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The light polarization has an effect on spectral properties of a multilayered photonic crystal infiltrated with a bistable chiral-tilted homeotropic nematic liquid crystal (LC) as a defect layer. By varying the direction of polarization of incident, linearly polarized light interacting with the birefringent LC, the tunability of defect modes in wavelength and amplitude and the broadening of the low-transmittance range can be realized in the transmission spectrum. The LC features two optically stable states and two voltage-sustained states. The bistability makes the device of low energy consumption. Such a hybrid can be used as not only a wavelength selector, optical shutter or multichannel switch but also a stopband-tunable device.
©2013 Optical Society of America
1. Introduction
Since the term “photonic crystals (PCs)” was coined more than two decades ago, numerous researchers have been fascinated by this field due to their unique optical properties. Among them, Yablonovitch and John independently proposed a novel PC conception in 1987 [1,2]. By 1991, Yablonovitch et al. fabricated a photonic band inverse-diamond structure [3]. Following his work, the next milestone was set by Krauss et al., who first produced a two-dimensional PC with a photonic bandgap (PBG) range located on the edge in the visible light [4]. With the rapid development of nanotechnology, a number of PCs designed for optical manipulation [5] or communications purposes [6] have been demonstrated. In recent years, this field of research has developed prosperously such as negative refraction [7] and well-designed interferometers [8] based on PCs.
One fascinating property of PCs is the PBG, which restrains the photon transport within a certain spectral range [9]. Even a one-dimensional (1D) PC (so-called dielectric mirrors) having no complete PBG can possess astonishing properties [10], such as optical resonant cavities that generate significantly collimated and coherent laser beams. In 2002, Ozaki et al. inserted a nematic liquid crystal (LC) as a defect layer in a 1D PC to make the defect modes electrically tunable in the PBG [11]. They later also demonstrated the 1D PC/LC color-tunable lasing and tunable spectral defect peaks [12–16]. Lately, Zyryanov et al. reported attractive optical properties of a similar photonic structure placed between two crossed polarizers, and analyzed the shift and superposition of defect modes in detail [17,18]. On the other hand, Hsiao et al. suggested a new bistable hybrid PC structure comprising a cholesteric liquid crystal (CLC) [19]. This device with powerful optical capability was structured by using a dual-frequency CLC as the defect layer [20]. Along this line, further progress was made with the demonstration of a novel device based on a 1D PC infiltrated with a polymer-stabilized cholesteric texture (PSCT) as the central defect layer [21]. This device, exhibiting optically tristable and multi-metastable states owing to the PSCT, possessed several alluring features including wavelength switchability, intensity tunability, polarizer-free construction and low power consumption.
In this paper, we investigated the spectral characteristics of a 1D multilayered PC stuffed with a bistable chiral-tilted homeotropic nematic LC (BHN) [22] in the single-polarizer condition or being positioned between two linear polarizers whose transmission axes were either parallel or perpendicular to each other. This work, as opposed to our previous research in electro-optical characteristics of a bistable PC/BHN cell [23], focuses on detailed observations of the light polarization effect under the three experimental schemes. A new interesting phenomenon looking like the broadening of the PBG was observed and its origin was analyzed in some specific experimental conditions.
2. Experimental
We prepared the BHN by mixing a dual-frequency LC host, MLC-2048 (Merck), and a chiral dopant, S-811 (Merck); the chiral agent yielded a 10.23-μm pitch length in the LC bulk. The mesogenic host used in this study possessed positive dielectric anisotropy at low frequencies, say, 1 kHz, and negative dielectric anisotropy at high frequencies, say, 100 kHz, beyond the crossover frequency of ~35 kHz at 26 °C. The concoction was introduced into empty PC cells with a gap ~10 μm by capillary action in the isotropic phase. Each PC cell was structured with two identical glass substrates coated with indium–tin oxide (ITO) and a 750-nm-thick dielectric multilayer. The periodic multilayer on each conducting substrate comprised a total of nine alternative layers including five layers of Ta2O5 (of high refractive index, nH = 2.18) and four layers of SiO2 (of low refractive index, nL = 1.47). The width of the resulting PBG increases with increasing difference in refractive index between the dielectric materials. With the two dielectric substances chosen and thus the refractive-index difference fixed, the larger the number of the layers in the dielectric mirror, the steeper and better-defined (and yet the slightly narrower) the PBG. Here we chose a total of nine layers so to generate the desired PBG in terms of the width and central forbidden wavelength. The thicknesses of Ta2O5 and SiO2 layers were determined to be 68.09 nm and 102.37 nm, respectively, leading to the central wavelength of the stopband at ~600 nm. Prior to cell assembly, a blend of polyimide SE-6414 (Nissan, 97.5 wt%) for planar alignment and polyimide IDL-V101 (Nissan, 2.5 wt%) for vertical alignment was spin-coated on the dielectric mirrors and then rubbed with a rubbing machine to promote an antiparallel tilted-alignment cell with a pretilt angle θ0 ~70° (measured from the substrate plane) for the LC molecules [23].
The filled cell was generally placed between a pair of linear polarizers for spectral observations as shown in Fig. 1. The transmission axes of the polarizers were either parallel or perpendicular to each other. In a particular case, the analyzer was removed to bring about the single-polarizer condition. Figure 1 illustrates a specific experimental geometry; i.e., the crossed-polarizer scheme, where the rubbing direction, transmission axis of the polarizer, and transmission axis of the analyzer are labeled as R, P, and A, respectively. A linearly polarized white light, with a polarization angle ϕ (0° ≤ ϕ ≤ 90°) defined as the angular span between P and R, was propagated through the cell along the z-axis. The transmission spectra of the PC/BHN were measured with a UV-visible spectrophotometer having a resolution of 0.2 nm (Shimadzu UV-1601PC). Various frequency-modulated square-wave pulses were supplied by an arbitrary function generator (Tektronix AFG-3022B) to induce reorientation of LC molecules in the PC/BHN cell. Note that the BHN possessed optical bistability—in the tilted-homeotropic (tH) and tilted-twist (tT) states at 0 Vrms—as well as two voltage-sustained states; namely, the biased-homeotropic (bH) state at 1 kHz and biased-twist (bT) state at 100 kHz. The dynamic behavior of the backflow effect in BHN was manifested from the bH to bT state [22]. Detailed operation principles for the frequency modulation and bistable switching of the 1D PC/BHN cell can be found elsewhere [23]. All the spectral observations were made at the temperature of 26 ± 1 °C.
Fig. 1 The sandwich structure of a hybrid cell based on 1D PC containing LC as a central defect layer (top) and the dynamic switching for the four states of the PC/BHN cell (bottom). The arrows in the side view indicate the transmission axes of the polarizer (P) and analyzer (A) as well as the rubbing direction (R).
3. Results and discussion
The PBG of the PC/BHN cell, located from ca. 500 to 700 nm, featured some spectral windows associated with the defect modes due to the central BHN defect layer. Figure 2 depicts the simulated spectra for the two homeotropic states under the parallel-polarizer scheme with various polarization angles. As a test, we calculated the optical responses for the bH and tH states by means of the transfer-matrix method that is generalized for anisotropic media [24,25]. Some of the unknown parameters have been acceptably tuned to reach a reasonable match with the experimental results. They are nITO = 1.5 + 0.04i and dITO = 100 nm for the ITO film, nSub = 1.47 for the glass substrate, nPI = 1.63 and dPI = 83 nm for the alignment layer, ne = 1.6168 + 0.00039i, no = 1.4978 + 0.00039i, d = 9600 nm and θ0 = 70° for the defect layer. The agreement is quite satisfactory between the simulated spectra and the experimental data (Fig. 3). The full width at half-maximum (FWHM) of the simulated defect-mode peaks is slightly narrower than that of the experimental data presumably. This is attributable to minor experimental uncertainties including interface roughness and imperfect parallelism of the constituent dielectric layers.
Fig. 2 Simulations of the transmission spectra of a PC/BHN cell under the parallel-polarizer scheme at various polarization angles. Left, the bH state; right, the tH state. (L = 9.6 μm and θ0 = 70°.)
Fig. 3 Transmission spectra within the PBG of a PC/BHN cell in four different states with parallel polarizers.
Figure 3 illustrates the experimental transmission spectra within the PBG of a PC/BHN cell in the bH, tH, bT, and tT states under the parallel-polarizer scheme. While the bH state exhibited the well-defined defect modes corresponding to the sole ordinary refractive index no of the LC bulk, all the other states displayed, to some extent, more complex spectral profiles or greater numbers of defect modes arising from the larger effective refractive index neff [18]:
where the integer N denotes the mode number, λ is the vacuum wavelength for the defect mode, and L is the defect (cavity) thickness. One can see from Fig. 3 that the defect modes of the bH state did not change with ϕ because of the LC molecules oriented vertically in this voltage-sustained state. Due to the continuum effect in the LC bulk with a tilt angle θ ~70°, the refractive index for the tH state, which can be simply calculated asis contributed by both no and the extraordinary refractive index ne and thus slightly higher than that for the bH state. Consequently, the number of defect modes increased and they were associated with extraordinary ray at ϕ = 0°. Note the emergence of the other set of defect modes associated with the ordinary-ray component at larger polarization angles (i.e., ϕ ≠ 0). This phenomenon along with the diminishing defect modes of the extraordinary-ray component with increasing polarization angle can easily be understood based on the explanation of an earlier report of a similarly photonic structure with a twisted-nematic (TN) defect layer [26]. Noticeably, the spectrum at ϕ = 90° in the tH state looks very much similar to that in the bH state because only a single ordinary-ray component remains. The conditions of ϕ = 0° and 90° allow the defect modes to be complementary in wavelength. This feature permits such device to be used as a polarization selector in particular wavelengths or an optical shutter.In order to ensure the optical bistability, the ratio of the BHN thickness to pitch has to be controlled within a certain range near unity [22]. As a result, the ~360°-twist configurations of both the bT and tT states in a BHN, with the bT state in particular, resembled a typical 90°-TN configuration with an approximately fourfold twist angle. Previously, transmission spectra of a 1D PC/TN cell at ϕ = 0°, 45°, and 90° have thoroughly been studied in the crossed-polarizer scheme [26]. Here one sees the dramatic change in the defect-mode spectral profile for the tT state at ϕ = 45°. The appearance of the companion peaks and suppression of some defect-mode peaks [26] revealed in Fig. 3 are due to the birefringent splitting of “defect modes” into two series with different polarizations. Each of these series can be additionally suppressed by polarizers, as in a mixed-mode TN or MTN [27]. The stable tT state was obtained from the bT state by turning off the high-frequency (100 kHz in this study) voltage. In comparison with the bT state, the tT state possessed a higher tilt angle, implying that the birefringence effect became more significant so that both the ordinary and extraordinary components were comparably conspicuous. Also note that the complementary nature in terms of defect-mode wavelengths between the conditions of ϕ = 0° and ϕ = 90° was clearly shown in the tT state as discussed above for the stable tH state (Fig. 3). It is worth mentioning that a slight change in defect-mode transmittance in the voltage-assisted bT state can be controlled by an externally applied voltage with amplitude beyond a threshold voltage. The nematic tilt angle in the bT state is factually dependent of the strength of the high-frequency electric field applied across the cell thickness. High voltage reduces the tilt angle and increases the contribution of the ne component to the resulting effective index of refraction. Moreover, the switching between the bistable tH and tT states can be achieved by applying short frequency-modulated voltage pulses. The switching scheme between them allows the PC/BHN to promptly transit through the intermediate bH and bT states. The interplay between the elastic torque and the suddenly changed electric torque leads to the subsequent backflow and thereby alters the configuration of the LC director field. Figure 4 shows the simulated director configurations using MATLAB for the bT and tT states. Giving its x- and y-component magnitudes at an arbitrary z coordinate within the LC thickness, each plot in this figure illustrates how the director is distributed in the x–y plane along the z-axis through the BHN bulk.
Fig. 4 MATLAB simulation of the director components nx, ny in the bT and tT states. Rubbing direction coincides with the y-axis.
Compared with the interesting optical proprieties in the parallel-polarizer scheme discussed above, the spectral variation in association with the defect modes in the PC/BHN cell between crossed polarizers seems relatively monotonous: The wavelengths of defect modes remain unchanged in the PBG as the input light polarization is varied. Moreover, the overall transmittance in the crossed-polarizer condition is lower than in the single- and parallel-polarizer schemes. It is worth mentioning, however, that a unique feature of the PC/BHN hybrid structure in the cross-polarizer scheme is the broadening of the spectral range where light transmission is blocked (stopband). That was never realized in a hybrid PC/LC system before. Figures 5 and 6 depict the transmittance of the bistable PC/BHN cell in the bT and tT states under the three schemes. One can see that different schemes yield distinct spectral profiles. In general, the width of spectral range with low transmittance can hardly be modified in such a hybrid device. In the optically stable tT state, especially, the transmissionspectra show obviously a larger stopband occupied by minimal defect-mode peaks in the crossed-polarizer condition as shown in Fig. 5(b). Notice that a hump and a valley in the spectrum were adjusted to the band edge in this particular case, causing the pseudo-broadening of the multilayer photonic forbidden region. If the valley is located beyond the bandgap, the breakup in the spectral cliff occurs as shown in both Figs. 5 and 6. It is worth noting that the FWHM of these defect-mode bands all are about 3 nm in the experimental data.
Fig. 5 Transmission spectra of the PC/BHN in (a) the bT and (b) tT states under three different experimental conditions (ϕ = 0°).
Fig. 6 Transmittances of the PC/BHN in (a) the bT and (b) tT states at various polarization angles (ϕ = 0°, 30°, and 60°) under crossed polarizers. Note that the polarization angle is measured between the rubbing direction and the transmission axis of the front polarizer.
4. Conclusions
A novel photonic structure with stopband widenability, defect-mode tunability and optical bistability, based on BHN as a defect layer infiltrated within a 1D PC, was investigated. To the best of our knowledge, this is the first study to reveal a broadened low-transmittance spectral range due to the combination of the PBG resulting from a 1D-PC multilayer structure and the polarization effect caused by the LC in the crossed-polarizer scheme. Under the parallel-polarizer condition, the defect modes in the bistable tT and tH states were tunable, shifting in wavelength with complementary nature. The PC/BHN possessed two voltage-sustained states (bT and bH) and the defect-mode bands in the bH state showed no obvious polarization-angle dependence. With the rich optical properties in association with the polarization effect, our results further open up new possible applications for the low-power-consumption photonic devices in tunable spectral bandwidth and optical multichannel technologies.
Acknowledgments
This work was financially supported by the National Science Council of the Republic of China (Taiwan) under Grant No. NSC 101-2112-M-009-018-MY3 and by the Siberian Branch of the Russian Academy of Sciences (SB RAS) through Grants Nos. 43, 101 and 24.29, 24.32 and by the Ministry of Education and Science of the Russian Federation (state contract no. 14.V37.21.0730).
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