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Abstract
In this work, optical properties of a cubic blue phase liquid crystal (BPLC) in photonic microstructures were investigated. The experiments were carried out in microcapillaries with different inner diameters and in a photonic crystal fiber (PCF). For the first time, white-light beam propagation through a BPLC (BP II) in a microcapillary with a 60-μm inner diameter at a distance of 26 mm was demonstrated. Furthermore, it was conclusively shown that the cylindrical geometry and the size of its inner diameter influence BP domains orientation, which can lead to a uniform texture of the BPLC with a dominant Bragg wavelength. This study also proves that a BPLC-filled PCF provides very attractive tunable properties. It was presented that by applying an external electric field, a control of the transmitted light intensity for particular wavelengths can be achieved, depending on the input polarization. Moreover, a range of the wavelengths corresponding to low transmission appeared to be tunable, whereas for x- and y-polarized light, respectively, both narrowing (from 16 nm to 9 nm) as well widening (from 13 nm to 22 nm) of the bandgaps were observed. Finally, the obtained experimental results were found qualitatively consistent.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Blue phase liquid crystal (BPLC) is a chiral mesophase with an exotic arrangement of liquid-crystalline molecules in two levels [1,2]. The first one refers to a three-dimensional highly chiral structure composed of rod-like molecules which constitute double-twist cylinders (DTCs) [3], resembling the chiral nematic phase in a capillary what is presented in Fig. 1(a). The second level is considered as a supramolecular cubic structure made by regularly ordered DTCs, forming body centered cubic and simple cubic in unity cell appropriate for BP I and BP II, respectively [Figs. 1(b) and 1(c)]. Moreover, BP III can also be distinguished. It is called the foggy phase, and has similar properties to the isotropic phase due to comprising an amorphous network of disclinations [4, 5]. All three structurally distinct types of the blue phase appear in order of increasing temperature from the chiral nematic phase to the isotropic and naturally exist in a relatively narrow temperature range of 0.1–5 °C. Taking into account that a BPLC has outstanding properties such as (i) optical isotropy and polarization insensitivity on a macroscopic scale for wavelengths outside of the resonance band [6,7], (ii) induced birefringence by an external electric field (Kerr-like effect) [8], (iii) sub-millisecond response time on electric field [9,10], (iv) existence of three-dimensional photonic band gap manifesting in Bragg reflections related to a cubic lattice structure [11, 12], all this makes BPLC a very attractive material for a wide range applications not only in novel displays but also in advanced photonic technology. In the latter case, BPLC can be potentially adapted for mirrorless liquid crystal lasers [13–15], polarization-insensitive liquid-crystalline microlenses [16–18] and a light valve or an optical attenuator based on photonic crystal fibers (PCFs) filled with BPLC [19–22]. From these papers it turns out that BPLC-filled PCFs can offer new functionalities in advanced photonic systems with a possible use of electro-optical modulation, switching, sensing, as well tunable filter applications, providing better transmission properties due to existence of optical isotropy in BPLC. It is a need to underline that BPLC-based complex photonic structures still suffer from some disadvantages in optical communication such as not fast enough response times as well a necessity to use of high driving voltage due to large cladding diameter of the PCF. However, new liquid-crystalline compounds with relatively high dielectric anisotropies or liquid crystals doped with nanoparticles may significantly lower threshold and speed up response times [23].
Fig. 1 Scheme of molecular ordering in: (a) double-twist cylinder, and cubic structures corresponding to a unit cell of (b) BP I and (c) BP II. Orange molecules mean connected helices in neighboring cylinders, and green rods correspond to an array of liquid-crystalline disclinations in a unit cell. It is worth to notice that the relation between chiral pitch p and lattice constant a (defined as the size of a cube) of presented cubic structures is as follows: p = a for BP I, and p = 2a for BP II.
To the best of our knowledge, only a few papers (aforementioned) describe optical and/or electrooptical properties of photonic devices utilizing the BPLC-infiltrated photonic crystal fibers. The performed studies include mainly an analysis of spectral properties of the complex photonic structures without investigating how cylindrical geometry affects BPLC orientation, especially when the PCF is consisted of an array of microcapillaries arranged periodically around the solid-core fiber in the cross section [24,25]. The preliminary studies of optical properties of BPLC cofined in a microcapillary for the first time were reported by Sala-Tefelska et al. [26]. They showed that a cylindrical geometry of the sample plays significant role on BP LC-crystals growth in comparison to standard cell commonly used in display technology. Moreover, it was presented that different alignment layers applied on the inner surface of cylindrical structure affects the crystal nucleation in blue phases leading to a specified orientation of BP domains.
In our paper, we decided to expand our research in this field by carrying out the studies of optical properties of cubic blue phases in photonic microstructures. Firstly, the examination in a single microcapillary for various diameters were performed, verifying how the size of the cylinder affects orientation of BP domains. Moreover, it was shown that the quasi-homogeneous texture of monodomain BP crystals was obtained, without applied the alignment layers, what is a crucial issue in low-loss optical transmission systems. Furthermore, the studies of PCF infiltrated with BPLC for two orthogonal linearly polarized light waves, in the presence of an external electric field were carried out. Additionally, preliminary simulations of modal analysis by means of commercially available software (COMSOL, Multiphysics) via the finite element method were performed based on physical properties of PCF and BPLC measured before. The presented work shows novel experimental results, extending earlier observations, that BPLC is a very attractive LC medium for photonic microstructures enabling relatively low-loss light beam propagation and providing simultaneously interesting tunable properties.
2. Materials and setup
In our experiment we used the 1912 chiral nematic LC mixture, which was synthetized in the Institute of Chemistry at the Military University of Technology. The major compositions of the 1912 mixture (85.8% by wt.) are photochemically stable fluorinated oligophenyls with fluorinated cyclohexyl- and bicyclohexylbiphenyls [27]. The dielectric and optical anisotropy of the base mixture are Δɛ = 12.6 (measured at ν = 1 kHz and T = 23 °C) and Δn = 0.178 (measured at λ = 589 nm and T = 23 °C). The BP phase is induced in the BPLC investigated by the presence of two optical active dopants added at an appropriate concentration: biphenyl-4,4-dicarboxylic acid bis-(1-methylheptyl) ester (7.0% by wt.) and [1,1;4,1] terphenyl-4,4-dicarboxylic acid bis-(1-methylheptyl) ester (7.2% by wt.), both synthetized at the Military University of Technology [28]. The average refractive index of the studied BPLC was measured by using the wedge-cell method [29] and was equal to 1.5558 at λ = 640 nm. The measured macroscopic parameters of the 1912 mixture can be found elsewhere [26].
Characterization of BPLC optical properties, including the exact specified temperature ranges of the BP phases, in cylindrical geometry was accomplished by means of a Nikon Eclipse Ts2R-FL polarized light microscope and Linkam THMS600 heating stage. The microcapillaries used in this work were manufactured at Maria Curie-Skłodowska University (MCSU) in Lublin (Poland), and made of pure silica glass with the following inner diameters: 15, 60, 80, 128 μm with about 200 mm outer diameter. The microcapillaries filled with the 1912 mixture by capillary action were placed on a heating stage between crossed polarizers. Each sample was heated over the temperature of clearing point (here 62 °C) and after that it was cooled gradually at the rate of 0.1 °C/min passing through the subsequent phases of the LC. The measurements show that BP II appears from 60.5 °C to 59.0 °C, and BP I appears from 58.9 °C to 56.2 °C. Below 56.2 °C the chiral nematic phase is obtained. The study of spectral properties of a more complex photonic structure was accomplished by the use of a PCF (fabricated at MCSU in Lublin, Poland), made of pure silica glass (which refractive index n = 1.4568 at λ = 640nm) with the inclusion diameter do = 2.4 μm, pitch Λ = 5.7 μm, and outer diameter D = 125 μm. The cross-section of the PCF is shown in Fig. 2(a). The PCF was filled with the 1912 mixture by capillary action with a length of 6 mm, and then was sandwiched between two glass plates with a conducting ITO layer (Indium Tin Oxide). The prepared sample was placed on a heating stage with temperature stability of 0.1 °C between crossed polarizers, and then a white linear polarized light beam was launched into the core of the PCF-type fiber. Next, spectral characteristics of the PCF infiltrated with liquid crystal and stabilized in BP, in the presence of an external (AC) electric field, were measured by using an Ocean Optics HR4000 spectrometer. The BPLC-filled PCF was driven by 1 kHz square-wave from a tunable function generator (Rigol, DG1022A) coupled to an amplifier (FLC Electronics, A800DI). The experimental setup is presented in Fig. 2(b).
Fig. 2 (a) Cross-section of the investigated PCF structure, and (b) scheme of the setup to study of the spectral properties of BPLC-filled PCF under the influence of an external electric field. Spectral properties of the BPLC-filled PCF were studied for two linear polarizations defined as follows: ‖ for y-axis and ⊥ for x-axis. The orientation of the coordinate frame is imposed by an external electric field E, where E ‖ y.
3. Results and discussion
3.1. Optical properties of BPLC in a single microcapillary
It is well known that PCF is manufactured of many microcapillaries arranged usually in a hexagonal lattice. Before a BP-filled PCF sample was characterized, optical properties of BPLC in a single cylinder were studied. Initially, the possibility of light propagation in a photonic microstructure consisted of microcapillary filled with the 1912 LC mixture was investigated for various temperatures. The inner diameter and the length of a microcapillary was equal to 60 μm and 26 mm, respectively. The sample was placed on a heating stage and a white light beam was launched into the BPLC-core of the fiber-optic microstructure. For the first time, the light guidance in a microcapillary filled with BP was achieved. The experimental results are presented in Fig. 3. On the left side the output of microcapillary infiltrated with BPLC can be found presented for isotropic, BP II, BP I and chiral nematic phases, respectively. Whereas on the right side, the longitudinal section of the analyzed BPLC-filled microcapillary for appropriate LC-phases are shown. The highest transmission of the light was obtained for higher temperatures corresponding to isotropic phase [Fig. 3(a)]. Taking into account that an average refractive index of BPLC is higher than that of the silica glass, the light beam propagation in the BPLC-core is allowed due to the total internal reflection (TIR) mechanism. It was very promising that the light beam was still guided through the LC medium in BP II and BP I for a distance of 26 mm [Figs. 3(b) and 3(c)]. It was noted that the propagating wavelengths were shifted from orange to red whereas the intensity of the light decreased for all wavelengths, but mostly for blue one. The color shift is caused most likely by changes in Bragg reflections due to structural changes, while signal intensity drop comes rather from light scattering. This is due to the signal attenuation caused by light scattering on unordered BP domains. However, the wavelength of the maximum intensity still remained for the red light like for spectrum of the light source (not shown here) what finally leads to obtain more vivid color. In the case of chiral nematic phase [Fig. 3(d)] the lack of light propagation is occurred caused by strong light scattering on highly anisotropic chiral structures.
Fig. 3 Fiber-optic structure composed of a microcapillary with 60 μm inner diameter filled with the 1912 mixture with a length of 26 mm in different temperatures corresponding to the following phases: (a) isotropic, (b) BP II, (c) BP I, and (d) chiral nematic (N*). The images on the left and the right side present the output of a BPLC-core fiber-optic microstructure and the longitudinal section of the analyzed BPLC-filled microcapillary for appropriate BPLC-phases, respectively. Textures of BP II and BP I were obtained for a rapid cooling process from the isotropic phase. However, texture of N* was recorded after filling the microcapillary by capillary action at room temperature.
In this work, an influence of cylindrical geometry inner dimensions (without applied alignment layers) on optical properties of BPLC was studied taking into account that the analyzed geometry differs significantly from a cell commonly used in display technology. However, the influence of aligning layers in cylindrical and rectangular geometries on BP domains in the 1912 LC mixture can be found elsewhere in [26], and [30], respectively. Polarizing microscope images of BP domains in a single microcapillary for different inner diameters are shown in Fig. 4. Textures of liquid crystal were taken at 59 °C (BP II) between crossed polarizers by two different conditions. Firstly, the sample was studied in the slow cooling process from isotropic phase to BP II [Figs. 4(a)–4(d)], and next the influence of a crystal growth process during the time of 60 min on BP crystals orientation was analyzed [Figs. 4(e)–4(h)], before the temperature of the testing sample was reached 59 °C.
Fig. 4 Polarizing microscope images of the BPLC in a microcapillary with different inner diameters: 15 μm [4(a) and 4(e)], 60 μm [4(b) and 4(f)], 80 μm [4(c) and 4(g)], and 128 μm [4(d) and 4(h)] obtained at 59 °C (for BP II). The images on the left and right sides correspond to the textures obtained in a cooling process from the isotropic phase with a speed of 0.1 °C/min without and with the crystal growth process near isotropic-BP II phase transition, respectively.
As it can be seen from the presented results, the quasi-uniform BPLC-texture with monodomain BP crystals can be achieved for microcapillary with relatively small inner diameter [Figs. 4(a) and 4(e)], without using alignment layers. Self-organizing BP domains in such a small volume leads to retain locally their orientation, in the direction transverse to the axis of the microcapillary, due to the influence of cylinder surface [Fig. 4(a)]. Hence, the BP platelets are formed as stable monocrystals, giving dominant selective reflection for blue light. However, for the microcapillaries with greater inner diameters, BP cubic structures are randomly oriented. Hence interactions between the inner microcapillary boundaries and BP platelets are much weaker. Finally, spontaneous orientation of the cubic structures in blue phase (manifesting in occurrence of BP polycrystals), for microcapillary with a 128-μm inner diameter was obtained [Fig. 4(d)].It has to be underlined that the greater diameter of sample, the more BP domains with various vivid colors for green and red occur. Moreover, close to the inner surface of cylinder [from Fig. 4(d)] many BP-platelets reflected also the green light. Whereas many red BP-platelets were formed in the bulk (near the axis of microcapillary). Possible explanations can be found in [31,32]. It was shown numerically and experimentally that new morphologies of blue phases arise due to their confinement in relatively small spherical geometry, resulting in a change of topological defects in a BP unit cell. However, it is known that the structure of disclination lines depend on chirality of the medium and can be altered by surface anchoring what can also influence Bragg reflection.
In the case of a crystal growth process, it can be seen that BPLC-textures [Figs. 4(e)–4(h), right side] are more uniform, having a dominant Bragg wavelength, in comparison to BPLC-textures presented in Figs. 4(a)–4(d). This process was initiated at the beginning of crystal nucleation in BP II, close to the temperature of clearing point (60.5 °C). During that time BP platelets were growing to the maximum size until a thermodynamic equilibrium state was achieved. Further cooling process caused expansion BP domains, maintaining their orientation in the volume of microcapillary. For cylinders with 60 μm and lower inner diameters, the quasi-homogeneous BPLC-texture with Bragg reflection for blue light on the entire length of the sample was obtained [compare e.g. Figs. 4(b) and 4(f)]. However, for microcapillary with the 128-μm inner diameter the BPLC-texture with dominant Bragg reflection for red light was occurred [Fig. 4(h)]. Therefore, we can conclude that for extreme inner diameters of microcapillary used, different BPLC textures can be obtained. Especially, for 15-μm and 128-μm diameters the Bragg reflections in BP II can vary essentially, having dominant selective light reflection for blue and red, respectively [compare Figs. 4(e) and 4(h)]. This is due to the fact that the BP crystal growth process enables to obtain a more uniform BPLC texture with dominant Bragg reflection. It is necessary to underline that the obtained results are repeatable. Similar effects in standard cells with thickness of 100 μm were observed in [33]. Chen et al. showed that the speed of cooling the BP sample and the time for the crystal growth process are crucial in a large BP monocrystal achieving, and thereby on optical properties of BPLC.
3.2. Spectral properties of PCF infiltrated with BPLC
Characterization of photonic structure consisting of PCF, which cross-section is shown in Fig. 2(a), filled with the 1912 chiral nematic mixture was performed in the setup presented in Fig. 2(b). In Fig. 5 the polarizing microscope images of BPLC in the investigated PCF are shown. It can be noticed that for BP II at 60 °C many BP monocrystals were obtained. This observation agrees with the previous results obtained for microcapillaries where it was demonstrated that already for cylinder diameter as small as 15 μm, the quasi-uniform texture of BPLC with blue light reflection can be achieved [compare Figs. 4(a) and 4(e) with Fig. 5(a)]. However, for BP I at 58 °C, much smaller BP polycrystals reflecting mainly blue and green wavelengths were occurred. This is due to existence of different topology of line defects in unit cell comparing to that in BP II [33]. However, Li et al. in [34] showed numerically and experimentally that it is possible to obtain uniform texture of BP I by applying specific pattern substrate on the surface of the cell. For chiral nematic phase (N*) at 56 °C the LC-texture with bright light reflection was obtained associated with strong light scattering.
Fig. 5 Polarizing microscope images of BPLC in PCF obtained at different temperatures: (a) 60 °C (BP II), (b) 58 °C (BP I), and (c) 56 °C (N*).
In the next step, measurements of the spectral characteristics of the light guided in the core of BPLC-filled PCF were done. Fig. 6 presents the results at selected temperatures of the photonic structure the BPLC-based PCF. Graphs show the results obtained for the following phases: isotropic (62 °C), BP II (60 °C), BP I (58 °C), and N* (56 °C), and for two orthogonal linearly polarized light waves (‖ for y-polarized light and ⊥ for x-polarized light; the orientation of coordinate frame is imposed by an external electric field E, where E ‖ y). From the presented results we can see that light propagation was limited to certain wavelengths. In our case, the refractive index of PCF core, made by silica glass, is lower than BPLC-filling, forming the cladding of PCF structure (ncore < ncladding). Therefore, the light is guided due to photonic band gaps (PBG) mechanism. A light propagation can be described by an ARROW model (Anti-Resonant Reflecting Optical Waveguide) [35, 36]. This model assumes that the light is trapped in the fiber core due to antiresonant reflection from the periodic structure of the cladding, giving the maximum transmission. Whereas for resonance, the leakage of the light outside the fiber is occurred, leading to absence of transmission.
Fig. 6 The spectral characteristics of BPLC-filled PCF obtained at different temperatures for the following phases: isotropic (62 °C), BP II (60 °C), BP I (58 °C), and N* (56 °C). The results were measured for two orthogonal linearly polarized light waves (a) parallel to y-axis (‖; y-polarized light) and (b) perpendicular to y-axis (⊥; x-polarized light).
The results from Fig. 6 show the highest transmission in isotropic phase (62 °C) for three wavelength ranges, for which λmax, corresponding to the maximum of intensity light, is equal to 535 nm (FWHM‖= 30 nm, FWHM⊥ = 36 nm), 575 nm (FWHM‖ = 27 nm, FWHM⊥ = 31 nm), and 615 nm (FWHM‖ = 43 nm, FWHM⊥ = 46 nm). Cooling the sample to blue phases generally caused decreasing of the optical signal. However, at 60 °C (BP II) for ‖ polarization, the intensity of light for all wavelengths is almost on the same level like for isotropic phase. Moreover, the spectra were asymmetrically shifted towards longer wavelengths. The shifts for mentioned λmax by cooling the sample from 62 °C to 58 °C were of the order of few nm, for both polarizations. However, at 56 °C for chiral nematic phase, the intensity of light was deacresed dramatically, and the light was guided only in the narrow range of wavelengths whith λmax equal to 570 nm and 573 nm (FWHM = 19 nm for both) for y- and x-polarized light, respectively.
In the last part of our experiment, an influence of an external electric field on transmission in PCF infiltrated with the 1912 LC mixture in BP II (60 °C) was studied. The effect of an electric field applying to BPLC-filled PCF is shown in Fig. 7. By cooling the LC-sample from isotropic phase to BP II, the LC-texture reflecting blue light is obtained [Fig. 7(a)]. Applying an electric field about 7 V/μm to the fiber, the selective light reflection from BP domains is spectrally shifted [Fig. 7(b)]. This may be the result of an electrostriction changing the size of BP unit cell by applying sufficiently high electric field [37]. Moreover, it can be noticed that the Bragg reflection is weakened what may results from the effect of local director reorientation on the periodicity of refractive index [38]. However, when the electric field was switched off the orientation of BP domains changed, comparing to the initial state, giving stable BP monocrystals reflecting red light [Fig. 7(c)]. It is a result of BP lattice reorientation due to applied high external electric field what can be explained by torque Γ⃗ = P⃗× E⃗ [39]. Similar effect for the 1912 LC mixture confined in a cylindrical geometry was obtained in [26].
Fig. 7 The effect of an electric field applied to PCF filled with BPLC at 60 °C (BP II). The images refer to: (a) the voltage-off state, (b) voltage-on state, and (c) voltage-off state after applied an electric field.
In Figs. 8 and 9, the influence of an external electric field on spectral properties of photonic structures analyzed in BP II (60 °C), for two orthogonal linearly polarized light waves, is shown. Graphs in Figs. 8(b) and 9(b) are enlargements the graphs in Figs. 8(a) and 9(a), respectively, limited to the shaded area. It has to be underlined that the electrodes of the cell are on top and bottom of the PCF sample. So then, the equipotential lines of the electric field are assumed to be parallel to the y-axis of the considered PCF structure. By applying an external electric field to the LC-sample, asymmetric shifting of the spectra for both light polarizations in the wavelength range between 560 nm and 585 nm towards longer wavelength was noticed. However, the asymmetric shift of spectra was greater for the initial linear polarization parallel to the electric field (‖; y-polarized light) than in the case of perpendicular (⊥; x-polarized light). This effect was also observed in previous work [22]. Wahle et al. explained the asymmetric band gaps shifting as a result of mixed polarization. Additionally in our experiment, either increasing or decreasing of the transmission signal was observed, depending on the initial light polarization. By applying the electric field of 4.8 V/μm, for y-polarized light, the intensity of light at 593 nm was decreased about 80% [vertical black arrow in Fig. 8(b)], while for x-polarized light at 588 nm circa 3.5-fold increase was noticed [vertical black arrow in Fig. 9(b)]. Furthermore, tunability of the range of wavelengths corresponding to the low transmission was obtained. In the case of y-polarized light, widening of bandgap from 13 nm (596÷609 nm) to 22 nm (590÷612 nm) was occurred by applying an electric field [horizontal violet arrows in Fig. 8(b)]. Whereas for x-polarized light and the same electric field the bandgap reduction from 16 nm (595÷611 nm) to 9 nm (600÷609 nm) was achieved [horizontal green arrows in Fig. 9(b)]. It is need to be emphasized that observed changes in the transmission spectra were occurred only for specific wavelengths, only in the shaded area in Figs. 8(a) and 9(a). It can be advantageous in designing of new filters or optical attenuators working only at certain wavelenghts especially that many articles focused so far on photonic devices having tunable properties in a wide wavelength range utilizing, for instance PCF filled with a nematic [40–42].
Fig. 8 The influence of an electric field on spectral properties of PCF infiltrated with BPLC at 60 °C (BP II). The results were obtained for light polarization parallel to the external electric field (y-polarized light). Graph from (b) represents results from the graph (a) in the shaded area.
Fig. 9 The influence of an electric field on spectral properties of PCF infiltrated with BPLC at 60 °C (BP II). The results were obtained for light polarization perpendicular to the external electric field (x-polarized light). Graph from (b) represents results from the graph (a) in the shaded area.
3.3. Modal analysis of PCF infiltrated with BPLC under the influence of electric field
The PCF structure filled with BPLC was analyzed numerically by using the commercially available software (COMSOL, Multiphysics) that is based on a fully vectorial finite-element algorithm. In order to study modal properties of the photonic structure, the values characterized the PCF from Section 2 were taken into simulations. However, for PCF-filling the refractive index of BPLC as a function of electric field was measured at 60 °C (BP II) for three wavelengths (442nm, 532nm and 640nm) by use of the wedge-cell method, which is described in details in [29]. Moreover, the obtained values are reliable and agree well with the theoretical predictions of the extended Kerr model [43]. The results of the measurements are listed in Table 1. The average refractive index n̄ equals to: 1.9817 (for 442nm), 1.6047 (for 532nm), 1.5558 (for 640nm). It should be emphasized that presented modal analysis relies on finding possible solutions of the modes guided in the studied complex photonic structure, considering only refractive indices of the PCF host structure and BPLC guest material. The optical activity and corresponding optical rotatory dispersion of BPLC [44] are not included currently in simulations, however, it is now the subject of further numerical analysis.
Table 1. The Refractive Index of 1912 LC Mixture in a Function of an Electric Field Measured in BP II
Preliminary numerical simulations were performed for x-polarized light, corresponding to the experimental results from Fig. 9, considering two cases. The first one is referred to PCF filled with BPLC in BP II without the external electric field. Therefore, BP is optically isotropic material, and can be described by the average refractive index. In the second one, it was assumed that by applying an external electric field to PCF filled with BPLC, the anisotropy is induced in BP structures. The electric field of 4.8 V/μm was taken in the analysis, and corresponding to this case, the index change of the BPLC as well. In simulations the refractive indices were included as follows [nxx = no; nyy = ne; nzz = no] for analyzed configuration of the sample.
The numerical results are presented in Figs. 10 and 11. In Figs. 10(a) and 11(a) the characteristics of an effective refractive index of the guided modes as a function of wavelength are presented, respectively for the voltage-off state and by applied electric field of 4.8 V/μm. The colorful points and area refer to the guided modes in the BPLC-filled PCF investigated. However, the points with red envelope correspond to guided modes with low power, usually for evanescent modes with the high light leakage to the cladding [look at mode no. 4 in Fig. 10(b) or mode no. 2 in Fig. 11(b)]. From Fig. 10 we can see that only higher order modes were found in the wavelength range of (582÷598 nm) and around 614 nm. At 600 nm the guided mode with low power was found (mode no. 4) which was associated with evanescent mode no. 3. The bandgap in a wavelength range of (598÷614 nm) corresponds to the absence of light propagation (or low transmission) what perfectly agrees with experimental results presented in Fig. 9(b). From calculations in the case of applying the electric field [Fig. 11], it turns out that the wavelength range for low transmission is narrower (602÷614 nm). However, fundamental modes for particular wavelengths were found, especially at 588 nm [mode no. 1 from Fig. 11(b)]. It indicates improvement in the light propagation, ensuring higher power of the mode guided in the PCF core [compare with experimental results, vertical black arrow from Fig. 9(b)]. It can be concluded that the performed calculations are in a good agreement with experimental results.
Fig. 10 (a) Effective refractive index of the modes in the BP-filled PCF as a function of the wavelength, and (b) profile of higher order modes allowing light propagating in considered photonic structure. The results were obtained for x-polarized light, and in the voltage-off state, assuming isotropic material inside the PCF. The points (and colorful area) on graph (a) refer to the modes for which light beam propagation is allowed, and the color indicates on guided mode for specific wavelengths. The points with red envelope correspond to guided modes with low power.
Fig. 11 (a) Effective refractive index of the modes in the BP-filled PCF as a function of the wavelength, and (b) profile of fundamental (1 and 2) and higher order (3–5) modes allowing light propagating in considered photonic structure. The results were obtained for x-polarized light, and the electric field of 4.8 V/μm. The points (and colorful area) on graph (a) refer to the modes for which light beam propagation is allowed, and the color indicates on guided mode for specific wavelengths. The points with red envelope correspond to guided modes with low power.
4. Conclusion
The optical properties of the cubic blue phase liquid crystal in photonic microstructures were investigated. It was shown for the first time that light beam propagation through BPLC medium (BP II) confined in a microcapillary with the 60-μm inner diameter can be achieved, even over few tens of millimeters. Also, it was revealed that the size of the microcapillary and the way of confining the BP phase in the cylindrical geometry affects the BP LC-crystals orientation. For lower inner diameters of the microcapillary the almost uniform texture with dominant Bragg wavelength was obtained without applying any alignment layers. This is of particular importance from the point of view of low-attenuation guidance of the optical signals in liquid-crystal fiber-optic microstructures. Furthermore, a PCF filled with BPLC was studied, showing its promising tunable properties. By applying an external electric field, depending on the input polarization, either increasing or decreasing of the light intensity for particular wavelengths can be achieved. The change in the level of transmission was about 80% obtained at 588 nm and 593 nm for x- and y-polarized light, respectively. Moreover, the range of wavelength corresponding to the low transmission was controlled by applied an external electric field. For x-polarized light, a narrowing of the bandgap from 16 nm (595÷611 nm) to 9 nm (600÷609 nm) was achieved, whereas for y-polarized light a widening of the bandgap from 13 nm (596÷609 nm) to 22 nm (590÷612 nm) was obtained. The experimental results obtained are qualitatively consistent with performed simulations. To summarize, the BP phase is a very promising material and holds a great potential for applications in photonic microstructures, offering possibilities to develop advanced LC-based devices with new functionalities.
Funding
National Science Centre, Poland (2015/19/D/ST3/02432, 2015/19/B/ST7/03650).
Acknowledgements
We would like to thank Dr. Paweł Mergo (Maria Curie-Skłodowska Univ., Lublin, Poland) for supporting us with microcapillaries and photonic crystal fibers, and Dr. Sławomir Ertman (Warsaw Univ. of Technology, Poland) for his valuable advice on performing simulations in PCF structures. We also would like to thank Mr. Wojciech Staniszewski from PRECOPTIC Co. for his technical support.
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