with a particular intensity and wavelength. As expected no change in tuning rate upon overlapping bandgap position with RHCP laser line was observed. Conversely, phototuning induced with LHCP slows considerably once the reflection peak overlaps the wavelength of the incident laser. Notably, the center of the reflection peak does slightly red-shift during continuous LHCP irradiation. However, tracking the red and blue band edges of the reflectance peak (Fig. 2(d)) confirms the reflection notch still enveloped the laser line even after 25 min of continuous irradiation. The red-shift during continuous illumination with the LHCP 514 nm can be quantified as the rate of change of the center of the reflection notch with time (tuning rate). Linear fits to the data indicate a tuning rate of 37 nm/min before and 2.3 nm/min after the red band edge overlaps with the incident LHCP laser line. The spectral position of this slope change occurs well before the maximum tuning range (photostationary state).

 figure: Fig. 2

Fig. 2 Reflection spectra taken as a function of exposure time of a LH CLC mixture with (a) RHCP 514 nm light and (b) LHCP 514 nm light. Plots of (c) the spectral position of the reflection peak central wavelength position as a function of time irradiated with LHCP and RHCP light and (d) the center, blue-edge, and red-edge of the reflection peak as a function of LHCP 514 nm light irradiation time. A horizontal line indicating position of radiation wavelength is included on (c) and (d) for reference. The same 8 µm LH CLC (5.7% QL76) cell was utilized to generate this data and the 514 nm LHCP/RHCP light intensity was 1.0 mW/cm2.

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The effective tuning range and time during which the reflection bandgap overlaps the irradiating wavelength were examined with respect to radiation intensity and wavelength. The photostationary state concentration of cis isomers in azobenzene materials and mixtures has been shown to depend on the radiation wavelength [25]. UV light in many cases almost completely converts trans to cis isomers. Increasing the intensity of the light at a particular wavelength has been shown to increase the photostationary state concentration of cis isomer [17], which in CLC mixtures such as those examined here strongly dictates the maximum change in the reflection notch upon light irradiation. Within Fig. 3(a) are plots of the central wavelength position of the reflection notch as a function of time for the same LH CLC cell irradiated with 1.0, 2.0, and 3.0 mW/cm2 LHCP 514 nm light. All three intensities show some dwell time at the laser line wavelength, but the tuning rate through the laser/peak overlap condition increases with increasing radiation intensity. The change in slope at the wavelength position indicated by the bottom horizontal line labeled ‘1’ within Fig. 3(a) corresponds to the red-edge of the bandgap overlapping the incident laser line causing a decrease in tuning rate. The unnumbered horizontal line within Fig. 3(a) indicates the wavelength of the laser. Wavelength position ‘2’ in Fig. 3(a) corresponds to the blue-edge of the bandgap passing through the incident radiation wavelength, resulting in an increase in slope as the reflection peak continues to red-shift toward its photostationary state as evident in the 2 and 3 mW/cm2 cases. Wavelength position ‘3’ indicates the wavelength position of the mixture at the photostationary state concentration induced by 514 nm light with intensity of 3 mW/cm2. Note: the photostationary state position of 2 mW/cm2 irradiation case is blue-shifted with respect to the wavelength of the 3 mW/cm2 photostationary state.

 figure: Fig. 3

Fig. 3 Plots of (a) the spectral position of the reflection peak central wavelength of LH CLC (4.0 wt% QL76, 8 µm) as a function of time irradiated with LHCP 514 nm light of 1.0, 2.0, and 3.0 mW/cm2 intensity. (b) Laser line/bandgap overlap duration (dwell time) of LH CLC cells (8 µm) composed with various concentrations of QL76 and irradiation with LHCP 514 nm light of 1, 2, and 3 mW/cm2 intensity. (c) The mean bandgap shift of various compositions of LH CLC cells irradiated with 3.0 mW RHCP 457, 488, and 514 nm light. (d) Plots of the spectral position of the LH CLC (5.7 wt% QL76, 8 µm) reflection peak central wavelength as a function of time irradiated with 1 mW LHCP 457, 488, and 514 nm light. Horizontal lines without symbols indicate wavelength position of the three stimulus wavelengths. Note: only the wavelength indicated in the legend was used for a particular curve.

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The duration of the overlap of the pump laser line and the phototuned bandgap strongly depended on radiation intensity as well as the concentration as summarized in Fig. 3(b). Not surprisingly, the dependence of laser line/bandgap overlap duration on intensity is evident at all three concentration levels. Increasing the wavelength of pump laser from 457 nm to 514 nm decreases the photostationary state concentration of cis isomer. The decreased photostationary state concentration with increasing pump laser wavelength is evident in Fig. 3(c) as a reduction in the mean bandgap shift for the three concentrations examined here. Concurrently, increasing the wavelength of the pump laser also increases the duration of overlap of the bandgap and the pump laser line, as shown in Fig. 3(d). Pump/reflection peak overlap duration is particularly evident in Fig. 3(d) as the slope of the spectral change deviates (slows) near the pump wavelength.

In addition to polarization, intensity, wavelength, and concentration, temperature can also affect the tuning range, rates, and ultimately the duration of overlap of the reflection bandgap and pump laser wavelength. To measure the dependence of tuning on temperature, cells were affixed to a Peltier cooler with heat sink compound. The 4 wt% QL76 CLC cells were equilibrated at the desired temperature for 2 min before irradiation with 1.0 mW/ cm2 514 nm light. The magnitude of the bandgap shift (Fig. 4(a) ) increased and the dwell times (Fig. 4(b)) decreased with increasing temperature. The maximum tuning range is governed by a relationship that is linear with the starting reflection notch wavelength and dependent on both the magnitude of the change in HTP as well as the magnitude of the HTP of the exposed state. The primary factor contributing to the increase in tuning range with temperature is thus caused by the red-shift in the starting wavelength for the phototuning experiments that vary linearly (slope of 3.1nm/⁰C from linear fit with R2 value = 0.98) with temperature. Pitch length dependence on temperature has previously been demonstrated [2730]. The primary contributing factor to the decrease in dwell time was attributed to the considerable increase in tuning rate due to the influence of temperature on the viscosity of the CLC mixture.

 figure: Fig. 4

Fig. 4 (a) Mean bandgap shift as a function of temperature. (b) Duration of bandgap overlap with incident laser wavelength as a function of temperature. All experiments conducted with 4 wt% QL76 mixture in 8 µm cells exposed to 514 nm laser with an intensity of 1.0 mW/cm2. Error bars represent range of three independent measurements. Linear regression fits for data in graphs (a) and (b) had R2 values of 0.988 and 0.964 respectively.

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All data presented here was based on reflection spectra collected in the set-up illustrated in Fig. 1. However, to further understand the nuances of the observations, transmission spectra for each of the examinations described here were also simultaneously collected. As shown in Fig. 5(a) , both the reflection and transmission spectra taken from a LH CLC exhibit asymmetrical tuning (broadening) of the transmission notch/reflection peak when irradiated with LHCP light. The broadening of the bandgap is indicative of an asymmetry, or non-uniform variation, of pitch length through the thickness of the cell. To elucidate this point, comparison of reflection and transmission spectra after 3, 4, and 7 min of irradiation with LHCP light shown in Fig. 5(a) indicate slower tuning (i.e., less red-shifted central wavelength position) of transmission notch versus reflection peak. No such differences were observed with RHCP irradiation (not shown here) which is expected to be transmitted through the LH CLC. Cell thickness effects have been noted in tuning of similar cells primarily due to absorption by the dye effectively attenuating the stimulus light through the thickness of the cell [17]. However, in this work the reflectivity of the LH CLC cell also causes attenuation of the LHCP laser line upon overlap of reflection peak with wavelength of pump laser. The proposed asymmetry of the bandgap tuning is depicted schematically in Fig. 5(b), which indicates a pitch change with color (i.e., color change from blue to green to orange to red corresponds to increasing pitch length). In the case where RHCP light is utilized, the pitch and thus the color of cell shifts uniformly, thus spectral changes due to pitch length are negligible when comparing transmission and reflection spectra. LHCP light behaves identically to RHCP light until after the pump wavelength overlaps the CLC bandgap (marked Time 1 in Fig. 5(b)). Under such conditions the LHCP pump light is selectively reflected. The input side of the cell is continually irradiated and may effectively tune as though it were being irradiated with RHCP light, but the attenuation of the LHCP light generates a slower response of the photosensitive chiral dopant through the thickness of the cell. The pitch length on the incident side of the cell becomes greater than that on the output side of the cell and significant differences between position of transmission notch and reflection peak are noted when comparing transmission and reflection spectra.

 figure: Fig. 5

Fig. 5 (a) Reflection and transmission spectra taken from a LH CLC after increasing irradiation time with LHCP 3.0 mW/cm2 488 nm laser line. Note: data points around laser line eliminated for clarity. (b) A schematic of symmetrical tuning proposed to occur upon irradiation with transmitted RHCP light vs. asymmetrical tuning within LH CLC observed when overlap of the CLC bandgap and wavelength of LHCP light occurs. Note: Red-shift in color indicates increase in pitch length and bandgap/pump wavelength overlap occurs at Time 1.

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3. Conclusions

Irradiation with circulary polarized blue/green light cued a rapid color change of a photosensitive CLC mixture until the reflection of the material matched the color of the input light. Utilizing low intensity, circularly polarized light of the same handedness as the periodic structure of the photoresponsive cholesteric liquid crystal (CLC) mixture enabled increased dwell time (i.e., laser line / bandgap overlap duration). Using longer wavelengths of light reduced the tuning range, increased the dwell time, and reduced the tuning rate of the bandgap toward the incident laser wavelength. Reducing temperature and decreasing light intensity also both increased the dwell time. Considering both the tuning rate and overlap duration at the incident laser line, a faster relaxing photosensitive chiral dopant would be most suitable for filtering applications whereas an irreversible, or slow relaxing photosensitive chiral dopant, would be best suited for data storage. Using light to control light with photoresponsive materials has focused on the chemistry of photosensitive molecules and the effects of such photoresponses on optical materials like CLCs with photosensitive nematics or chiral dopants. Building upon the burgeoning field of photosensitive materials research, this work shows that new optical functions and applications may be demonstrated with careful consideration of the photosensitive component, light wavelength, temperature, and polarization state of light.

4. Experimental methods

The cholesteric liquid crystal (CLC) mixtures were composed of a nematic liquid crystal host, MDA-00-1444 (Merck), a non-photosensitive left-handed (LH) chiral dopant, (MSB-10 shown in Fig. 1(b), synthesis detailed in [22]) and a photosensitive chiral dopant (QL76 shown in Fig. 1(a), synthesis detailed in [23]). The helical twisting power of the QL76 and MSB-10 in MDA-00-1444 LC host were estimated to be ~58 µm−1 and 49 µm−1 respectively. HTP was estimated by adding a single chiral dopant to the nematic liquid crystal and determining the central wavelength of the CLC bandgap via FWHM of the reflection spectrum. HTP was calculated from Eq. (1) assuming <n> was 1.6. The compositions of the three mixtures explored are summarized in Table 1 . The wt% values reported for the QL76 were calculated omitting the weight of the MSB-10.

Tables Icon

Table 1. Composition and Properties of CLC Mixtures

The CLC compositions were tested in cells constructed with CCC166 uncoated 25 x 38 x 1.1 mm plates of EXG Boro-Aluminosilicate glass (Corning). Each glass substrate was rinsed with acetone, rinsed with methanol, and then air plasma etched for 10 min at ~260 mTorr via plasma cleaner (PDC-32G, Harrick). After plasma cleaning each glass substrate was spin coated on one side with a polyimide (PI) solution [prepared by mixing PI-2555 (HD MicroSystems) (8 mL) with reagent grade N-Methyl-2-pyrrolidone (32.5 mL) and reagent grade1-Methoxy-2-propanol (9.1 mL).] The polyimide solution was applied via syringe outfitted with a 0.45 µm GHP membrane (Pall Acrodisc) filter. Spin coating was conducted in a wafer spinner (Spin 150, Semiconductor Production Systems) programmed to spin at 1500 rpm for 15 s and then 3000 rpm for 60 s. Coated glass substrates were then dried on a hotplate for 30 min at 200°C and subsequently uniaxially rubbed with a felt cloth.

The gap between the glass substrates was set by glass rod spacers of 8, 20 and 30 µm thicknesses dispersed in UV curable optical adhesive (Norland 68). CLC mixture was drawn into the constructed cells above clearing temperature and allowed to cool at ~1°C/min to room temperature utilizing a heating/cooling stage (FP82HT, Mettler) with temperature controller (FP90 Central Processor, Mettler). The changes in transmission and reflection of CLC cells were tested at all three blue/green laser lines from a Multi-line Stellar-Pro-Select Argon-Ion laser (Modu-Laser, LLC) utilizing the experimental setup depicted in Fig. 1(c). Each composition of interrogated cells was matched with a reference cell. However, opposite handedness MSB-10 was utilized in reference cells so that the reflection peak did not interfere with the spectral range interrogated in the phototuning cells, and matching compositions would account for absorbance of the CLC mixture. The linear polarization of the Ar + beam was converted into circular polarization using a half Fresnel Rhomb (Broadband Polarization Rotator, Model Pr-550, Newport Corp.) followed by a 1/4 Fresnel Rhomb (Newport Corporation), rotation of the 1/2 Fresnel Rhomb allowed for expedient changing between LH and RH CP light. All power measurements were made with a PM100A power meter and S302C detector (Thorlabs, Inc.). Exposure areas used to calculate intensity were defined by 5 mm metal iris. The tungsten halogen lamp source (LS-1, Ocean Optics) was incident at ~4.4 degrees from normal to the CLC cell. USB2000 + VIS-NIR spectrometers (Ocean Optics, Inc.) collected reflection and transmission spectra every 0.27 s via custom LabVIEW (National Instruments) program. Samples were exposed to a laser line for anywhere from 5 min to 1 hr depending on the laser line/bandgap overlap duration. For temperature-controlled experiments, CLC cells were affixed with silicone heat sink compound (340, Dow Corning, Corp.) to a Peltier cooler, which was adhered via heat sink compound to a 9.0 x 8.5 x 5 cm aluminum block that was controlled with a 2510 TEC Sourcemeter (Keithley Instruments, Inc.).

Acknowledgments

This work was funded by the Air Force Office of Scientific Research, the Materials and Manufacturing Directorate of the Air Force Research Laboratory, and the DoD SBIR program.

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Figures (5)

Fig. 1
Fig. 1 Skeletal formulas of (a) the bis(azobenzene) chiral dopant (QL76) and (b) the non-photosensitive chiral dopant (MSB-10). (c) Schematic illustration of experimental set-up utilized to simultaneously collect transmission and reflection spectra from CLC cells irradiated with either RHCP light or LHCP laser light.
Fig. 2
Fig. 2 Reflection spectra taken as a function of exposure time of a LH CLC mixture with (a) RHCP 514 nm light and (b) LHCP 514 nm light. Plots of (c) the spectral position of the reflection peak central wavelength position as a function of time irradiated with LHCP and RHCP light and (d) the center, blue-edge, and red-edge of the reflection peak as a function of LHCP 514 nm light irradiation time. A horizontal line indicating position of radiation wavelength is included on (c) and (d) for reference. The same 8 µm LH CLC (5.7% QL76) cell was utilized to generate this data and the 514 nm LHCP/RHCP light intensity was 1.0 mW/cm2.
Fig. 3
Fig. 3 Plots of (a) the spectral position of the reflection peak central wavelength of LH CLC (4.0 wt% QL76, 8 µm) as a function of time irradiated with LHCP 514 nm light of 1.0, 2.0, and 3.0 mW/cm2 intensity. (b) Laser line/bandgap overlap duration (dwell time) of LH CLC cells (8 µm) composed with various concentrations of QL76 and irradiation with LHCP 514 nm light of 1, 2, and 3 mW/cm2 intensity. (c) The mean bandgap shift of various compositions of LH CLC cells irradiated with 3.0 mW RHCP 457, 488, and 514 nm light. (d) Plots of the spectral position of the LH CLC (5.7 wt% QL76, 8 µm) reflection peak central wavelength as a function of time irradiated with 1 mW LHCP 457, 488, and 514 nm light. Horizontal lines without symbols indicate wavelength position of the three stimulus wavelengths. Note: only the wavelength indicated in the legend was used for a particular curve.
Fig. 4
Fig. 4 (a) Mean bandgap shift as a function of temperature. (b) Duration of bandgap overlap with incident laser wavelength as a function of temperature. All experiments conducted with 4 wt% QL76 mixture in 8 µm cells exposed to 514 nm laser with an intensity of 1.0 mW/cm2. Error bars represent range of three independent measurements. Linear regression fits for data in graphs (a) and (b) had R2 values of 0.988 and 0.964 respectively.
Fig. 5
Fig. 5 (a) Reflection and transmission spectra taken from a LH CLC after increasing irradiation time with LHCP 3.0 mW/cm2 488 nm laser line. Note: data points around laser line eliminated for clarity. (b) A schematic of symmetrical tuning proposed to occur upon irradiation with transmitted RHCP light vs. asymmetrical tuning within LH CLC observed when overlap of the CLC bandgap and wavelength of LHCP light occurs. Note: Red-shift in color indicates increase in pitch length and bandgap/pump wavelength overlap occurs at Time 1.

Tables (1)

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Table 1 Composition and Properties of CLC Mixtures

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λ B =<n>/( HTP*c )
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