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Abstract
We introduce an optically controllable color filter model using bi-layered CLC structure. From mathematical parameter sweep analysis using 4×4 matrix method, wavelength controls of red, green, and blue optical color filters and tailored tuning of optical purity in terms of FWHM from 105 nm down to 21 nm at green colored position were confirmed. In addition, an improved color gamut of optical color filters up to 162% of sRGB space in CIE 1931 was first reported. Facile design of custom color filter with controlled wavelength and FWHM, along with enhanced color gamut, can be used for various optical applications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The influence of optical sensing devices has grown drastically over recent decades [1–8]. The progress in optical sensing technology has been driven by the increasing demands of optical sensing applications, such as image sensors [9], thermal infrared detecting devices [10], and ultrasound imaging devices [11]. An image sensor is a representative optical sensing device that converts external image information into a digitized signal and is conventionally composed of a micro-lens, a photodiode, and a color filter [12]. Major characteristics of the image sensor including resolution, color purity, and signal-to-noise ratio are dominantly determined by the characteristics of the color filter [13–15]. This is due to the color filter selectively controlling the flow of light entering the optical sensor dependent on its wavelength. In recent years, many optical color filter applications have been investigated: pigment-dye based color filters [16], dielectric color filters [17], and plasmonic color filters [18,19]. The dielectric color filters that exploit structural color provide many benefits over traditional pigment-dye based color filters, yielding high color purity, robustness, and environmental friendliness [20,21]. A promising dielectric filter candidate is chiral liquid crystal (CLC).
A periodic helical structure of CLC can be spontaneously arranged by doping chiral molecules into achiral nematic liquid crystals (NLCs). As a result, CLC selectively reflects the circularly polarized light which has the same handedness as the helical structure and the wavelength λ corresponding to nop < λ < nep, where no and ne are refractive indices of the ordinary and extraordinary ray, and p is the pitch of the helical structure [22,23]. Photonic bandgap (PBG), where selective reflection happens in CLC, can be controlled by modifying the principal parameters, helical pitch p and birefringence Δn = ne - no. The helical pitch p can be simply manipulated by adjusting the weight concentration of the chiral dopant c because p can be defined as
where β is the helical twisting power of the chiral molecule [24]. This enables control over the wavelength position and bandwidth of PBG. Birefringence Δn is determined by the molecular structure of the achiral NLC material. Furthermore, PBG formed by the helical structure of CLC can be easily tuned through various external stimuli.These optical benefits have led to CLC being studied extensively for diverse applications, such as display [25,26], low-threshold lasing [27–32], and anti-counterfeiting technologies [20,33,34]. Especially, CLC can be approached as various stimulus-responsive sensors owing to its intrinsic properties of soft matter. The helical molecular arrangements in CLC can be altered by numerous external stimuli such as light [35–38], temperature [39–45], mechanical deformation [46–48], electric field [49–54], chemical gas [55–58], pH change [59–61], humidity [62–64], and bio-molecules [65–67]. In particular, when PBG of CLC is located and tuned in accordance with the visible spectrum, vivid color change can be observed even with the naked eyes, so it can be used as a visible stimulus-responsive sensor. More recently, by using CLC elastomer so-called chiral photonic gels, a tensile/pressure sensor beyond optical sensors [68] and electro-mechanic optical system of electrically stretchable chiral photonic gels [69] were suggested.
Optical filters using the peculiar reflection characteristics of CLC have been also widely explored. For instance, many researchers have devised optical notch filters and bandpass filters that are essential for optical communications and signal processing technologies using single or bi-layered CLC [70–72]. As another example, polarization independent optical filters stacking double CLC layers were reported [73]. CLC color filters that improved the angular dependency, which could be the weak point of standing helix of CLC [74], or used it as a tunable factor were investigated [75]. Moreover, tunable CLC filters have been studied by applying external stimulation of several kinds [76–78]. It should be noted, however, that most of the color control in CLC has been limited to using selectively reflected light rather than transmissive light. In fact, light-transmitting color of conventional color filter is based on an absorption band and is different from that of the CLC color filter based on selective reflection. Therefore, obtaining a transmissive CLC color filter with high optical quality requires an in-depth discussion on the implementation of delicate optical properties, including fine positioning of the PBG and tailoring of full-width at half-maximum (FWHM).
In this study, we propose a systematic approach to designing a bi-layered CLC color filter by sweeping the principal parameter, helical pitch p, which substantially contributes to the optical performance. By stacking two CLC layers that reflect different wavelengths of light, the optical color filter only transmitting the desired wavelength band in the visible spectrum can be obtained. With our proposed design method applying to this bi-layered structure, the parametric controls of sufficiently narrow FWHM and nearly continuous central wavelength position could be achieved. A design based on presented theoretical analysis may facilitate the optimization of color filter performance while minimizing trial and error in the experimental point of view. Especially, it is believed that superb optical characteristics of bi-layered CLC color filter found in this study will contribute to the potential advancement of hyperspectral resolution imaging which requires continuous central wavelength and sufficiently narrow FWHM [79,80].
2. Methods
2.1 Design configuration of the optical color filter using bi-layered CLC
A CLC color filter consists of bi-layered structure of two CLC layers sandwiched between two substrates at the top and the bottom side of the device, as illustrated in Fig. 1. When the color filter is exposed to light, CLC layers reflect the light with the central wavelength λ1 and λ2 corresponding to their PBG formed by helical pitches p1 and p2. As a result, the light with the central transmitting wavelength λT which is not blocked by two CLC layers is transmitted through the color filter. For example, if each CLC layer 1 and 2 reflects the light with the blue and green wavelength band respectively, the color filter as a whole transmitting red light can be realized in the visible spectrum. This method allows for on-demand controls of the desired central transmission wavelength and tailored FWHM for an optical color filter.
2.2 Mathematical approach
This study utilizes a 4×4 matrix method to scrutinize the optical phenomena occurring in the bi-layered CLC color filter. The 4×4 matrix method has advantages over the conventional analysis methods, such as the Jones matrix. Using the Jones matrix, the polarization state of the incident light can be examined by treating CLC as a birefringent layered media [81]. However, Jones matrix method has a limitation omitting the reflections and interferences that occur at the surface of the media to simply approximate the optical phenomena [23]. In particular, selective reflection, one of the most important optical phenomena in CLC, cannot be analyzed in this way as it ignores all reflections [82]. Although it is possible to analyze single reflections using the extended Jones matrix, this method still introduces inaccuracies in the analysis of multiple reflections caused by dielectric discontinuities at the interface of the CLC structure [23]. This is why these methods are not applicable to exhaustively calculating the exact solution of stratified anisotropic media such as CLC. On the other hand, the 4×4 matrix method considers all reflections and interferences occurring at the interface of each layer, making it a highly suitable way to calculate the exact solutions. Many researchers have analyzed the chiral and stratified structures using the 4×4 matrix method [83–86], but few papers have investigated bi-layered CLC structures as discussed in this study. A detailed description of the 4×4 matrix method has been given in previous studies [87,88]; thus, we will only outline the key details here.
To apply 4×4 matrix method, a bi-layered CLC medium with thickness d is divided into discrete N waveplates, as shown in Fig. 2(a). Here we set d = 20 µm and N = 1000 for all simulation results for the CLC color filter. The thickness of each plate is defined as t = d/N and the thickness of the substrates at w = 0 and N + 1 is neglected. In each plate, a director vector c(w) which indicates the direction along NLC molecule is defined as c(w) = (cosθ(w), sinθ(w), 0) where θ(w) is 2πwd/p1N for CLC layer 1 (w = 1, …, N/2), and 2πwd/p2N for CLC layer 2 (w = N/2 + 1, …, N), as shown in Fig. 2(b). Wave vectors are given in the form kδ(w) = (0, 0, γδ(w)) since the normal incidence condition is assumed where k1(w) and k3(w) are the propagating light, with k2(w) and k4(w) as the reflected light at each w-th plate. The subscripts indicate the ordinary ray where δ is 1, 2 and the extraordinary ray where δ is 3, 4. To give the exact solution for the wave vector kδ(w), the wave equation is solved as follow:
where E is the electric field vector, ω is the angular velocity, μ0 is the magnetic permeability, and ε(w) is the dielectric permittivity tensor. At w = 0 and N + 1, kδ(w) can be defined as k1(w) = k3(w) = (0, 0, nsk0) and k2(w) = k4(w) = (0, 0, - nsk0) where ns is the refractive index of the substrate and k0 is the wave number.
Fig. 2. (a) Discrete N waveplates of bi-layered CLC color filter; (b) wave vector kδ(w) and the director vector c(w) in Cartesian coordinate.
Next, the polarization vectors pδ(w) and qδ(w) each representing the direction of the electric and the magnetic field are calculated. Given the continuity of the electric and the magnetic waves at the interfaces, the relationship between the amplitude of the electromagnetic field Aδ at the (w − 1)-th and the w-th layer can be expressed as
3. Results and discussion
3.1 Basic characteristics of bi-layered CLC color filter
The simulated optical spectrum of the bi-layered CLC color filter which transmits a chosen wavelength band based on the 4×4 matrix method is presented below for assessing the controllability of the central transmission wavelength of a color filter. The calculated results are smoothed by the adjacent average algorithm to extract more reliable central wavelengths and FWHMs from the spectra. Figure 3 shows the simulated transmission spectra of the CLC color filter and the simulated reflection spectra of each CLC layer used to construct the color filter. Because the visible spectrum of device applications is the focus in this study (between 400 nm and 700 nm), the transmission spectrum outside this region was considered as filtered by conventional IR cutoff filter and was notated in the figure by the dotted lines. In Fig. 3(a), CLC layers 1 and 2 reflect light with central wavelength λ1 = 434 nm and λ2 = 550 nm, representing blue and green colors, respectively. This configuration results in red-colored light with a central transmission wavelength λT = 662 nm. The optical spectra of the color filter transmitting the green and the blue color are shown in Figs. 3(b) and (c). In result, the color filter which possesses the desired central transmission wavelength could be realized.
Fig. 3. Simulated optical spectra of the bi-layered CLC color filter which transmits (a) red, (b) green, and (c) blue light. The colored line in each graph indicates the transmission spectrum. The black solid lines and black dash-dot lines indicate the reflection spectra of each CLC layer, 1 and 2, respectively. The pitches of single CLC layers are 257 nm, 324 nm for red color filter, 248 nm, 394 nm for green color filter, and 324 nm, 405 nm for blue color filter, respectively. The average refractive index navg is 1.70 and the birefringence Δn is 0.40 for all CLC layers.
We fabricated the red, green, and blue color filter and measured the optical spectra as shown in Fig. S1 (Supplement 1). The shapes of transmission spectra in Fig. S1 were in good agreement with those of the simulation data in Fig. 3. The central wavelength of each color filter was slightly different from the simulation data since we used NLC which has navg = 1.715 and Δn = 0.402 due to the material availability. Also, optical color filters transmitted desired colors, which were red, green, and blue, as shown in Fig. S2 (Supplement 1). Here, we stacked two CLC cells to form bi-layered CLC system that have different pitches at each layer respectively, considering that the substrates between CLC layers barely affect the central transmission wavelength of the color filter. The fabrication of bi-layered CLC in single cell is currently under investigation. Based on this empirical implementation, the rest of the study will focus on designing the optical characteristics of the color filter through analytical studies.
To determine which variables to select as control parameters in further studies, the constant contour diagram of the central reflection wavelength and FWHM of the single CLC layer was examined, as shown in Fig. S3 (Supplement 1). We investigated the influence of navg and p on the central reflection wavelength in the visible spectrum based on the equation, λc = navgp, as shown in Fig. S3(a). Both navg and p demonstrated similar contributions to the central reflection wavelength so that either navg or p could be used to control wavelength position. Next, we examined the effect of Δn and p on FWHM based on the well-known de Vries equation [81], Δλ = (Δn)p. In this case, FWHM was dominantly controlled depending on Δn due to the much greater change of FWHM as a function of Δn rather than the pitch length p. From this perspective, we focused on the change in optical properties according to the control of p and Δn in the remainder of this study.
Next, we investigated the influence of the principal parameters, the helical pitch p and the birefringence Δn, on the color purity of the optical color filter in terms of FWHM. The transmission spectra of the bi-layered CLC color filter are manipulated by changing the helical pitch of each layer (p1 and p2), leading to a change in Δp = p2 - p1. The individual birefringence Δn of both CLC layers are identical and changed together when used to construct a combined color filter. In Figs. 4(a)–(c), with Δn of 0.25, we observed that FWHM decreases from 105 nm (Fig. 4(a)) to 88 nm (Fig. 4(b)) to 65 nm (Fig. 4(c)) as Δp decreases. This is because the difference of the central reflection wavelength Δλ = λ2 - λ1 is compressed as Δp decreases under the same Δn. The same decreasing trend for FWHM with decreasing Δp is also seen for Δn = 0.30 (Figs. 4(d)–(f)) and Δn = 0.40 (Figs. 4(g)–(i)). FWHM decreases from 105 nm (Fig. 4(a)) to 88 nm (Fig. 4(d)) to 59 nm (Fig. 4(g)) as Δn increases under the same combination of p1 and p2. When Δn increases, the PBG of each CLC layer expands, causing a decrease in the bandwidth of the light transmitted through the color filter. This shows that with control of p and Δn, the FWHM of the CLC color filter can be selected in a range 105–21 nm. Note that the FWHM can be further tuned depending on how the parameter conditions are set.
Fig. 4. Transmission spectra of the bi-layered CLC color filter which transmits light with a central wavelength that ranges from 540 nm to 550 nm (green). The pitch lengths of the CLC layers constructing the color filter are (a,d,g) p1 = 268 nm, p2 = 382 nm, (b,e,h) p1 = 274 nm, p2 = 376 nm, and (c,f,i) p1 = 280 nm, p2 = 370 nm. The birefringence of the CLC layers is (a–c) Δn = 0.25, (d–f) Δn = 0.30, and (g–i) Δn = 0.40. The average refractive index of all CLC layers is navg = 1.70.
Figure 5 illustrates the FWHM of the color filter with respect to the change of Δp and Δn. In Fig. 5(a), the FWHM of the color filter decreases with decreasing Δp under the constant value of Δn = 0.40 with a minimum value of 21 nm when Δp is 90 nm. In Fig. 5(b), the FWHM decreases as Δn increases under the constant combination of pitches. Considering the results of Fig. 4 and Fig. 5 to control the FWHM in practice, the property that is more easily changed can be used. Note that it is difficult to control Δn without further chemical synthesis technique, as it is the material property of achiral NLC constituting the CLC layer. On the other hand, the pitch length p is easier to control because it can be adjusted by the concentration of the chiral dopant c, as shown in Eq. (1). The remainder of the paper is therefore focused on designing bi-layered CLC color filters by adjusting p.
Fig. 5. FWHM of bi-layered CLC color filter that gives a central transmission wavelength ranging from 540 nm to 550 nm (green) with changing (a) Δp, where Δn = 0.25, Δn = 0.30, and Δn = 0.40, and (b) Δn where Δp = 90 nm, Δp = 102 nm, and Δp = 114 nm with navg = 1.70.
3.2 Systematic design of bi-layered CLC color filter
A parameter sweep analysis with respect to the principal factors, p1 and p2, which are the helical pitches of each CLC layer, was performed using the abovementioned mathematical approach and design characteristics with Δn = 0.40 and navg = 1.70. Figure 6 shows the resultant two-dimensional constant contour diagrams of the central transmission wavelength and the FWHM of the bi-layered CLC color filter obtained as a function of the helical pitch p and the pitch difference Δp. Figure 6(a) shows the constant contour diagram of the central transmission wavelength ranging from 520 nm to 566 nm where p1 and Δp are swept from 265 nm to 280 nm and from 95 nm to 120 nm, respectively. This result of the constant contour diagram illustrates that the central transmission wavelength of the color filter can be almost continuously fine-tuned. Figure 6(b) represents the constant contour diagram where the FWHM ranges from 69 nm down to 23 nm with the identical parameter sweep range shown in Fig. 6(a). Consequently, this result demonstrated that FWHM was able to design with high controllability from the wide bandwidth to narrow bandwidth by adjusting p.
Fig. 6. Constant contour diagram of (a) the central transmission wavelength, and (b) FWHM of the bi-layered CLC color filter where Δn = 0.40 and navg = 1.70.
From these results, the color filter with a desired central wavelength and FWHM was able to be designed systematically for given Δn and navg. First, we approached by selecting the pitch region with target central transmission wavelength from the constant wavelength contour diagram, as noted with the yellow line in Fig. 7(a). Next, we could obtain the required specific properties of the color filter by extracting p1 and p2 which correspond to the desired FWHM from the constant FWHM contour diagram, as shown in Fig. 7(b). Once the values of p1 and p2 are selected, CLC layers can be manufactured and the color filter satisfying the demanding optical performance could be obtained by stacking bi-layered chiral structures, as shown in Fig. 7(c). Here, we selected the desired central wavelength region from 526 nm to 532 nm and FWHM region from 28 nm to 34 nm. The resulting spectrum in Fig. 7(c) demonstrated the central transmission wavelength at 531 nm and FWHM of 29 nm with p1 = 268 nm and Δp = 97 nm. Note that the center wavelength position and FWHM were slightly adjusted to obtain a wider color gamut of the optical color filter rather than the direct use of the very narrow condition of the optical color filter with a central wavelength of 544 nm and FWHM of 21 nm in Fig. 4(i).
Fig. 7. An example of the systematic design of bi-layered CLC color filter using constant contour diagrams of (a) central transmission wavelength, and (b) FWHM. (c) The resultant transmission spectrum of the designed color filter.
Figure 8 shows the CIE 1931 color space of the designed color filter when D65 light was illuminated. In Fig. 8, the white dashed line indicates the color gamut of red, green, and blue color filter shown in Fig. 3 as an example of RGB color filters for image sensor applications. The black dashed line illustrates the color coordinate of the same color filter for red and blue as the white dashed line, except for the green color filter which has the same configuration with the color filter shown in Fig. 7(c) to manifest the controllability of the color gamut. Consequently, the color gamut of the designed color filters was enhanced from 116% (white dashed line) to 162% (black dashed line) of sRGB space. These results further elucidate that the bi-layered CLC color filter with desired property can be easily designed through the proposed analysis method.
4. Conclusions
This study has explored the optical characteristics and design strategy of tailored optical color filters with a bi-layered CLC structure. Analytical investigation of the possible optical conditions in the multilayered birefringent media was studied using 4×4 matrix method, resulting in design conditions to obtain the controllability of the central wavelength position corresponding to red, green, and blue color regions. The FWHM was controllable by manipulating the principal parameters, p and Δn. The green color filter exhibited high optical purity, down to a 21 nm FWHM, showing that this method can be exploited in optical color filter applications requiring fine positioning of the central wavelength and a narrow FWHM, which enable the implementation of high color purity. Through parameter sweep analysis, a facile design of the optical color filter for the target central wavelength and FWHM can be implemented without trial and error in the experimental perspective. Furthermore, the color gamut of bi-layered CLC color filter in CIE 1931 could be improved up to 162% of sRGB space by abovementioned design method. A color filter that transmits a different (i.e., non-visible) spectral range of the wavelength can also be analyzed and designed using this analysis approach. The scope of future studies could be expanded by broadening the PBG of each CLC layer, resulting in a wider range of the central wavelength and a narrower FWHM being realized. The optical color filter independent of the incident polarization could be implemented with the stacked structure of CLC layers having right- and left-handed helix, respectively. The authors believe that the remarkable design of the bi-layered CLC color filter found in this study will contribute to the development of the various potential optical color filter technologies.
Funding
Samsung Science and Technology Foundation (SRFC-TC2103-01); Samsung Electronics (IO201211-08048-01).
Acknowledgments
This research was funded by Samsung Electronics Co Ltd, grant number IO 201211 08048 01 and Samsung Research Funding and Incubation Center of Samsung Electronics under Project Number SRFC TC 2103 01.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. L. C. P. Gouveia and B. Choubey, “Advances on CMOS image sensors,” Sens. Rev. 36(3), 231–239 (2016). [CrossRef]
2. M. Bigas, E. Cabruja, J. Forest, and J. Salvi, “Review of CMOS image sensors,” Microelectronics J. 37(5), 433–451 (2006). [CrossRef]
3. B. Luo, F. Yang, and L. Yan, “Key technologies and research development of CMOS image sensors,” in2nd IITA Int. Conf. Geosci. Remote Sensing (IITA-GRS) (2010), pp. 322–325.
4. E. G. Camargo, S. Tokuo, H. Goto, and N. Kuze, “Nondispersive infrared gas sensor using InSb-based photovoltaic-type infrared sensor,” Sensors Mater. 26(4), 253–262 (2014).
5. A. Gnanasambandam, O. Elgendy, J. Ma, and S. H. Chan, “Megapixel photon-counting color imaging using quanta image sensor,” Opt. Express 27(12), 17298 (2019). [CrossRef]
6. L. Duan, P. Zhang, M. Tang, R. Wang, Z. Zhao, S. Fu, L. Gan, B. Zhu, W. Tong, D. Liu, and P. P. Shum, “Heterogeneous all-solid multicore fiber based multipath Michelson interferometer for high temperature sensing,” Opt. Express 24(18), 20210 (2016). [CrossRef]
7. H. Taguchi and M. Enokido, “Technology of color filter materials for image sensor,” Proc. 2011 Int. Image Sens. Work. (2011), pp. 34–37.
8. Y. Oike, “Evolution of image sensor architectures with stacked device technologies,” IEEE Trans. Electron Devices 15(1), 1–9 (2021). [CrossRef]
9. Y. Yoo, S. Lee, W. Choe, and C.-Y. Kim, “CMOS image sensor noise reduction method for image signal processor in digital cameras and camera phones,” Digit. Photogr. III 6502, 65020S (2007). [CrossRef]
10. J. J. Talghader, A. S. Gawarikar, and R. P. Shea, “Spectral selectivity in infrared thermal detection,” Light: Sci. Appl. 1(8), e24 (2012). [CrossRef]
11. R. Wang, Z. Fang, J. Gu, Y. Guo, S. Zhou, Y. Wang, C. Chang, and J. Yu, “High-resolution image reconstruction for portable ultrasound imaging devices,” EURASIP J. Adv. Signal Process. 2019, 56 (2019). [CrossRef]
12. K. F. Lin, Y. K. Hsiao, C. C. Hsieh, S. C. Hsin, and W. F. Hsieh, “Controlling electromagnetic wave through dual heights micro-lens array of a CMOS image sensor,” Opt. Commun. 367, 254–258 (2016). [CrossRef]
13. H.-K. Kim, B. Kim, J.-S. Kim, J. Park, Y. Lee, T. Jung, and K. Lee, “Development of lensed color filter technology for higher SNR and lower crosstalk CMOS image sensor development of lensed color filter technology,” in IEEE Int. Image Sens. Work. (2013).
14. K. Hirakawa and P. J. Wolfe, “Second-generation color filter array and demosaicking designs,” in Visual Communications and Image Processing (International Society for Optics and Photonic, 2008), 6822, p. 68221P.
15. T. M. Lee, Y. J. Choi, S. Y. Nam, C. W. You, D. Y. Na, H. C. Choi, D. Y. Shin, K. Y. Kim, and K. Il Jung, “Color filter patterned by screen printing,” Thin Solid Films 516(21), 7875–7880 (2008). [CrossRef]
16. J. Y. Kim, C. Sakong, S. A. Choi, H. Jang, S. H. Kim, K. S. Chang, M. S. Han, J. S. Lee, and J. P. Kim, “The effect of fluorescence of perylene red dyes on the contrast ratio of LCD color filters,” Dyes Pigm. 131, 293–300 (2016). [CrossRef]
17. Q. H. Wang, D. H. Li, B. J. Peng, Y. H. Tao, and W. X. Zhao, “Multilayer dielectric color filters for optically written display using up-conversion of near infrared light,” J. Display Technol. 4(2), 250–253 (2008). [CrossRef]
18. G. Ro, Y. Choi, M. Kang, S. Hong, and Y. Kim, “Novel color filters for the correction of red-green color vision deficiency based on the localized surface plasmon resonance effect of Au nanoparticles,” Nanotechnology 30(40), 1 (2019). [CrossRef]
19. A. Miyamichi, A. Ono, K. Kagawa, K. Yasutomi, and S. Kawahito, “Plasmonic color filter array with high color purity for CMOS image sensors,” Sensors 19(8), 1750 (2019). [CrossRef]
20. S. U. Kim, Y. J. Lee, J. Liu, D. S. Kim, H. Wang, and S. Yang, “Broadband and pixelated camouflage in inflating chiral nematic liquid crystalline elastomers,” Nat. Mater. 21(1), 41–46 (2022). [CrossRef]
21. S. S. Panda and R. S. Hegde, “Transmission-mode all-dielectric metasurface color filter arrays designed by evolutionary search,” J. Nanophotonics 14(01), 1 (2020). [CrossRef]
22. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon Press, 1993).
23. P. Yeh and C. Gu, Optics of Liquid Crystal Displays, 2nd ed. (John Wiley & Sons, 2009).
24. G. Gottarelli and G. P. Spada, “Induced cholesteric mesophases: origin and application,” Mol. Cryst. Liq. Cryst. 123(1), 377–388 (1985). [CrossRef]
25. Q. Chen, Z. Peng, Y. Li, S. Liu, P. Zhou, J. Gu, J. Lu, L. Yao, M. Wang, and Y. Su, “Multi-plane augmented reality display based on cholesteric liquid crystal reflective films,” Opt. Express 27(9), 12039 (2019). [CrossRef]
26. J. K. Kim, S. H. Joo, and J. K. Song, “Reflective-emissive photoluminescent cholesteric liquid crystal display,” Appl. Opt. 52(34), 8280–8286 (2013). [CrossRef]
27. A. H. Gevorgyan and K. B. Oganesyan, “Lasing in cholesteric liquid crystal cells with an isotropic defect layer inside,” Laser Phys. Lett. 12(12), 125805 (2015). [CrossRef]
28. Y. Watanabe, M. Uchimura, F. Araoka, G. I. Konishi, J. Watanabe, and H. Takezoe, “Extremely low threshold in a pyrene-doped distributed feedback cholesteric liquid crystal laser,” Appl. Phys. Express 2(10), 102501 (2009). [CrossRef]
29. F. Castles, F. V. Day, S. M. Morris, D. H. Ko, D. J. Gardiner, M. M. Qasim, S. Nosheen, P. J. W. Hands, S. S. Choi, R. H. Friend, and H. J. Coles, “Blue-phase templated fabrication of three-dimensional nanostructures for photonic applications,” Nat. Mater. 11(7), 599–603 (2012). [CrossRef]
30. B. Taheri, A. F. Munoz, P. Palffy-Muhoray, and R. Twieg, “Low threshold lasing in cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 358(1), 73–82 (2001). [CrossRef]
31. S. M. Morris, P. J. Hands, S. Findeisen-Tandel, R. H. Cole, T. D. Wilkinson, and H. J. Coles, “Polychromatic liquid crystal laser arrays towards display applications,” Opt. Express 16(23), 18827 (2008). [CrossRef]
32. H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics 4(10), 676–685 (2010). [CrossRef]
33. W.-S. Li, Y. Shen, Z.-J. Chen, Q. Cui, S.-S. Li, and L.-J. Chen, “Demonstration of patterned polymer-stabilized cholesteric liquid crystal textures for anti-counterfeiting two-dimensional barcodes,” Appl. Opt. 56(3), 601 (2017). [CrossRef]
34. S. Hussain, S. Haider, W. Al-Masry, and S. Y. Park, “Optical anticounterfeiting photonic bilayer film based on handedness of solid-state helicoidal structure,” RSC Adv. 11(59), 37498–37503 (2021). [CrossRef]
35. U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, and T. J. Bunning, “Optical tuning of the reflection of cholesterics doped with azobenzene liquid crystals,” Adv. Funct. Mater. 17(11), 1735–1742 (2007). [CrossRef]
36. T. White, R. L. Bricker, L. V. Natarajan, N. V. Tabiryan, L. Green, Q. Li, and T. J. Bunning, “Phototunable azobenzene cholesteric liquid crystals with 2000nm range,” Adv. Funct. Mater. 19(21), 3484–3488 (2009). [CrossRef]
37. J. Ma, Y. Li, T. White, A. Urbas, and Q. Li, “Light-driven nanoscale chiral molecular switch: reversible dynamic full range color phototuning,” Chem. Commun. 46(20), 3463–3465 (2010). [CrossRef]
38. Y. Li, A. Urbas, and Q. Li, “Reversible light-directed red, green, and blue reflection with thermal stability enabled by a self-organized helical superstructure,” J. Am. Chem. Soc. 134(23), 9573–9576 (2012). [CrossRef]
39. K. Funamoto, M. Ozaki, and K. Yoshino, “Discontinuous shift of lasing wavelength with temperature in cholesteric liquid crystal,” Jpn. J. Appl. Phys. 42(12 B), 1 (2003). [CrossRef]
40. Y. 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 (2006). [CrossRef]
41. M. Humar and I. Muševič, “3D microlasers from self-assembled cholesteric liquid-crystal microdroplets,” Opt. Express 18(26), 26995 (2010). [CrossRef]
42. S. Y. T. Tzeng, C. N. Chen, and Y. Tzeng, “Thermal tuning band gap in cholesteric liquid crystals,” Liq. Cryst. 37(9), 1221–1224 (2010). [CrossRef]
43. B. A. San Jose, J. Yan, and K. Akagi, “Dynamic switching of the circularly polarized luminescence of disubstituted polyacetylene by selective transmission through a thermotropic chiral nematic liquid crystal,” Angew. Chemie - Int. Ed. 53(40), 10641–10644 (2014). [CrossRef]
44. G. Petriashvili, M. D. L. Bruno, M. P. De Santo, and R. Barberi, “Temperature-tunable lasing from dye-doped chiral microdroplets encapsulated in a thin polymeric film,” Beilstein J. Nanotechnol. 9(1), 379–383 (2018). [CrossRef]
45. W. Zhang, A. A. F. Froyen, A. P. H. J. Schenning, G. Zhou, M. G. Debije, and L. T. de Haan, “Temperature-Responsive Photonic Devices Based on Cholesteric Liquid Crystals,” Adv. Photonics Res. 2(7), 2100016 (2021). [CrossRef]
46. P. V. Shibaev, P. Rivera, D. Teter, S. Marsico, M. Sanzari, V. Ramakrishnan, and E. Hanelt, “Color changing and lasing stretchable cholesteric films,” Opt. Express 16(5), 2965 (2008). [CrossRef]
47. F. Castles, S. M. Morris, J. M. C. Hung, M. M. Qasim, A. D. Wright, S. Nosheen, S. S. Choi, B. I. Outram, S. J. Elston, C. Burgess, L. Hill, T. D. Wilkinson, and H. J. Coles, “Stretchable liquid-crystal blue-phase gels,” Nat. Mater. 13(8), 817–821 (2014). [CrossRef]
48. H. Finkelmann, S. T. Kim, A. Muñoz, P. Palffy-Muhoray, and B. Taheri, “Tunable mirrorless lasing in cholesteric liquid crystalline elastomers,” Adv. Mater. 13(14), 1069–1072 (2001). [CrossRef]
49. J. Xiang, Y. Li, Q. Li, D. A. Paterson, J. M. D. Storey, C. T. Imrie, and O. D. Lavrentovich, “Electrically tunable selective reflection of light from ultraviolet to visible and infrared by heliconical cholesterics,” Adv. Mater. 27(19), 3014–3018 (2015). [CrossRef]
50. G. Nava, F. Ciciulla, F. Simoni, O. Iadlovska, O. D. Lavrentovich, and L. Lucchetti, “Heliconical cholesteric liquid crystals as electrically tunable optical filters in notch and bandpass configurations,” Liq. Cryst. 00(00), 1–10 (2021). [CrossRef]
51. S. S. Choi, S. M. Morris, H. J. Coles, and W. T. S. Huck, “Wavelength tuning the photonic band gap in chiral nematic liquid crystals using electrically commanded surfaces,” Appl. Phys. Lett. 91(23), 98–101 (2007). [CrossRef]
52. 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]
53. S. S. Choi, S. M. Morris, W. T. S. Huck, and H. J. Coles, “Electrically tuneable liquid crystal photonic bandgaps,” Adv. Mater. 21(38), 3915–3918 (2009). [CrossRef]
54. 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]
55. Y. Han, K. Pacheco, C. W. M. Bastiaansen, D. J. Broer, and R. P. Sijbesma, “Optical monitoring of gases with cholesteric liquid crystals,” J. Am. Chem. Soc. 132(9), 2961–2967 (2010). [CrossRef]
56. D. A. Winterbottom, R. Narayanaswamy, and I. M. Raimundo, “Cholesteric liquid crystals for detection of organic vapours,” Sens. Actuators, B 90(1-3), 52–57 (2003). [CrossRef]
57. L. Sutarlie, J. Y. Lim, and K. L. Yang, “Cholesteric liquid crystals doped with dodecylamine for detecting aldehyde vapors,” Anal. Chem. 83(13), 5253–5258 (2011). [CrossRef]
58. A. Mujahid, H. Stathopulos, P. A. Lieberzeit, and F. L. Dickert, “Solvent vapour detection with cholesteric liquid crystals-optical and mass-sensitive evaluation of the sensor mechanism,” Sensors 10(5), 4887–4897 (2010). [CrossRef]
59. J. H. Jang and S. Y. Park, “pH-responsive cholesteric liquid crystal double emulsion droplets prepared by microfluidics,” Sens. Actuators, B 241, 636–643 (2017). [CrossRef]
60. Z. H. Guo, X. F. Liu, J. S. Hu, L. Q. Yang, and Z. P. Chen, “Synthesis and self-assembled behavior of pH-responsive chiral liquid crystal amphiphilic copolymers based on diosgenyl-functionalized aliphatic polycarbonate,” Nanomaterials 7(7), 169 (2017). [CrossRef]
61. D. J. Mulder, A. P. H. J. Schenning, and C. W. M. Bastiaansen, “Chiral-nematic liquid crystals as one dimensional photonic materials in optical sensors,” J. Mater. Chem. C 2(33), 6695–6705 (2014). [CrossRef]
62. N. Herzer, H. Guneysu, D. J. D. Davies, D. Yildirim, A. R. Vaccaro, D. J. Broer, C. W. M. Bastiaansen, and A. P. H. J. Schenning, “Printable optical sensors based on H-bonded supramolecular cholesteric liquid crystal networks,” J. Am. Chem. Soc. 134(18), 7608–7611 (2012). [CrossRef]
63. A. Saha, Y. Tanaka, Y. Han, C. M. W. Bastiaansen, D. J. Broer, and R. P. Sijbesma, “Irreversible visual sensing of humidity using a cholesteric liquid crystal,” Chem. Commun. 48(38), 4579–4581 (2012). [CrossRef]
64. D. bi Myung, S. Hussain, and S. Y. Park, “Photonic calcium and humidity array sensor prepared with reactive cholesteric liquid crystal mesogens,” Sens. Actuators, B 298, 126894 (2019). [CrossRef]
65. B. Gollapelli, A. K. Tatipamula, S. Dewanjee, R. S. Pathinti, and J. Vallamkondu, “Detection of bile acids using optical biosensors based on cholesteric liquid crystal droplets,” J. Mater. Chem. C 9(39), 13991–14002 (2021). [CrossRef]
66. H. G. Lee, S. Munir, and S. Y. Park, “Cholesteric liquid crystal droplets for biosensors,” ACS Appl. Mater. Interfaces 8(39), 26407–26417 (2016). [CrossRef]
67. S. Hussain and S. Y. Park, “Optical glucose biosensor based on photonic interpenetrating polymer network with solid-state cholesteric liquid crystal and cationic polyelectrolyte,” Sens. Actuators, B 316, 128099 (2020). [CrossRef]
68. R. Kizhakidathazhath, Y. Geng, V. S. R. Jampani, C. Charni, A. Sharma, and J. P. F. Lagerwall, “Facile anisotropic deswelling method for realizing large-area cholesteric liquid crystal elastomers with uniform structural color and broad-range mechanochromic response,” Adv. Funct. Mater. 30(7), 1909537 (2020). [CrossRef]
69. S. Nam, D. Wang, G. Lee, and S. S. Choi, “Broadband wavelength tuning of electrically stretchable chiral photonic gel,” Nanophotonics 7729, 1–10 (2022). [CrossRef]
70. M. Y. Jeong and K. Kwak, “Continuously tunable and bandwidth variable optical notch/band-pass filters over 500 nm spectral range using cholesteric liquid crystals,” IEEE Photonics J. 11(1), 1–11 (2019). [CrossRef]
71. M.-Y. Jeong and J. Y. Mang, “Continuously tunable optical notch filter and band-pass filter systems that cover the visible to near-infrared spectral ranges,” Appl. Opt. 57(8), 1962 (2018). [CrossRef]
72. M. Mohammadimasoudi, J. Beeckman, J. Shin, K. Lee, and K. Neyts, “Widely tunable chiral nematic liquid crystal optical filter with microsecond switching time,” Opt. Express 22(16), 19098 (2014). [CrossRef]
73. Y. Huang, M. Jin, and S. Zhang, “Polarization-independent bandwidth-variable tunable optical filter based on cholesteric liquid crystals,” Jpn. J. Appl. Phys. 53(7), 072601 (2014). [CrossRef]
74. W. G. Jang, T. W. Beom, H. Cui, J. R. Park, S. J. Hwang, Y. J. Lim, and S. H. Lee, “Reduction of viewing-angle dependent color shift in a reflective type cholesteric liquid crystal color filter,” Appl. Phys. Express 1(3), 0320011 (2008). [CrossRef]
75. V. N. H. Silva, K. Sathaye, L. Dupont, D. Stoenescu, D. S. V. Medeiros, R. M. Ribeiro, and A. P. L. Barbero, “Angle-Tuned filters from cholesteric liquid-Crystal for visible wavelength-Division multiplexing,” IEEE Photonics Technol. Lett. 26(5), 423–425 (2014). [CrossRef]
76. Y. Huang and S. Zhang, “Optical filter with tunable wavelength and bandwidth based on cholesteric liquid crystals,” Opt. Lett. 36(23), 4563 (2011). [CrossRef]
77. Y. Huang and S. Zhang, “Widely tunable optical filter with variable bandwidth based on the thermal effect on cholesteric liquid crystals,” Appl. Opt. 51(24), 5780–5784 (2012). [CrossRef]
78. D. Chen, X. B. Yin, Y. J. Liu, L. L. Zhang, J. Ma, and W. M. Sun, “Tunable optical filters based on different configurations with cholesteric liquid crystals,” Chinese Phys. Lett. 32(7), 074208 (2015). [CrossRef]
79. A. Wang and Y. Dan, “Mid-infrared plasmonic multispectral filters,” Sci. Rep. 8(1), 1–7 (2018). [CrossRef]
80. F. Gildas and Y. Dan, “Review of nanostructure color filters,” J. Nanophotonics 13(02), 1 (2019). [CrossRef]
81. S. Chandrasekhar, Liquid Crystals (Cambridge University Press, 1992).
82. Z. Zhuang, Y. J. Kim, and J. S. Patel, “Behavior of the cholesteric liquid-crystal Fabry-Perot cavity in the Bragg reflection band,” Phys. Rev. Lett. 84(6), 1168–1171 (2000). [CrossRef]
83. D. Grzelczyk and J. Awrejcewicz, “Reflectivity of cholesteric liquid crystals with an anisotropic defect layer inside,” Photonics 7(3), 58 (2020). [CrossRef]
84. O. V. Ivanov and D. I. Sementsov, “Light propagation in stratified chiral media: the 4 × 4 matrix method,” Crystallogr. Rep. 45(3), 487–492 (2000). [CrossRef]
85. J. Ortega, C. L. Folcia, and J. Etxebarria, “Upgrading the performance of cholesteric liquid crystal lasers: Improvement margins and limitations,” Materials 11(1), 5 (2018). [CrossRef]
86. N. Y. Ha, Y. Ohtsuka, S. M. Jeong, S. Nishimura, G. Suzaki, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Fabrication of a simultaneous red-green-blue reflector using single-pitched cholesteric liquid crystals,” Nat. Mater. 7(1), 43–47 (2008). [CrossRef]
87. P. Yeh, “Electromagnetic propagation in birefringent layered media,” J. Opt. Soc. Am. 69(5), 742–756 (1979). [CrossRef]
88. D. Grzelczyk and J. Awrejcewicz, “Calculation of reflectance and transmittance of optical birefringent networks based on cholesteric liquid crystals,” Lat. Am. J. Solids Struct. 16(1), 1–20 (2019). [CrossRef]
