Abstract

A wavelength shift of the photonic band gap of 141 nm is obtained by electric switching of a partly polymerized chiral liquid crystal. The devices feature high reflectivity in the photonic band gap without any noticeable degradation or disruption and have response times of 50 µs and 20 µs for switching on and off. The device consists of a mixture of photo-polymerizable liquid crystal, non-reactive nematic liquid crystal and a chiral dopant that has been polymerized with UV light. We investigate the influence of the amplitude of the applied voltage on the width and the depth of the reflection band.

© 2014 Optical Society of America

1. Introduction

Chiral nematic liquid crystals (CLC) are well known for their spontaneous arrangement into a helical structure with periodicity of a few hundred nanometer and modulation of the refractive index profile [1]. The periodicity of a CLC, similar to a distributed Bragg reflector (DBR), possesses a 1D photonic band gap (PBG). The width of the photonic band gap is Δλ=ΔnPwith Δn = ne-no the LC birefringence and P the pitch, which is equal to the distance to reach 360° rotation of the director. The long-wavelength band-edge, λL, and short- wavelength band-edge, λS are given by neP and noP, respectively. When an unpolarized light beam is incident on the planar CLC cell along the helical axis, the circularly polarized light of the same handedness as the chiral helix is reflected while the opposite handedness can propagate unhindered [1, 2].

CLCs have been used in applications such as lasers and displays [38]. Nevertheless direct control and tuning of the PBG are of crucial importance to several emerging applications: photonic information technology, lab-on-a-chip devices, and switchable optical devices such as sensors [9], reflectors, diffraction gratings, polarizers, shutters, notch- and band-pass filters, reflective displays, mirror-less and ultralow threshold tunable lasers, and modulators. Significant efforts have been devoted to tuning of the PBG using external stimuli such as heat [1013], light [1416], elasticity [17] and electricity [1829]. Up to this point, almost all CLC devices have relatively slow switching characteristics in the order of several ms or a small tuning range which encumbers the use in practical applications. The most common technique for tuning is changing the pitch P [921]. Direct electronic control of the PBG is difficult because the periodic structure may deform non-uniformly and the Bragg reflection may be disrupted under the application of an electric field [2, 26, 29]. When an electric field is applied parallel to the helical axis, the CLC molecules (with positive dielectric anisotropy) tend to align parallel to the direction of electric field and the homogeneity of the structure is distorted [30, 31]. Helfrich has shown that the orientation pattern of cholesteric liquid crystals can be unstable in electric and magnetic fields and proposed a model for the so-called Helfrich deformation [32, 33]. In addition there can be a deterioration of the helical structure due to the presence of electro-hydrodynamic instabilities (EHDIs) at low frequencies [1, 12, 34]. The so-called focal conic structure is highly scattering and is used in certain devices such as the eReader LCDs from Kent Displays. Some researchers have used polymer-stabilized CLC to tune the PBG [23, 3542]. Yet the deterioration of the structure has remained a significant problem. Choi et al. [21] controlled the PBG by using ferroelectric liquid crystal (FLC) in CLC with a relatively large tuning range of ~101 nm but a slow response time of ~280 s. A further limitation of this method is the fact that the liquid crystalline mixtures possess negative dielectric anisotropy and therefore have a small birefringence and narrow PBG.

Choi et al. [22] have demonstrated wavelength tuning of the PBG from a hybrid structure consisting of an achiral nematic liquid crystal and a periodic polymer template. The resulting wavelength tuning is relatively fast and broadband with a response time of ~43 µs and a bandgap of ~100 nm. However only the long wavelength photonic band edge shifts to the blue, while the short band edge is fixed. In this method there is a reduction of the reflectivity in the reflection band, which makes them less suitable for some applications such as liquid crystal lasers. Recently Inoue et al. [24] fabricated a CLC laser that can be tuned continuously with a response time of less than 1 ms with a 30 nm blue shift, based on the modulation of the refractive index to control the selective reflection band. It is desirable to have a switchable PBG with fast response to electrical addressing and tuning over a broad range wavelength with high reproducibility without deformation and degradation.

In this work, a shift of the photonic band gap of up to 141 nm and response times of 50 µs (switching ON) and 20 µs (switching OFF) is reported. This method features high stability and reflectivity without any noticeable degradation and disruption. The shift is performed by applying an electric field on a mixture of photo-polymerizable LC and non-reactive nematic LC including a chiral dopant. The influence of amplitude of the applied voltage on the location of the PBG are investigated.

2. Fabrication

Chiral liquid crystal mixtures are made by dissolving a reactive LC which is a blend of different compounds from Merck, non-reactive nematic LC (MDA-00-3536, Merck) and right handed chiral dopant (BDH1305, Merck) in chloroform after stirring it for 20 minutes. The relative ratio of reactive and non-reactive LC is varied and different mixtures are prepared with non-reactive LC ranging from 40 to 60 wt%. It is possible to make devices for different operation wavelengths by selecting the appropriate chiral dopant concentration. For the results obtained in this manuscript, the concentration of chiral dopant is fixed to 3.7 wt%.

The clearing point of the mixture is close to 102°C for all the mixtures. The composite mixture is injected into an empty cell using the capillary effect in vacuum on a hot plate in the isotropic phase. The cell consists of two glass substrates with 30 nm thick conductive Indium-Tin-Oxide (ITO) electrodes, coated with a nylon layer and rubbed anti-parallel. In this way the CLC is stabilized in the planar texture with the helical axis perpendicular to the glass substrates. The empty cell is sealed with different spacers of 4, 6.75 or 8 µm. The cell is cooled to room temperature to form a homogeneous film without domains. Then the cell is exposed to 365 nm UV light for 1 minute to polymerize the CLC mixture.

After polymerization, a chiral LC polymer is formed with selective reflection of right circularly polarized light. For the compositions and UV intensities we investigated the cell remains transparent without observable scattering. This indicates that droplets of nonreactive LC formed in the cross-linked network are smaller than 50 nm. To control the behaviour of the CLC films, the concentration of nematic LC and the UV dose for curing are controlled.

3. Results and discussion

To investigate the influence of the concentration of nonreactive LC inside the network, mixtures with 40, 50 and 60 wt% of MDA concentration are used in cells with 4 µm thickness. After fabrication, the transmission spectra of the samples are measured by a spectrometer (Perkin Elmer) while applying a sine shape voltage signal of 1 kHz with 0 to 247 V/µm RMS electric field. The fabricated CLC films exhibit a broad PBG centered between 800 and 900 nm with a total bandwidth of approximately 100 nm. The blue shift of the PBG of the devices with 40-50 and 60 wt% MDA concentrations are shown in Figs. 1(a)1(c) respectively. The devices with 40 wt% nematic LC show the strongest blue shift, equal to 141 nm. Unfortunately this mixture exhibits the highest threshold voltage (90 V/µm) and suffers from electric breakdown before the saturation of the wavelength shift is observed. The sample with 50 wt% MDA shows a 114 nm blue shift, with a 65 V/µm threshold. The cell with 60 wt% MDA shows a low threshold voltage of 35 V/µm but breakdown occurs after a 48 nm shifting. Apparently the non-reactive LC exhibits a lower breakdown electric field than the polymerized components. In principle other liquid crystal materials with a higher breakdown voltage may be used, based on fluorinated compounds which typically exhibit a lower ionic content. In principle a higher concentration of nematic LC causes more and larger voids inside the polymer network which facilitates the reorientation of the nematic LC. This leads to the lowest threshold in the device with 60 wt% MDA. The shift of the long band edge wavelength of the PBG as a function of the applied electric field for devices with 40, 50 and 60 wt% MDA concentration is shown in Fig. 1(d). It illustrates that the shift is continuous and the degree of modulation of the device with 40 wt% MDA concentration is larger than the others. Note that the IR absorption in Figs. 1(a) and 1(c) is slightly higher due to thicker ITO electrodes (200 nm) compared to Fig. 1(b) (30 nm).

 

Fig. 1 Transmission spectra for unpolarized light, a) 40 wt%, b) 50 wt% and c) 60 wt% MDA concentration for different applied electrical fields. d) Shifting of the long band edge position of the photonic band gap as a function of the applied electric field for mixtures with 40, 50 and 60 wt% MDA concentration.

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In order to rule out polarization dependencies of the spectrometer, the transmission measurements have been performed for right handed circularly polarized light, that is produced with a linear polarizer and a zero order quarter wave plate at 850 nm. The transmission spectra of 4 samples with 50 wt% MDA and 4 µm thickness in Fig. 2 illustrate the reproducibility of the procedure.

 

Fig. 2 Transmission spectra of 4 devices with 50 wt% MDA and 4 µm thickness, for right handed circularly polarized light.

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Obtaining high reflectivity and low transmittance in the bandgap is essential for an effective distributed Bragg reflector. The theory of light propagation in CLC can be found in different books [43]. Equation (1) gives the reflectance for a CLC layer with thickness L for normal incidence when absorption and partial reflections at the interface with the substrate can be neglected:

R=|κ|2sinh2sLs2cosh2sL+(Δk2)2sinh2sL
Where:
κ=π(ne2no2)λ2(ne2+no2)
k=2πλne2+no22
Δk=2k4πp
s2=κ2(Δk2)2
ne and no are the extra-ordinary and ordinary refractive indices of the liquid crystal and p is the pitch. The transmission is simply T = 1- R. At the center of the PBG, ∆k = 0 and the reflectance is maximum:
R=tanh2κL
High reflectivity can be obtained by increasing the anisotropy and the thickness of the CLC. Figure 3(a) shows the simulated transmission for samples with 4 µm thickness and different birefringence values. Figure 3(b) shows the simulated transmission of samples with ∆n = 0.163 and different thicknesses. The reflectivity within the PBG increases with increasing thickness or increasing birefringence. A fit of the measurement results with the theoretical curves reveals that the polymerized mixture has a birefringence of 0.16.

 

Fig. 3 Simulated transmission spectra for right handed polarized light for a) cells with 4 µm thickness and 3 different values of the birefringence; b) cells with ∆n = 0.163 and different thicknesses (the dotted line is a measured transmission spectrum).

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To avoid electric breakdown for strong electric fields and to achieve low transmission in the reflection band, the thickness of the cells is increased to 6.75 and 8 µm. Figure 4 shows the transmission spectra for a thickness of 8 µm for right handed circularly polarized light. As a figure of merit we define the contrast ratio as the ratio between the transmission for zero volt and for a high voltage for a certain wavelength. The contrast ratio is 16.5 and 21.5 respectively for 6.75 and 8 µm thickness. This value is larger than the contrast ratio of 9 of the device with 4 µm thickness.

 

Fig. 4 Transmission spectra for right handed polarized light for devices with 50 wt% MDA and 8 µm thickness, for different applied electrical fields.

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The transmission in the center of the PBG is practically independent of the applied electric field and the width of the photonic band gap is only slightly reduced. This proves that the uniform helical order is maintained. The transmission in the PBG of samples with 8 µm thickness is reduced with respect to the 4 µm samples, but not as much as expected from the theoretical calculations shown in Fig. 3(b): the measured transmission in the middle of the PBG is 3.55%, while the theoretical estimation is below 0.01%. To understand this mismatch, the Stokes parameters of the transmitted light for linearly polarized incident light (equal amounts of RH and LH polarization) are measured for a wavelength near the center of the bandgap [44]. The Stokes parameters for samples with 4 µm and 8 µm thicknesses are shown in Table 1. S0 represents the total intensity and is normalized to 1. The Stokes parameters S1, S2 and S3 are obtained using the method described by Xie et al. [44] The degree of polarization p follows fromp2=S12+S22+S32. The ellipticity angle χ is determined from sin2χ = S3/p and the result is 33.2° and 42.9° for the samples with 4 µm and 8 µm thickness respectively. The transmitted light for the thinner (4 µm) sample has a high degree of polarization (0.988) but the ellipticity angle deviates strongly from 45°, indicating that there is also an important transmission of right handed circularly polarized light. This is in agreement with the experiments of Fig. 2 and the simulation of Fig. 3(b). For the thicker (8 µm) sample the transmitted light is mainly circularly polarized (S3), but the degree of polarization is decreased to 0.958 which means there is an important contribution from scattered light.

Tables Icon

Table 1. Stokes parameters of the transmission of linearly polarized light with a wavelength near the band center.

A CLC reflector with a 1 × 1 cm2 active region with band gap in the visible region is placed on a black sheet of paper which the word ‘Mohammad’ in white colour. Figure 5 shows the photographs of the device with and without applied electric field. This shows that the field-tuning of the PBG keeps good transmission for white light without scattering in the visible region which is usually not the case for polymer-CLC composites [23].

 

Fig. 5 A macroscopic photograph of a CLC orange reflector with 1 × 1 cm2 active region placed on a black sheet on which the word Mohammad is printed, a) without and b) with applied electric field.

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To explain the blue-shift of both the right and the left band edge one has to consider the fact that light at the right band edge is traveling through the medium with an electric field vector aligned along the director of the helix. Light with a wavelength at the left band edge is traveling with an electric field vector perpendicular to the director. This explains why the right and left band edges are located at neP and noP respectively. The blue shift means that the refractive indices ne and no both decrease with increasing applied voltage. The orientation of the nematic LC inside the voids is initially random as shown in Fig. 6(a), contributing with the average refractive index navgLC to the ne and the no of the mixture. By applying an electric field, the nematic LC inside the voids is oriented and aligned parallel to the electric field due to the positive dielectric anisotropy of the material. In this case only the ordinary refractive index of the liquid crystal noLC contributes and both refractive indices of the mixture decrease. As the pitch is fixed by the polymer template, and the refractive index decreases, the photonic band edges both shift to the blue and the reflected colour changes. By removing the electric field, everything returns to its original state.

 

Fig. 6 Scheme of the pattern with a polymerized CLC network and dispersed nano droplets with nematic LC a) without b) with applying electric field.

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Figure 6 illustrates the switching of the liquid crystal under influence of an electric field. The response time of the device with 50 wt% MDA, 8 µm thickness and long band edge of 870 nm is measured with a microscope (Nikon, eclipse,E400 POL), 850 nm light emitting diodes for the illumination and a silicon photodiode for the detection. When the voltage is off, the transmission is low as shown in Fig. 7, because the wavelength is inside the PBG. When applying a voltage, the nematic LC orients perpendicular to the substrates and the photonic band gap shifts to smaller wavelengths. The wavelength of 850 nm is now above the PBG and right circularly polarized light is strongly reflected. The 10–90% response times are 50 µs and 20 µs for respectively turning on and off, when switching between zero voltage and a block wave voltage signal with amplitude 150 V/µm and frequency 1 kHz. These switching times are drastically shorter than in previously reported work [21, 22, 24].

 

Fig. 7 Electrical response of the 50 wt% MDA device with 8 µm thickness for an block wave electric field with amplitude 150 V/µm and frequency 1 kHz.

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It should be noted that the device does not switch anymore for frequencies larger than 10 kHz. It is found that this is due to speed limitations of the voltage amplifier. The slew rate of the amplifier (Trek model 50/750) is 125 V/µs which limits the driving frequency. The slew rate of the amplifier also explains the fact that the switching off time is shorter than the switching on time.

4. Conclusions

In conclusion, we have demonstrated a wide and fast shifting of the photonic band gap of a mixture of photo-polymerizable LC and nematic LC including a chiral dopant assisted by applying an alternative electric field. The wavelength tuning has been shown to be maximum 141 nm with relatively high stability and reflectivity and without any noticeable degradation and disruption. The response time is 50 µs and 20 µs for turning on and off an electric field, respectively.

Acknowledgments

This research was supported by the Interuniversity Attraction Poles program of the Belgian Science Policy Office, under grant IAP P7-35 «photonics@be»

References and links

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9. S. Kado, Y. Takeshima, Y. Nakahara, and K. Kimura, “Potassium-ion-selective sensing based on selective reflection of cholesteric liquid crystal membranes,” J. Incl. Phenom. Macrocycl. Chem. 72(1-2), 227–232 (2012). [CrossRef]  

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References

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  1. P. G. De Gennes, The Physics of Liquid Crystals (Clarendon, 1974).
  2. D. K. Yang, J. L. West, L. C. Chien, and J. W. Doane, “Control of reflectivity and bistability in displays using cholesteric liquid crystals,” J. Appl. Phys. 76(2), 1331–1333 (1994).
    [CrossRef]
  3. V. A. Belyakov, “Low threshold DFB lasing at the edge and defect modes in chiral liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 488(1), 279–308 (2008).
    [CrossRef]
  4. A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
    [CrossRef]
  5. H. Shirvani-Mahdavi, E. Mohajerani, and S. T. Wu, “Circularly polarized high-efficiency cholesteric liquid crystal lasers with a tunable nematic phase retarder,” Opt. Express 18(5), 5021–5027 (2010).
    [CrossRef] [PubMed]
  6. A. D. Ford, S. M. Morris, and H. J. Coles, “Phototonics and lasing in liquid crystals,” Mater. Today 9(7-8), 36–42 (2006).
    [CrossRef]
  7. L. Penninck, J. Beeckman, P. De Visschere, and K. Neyts, “Numerical simulation of stimulated emission and lasing in dye doped cholesteric liquid crystal films,” J. Appl. Phys. 113(6), 063106 (2013).
    [CrossRef]
  8. Y. Inoue, H. Yoshida, K. Inoue, A. Fujii, and M. Ozaki, “Improved lasing threshold of cholesteric liquid crystal lasers with In-Plane Helix Alignment,” Jpn. J. Appl. Phys. 3, 102702 (2010).
  9. S. Kado, Y. Takeshima, Y. Nakahara, and K. Kimura, “Potassium-ion-selective sensing based on selective reflection of cholesteric liquid crystal membranes,” J. Incl. Phenom. Macrocycl. Chem. 72(1-2), 227–232 (2012).
    [CrossRef]
  10. Y. H. Huang, Y. Zhou, C. Doyle, and S. T. Wu, “Tuning the photonic band gap in cholesteric liquid crystals by temperature-dependent dopant solubility,” Opt. Express 14(3), 1236–1242 (2006).
    [CrossRef] [PubMed]
  11. K. Funamoto, M. Ozaki, and K. Yoshino, “Discontinuous shift of lasing wavelength with temperature in cholesteric liquid crystal,” Jpn. J. Appl.Phys. Part 2 Lett 42(Part 2, No. 12B), L1523–L1525 (2003).
    [CrossRef]
  12. L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008).
    [CrossRef]
  13. S. Furumi and N. Tamaoki, “Glass-Forming Cholesteric Liquid Crystal Oligomers for New Tunable Solid-State Laser,” Adv. Mater. 22(8), 886–891 (2010).
    [CrossRef] [PubMed]
  14. S. Kurihara, Y. Hatae, T. Yoshioka, M. Moritsugu, T. Ogata, and T. Nonaka, “Photo-tuning of lasing from a dye-doped cholesteric liquid crystals by photoisomerization of a sugar derivative having plural azobenzene groups,” Appl. Phys. Lett. 88(10), 103121 (2006).
    [CrossRef]
  15. G. S. Chilaya, “Light-controlled change in the helical pitch and broadband tunable cholesteric liquid-crystal lasers,” Crystallogr. Rep. 51(S1), S108–S118 (2006).
    [CrossRef]
  16. T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
    [CrossRef]
  17. H. Finkelmann, S. T. Kim, A. Munoz, P. Palffy-Muhoray, and B. Taheri, “Tunable mirrorless lasing in cholesteric liquid crystalline elastomers,” Adv. Mater. 13(14), 1069–1072 (2001).
    [CrossRef]
  18. H. P. Yu, B. Y. Tang, J. H. Li, and L. Li, “Electrically tunable lasers made from electro-optically active photonics band gap materials,” Opt. Express 13(18), 7243–7249 (2005).
    [CrossRef] [PubMed]
  19. Y. Inoue, Y. Matsuhisa, H. Yoshida, R. Ozaki, H. Moritake, A. Fujii, and M. Ozaki, “Electric field dependence of lasing wavelength in cholesteric liquid crystal with an in-plane helix alignment,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 516(1), 182–189 (2010).
    [CrossRef]
  20. H. Yoshida, Y. Inoue, T. Isomura, Y. Matsuhisa, A. Fujii, and M. Ozaki, “Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment,” Appl. Phys. Lett. 94(9), 093306 (2009).
    [CrossRef]
  21. S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Electrically tuneable liquid crystal photonic bandgaps,” Adv. Mater. 21(38–39), 3915–3918 (2009).
    [CrossRef]
  22. S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Simultaneous red-green-blue reflection and wavelength tuning from an achiral liquid crystal and a polymer template,” Adv. Mater. 22(1), 53–56 (2010).
    [CrossRef] [PubMed]
  23. B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
    [CrossRef]
  24. Y. Inoue, H. Yoshida, K. Inoue, Y. Shiozaki, H. Kubo, A. Fujii, and M. Ozaki, “Tunable lasing from a cholesteric liquid crystal film embedded with a liquid crystal nanopore network,” Adv. Mater. 23(46), 5498–5501 (2011).
    [CrossRef] [PubMed]
  25. B. W. Liu, Z. G. Zheng, X. C. Chen, and D. Shen, “Low-voltage-modulated laser based on dye-doped polymer stabilized cholesteric liquid crystal,” Opt. Mater. Express 3(4), 519–526 (2013).
    [CrossRef]
  26. J. Schmidtke, G. Junnemann, S. Keuker-Baumann, and H. S. Kitzerow, “Electrical fine tuning of liquid crystal lasers,” Appl. Phys. Lett. 101(5), 051117 (2012).
    [CrossRef]
  27. C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
    [CrossRef]
  28. S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “The switching properties of chiral nematic liquid crystals using electrically commanded surfaces,” Soft Matter 5(2), 354–362 (2009).
    [CrossRef]
  29. S. Furumi, S. Yokoyama, A. Otomo, and S. Mashiko, “Control of photonic bandgaps in chiral liquid crystals for distributed feedback effect,” Thin Solid Films 499(1-2), 322–328 (2006).
    [CrossRef]
  30. M. Kawachi and O. Kogure, “Hysteresis behavior of texture in field-induced nematic-cholesteric relaxation,” Jpn. J. Appl. Phys. 16(9), 1673–1678 (1977).
    [CrossRef]
  31. F. J. Kahn, “Electric-field-induced color changes and pitch dilation in cholesteric liquid crystals,” Phys. Rev. Lett. 24(5), 209–212 (1970).
    [CrossRef]
  32. W. Helfrich, “Electrohydrodynamic and dielectric instabilities of cholesteric liquid crystals,” J. Chem. Phys. 55(2), 839–842 (1971).
    [CrossRef]
  33. W. Helfrich, “Deformation of cholesteric liquid crystals with low threshold voltage,” Appl. Phys. Lett. 17(12), 531–532 (1970).
    [CrossRef]
  34. T. H. Lin, H. C. Jau, C. H. Chen, Y. J. Chen, T. H. Wei, C. W. Chen, and A. Y. G. Fuh, “Electrically controllable laser based on cholesteric liquid crystal with negative dielectric anisotropy,” Appl. Phys. Lett. 88(6), 061122 (2006).
    [CrossRef]
  35. R. A. M. Hikmet and H. Kemperman, “Electrically switchable mirrors and optical components made from liquid-crystal gels,” Nature 392(6675), 476–479 (1998).
    [CrossRef]
  36. R. A. M. Hikmet and H. Kemperman, “Switchable mirrors of chiral liquid crystal gels,” Liq. Cryst. 26(11), 1645–1653 (1999).
    [CrossRef]
  37. A. Bobrovsky and V. Shibaev, “Novel type of combined photopatternable and electro-switchable polymer-stabilized cholesteric materials,” J. Mater. Chem. 19(3), 366–372 (2008).
    [CrossRef]
  38. J. Chen, S. M. Morris, T. D. Wilkinson, and H. J. Coles, “Reversible color switching from blue to red in a polymer stabilized chiral nematic liquid crystals,” Appl. Phys. Lett. 91(12), 121118 (2007).
    [CrossRef]
  39. M. Mitov, E. Nouvet, and N. Dessaud, “Polymer-stabilized cholesteric liquid crystals as switchable photonic broad bandgaps,” Eur Phys J E Soft Matter 15(4), 413–419 (2004).
    [CrossRef] [PubMed]
  40. K. G. Kang, L. C. Chien, and S. Sprunt, “Polymer-stabilized cholesteric liquid crystal microgratings: a comparison of polymer network formation and electro-optic properties for mesogenic and non-mesogenic monomers,” Liq. Cryst. 29(1), 9–18 (2002).
    [CrossRef]
  41. M. E. McConney, V. P. Tondiglia, L. V. Natarajan, K. M. Lee, T. J. White, and T. J. Bunning, “Electrically induced color changes in polymer-stabilized cholesteric liquid crystals,” Adv. Opt. Mater. 1(6), 417–421 (2013).
    [CrossRef]
  42. S.-Y. Lu and L.-C. Chien, “A polymer-stabilized single-layer color cholesteric liquid crystal display with anisotropic reflection,” Appl. Phys. Lett. 91(13), 131119 (2007).
    [CrossRef]
  43. T. Scharf, Polarized Light in Liquid Crystals and Polymers (John Wiley, 2007).
  44. X. Yi, J. Beeckman, W. Woestenborghs, K. Panajotov, and K. Neyts, “VCSEL with photo-aligned liquid crystal overlay,” IEEE Photon. Technol. Lett. 24(17), 1509–1512 (2012).
    [CrossRef]

2013 (3)

L. Penninck, J. Beeckman, P. De Visschere, and K. Neyts, “Numerical simulation of stimulated emission and lasing in dye doped cholesteric liquid crystal films,” J. Appl. Phys. 113(6), 063106 (2013).
[CrossRef]

B. W. Liu, Z. G. Zheng, X. C. Chen, and D. Shen, “Low-voltage-modulated laser based on dye-doped polymer stabilized cholesteric liquid crystal,” Opt. Mater. Express 3(4), 519–526 (2013).
[CrossRef]

M. E. McConney, V. P. Tondiglia, L. V. Natarajan, K. M. Lee, T. J. White, and T. J. Bunning, “Electrically induced color changes in polymer-stabilized cholesteric liquid crystals,” Adv. Opt. Mater. 1(6), 417–421 (2013).
[CrossRef]

2012 (3)

X. Yi, J. Beeckman, W. Woestenborghs, K. Panajotov, and K. Neyts, “VCSEL with photo-aligned liquid crystal overlay,” IEEE Photon. Technol. Lett. 24(17), 1509–1512 (2012).
[CrossRef]

J. Schmidtke, G. Junnemann, S. Keuker-Baumann, and H. S. Kitzerow, “Electrical fine tuning of liquid crystal lasers,” Appl. Phys. Lett. 101(5), 051117 (2012).
[CrossRef]

S. Kado, Y. Takeshima, Y. Nakahara, and K. Kimura, “Potassium-ion-selective sensing based on selective reflection of cholesteric liquid crystal membranes,” J. Incl. Phenom. Macrocycl. Chem. 72(1-2), 227–232 (2012).
[CrossRef]

2011 (1)

Y. Inoue, H. Yoshida, K. Inoue, Y. Shiozaki, H. Kubo, A. Fujii, and M. Ozaki, “Tunable lasing from a cholesteric liquid crystal film embedded with a liquid crystal nanopore network,” Adv. Mater. 23(46), 5498–5501 (2011).
[CrossRef] [PubMed]

2010 (7)

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Simultaneous red-green-blue reflection and wavelength tuning from an achiral liquid crystal and a polymer template,” Adv. Mater. 22(1), 53–56 (2010).
[CrossRef] [PubMed]

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

Y. Inoue, H. Yoshida, K. Inoue, A. Fujii, and M. Ozaki, “Improved lasing threshold of cholesteric liquid crystal lasers with In-Plane Helix Alignment,” Jpn. J. Appl. Phys. 3, 102702 (2010).

H. Shirvani-Mahdavi, E. Mohajerani, and S. T. Wu, “Circularly polarized high-efficiency cholesteric liquid crystal lasers with a tunable nematic phase retarder,” Opt. Express 18(5), 5021–5027 (2010).
[CrossRef] [PubMed]

S. Furumi and N. Tamaoki, “Glass-Forming Cholesteric Liquid Crystal Oligomers for New Tunable Solid-State Laser,” Adv. Mater. 22(8), 886–891 (2010).
[CrossRef] [PubMed]

T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
[CrossRef]

Y. Inoue, Y. Matsuhisa, H. Yoshida, R. Ozaki, H. Moritake, A. Fujii, and M. Ozaki, “Electric field dependence of lasing wavelength in cholesteric liquid crystal with an in-plane helix alignment,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 516(1), 182–189 (2010).
[CrossRef]

2009 (4)

H. Yoshida, Y. Inoue, T. Isomura, Y. Matsuhisa, A. Fujii, and M. Ozaki, “Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment,” Appl. Phys. Lett. 94(9), 093306 (2009).
[CrossRef]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Electrically tuneable liquid crystal photonic bandgaps,” Adv. Mater. 21(38–39), 3915–3918 (2009).
[CrossRef]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “The switching properties of chiral nematic liquid crystals using electrically commanded surfaces,” Soft Matter 5(2), 354–362 (2009).
[CrossRef]

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

2008 (3)

A. Bobrovsky and V. Shibaev, “Novel type of combined photopatternable and electro-switchable polymer-stabilized cholesteric materials,” J. Mater. Chem. 19(3), 366–372 (2008).
[CrossRef]

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008).
[CrossRef]

V. A. Belyakov, “Low threshold DFB lasing at the edge and defect modes in chiral liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 488(1), 279–308 (2008).
[CrossRef]

2007 (2)

J. Chen, S. M. Morris, T. D. Wilkinson, and H. J. Coles, “Reversible color switching from blue to red in a polymer stabilized chiral nematic liquid crystals,” Appl. Phys. Lett. 91(12), 121118 (2007).
[CrossRef]

S.-Y. Lu and L.-C. Chien, “A polymer-stabilized single-layer color cholesteric liquid crystal display with anisotropic reflection,” Appl. Phys. Lett. 91(13), 131119 (2007).
[CrossRef]

2006 (6)

T. H. Lin, H. C. Jau, C. H. Chen, Y. J. Chen, T. H. Wei, C. W. Chen, and A. Y. G. Fuh, “Electrically controllable laser based on cholesteric liquid crystal with negative dielectric anisotropy,” Appl. Phys. Lett. 88(6), 061122 (2006).
[CrossRef]

S. Furumi, S. Yokoyama, A. Otomo, and S. Mashiko, “Control of photonic bandgaps in chiral liquid crystals for distributed feedback effect,” Thin Solid Films 499(1-2), 322–328 (2006).
[CrossRef]

A. D. Ford, S. M. Morris, and H. J. Coles, “Phototonics and lasing in liquid crystals,” Mater. Today 9(7-8), 36–42 (2006).
[CrossRef]

Y. H. Huang, Y. Zhou, C. Doyle, and S. T. Wu, “Tuning the photonic band gap in cholesteric liquid crystals by temperature-dependent dopant solubility,” Opt. Express 14(3), 1236–1242 (2006).
[CrossRef] [PubMed]

S. Kurihara, Y. Hatae, T. Yoshioka, M. Moritsugu, T. Ogata, and T. Nonaka, “Photo-tuning of lasing from a dye-doped cholesteric liquid crystals by photoisomerization of a sugar derivative having plural azobenzene groups,” Appl. Phys. Lett. 88(10), 103121 (2006).
[CrossRef]

G. S. Chilaya, “Light-controlled change in the helical pitch and broadband tunable cholesteric liquid-crystal lasers,” Crystallogr. Rep. 51(S1), S108–S118 (2006).
[CrossRef]

2005 (1)

2004 (2)

M. Mitov, E. Nouvet, and N. Dessaud, “Polymer-stabilized cholesteric liquid crystals as switchable photonic broad bandgaps,” Eur Phys J E Soft Matter 15(4), 413–419 (2004).
[CrossRef] [PubMed]

A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
[CrossRef]

2003 (1)

K. Funamoto, M. Ozaki, and K. Yoshino, “Discontinuous shift of lasing wavelength with temperature in cholesteric liquid crystal,” Jpn. J. Appl.Phys. Part 2 Lett 42(Part 2, No. 12B), L1523–L1525 (2003).
[CrossRef]

2002 (1)

K. G. Kang, L. C. Chien, and S. Sprunt, “Polymer-stabilized cholesteric liquid crystal microgratings: a comparison of polymer network formation and electro-optic properties for mesogenic and non-mesogenic monomers,” Liq. Cryst. 29(1), 9–18 (2002).
[CrossRef]

2001 (1)

H. Finkelmann, S. T. Kim, A. Munoz, P. Palffy-Muhoray, and B. Taheri, “Tunable mirrorless lasing in cholesteric liquid crystalline elastomers,” Adv. Mater. 13(14), 1069–1072 (2001).
[CrossRef]

1999 (1)

R. A. M. Hikmet and H. Kemperman, “Switchable mirrors of chiral liquid crystal gels,” Liq. Cryst. 26(11), 1645–1653 (1999).
[CrossRef]

1998 (1)

R. A. M. Hikmet and H. Kemperman, “Electrically switchable mirrors and optical components made from liquid-crystal gels,” Nature 392(6675), 476–479 (1998).
[CrossRef]

1994 (1)

D. K. Yang, J. L. West, L. C. Chien, and J. W. Doane, “Control of reflectivity and bistability in displays using cholesteric liquid crystals,” J. Appl. Phys. 76(2), 1331–1333 (1994).
[CrossRef]

1977 (1)

M. Kawachi and O. Kogure, “Hysteresis behavior of texture in field-induced nematic-cholesteric relaxation,” Jpn. J. Appl. Phys. 16(9), 1673–1678 (1977).
[CrossRef]

1971 (1)

W. Helfrich, “Electrohydrodynamic and dielectric instabilities of cholesteric liquid crystals,” J. Chem. Phys. 55(2), 839–842 (1971).
[CrossRef]

1970 (2)

W. Helfrich, “Deformation of cholesteric liquid crystals with low threshold voltage,” Appl. Phys. Lett. 17(12), 531–532 (1970).
[CrossRef]

F. J. Kahn, “Electric-field-induced color changes and pitch dilation in cholesteric liquid crystals,” Phys. Rev. Lett. 24(5), 209–212 (1970).
[CrossRef]

Bailey, C.

T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
[CrossRef]

Bailey, C. A.

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

Barberi, R.

A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
[CrossRef]

Bartolino, R.

A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
[CrossRef]

Beeckman, J.

L. Penninck, J. Beeckman, P. De Visschere, and K. Neyts, “Numerical simulation of stimulated emission and lasing in dye doped cholesteric liquid crystal films,” J. Appl. Phys. 113(6), 063106 (2013).
[CrossRef]

X. Yi, J. Beeckman, W. Woestenborghs, K. Panajotov, and K. Neyts, “VCSEL with photo-aligned liquid crystal overlay,” IEEE Photon. Technol. Lett. 24(17), 1509–1512 (2012).
[CrossRef]

Belyakov, V. A.

V. A. Belyakov, “Low threshold DFB lasing at the edge and defect modes in chiral liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 488(1), 279–308 (2008).
[CrossRef]

Bobrovsky, A.

A. Bobrovsky and V. Shibaev, “Novel type of combined photopatternable and electro-switchable polymer-stabilized cholesteric materials,” J. Mater. Chem. 19(3), 366–372 (2008).
[CrossRef]

Bricker, R. L.

T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
[CrossRef]

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

Bunning, T. J.

M. E. McConney, V. P. Tondiglia, L. V. Natarajan, K. M. Lee, T. J. White, and T. J. Bunning, “Electrically induced color changes in polymer-stabilized cholesteric liquid crystals,” Adv. Opt. Mater. 1(6), 417–421 (2013).
[CrossRef]

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
[CrossRef]

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008).
[CrossRef]

Chanishvili, A.

A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
[CrossRef]

Chen, C. H.

T. H. Lin, H. C. Jau, C. H. Chen, Y. J. Chen, T. H. Wei, C. W. Chen, and A. Y. G. Fuh, “Electrically controllable laser based on cholesteric liquid crystal with negative dielectric anisotropy,” Appl. Phys. Lett. 88(6), 061122 (2006).
[CrossRef]

Chen, C. W.

T. H. Lin, H. C. Jau, C. H. Chen, Y. J. Chen, T. H. Wei, C. W. Chen, and A. Y. G. Fuh, “Electrically controllable laser based on cholesteric liquid crystal with negative dielectric anisotropy,” Appl. Phys. Lett. 88(6), 061122 (2006).
[CrossRef]

Chen, J.

J. Chen, S. M. Morris, T. D. Wilkinson, and H. J. Coles, “Reversible color switching from blue to red in a polymer stabilized chiral nematic liquid crystals,” Appl. Phys. Lett. 91(12), 121118 (2007).
[CrossRef]

Chen, X. C.

Chen, Y. J.

T. H. Lin, H. C. Jau, C. H. Chen, Y. J. Chen, T. H. Wei, C. W. Chen, and A. Y. G. Fuh, “Electrically controllable laser based on cholesteric liquid crystal with negative dielectric anisotropy,” Appl. Phys. Lett. 88(6), 061122 (2006).
[CrossRef]

Chien, L. C.

K. G. Kang, L. C. Chien, and S. Sprunt, “Polymer-stabilized cholesteric liquid crystal microgratings: a comparison of polymer network formation and electro-optic properties for mesogenic and non-mesogenic monomers,” Liq. Cryst. 29(1), 9–18 (2002).
[CrossRef]

D. K. Yang, J. L. West, L. C. Chien, and J. W. Doane, “Control of reflectivity and bistability in displays using cholesteric liquid crystals,” J. Appl. Phys. 76(2), 1331–1333 (1994).
[CrossRef]

Chien, L.-C.

S.-Y. Lu and L.-C. Chien, “A polymer-stabilized single-layer color cholesteric liquid crystal display with anisotropic reflection,” Appl. Phys. Lett. 91(13), 131119 (2007).
[CrossRef]

Chilaya, G.

A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
[CrossRef]

Chilaya, G. S.

G. S. Chilaya, “Light-controlled change in the helical pitch and broadband tunable cholesteric liquid-crystal lasers,” Crystallogr. Rep. 51(S1), S108–S118 (2006).
[CrossRef]

Cho, G. S.

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Choi, E. H.

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Choi, S. S.

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Simultaneous red-green-blue reflection and wavelength tuning from an achiral liquid crystal and a polymer template,” Adv. Mater. 22(1), 53–56 (2010).
[CrossRef] [PubMed]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Electrically tuneable liquid crystal photonic bandgaps,” Adv. Mater. 21(38–39), 3915–3918 (2009).
[CrossRef]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “The switching properties of chiral nematic liquid crystals using electrically commanded surfaces,” Soft Matter 5(2), 354–362 (2009).
[CrossRef]

Cipparrone, G.

A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
[CrossRef]

Coles, H. J.

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Simultaneous red-green-blue reflection and wavelength tuning from an achiral liquid crystal and a polymer template,” Adv. Mater. 22(1), 53–56 (2010).
[CrossRef] [PubMed]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Electrically tuneable liquid crystal photonic bandgaps,” Adv. Mater. 21(38–39), 3915–3918 (2009).
[CrossRef]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “The switching properties of chiral nematic liquid crystals using electrically commanded surfaces,” Soft Matter 5(2), 354–362 (2009).
[CrossRef]

J. Chen, S. M. Morris, T. D. Wilkinson, and H. J. Coles, “Reversible color switching from blue to red in a polymer stabilized chiral nematic liquid crystals,” Appl. Phys. Lett. 91(12), 121118 (2007).
[CrossRef]

A. D. Ford, S. M. Morris, and H. J. Coles, “Phototonics and lasing in liquid crystals,” Mater. Today 9(7-8), 36–42 (2006).
[CrossRef]

De Visschere, P.

L. Penninck, J. Beeckman, P. De Visschere, and K. Neyts, “Numerical simulation of stimulated emission and lasing in dye doped cholesteric liquid crystal films,” J. Appl. Phys. 113(6), 063106 (2013).
[CrossRef]

Dessaud, N.

M. Mitov, E. Nouvet, and N. Dessaud, “Polymer-stabilized cholesteric liquid crystals as switchable photonic broad bandgaps,” Eur Phys J E Soft Matter 15(4), 413–419 (2004).
[CrossRef] [PubMed]

Doane, J. W.

D. K. Yang, J. L. West, L. C. Chien, and J. W. Doane, “Control of reflectivity and bistability in displays using cholesteric liquid crystals,” J. Appl. Phys. 76(2), 1331–1333 (1994).
[CrossRef]

Doyle, C.

Duning, M. M.

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

Durstock, M. F.

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

Finkelmann, H.

H. Finkelmann, S. T. Kim, A. Munoz, P. Palffy-Muhoray, and B. Taheri, “Tunable mirrorless lasing in cholesteric liquid crystalline elastomers,” Adv. Mater. 13(14), 1069–1072 (2001).
[CrossRef]

Ford, A. D.

A. D. Ford, S. M. Morris, and H. J. Coles, “Phototonics and lasing in liquid crystals,” Mater. Today 9(7-8), 36–42 (2006).
[CrossRef]

Fuh, A. Y. G.

T. H. Lin, H. C. Jau, C. H. Chen, Y. J. Chen, T. H. Wei, C. W. Chen, and A. Y. G. Fuh, “Electrically controllable laser based on cholesteric liquid crystal with negative dielectric anisotropy,” Appl. Phys. Lett. 88(6), 061122 (2006).
[CrossRef]

Fujii, A.

Y. Inoue, H. Yoshida, K. Inoue, Y. Shiozaki, H. Kubo, A. Fujii, and M. Ozaki, “Tunable lasing from a cholesteric liquid crystal film embedded with a liquid crystal nanopore network,” Adv. Mater. 23(46), 5498–5501 (2011).
[CrossRef] [PubMed]

Y. Inoue, Y. Matsuhisa, H. Yoshida, R. Ozaki, H. Moritake, A. Fujii, and M. Ozaki, “Electric field dependence of lasing wavelength in cholesteric liquid crystal with an in-plane helix alignment,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 516(1), 182–189 (2010).
[CrossRef]

Y. Inoue, H. Yoshida, K. Inoue, A. Fujii, and M. Ozaki, “Improved lasing threshold of cholesteric liquid crystal lasers with In-Plane Helix Alignment,” Jpn. J. Appl. Phys. 3, 102702 (2010).

H. Yoshida, Y. Inoue, T. Isomura, Y. Matsuhisa, A. Fujii, and M. Ozaki, “Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment,” Appl. Phys. Lett. 94(9), 093306 (2009).
[CrossRef]

Funamoto, K.

K. Funamoto, M. Ozaki, and K. Yoshino, “Discontinuous shift of lasing wavelength with temperature in cholesteric liquid crystal,” Jpn. J. Appl.Phys. Part 2 Lett 42(Part 2, No. 12B), L1523–L1525 (2003).
[CrossRef]

Furumi, S.

S. Furumi and N. Tamaoki, “Glass-Forming Cholesteric Liquid Crystal Oligomers for New Tunable Solid-State Laser,” Adv. Mater. 22(8), 886–891 (2010).
[CrossRef] [PubMed]

S. Furumi, S. Yokoyama, A. Otomo, and S. Mashiko, “Control of photonic bandgaps in chiral liquid crystals for distributed feedback effect,” Thin Solid Films 499(1-2), 322–328 (2006).
[CrossRef]

Green, L.

T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
[CrossRef]

Hatae, Y.

S. Kurihara, Y. Hatae, T. Yoshioka, M. Moritsugu, T. Ogata, and T. Nonaka, “Photo-tuning of lasing from a dye-doped cholesteric liquid crystals by photoisomerization of a sugar derivative having plural azobenzene groups,” Appl. Phys. Lett. 88(10), 103121 (2006).
[CrossRef]

Helfrich, W.

W. Helfrich, “Electrohydrodynamic and dielectric instabilities of cholesteric liquid crystals,” J. Chem. Phys. 55(2), 839–842 (1971).
[CrossRef]

W. Helfrich, “Deformation of cholesteric liquid crystals with low threshold voltage,” Appl. Phys. Lett. 17(12), 531–532 (1970).
[CrossRef]

Hikmet, R. A. M.

R. A. M. Hikmet and H. Kemperman, “Switchable mirrors of chiral liquid crystal gels,” Liq. Cryst. 26(11), 1645–1653 (1999).
[CrossRef]

R. A. M. Hikmet and H. Kemperman, “Electrically switchable mirrors and optical components made from liquid-crystal gels,” Nature 392(6675), 476–479 (1998).
[CrossRef]

Huang, Y. H.

Huck, W. T. S.

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Simultaneous red-green-blue reflection and wavelength tuning from an achiral liquid crystal and a polymer template,” Adv. Mater. 22(1), 53–56 (2010).
[CrossRef] [PubMed]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Electrically tuneable liquid crystal photonic bandgaps,” Adv. Mater. 21(38–39), 3915–3918 (2009).
[CrossRef]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “The switching properties of chiral nematic liquid crystals using electrically commanded surfaces,” Soft Matter 5(2), 354–362 (2009).
[CrossRef]

Inoue, K.

Y. Inoue, H. Yoshida, K. Inoue, Y. Shiozaki, H. Kubo, A. Fujii, and M. Ozaki, “Tunable lasing from a cholesteric liquid crystal film embedded with a liquid crystal nanopore network,” Adv. Mater. 23(46), 5498–5501 (2011).
[CrossRef] [PubMed]

Y. Inoue, H. Yoshida, K. Inoue, A. Fujii, and M. Ozaki, “Improved lasing threshold of cholesteric liquid crystal lasers with In-Plane Helix Alignment,” Jpn. J. Appl. Phys. 3, 102702 (2010).

Inoue, Y.

Y. Inoue, H. Yoshida, K. Inoue, Y. Shiozaki, H. Kubo, A. Fujii, and M. Ozaki, “Tunable lasing from a cholesteric liquid crystal film embedded with a liquid crystal nanopore network,” Adv. Mater. 23(46), 5498–5501 (2011).
[CrossRef] [PubMed]

Y. Inoue, H. Yoshida, K. Inoue, A. Fujii, and M. Ozaki, “Improved lasing threshold of cholesteric liquid crystal lasers with In-Plane Helix Alignment,” Jpn. J. Appl. Phys. 3, 102702 (2010).

Y. Inoue, Y. Matsuhisa, H. Yoshida, R. Ozaki, H. Moritake, A. Fujii, and M. Ozaki, “Electric field dependence of lasing wavelength in cholesteric liquid crystal with an in-plane helix alignment,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 516(1), 182–189 (2010).
[CrossRef]

H. Yoshida, Y. Inoue, T. Isomura, Y. Matsuhisa, A. Fujii, and M. Ozaki, “Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment,” Appl. Phys. Lett. 94(9), 093306 (2009).
[CrossRef]

Isomura, T.

H. Yoshida, Y. Inoue, T. Isomura, Y. Matsuhisa, A. Fujii, and M. Ozaki, “Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment,” Appl. Phys. Lett. 94(9), 093306 (2009).
[CrossRef]

Jang, W.

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Jau, H. C.

T. H. Lin, H. C. Jau, C. H. Chen, Y. J. Chen, T. H. Wei, C. W. Chen, and A. Y. G. Fuh, “Electrically controllable laser based on cholesteric liquid crystal with negative dielectric anisotropy,” Appl. Phys. Lett. 88(6), 061122 (2006).
[CrossRef]

Junnemann, G.

J. Schmidtke, G. Junnemann, S. Keuker-Baumann, and H. S. Kitzerow, “Electrical fine tuning of liquid crystal lasers,” Appl. Phys. Lett. 101(5), 051117 (2012).
[CrossRef]

Kado, S.

S. Kado, Y. Takeshima, Y. Nakahara, and K. Kimura, “Potassium-ion-selective sensing based on selective reflection of cholesteric liquid crystal membranes,” J. Incl. Phenom. Macrocycl. Chem. 72(1-2), 227–232 (2012).
[CrossRef]

Kahn, F. J.

F. J. Kahn, “Electric-field-induced color changes and pitch dilation in cholesteric liquid crystals,” Phys. Rev. Lett. 24(5), 209–212 (1970).
[CrossRef]

Kang, K. G.

K. G. Kang, L. C. Chien, and S. Sprunt, “Polymer-stabilized cholesteric liquid crystal microgratings: a comparison of polymer network formation and electro-optic properties for mesogenic and non-mesogenic monomers,” Liq. Cryst. 29(1), 9–18 (2002).
[CrossRef]

Kawachi, M.

M. Kawachi and O. Kogure, “Hysteresis behavior of texture in field-induced nematic-cholesteric relaxation,” Jpn. J. Appl. Phys. 16(9), 1673–1678 (1977).
[CrossRef]

Kemperman, H.

R. A. M. Hikmet and H. Kemperman, “Switchable mirrors of chiral liquid crystal gels,” Liq. Cryst. 26(11), 1645–1653 (1999).
[CrossRef]

R. A. M. Hikmet and H. Kemperman, “Electrically switchable mirrors and optical components made from liquid-crystal gels,” Nature 392(6675), 476–479 (1998).
[CrossRef]

Keuker-Baumann, S.

J. Schmidtke, G. Junnemann, S. Keuker-Baumann, and H. S. Kitzerow, “Electrical fine tuning of liquid crystal lasers,” Appl. Phys. Lett. 101(5), 051117 (2012).
[CrossRef]

Kim, M.

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Kim, S. T.

H. Finkelmann, S. T. Kim, A. Munoz, P. Palffy-Muhoray, and B. Taheri, “Tunable mirrorless lasing in cholesteric liquid crystalline elastomers,” Adv. Mater. 13(14), 1069–1072 (2001).
[CrossRef]

Kim, S. W.

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Kim, Y.

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Kimura, K.

S. Kado, Y. Takeshima, Y. Nakahara, and K. Kimura, “Potassium-ion-selective sensing based on selective reflection of cholesteric liquid crystal membranes,” J. Incl. Phenom. Macrocycl. Chem. 72(1-2), 227–232 (2012).
[CrossRef]

Kitzerow, H. S.

J. Schmidtke, G. Junnemann, S. Keuker-Baumann, and H. S. Kitzerow, “Electrical fine tuning of liquid crystal lasers,” Appl. Phys. Lett. 101(5), 051117 (2012).
[CrossRef]

Koerner, H.

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008).
[CrossRef]

Kogure, O.

M. Kawachi and O. Kogure, “Hysteresis behavior of texture in field-induced nematic-cholesteric relaxation,” Jpn. J. Appl. Phys. 16(9), 1673–1678 (1977).
[CrossRef]

Kong, S. O.

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Kubo, H.

Y. Inoue, H. Yoshida, K. Inoue, Y. Shiozaki, H. Kubo, A. Fujii, and M. Ozaki, “Tunable lasing from a cholesteric liquid crystal film embedded with a liquid crystal nanopore network,” Adv. Mater. 23(46), 5498–5501 (2011).
[CrossRef] [PubMed]

Kurihara, S.

S. Kurihara, Y. Hatae, T. Yoshioka, M. Moritsugu, T. Ogata, and T. Nonaka, “Photo-tuning of lasing from a dye-doped cholesteric liquid crystals by photoisomerization of a sugar derivative having plural azobenzene groups,” Appl. Phys. Lett. 88(10), 103121 (2006).
[CrossRef]

Lee, K. M.

M. E. McConney, V. P. Tondiglia, L. V. Natarajan, K. M. Lee, T. J. White, and T. J. Bunning, “Electrically induced color changes in polymer-stabilized cholesteric liquid crystals,” Adv. Opt. Mater. 1(6), 417–421 (2013).
[CrossRef]

Li, J. H.

Li, L.

Li, Q. A.

T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
[CrossRef]

Lin, T. H.

T. H. Lin, H. C. Jau, C. H. Chen, Y. J. Chen, T. H. Wei, C. W. Chen, and A. Y. G. Fuh, “Electrically controllable laser based on cholesteric liquid crystal with negative dielectric anisotropy,” Appl. Phys. Lett. 88(6), 061122 (2006).
[CrossRef]

Liu, B. W.

Lu, S.-Y.

S.-Y. Lu and L.-C. Chien, “A polymer-stabilized single-layer color cholesteric liquid crystal display with anisotropic reflection,” Appl. Phys. Lett. 91(13), 131119 (2007).
[CrossRef]

Mashiko, S.

S. Furumi, S. Yokoyama, A. Otomo, and S. Mashiko, “Control of photonic bandgaps in chiral liquid crystals for distributed feedback effect,” Thin Solid Films 499(1-2), 322–328 (2006).
[CrossRef]

Matsuhisa, Y.

Y. Inoue, Y. Matsuhisa, H. Yoshida, R. Ozaki, H. Moritake, A. Fujii, and M. Ozaki, “Electric field dependence of lasing wavelength in cholesteric liquid crystal with an in-plane helix alignment,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 516(1), 182–189 (2010).
[CrossRef]

H. Yoshida, Y. Inoue, T. Isomura, Y. Matsuhisa, A. Fujii, and M. Ozaki, “Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment,” Appl. Phys. Lett. 94(9), 093306 (2009).
[CrossRef]

Mazzulla, A.

A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
[CrossRef]

McConney, M. E.

M. E. McConney, V. P. Tondiglia, L. V. Natarajan, K. M. Lee, T. J. White, and T. J. Bunning, “Electrically induced color changes in polymer-stabilized cholesteric liquid crystals,” Adv. Opt. Mater. 1(6), 417–421 (2013).
[CrossRef]

Mitov, M.

M. Mitov, E. Nouvet, and N. Dessaud, “Polymer-stabilized cholesteric liquid crystals as switchable photonic broad bandgaps,” Eur Phys J E Soft Matter 15(4), 413–419 (2004).
[CrossRef] [PubMed]

Mohajerani, E.

Moritake, H.

Y. Inoue, Y. Matsuhisa, H. Yoshida, R. Ozaki, H. Moritake, A. Fujii, and M. Ozaki, “Electric field dependence of lasing wavelength in cholesteric liquid crystal with an in-plane helix alignment,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 516(1), 182–189 (2010).
[CrossRef]

Moritsugu, M.

S. Kurihara, Y. Hatae, T. Yoshioka, M. Moritsugu, T. Ogata, and T. Nonaka, “Photo-tuning of lasing from a dye-doped cholesteric liquid crystals by photoisomerization of a sugar derivative having plural azobenzene groups,” Appl. Phys. Lett. 88(10), 103121 (2006).
[CrossRef]

Morris, S. M.

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Simultaneous red-green-blue reflection and wavelength tuning from an achiral liquid crystal and a polymer template,” Adv. Mater. 22(1), 53–56 (2010).
[CrossRef] [PubMed]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Electrically tuneable liquid crystal photonic bandgaps,” Adv. Mater. 21(38–39), 3915–3918 (2009).
[CrossRef]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “The switching properties of chiral nematic liquid crystals using electrically commanded surfaces,” Soft Matter 5(2), 354–362 (2009).
[CrossRef]

J. Chen, S. M. Morris, T. D. Wilkinson, and H. J. Coles, “Reversible color switching from blue to red in a polymer stabilized chiral nematic liquid crystals,” Appl. Phys. Lett. 91(12), 121118 (2007).
[CrossRef]

A. D. Ford, S. M. Morris, and H. J. Coles, “Phototonics and lasing in liquid crystals,” Mater. Today 9(7-8), 36–42 (2006).
[CrossRef]

Munoz, A.

H. Finkelmann, S. T. Kim, A. Munoz, P. Palffy-Muhoray, and B. Taheri, “Tunable mirrorless lasing in cholesteric liquid crystalline elastomers,” Adv. Mater. 13(14), 1069–1072 (2001).
[CrossRef]

Nakahara, Y.

S. Kado, Y. Takeshima, Y. Nakahara, and K. Kimura, “Potassium-ion-selective sensing based on selective reflection of cholesteric liquid crystal membranes,” J. Incl. Phenom. Macrocycl. Chem. 72(1-2), 227–232 (2012).
[CrossRef]

Natarajan, L. V.

M. E. McConney, V. P. Tondiglia, L. V. Natarajan, K. M. Lee, T. J. White, and T. J. Bunning, “Electrically induced color changes in polymer-stabilized cholesteric liquid crystals,” Adv. Opt. Mater. 1(6), 417–421 (2013).
[CrossRef]

T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
[CrossRef]

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008).
[CrossRef]

Neyts, K.

L. Penninck, J. Beeckman, P. De Visschere, and K. Neyts, “Numerical simulation of stimulated emission and lasing in dye doped cholesteric liquid crystal films,” J. Appl. Phys. 113(6), 063106 (2013).
[CrossRef]

X. Yi, J. Beeckman, W. Woestenborghs, K. Panajotov, and K. Neyts, “VCSEL with photo-aligned liquid crystal overlay,” IEEE Photon. Technol. Lett. 24(17), 1509–1512 (2012).
[CrossRef]

Nonaka, T.

S. Kurihara, Y. Hatae, T. Yoshioka, M. Moritsugu, T. Ogata, and T. Nonaka, “Photo-tuning of lasing from a dye-doped cholesteric liquid crystals by photoisomerization of a sugar derivative having plural azobenzene groups,” Appl. Phys. Lett. 88(10), 103121 (2006).
[CrossRef]

Nouvet, E.

M. Mitov, E. Nouvet, and N. Dessaud, “Polymer-stabilized cholesteric liquid crystals as switchable photonic broad bandgaps,” Eur Phys J E Soft Matter 15(4), 413–419 (2004).
[CrossRef] [PubMed]

Ogata, T.

S. Kurihara, Y. Hatae, T. Yoshioka, M. Moritsugu, T. Ogata, and T. Nonaka, “Photo-tuning of lasing from a dye-doped cholesteric liquid crystals by photoisomerization of a sugar derivative having plural azobenzene groups,” Appl. Phys. Lett. 88(10), 103121 (2006).
[CrossRef]

Oriol, L.

A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
[CrossRef]

Otomo, A.

S. Furumi, S. Yokoyama, A. Otomo, and S. Mashiko, “Control of photonic bandgaps in chiral liquid crystals for distributed feedback effect,” Thin Solid Films 499(1-2), 322–328 (2006).
[CrossRef]

Ozaki, M.

Y. Inoue, H. Yoshida, K. Inoue, Y. Shiozaki, H. Kubo, A. Fujii, and M. Ozaki, “Tunable lasing from a cholesteric liquid crystal film embedded with a liquid crystal nanopore network,” Adv. Mater. 23(46), 5498–5501 (2011).
[CrossRef] [PubMed]

Y. Inoue, Y. Matsuhisa, H. Yoshida, R. Ozaki, H. Moritake, A. Fujii, and M. Ozaki, “Electric field dependence of lasing wavelength in cholesteric liquid crystal with an in-plane helix alignment,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 516(1), 182–189 (2010).
[CrossRef]

Y. Inoue, H. Yoshida, K. Inoue, A. Fujii, and M. Ozaki, “Improved lasing threshold of cholesteric liquid crystal lasers with In-Plane Helix Alignment,” Jpn. J. Appl. Phys. 3, 102702 (2010).

H. Yoshida, Y. Inoue, T. Isomura, Y. Matsuhisa, A. Fujii, and M. Ozaki, “Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment,” Appl. Phys. Lett. 94(9), 093306 (2009).
[CrossRef]

K. Funamoto, M. Ozaki, and K. Yoshino, “Discontinuous shift of lasing wavelength with temperature in cholesteric liquid crystal,” Jpn. J. Appl.Phys. Part 2 Lett 42(Part 2, No. 12B), L1523–L1525 (2003).
[CrossRef]

Ozaki, R.

Y. Inoue, Y. Matsuhisa, H. Yoshida, R. Ozaki, H. Moritake, A. Fujii, and M. Ozaki, “Electric field dependence of lasing wavelength in cholesteric liquid crystal with an in-plane helix alignment,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 516(1), 182–189 (2010).
[CrossRef]

Palffy-Muhoray, P.

H. Finkelmann, S. T. Kim, A. Munoz, P. Palffy-Muhoray, and B. Taheri, “Tunable mirrorless lasing in cholesteric liquid crystalline elastomers,” Adv. Mater. 13(14), 1069–1072 (2001).
[CrossRef]

Panajotov, K.

X. Yi, J. Beeckman, W. Woestenborghs, K. Panajotov, and K. Neyts, “VCSEL with photo-aligned liquid crystal overlay,” IEEE Photon. Technol. Lett. 24(17), 1509–1512 (2012).
[CrossRef]

Park, B.

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Penninck, L.

L. Penninck, J. Beeckman, P. De Visschere, and K. Neyts, “Numerical simulation of stimulated emission and lasing in dye doped cholesteric liquid crystal films,” J. Appl. Phys. 113(6), 063106 (2013).
[CrossRef]

Petriashvili, G.

A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
[CrossRef]

Schmidtke, J.

J. Schmidtke, G. Junnemann, S. Keuker-Baumann, and H. S. Kitzerow, “Electrical fine tuning of liquid crystal lasers,” Appl. Phys. Lett. 101(5), 051117 (2012).
[CrossRef]

Seo, Y. H.

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Shen, D.

Shibaev, V.

A. Bobrovsky and V. Shibaev, “Novel type of combined photopatternable and electro-switchable polymer-stabilized cholesteric materials,” J. Mater. Chem. 19(3), 366–372 (2008).
[CrossRef]

Shiozaki, Y.

Y. Inoue, H. Yoshida, K. Inoue, Y. Shiozaki, H. Kubo, A. Fujii, and M. Ozaki, “Tunable lasing from a cholesteric liquid crystal film embedded with a liquid crystal nanopore network,” Adv. Mater. 23(46), 5498–5501 (2011).
[CrossRef] [PubMed]

Shirvani-Mahdavi, H.

Sprunt, S.

K. G. Kang, L. C. Chien, and S. Sprunt, “Polymer-stabilized cholesteric liquid crystal microgratings: a comparison of polymer network formation and electro-optic properties for mesogenic and non-mesogenic monomers,” Liq. Cryst. 29(1), 9–18 (2002).
[CrossRef]

Sutherland, R. L.

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008).
[CrossRef]

Taheri, B.

H. Finkelmann, S. T. Kim, A. Munoz, P. Palffy-Muhoray, and B. Taheri, “Tunable mirrorless lasing in cholesteric liquid crystalline elastomers,” Adv. Mater. 13(14), 1069–1072 (2001).
[CrossRef]

Takeshima, Y.

S. Kado, Y. Takeshima, Y. Nakahara, and K. Kimura, “Potassium-ion-selective sensing based on selective reflection of cholesteric liquid crystal membranes,” J. Incl. Phenom. Macrocycl. Chem. 72(1-2), 227–232 (2012).
[CrossRef]

Takezoe, H.

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Tamaoki, N.

S. Furumi and N. Tamaoki, “Glass-Forming Cholesteric Liquid Crystal Oligomers for New Tunable Solid-State Laser,” Adv. Mater. 22(8), 886–891 (2010).
[CrossRef] [PubMed]

Tang, B. Y.

Tondiglia, V. P.

M. E. McConney, V. P. Tondiglia, L. V. Natarajan, K. M. Lee, T. J. White, and T. J. Bunning, “Electrically induced color changes in polymer-stabilized cholesteric liquid crystals,” Adv. Opt. Mater. 1(6), 417–421 (2013).
[CrossRef]

T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
[CrossRef]

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008).
[CrossRef]

Vaia, R. A.

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008).
[CrossRef]

Wei, T. H.

T. H. Lin, H. C. Jau, C. H. Chen, Y. J. Chen, T. H. Wei, C. W. Chen, and A. Y. G. Fuh, “Electrically controllable laser based on cholesteric liquid crystal with negative dielectric anisotropy,” Appl. Phys. Lett. 88(6), 061122 (2006).
[CrossRef]

West, J. L.

D. K. Yang, J. L. West, L. C. Chien, and J. W. Doane, “Control of reflectivity and bistability in displays using cholesteric liquid crystals,” J. Appl. Phys. 76(2), 1331–1333 (1994).
[CrossRef]

White, T. J.

M. E. McConney, V. P. Tondiglia, L. V. Natarajan, K. M. Lee, T. J. White, and T. J. Bunning, “Electrically induced color changes in polymer-stabilized cholesteric liquid crystals,” Adv. Opt. Mater. 1(6), 417–421 (2013).
[CrossRef]

T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
[CrossRef]

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

Wilkinson, T. D.

J. Chen, S. M. Morris, T. D. Wilkinson, and H. J. Coles, “Reversible color switching from blue to red in a polymer stabilized chiral nematic liquid crystals,” Appl. Phys. Lett. 91(12), 121118 (2007).
[CrossRef]

Woestenborghs, W.

X. Yi, J. Beeckman, W. Woestenborghs, K. Panajotov, and K. Neyts, “VCSEL with photo-aligned liquid crystal overlay,” IEEE Photon. Technol. Lett. 24(17), 1509–1512 (2012).
[CrossRef]

Wofford, J. M.

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008).
[CrossRef]

Wu, S. T.

Yang, D. K.

D. K. Yang, J. L. West, L. C. Chien, and J. W. Doane, “Control of reflectivity and bistability in displays using cholesteric liquid crystals,” J. Appl. Phys. 76(2), 1331–1333 (1994).
[CrossRef]

Yi, X.

X. Yi, J. Beeckman, W. Woestenborghs, K. Panajotov, and K. Neyts, “VCSEL with photo-aligned liquid crystal overlay,” IEEE Photon. Technol. Lett. 24(17), 1509–1512 (2012).
[CrossRef]

Yokoyama, S.

S. Furumi, S. Yokoyama, A. Otomo, and S. Mashiko, “Control of photonic bandgaps in chiral liquid crystals for distributed feedback effect,” Thin Solid Films 499(1-2), 322–328 (2006).
[CrossRef]

Yoshida, H.

Y. Inoue, H. Yoshida, K. Inoue, Y. Shiozaki, H. Kubo, A. Fujii, and M. Ozaki, “Tunable lasing from a cholesteric liquid crystal film embedded with a liquid crystal nanopore network,” Adv. Mater. 23(46), 5498–5501 (2011).
[CrossRef] [PubMed]

Y. Inoue, H. Yoshida, K. Inoue, A. Fujii, and M. Ozaki, “Improved lasing threshold of cholesteric liquid crystal lasers with In-Plane Helix Alignment,” Jpn. J. Appl. Phys. 3, 102702 (2010).

Y. Inoue, Y. Matsuhisa, H. Yoshida, R. Ozaki, H. Moritake, A. Fujii, and M. Ozaki, “Electric field dependence of lasing wavelength in cholesteric liquid crystal with an in-plane helix alignment,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 516(1), 182–189 (2010).
[CrossRef]

H. Yoshida, Y. Inoue, T. Isomura, Y. Matsuhisa, A. Fujii, and M. Ozaki, “Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment,” Appl. Phys. Lett. 94(9), 093306 (2009).
[CrossRef]

Yoshino, K.

K. Funamoto, M. Ozaki, and K. Yoshino, “Discontinuous shift of lasing wavelength with temperature in cholesteric liquid crystal,” Jpn. J. Appl.Phys. Part 2 Lett 42(Part 2, No. 12B), L1523–L1525 (2003).
[CrossRef]

Yoshioka, T.

S. Kurihara, Y. Hatae, T. Yoshioka, M. Moritsugu, T. Ogata, and T. Nonaka, “Photo-tuning of lasing from a dye-doped cholesteric liquid crystals by photoisomerization of a sugar derivative having plural azobenzene groups,” Appl. Phys. Lett. 88(10), 103121 (2006).
[CrossRef]

Yu, H. P.

Zheng, Z. G.

Zhou, Y.

Adv. Mater. (7)

A. Chanishvili, G. Chilaya, G. Petriashvili, R. Barberi, R. Bartolino, G. Cipparrone, A. Mazzulla, and L. Oriol, “Lasing in dye-doped cholesteric liquid crystals: two new tuning strategies,” Adv. Mater. 16(910), 791–795 (2004).
[CrossRef]

S. Furumi and N. Tamaoki, “Glass-Forming Cholesteric Liquid Crystal Oligomers for New Tunable Solid-State Laser,” Adv. Mater. 22(8), 886–891 (2010).
[CrossRef] [PubMed]

H. Finkelmann, S. T. Kim, A. Munoz, P. Palffy-Muhoray, and B. Taheri, “Tunable mirrorless lasing in cholesteric liquid crystalline elastomers,” Adv. Mater. 13(14), 1069–1072 (2001).
[CrossRef]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Electrically tuneable liquid crystal photonic bandgaps,” Adv. Mater. 21(38–39), 3915–3918 (2009).
[CrossRef]

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Simultaneous red-green-blue reflection and wavelength tuning from an achiral liquid crystal and a polymer template,” Adv. Mater. 22(1), 53–56 (2010).
[CrossRef] [PubMed]

B. Park, M. Kim, S. W. Kim, W. Jang, H. Takezoe, Y. Kim, E. H. Choi, Y. H. Seo, G. S. Cho, and S. O. Kong, “Electrically controllable omnidirectional laser emission from a helical-Polymer network composite film,” Adv. Mater. 21(7), 771–775 (2009).
[CrossRef]

Y. Inoue, H. Yoshida, K. Inoue, Y. Shiozaki, H. Kubo, A. Fujii, and M. Ozaki, “Tunable lasing from a cholesteric liquid crystal film embedded with a liquid crystal nanopore network,” Adv. Mater. 23(46), 5498–5501 (2011).
[CrossRef] [PubMed]

Adv. Opt. Mater. (1)

M. E. McConney, V. P. Tondiglia, L. V. Natarajan, K. M. Lee, T. J. White, and T. J. Bunning, “Electrically induced color changes in polymer-stabilized cholesteric liquid crystals,” Adv. Opt. Mater. 1(6), 417–421 (2013).
[CrossRef]

Appl. Phys. Lett. (7)

S.-Y. Lu and L.-C. Chien, “A polymer-stabilized single-layer color cholesteric liquid crystal display with anisotropic reflection,” Appl. Phys. Lett. 91(13), 131119 (2007).
[CrossRef]

J. Chen, S. M. Morris, T. D. Wilkinson, and H. J. Coles, “Reversible color switching from blue to red in a polymer stabilized chiral nematic liquid crystals,” Appl. Phys. Lett. 91(12), 121118 (2007).
[CrossRef]

H. Yoshida, Y. Inoue, T. Isomura, Y. Matsuhisa, A. Fujii, and M. Ozaki, “Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment,” Appl. Phys. Lett. 94(9), 093306 (2009).
[CrossRef]

J. Schmidtke, G. Junnemann, S. Keuker-Baumann, and H. S. Kitzerow, “Electrical fine tuning of liquid crystal lasers,” Appl. Phys. Lett. 101(5), 051117 (2012).
[CrossRef]

W. Helfrich, “Deformation of cholesteric liquid crystals with low threshold voltage,” Appl. Phys. Lett. 17(12), 531–532 (1970).
[CrossRef]

T. H. Lin, H. C. Jau, C. H. Chen, Y. J. Chen, T. H. Wei, C. W. Chen, and A. Y. G. Fuh, “Electrically controllable laser based on cholesteric liquid crystal with negative dielectric anisotropy,” Appl. Phys. Lett. 88(6), 061122 (2006).
[CrossRef]

S. Kurihara, Y. Hatae, T. Yoshioka, M. Moritsugu, T. Ogata, and T. Nonaka, “Photo-tuning of lasing from a dye-doped cholesteric liquid crystals by photoisomerization of a sugar derivative having plural azobenzene groups,” Appl. Phys. Lett. 88(10), 103121 (2006).
[CrossRef]

Crystallogr. Rep. (1)

G. S. Chilaya, “Light-controlled change in the helical pitch and broadband tunable cholesteric liquid-crystal lasers,” Crystallogr. Rep. 51(S1), S108–S118 (2006).
[CrossRef]

Eur Phys J E Soft Matter (1)

M. Mitov, E. Nouvet, and N. Dessaud, “Polymer-stabilized cholesteric liquid crystals as switchable photonic broad bandgaps,” Eur Phys J E Soft Matter 15(4), 413–419 (2004).
[CrossRef] [PubMed]

IEEE Photon. Technol. Lett. (1)

X. Yi, J. Beeckman, W. Woestenborghs, K. Panajotov, and K. Neyts, “VCSEL with photo-aligned liquid crystal overlay,” IEEE Photon. Technol. Lett. 24(17), 1509–1512 (2012).
[CrossRef]

J. Appl. Phys. (4)

L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, H. Koerner, R. A. Vaia, and T. J. Bunning, “Electro-thermal tuning in a negative dielectric cholesteric liquid crystal material,” J. Appl. Phys. 103(9), 093107 (2008).
[CrossRef]

D. K. Yang, J. L. West, L. C. Chien, and J. W. Doane, “Control of reflectivity and bistability in displays using cholesteric liquid crystals,” J. Appl. Phys. 76(2), 1331–1333 (1994).
[CrossRef]

L. Penninck, J. Beeckman, P. De Visschere, and K. Neyts, “Numerical simulation of stimulated emission and lasing in dye doped cholesteric liquid crystal films,” J. Appl. Phys. 113(6), 063106 (2013).
[CrossRef]

C. A. Bailey, V. P. Tondiglia, L. V. Natarajan, M. M. Duning, R. L. Bricker, R. L. Sutherland, T. J. White, M. F. Durstock, and T. J. Bunning, “Electromechanical tuning of cholesteric liquid crystals,” J. Appl. Phys. 107(1), 013105 (2010).
[CrossRef]

J. Chem. Phys. (1)

W. Helfrich, “Electrohydrodynamic and dielectric instabilities of cholesteric liquid crystals,” J. Chem. Phys. 55(2), 839–842 (1971).
[CrossRef]

J. Incl. Phenom. Macrocycl. Chem. (1)

S. Kado, Y. Takeshima, Y. Nakahara, and K. Kimura, “Potassium-ion-selective sensing based on selective reflection of cholesteric liquid crystal membranes,” J. Incl. Phenom. Macrocycl. Chem. 72(1-2), 227–232 (2012).
[CrossRef]

J. Mater. Chem. (1)

A. Bobrovsky and V. Shibaev, “Novel type of combined photopatternable and electro-switchable polymer-stabilized cholesteric materials,” J. Mater. Chem. 19(3), 366–372 (2008).
[CrossRef]

Jpn. J. Appl. Phys. (2)

Y. Inoue, H. Yoshida, K. Inoue, A. Fujii, and M. Ozaki, “Improved lasing threshold of cholesteric liquid crystal lasers with In-Plane Helix Alignment,” Jpn. J. Appl. Phys. 3, 102702 (2010).

M. Kawachi and O. Kogure, “Hysteresis behavior of texture in field-induced nematic-cholesteric relaxation,” Jpn. J. Appl. Phys. 16(9), 1673–1678 (1977).
[CrossRef]

Jpn. J. Appl.Phys. Part 2 Lett (1)

K. Funamoto, M. Ozaki, and K. Yoshino, “Discontinuous shift of lasing wavelength with temperature in cholesteric liquid crystal,” Jpn. J. Appl.Phys. Part 2 Lett 42(Part 2, No. 12B), L1523–L1525 (2003).
[CrossRef]

Liq. Cryst. (2)

R. A. M. Hikmet and H. Kemperman, “Switchable mirrors of chiral liquid crystal gels,” Liq. Cryst. 26(11), 1645–1653 (1999).
[CrossRef]

K. G. Kang, L. C. Chien, and S. Sprunt, “Polymer-stabilized cholesteric liquid crystal microgratings: a comparison of polymer network formation and electro-optic properties for mesogenic and non-mesogenic monomers,” Liq. Cryst. 29(1), 9–18 (2002).
[CrossRef]

Mater. Today (1)

A. D. Ford, S. M. Morris, and H. J. Coles, “Phototonics and lasing in liquid crystals,” Mater. Today 9(7-8), 36–42 (2006).
[CrossRef]

Mol. Cryst. Liq. Cryst. (Phila. Pa.) (2)

V. A. Belyakov, “Low threshold DFB lasing at the edge and defect modes in chiral liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 488(1), 279–308 (2008).
[CrossRef]

Y. Inoue, Y. Matsuhisa, H. Yoshida, R. Ozaki, H. Moritake, A. Fujii, and M. Ozaki, “Electric field dependence of lasing wavelength in cholesteric liquid crystal with an in-plane helix alignment,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 516(1), 182–189 (2010).
[CrossRef]

Nature (1)

R. A. M. Hikmet and H. Kemperman, “Electrically switchable mirrors and optical components made from liquid-crystal gels,” Nature 392(6675), 476–479 (1998).
[CrossRef]

Opt. Commun. (1)

T. J. White, R. L. Bricker, L. V. Natarajan, V. P. Tondiglia, C. Bailey, L. Green, Q. A. Li, and T. J. Bunning, “Electromechanical and light tunable cholesteric liquid crystals,” Opt. Commun. 283(18), 3434–3436 (2010).
[CrossRef]

Opt. Express (3)

Opt. Mater. Express (1)

Phys. Rev. Lett. (1)

F. J. Kahn, “Electric-field-induced color changes and pitch dilation in cholesteric liquid crystals,” Phys. Rev. Lett. 24(5), 209–212 (1970).
[CrossRef]

Soft Matter (1)

S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “The switching properties of chiral nematic liquid crystals using electrically commanded surfaces,” Soft Matter 5(2), 354–362 (2009).
[CrossRef]

Thin Solid Films (1)

S. Furumi, S. Yokoyama, A. Otomo, and S. Mashiko, “Control of photonic bandgaps in chiral liquid crystals for distributed feedback effect,” Thin Solid Films 499(1-2), 322–328 (2006).
[CrossRef]

Other (2)

P. G. De Gennes, The Physics of Liquid Crystals (Clarendon, 1974).

T. Scharf, Polarized Light in Liquid Crystals and Polymers (John Wiley, 2007).

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Figures (7)

Fig. 1
Fig. 1

Transmission spectra for unpolarized light, a) 40 wt%, b) 50 wt% and c) 60 wt% MDA concentration for different applied electrical fields. d) Shifting of the long band edge position of the photonic band gap as a function of the applied electric field for mixtures with 40, 50 and 60 wt% MDA concentration.

Fig. 2
Fig. 2

Transmission spectra of 4 devices with 50 wt% MDA and 4 µm thickness, for right handed circularly polarized light.

Fig. 3
Fig. 3

Simulated transmission spectra for right handed polarized light for a) cells with 4 µm thickness and 3 different values of the birefringence; b) cells with ∆n = 0.163 and different thicknesses (the dotted line is a measured transmission spectrum).

Fig. 4
Fig. 4

Transmission spectra for right handed polarized light for devices with 50 wt% MDA and 8 µm thickness, for different applied electrical fields.

Fig. 5
Fig. 5

A macroscopic photograph of a CLC orange reflector with 1 × 1 cm2 active region placed on a black sheet on which the word Mohammad is printed, a) without and b) with applied electric field.

Fig. 6
Fig. 6

Scheme of the pattern with a polymerized CLC network and dispersed nano droplets with nematic LC a) without b) with applying electric field.

Fig. 7
Fig. 7

Electrical response of the 50 wt% MDA device with 8 µm thickness for an block wave electric field with amplitude 150 V/µm and frequency 1 kHz.

Tables (1)

Tables Icon

Table 1 Stokes parameters of the transmission of linearly polarized light with a wavelength near the band center.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

R= | κ | 2 sin h 2 sL s 2 cos h 2 sL+ ( Δk 2 ) 2 sin h 2 sL
κ= π( n e 2 n o 2 ) λ 2( n e 2 + n o 2 )
k= 2π λ n e 2 + n o 2 2
Δk=2k 4π p
s 2 = κ 2 ( Δk 2 ) 2
R = tan h 2 κL

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