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Abstract
Transmission optical diffraction gratings composed of periodic slices of a ferromagnetic liquid crystal and a conventional photoresist polymer are demonstrated. Dependence of diffraction efficiencies of various diffraction orders on an in-plane external magnetic field is investigated. It is shown that diffraction properties can be effectively tuned by magnetic fields as low as a few mT. The tuning mechanism is explained in the framework of a simple empirical model and also by numerical simulations based on the rigorous coupled wave analysis (RCWA). The obtained results provide a proof of principle of operation of magnetically tunable liquid crystalline diffractive optical elements applicable in contactless schemes for control of optical signals.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Diffractive optical elements (DOEs) are inevitable building blocks of modern photonic technologies. They are used for beam switching, splitting, steering, filtering, shaping, correcting, etc. and are consequently applied in a broad range of systems and devices [1,2]. Most applications demand DOEs with tunable diffractive properties. In components that operate with relatively low optical intensities (∼1 mW/mm2) and that need moderate response times (∼1 ms), a suitable tunability can be achieved by use of liquid crystals (LCs). The main advantages of LCs as optical materials are their large optical birefringence and strong response to various external stimuli [3]. A broad range of methods for assembling LC media into diffractive optical gratings and other diffractive structures was developed. They can be grouped into surface and volume-based patterning approaches. In the former group, patterning is performed on the substrates that surround the LC medium and typically involves micro-structuring of the driving electrodes and different ways of patterning of surface alignment layers [4–18]. In the latter group, LC materials are usually combined with photo-polymeric materials and the entailed patterning is achieved via photolithography, holographic lithography, direct laser writing, etc [19–27].
Similar to LC display (LCD) devices, also LC DOEs are predominantly controlled by an external electric field. The origin of the strong responsivity of LC materials to an electric field is a large anisotropy of their (quasi)static dielectric permittivity (∼10), due to which even relatively weak applied fields (∼1 V/μm) cause large reorientation of the LC molecules that leads to large modification of optical properties. In contrast to dielectric permittivity, the anisotropy of magnetic permeability of conventional LC materials is very low (∼10−6) and therefore strong magnetic fields (∼10 T) are required to generate comparable modifications of optical properties. For this reason, investigations of magnetic field-driven LC DOEs and other optical elements were up till now relatively rare and focused mostly on applications in the microwave spectral region in which millimetre scale structures are required [28–33].
However, recent development of ferromagnetic LC materials that can be manipulated by weak external magnetic fields (∼mT), opened up new perspectives for construction of magnetically tunable DOEs with micrometre scale structures that are applicable in the spectral region of visible light. In 1970, Brochard and de Gennes proposed that introduction of magnetic particles into the LC medium can increase its sensitivity to magnetic field [34,35]. Several groups investigated different types of dopants, however, pioneering studies encountered problems with particle aggregation [36–42], which was solved by surface functionalization of nanoparticles. Using dendritic-type surface coating, Prodanov et al. have recently succeeded to fabricate a thermodynamically stable colloid of spherical ferromagnetic nanoparticles in commercially available nematic mixture [43]. In their system, magneto-optic response to fields below 50 mT was detected. Highly sensitive suspensions were recently developed also in our group and are based on nanoparticles with a platelet shape [44–49]. A comprehensive review on the development of ferronematics can be found in [50].
In this work we report on fabrication, characterization and theoretical analysis of optical transmission gratings for visible light whose diffraction efficiency can be effectively tuned by magnetic fields as low as a few mT. In-plane switching (IPS) geometry in which the driving field is oriented along the plane of the grating structure was selected for this investigation, because it is quite difficult to realize this geometry by electrically tuneable structures. The subsequent investigation aims at providing a proof of principle of operation of this new type of tunable LC DOEs and intends to pave the way towards novel contactless schemes for magnetic control of optical diffraction phenomena.
2. Experimental
At first, a periodic array (one-dimensional gratings) of polymeric ribbons from a negative photoresist (SU-8 3000, MicroChem) was fabricated on a cleaned ITO-coated glass substrate by a direct laser writing method based on two-photon polymerization (TPP) as described in details in our previous work [51,52]. The ITO layer serves as reflection layer for generation of an interference pattern that results in a periodic surface relief of the ribbon side walls, as depicted in Fig. 1(a). This surface relief generates planar alignment of the LC medium via minimization of the elastic strain energy of the LC phase [53]. The patterned area had a size of 1 x 2 mm2. Patterns were produced with grating spacings Λ in the range of 5-20 μm and the thickness D of the grating structures was 9 μm, as shown in Fig. 1(a). After the required baking and development processes, the grating structure was covered by another ITO-coated glass plate and the assembly was fixed together. Two polymeric spacers of thickness D, fabricated on the initial substrate (prior to the TPP process) by UV illumination through a conventional photolithographic mask, provided mechanical stability of the entire assembly and ensured a tight contact between the cover glass plate and the top of the polymeric scaffold.
Fig. 1 (a) Schematic drawing of the polymeric grating structure fabricated by a TPP-based direct laser writing technique. (b) Polarization optical microscopy (POM) image of the grating structure with Λ = 20 μm that is filled with a ferromagnetic LC material. Arrow-ended lines in the top left corner indicate the orientations of the polarizer (P) and the analyzer (A). (c) Position of the sample between the two poles of electromagnet core.
A ferromagnetic nematic liquid crystalline material was composed of the commercial LC mixture E7 (Merck Ltd.) and of ferromagnetic scandium doped barium hexaferrite (BaFe12-xScxO19, BaHF) single-crystal nanoplatelets [45]. It was introduced into the channels of the polymer grating structure by capillary action at room temperature. Figure 1(b) shows a transmission polarization optical microscopy (POM) image of the patterned as well as non-patterned region of the assembly. Since ITO-coated glass substrates induce homeotropic anchoring of the ferromagnetic LC phase in which the optical axis of the material is perpendicular to the glass plates, the region outside the grating structure looks dark. In contrast, the LC in the planes within the grating structure is aligned along the polymer ribbons (planar alignment) and therefore appears bright. This alignment, as mentioned before, is induced by the surface relief gratings on the side walls of the ribbons [52]. Optical video-microscopy visualization of the effect of the magnetic field on optical properties of the gratings was performed by a monochrome CCD camera (Pixelink PL-B957U) and the images were analyzed by a program written in Python.
Optical diffraction efficiency of the gratings was probed with a low-power (< 1 mW) beam from a HeNe laser operating at a wavelength of λP = 632.8 nm. The beam was linearly polarized and entered the film at normal incidence. For analysing the polarization dependence of the diffraction properties its polarization direction was switched from s-polarization (parallel to grating planes) to p-polarization (perpendicular to grating planes) by using a λ/2 plate. The diameter of the probe beam in the sample was around 100 μm. The intensities of the 0th (transmission direction), ± 1st and ± 2nd order diffraction peaks were measured by photodiodes. Intensities of the peaks of higher order were negligible. To probe the effect of an external magnetic field on the diffraction efficiency of the gratings, the sample was placed in between the poles of a home-made electromagnet that generated static magnetic field with magnitudes up to 60 mT. The magnetic field vector B was parallel to the plane of the grating assembly and was oriented at an angle of 45° with respect to the polymeric ribbons (see Fig. 2). The diffraction efficiency ηi defined as the ratio between the intensity of the selected diffraction peak Ii and the sum of the intensities of all other detected peaks, namely
was investigated. By this definition, which is often used in holographic polymer dispersed LCs (HPDLCs) and similar type of diffractive structures [54,55], absorption and scattering losses of the probe beam are disregarded.Fig. 2 Polarization optical microscopy (POM) image of a ferromagnetic LC-filled grating structure with a grating period of Λ = 5 μm (a) at zero magnetic field and (b) at a magnetic field of B = 57 mT. The field was oriented at 45° deg with respect to the grating planes. Arrow-ended white lines denote the orientations of the polarizer (P) and the analyzer (A). Yellow arrows indicate the coordinate axes used in the theoretical description. The insets in the lower left corners indicate orientation of the LC molecules. Red squares denote the region of interest (ROI) that was selected for analysis of the average grayscale level of the image. (c) Average grayscale level in the selected ROI as a function of the magnetic field B. Full circles: values obtained for increasing field, open circles: values obtained for decreasing field. Practically no hysteresis is observed.
3. Results
3.1 Optical transmission properties
Most of the experiments were performed on gratings with a grating spacing of Λ = 5 μm. Figure 2(a) shows the transmission POM image of one of such gratings. The grating planes are oriented at α = 45° with respect to the transmission axes of the polarizer (P) and the analyzer (A). The polymer ribbons appear dark, while the LC planes appear bright. When comparing this image to the image shown in Fig. 1(b), one can notice that the optical homogeneity of the LC material in this grating structure is poorer than in the grating with Λ = 20 μm. Nevertheless, one can find regions of a size of 100 x 100 μm2 (∼laser spot size in diffraction experiments) that appear quite homogeneous. Figure 2(c) shows modifications of the average grayscale level in one of such regions, which is denoted in Fig. 2(a) and Fig. 2(b) by a red square, in response to the magnetic field in the range −60 mT < B < 60 mT. The field was applied in the direction of the polarizer (P). The average grayscale value detected in the same region when the sample was oriented so that the grating planes were parallel to the direction of the polarizer was subtracted as background. The greyscale values obtained during increasing and decreasing magnetic fields are very similar. However, even for the largest applied fields the grayscale value drops only to about 50% of the initial value.
The transmittance of the planarly aligned LC material placed between two crossed polarizers is given as [56]
where α is the angle between the preferential orientation of the LC molecules known as the nematic director n and the transmission direction of the polarizer, while the optical retardation in the LC medium given aswhere ne and no are extraordinary and ordinary refractive indices, respectively, and λ is optical wavelength. From Eq. (2) it follows that a complete reorientation of the LC medium from α = 45° to α = 0 should result in grayscale level zero. The fact that this does not happen in our samples is attributed to various reasons. The main one is aggregation of ferromagnetic nanoplatelets, which causes that parts of the LC material do not respond to the magnetic field. This effect increases with sample aging. Typical “operation time” of a freshly prepared sample was one day. With each sample we performed several experiments with increasing and decreasing magnetic field. When samples were several days old, they became practically insensitive to the magnetic field and aggregates were observed by optical microscopy. Another reason is anchoring of the LC at the interface with polymer ribbons, which keeps the interface layer aligned along α = 45°. With prolonged exposure to magnetic field some parts of the sample also get pinned along the field-directed orientation. Nevertheless, from these observations one can expect that there should be a noticeable effect on the diffraction properties, despite of the fact that the magnetic field-induced LC reorientation process is incomplete.3.2 Optical diffraction properties
The setup for analysis of diffraction properties is schematically depicted in Fig. 3. Images of the far-field diffraction pattern observed at B = 0 are shown in the top right corner. For an s-polarized beam the intensity of the ± 1st order diffraction peaks is larger than the intensity of the 0th order peak. For a p-polarized beam the situation is reversed. The intensities of the ± 2nd order peaks remain in both cases relatively low. The symmetry between the diffraction peaks on the right and the left side of the 0th order peak is evident. Therefore in all further experiments only the 0th, the + 1st and the + 2nd order diffraction peaks were measured.
Fig. 3 Schematic drawing of the diffraction experiment. A linearly polarized laser beam with either s or p polarization direction enters the sample at normal incidence with respect to the grating plane. The intensities of the 0th, + 1st and + 2nd diffraction orders are measured. In the top right corner, the far field diffraction patterns at B = 0 are shown for s and for p polarized light, respectively.
Figure 4 shows the diffraction efficiencies of different diffraction orders as a function of the applied magnetic field. The efficiencies of the 0th and the 1st order peaks exhibit opposite behavior, i.e. when one of them is increasing the other one is decreasing and vice versa, while the diffraction efficiency of the 2nd order peaks is practically constant. It can also be noticed that for B = 50 mT the values of diffraction efficiencies of the same diffraction orders became very similar for both polarizations. As can be noticed in Fig. 2(b), the reorientation process induced by the magnetic field takes place in an inhomogeneous manner associated with microscale “reorientation domains”. Due to this, step-like changes of the diffraction efficiency, as those shown in Fig. 4(b), are often detected.
Fig. 4 Diffraction efficiencies of different diffraction orders as a function of an applied magnetic field (a) for an s-polarized beam and (b) for a p-polarized beam.
We analyzed also the time dependence of the diffraction efficiencies after switching on and switching off the magnetic field. The results obtained for B = 35 mT are shown in Fig. 5. Gray vertical lines indicate the switching events. Response times in the range of 0.1-1 s are observed, which is about one order of magnitude longer than expected for visco-elastic relaxation of a pure nematic LC material (E7) confined to planar slices with a thickness of Λ/2 (2.5 µm) [57]. The observed slowing-down effect is attributed to the weakening of surface anchoring that is associated with weakening of the magneto-nematic coupling due to segregation of the nanoplatelets onto the side-walls of polymer ribbons. Particles adsorbed onto polymer walls can reduce surface anchoring and consequently decrease the associated surface torque that is responsible for LC reorientation after switching off the magnetic field [58,59].
Fig. 5 Time dependence of diffraction efficiencies of different diffraction orders after switching on and switching off a magnetic field of 35 mT (a) for an s-polarized beam and (b) for a p-polarized beam.
4. Theoretical analysis
In the theoretical analysis we assume that the polymeric and the LC slices of the investigated grating structures have both a thickness of Λ/2. Polymer slices are described as optically isotropic material with refractive index np and LC slices as an optically uniaxial material with principal refractive indices ne and no. In the absence of a magnetic field, the optical axis of the LC material that is parallel to the nematic director n, points along the grating planes, i.e. it is oriented along the y-axis in Figs. 2 and 3. When a magnetic field is applied to the sample, the optical axis rotates in the xy plane so that the intermediate angle β between the n and the y-axis increases with increasing magnetic field until it reaches an orientation parallel to B corresponding to β = 45° (see Fig. 3). If various possible beam coupling effects are fully neglected (thin grating approximation), then one can empirically predict the behavior of the diffraction efficiencies as a function of β by simply considering the decomposition of the incident optical polarization into the ordinary and extraordinary polarization directions of the LC phase, namely
where ηis0 and ηip0 are diffraction efficiencies of the i-th diffraction order for s- and for p-polarized beams at zero magnetic field, i.e. at β = 0.As the diffraction efficiencies of the 2nd diffraction orders were found to be practically independent of the magnetic field and as all higher diffraction orders had negligible intensities, we show dependencies predicted by Eq. (4) only for the efficiencies of the 0th and the 1st diffraction orders. The values of the parameters ηis0 and ηip0 for i = 0,1 were taken from the data shown in Fig. 4. The resulting calculated dependencies of the diffraction efficiencies for s and p polarizations are shown in Fig. 6. The predicted behavior agrees quite well with the observed dependence.
Fig. 6 Calculated diffraction efficiencies of the 0th and the 1st diffraction orders as a function of the rotation angle β obtained from Eq. (4). (a) Results obtained for an s-polarized beam and (b) for a p-polarized beam. The definition of β is shown Fig. 3. The value β = 0 corresponds to n pointing along the grating planes, i.e. along the y axis.
In the thin grating (Raman-Nath) diffraction regime, rectangular-type gratings exhibit zero intensity for all even-order diffraction peaks. The nonzero intensity of the 2nd order peak observed in our experiments is attributed to a deviation from the Raman-Nath regime. This deviation primarily depends on the ratio between the grating thickness D and the grating pitch Λ and is consequently not very sensitive to the orientation of the LC within the grating structure. In accordance with Gaylord and Moharam [60], the gratings investigated in our work do not belong to the category of thin gratings, but they fall into the so-called mixed diffraction regime, which is an intermediate regime between the Raman-Nath and the thick (Bragg) gratings. Consequently, the rigorous coupled wave analysis (RCWA) should be used to describe their diffractive properties. We performed such an analysis by the use of the Stanford Stratified Structure Solver (S4), which is a frequency domain code to solve the Maxwell’s equations in layered periodic structures based on the RCWA [61]. A schematic drawing of the unit cell used for the calculations is shown in Fig. 7. The thicknesses of the glass and the ITO layers confining the grating assembly from both sides were 1 mm and 220 nm, respectively. However, those layers in general have a relatively minor (indirect) effect on the diffractive properties. As already mentioned before, the polymer and the ferromagnetic LC slices forming the grating structure were taken to have the same thickness, namely Λ/2. Optical properties of the LC slices were described by a uniaxial dielectric tensor that was rotated for an angle β in the xy plane. The values of β were varied in the range 0 < β < 45°.
The values of the optical dielectric constants of different materials used for this calculation were taken from the literature and were the following: εg = (1.52)2 for glass [62], εITO = 3.18 + 0.01i for ITO [63], εp = (1.7)2 for post-exposure baked SU-8 polymer [64], and εe = (1.73)2 for extraordinary and εo = (1.52)2 for ordinary dielectric constants of the LC material [65]. The latter values are given for a pure E7 LC compound, however, because of low concentration of added nanoplatelets (< 0.3 wt%) in the used ferromagnetic mixture it is reasonable to use them also for our case. The result is shown in Fig. 8. The agreement between the experimental results shown in Fig. 4, the phenomenological results shown in Fig. 6 and the numerical calculation shown in Fig. 8 is qualitatively quite good, but some quantitative differences are evident. We believe that better agreement can be obtained by suitable adjustment of the material parameters. For instance, the refractive index of the SU-8 polymer can be different from the one reported in the literature due to different details of the baking and development processes. Another parameter that can be adjusted is lateral thicknesses of the LC and the polymer planes. An additional improvement is possible also by taking into account an inhomogeneous, instead of a homogeneous, LC reorientation between the adjacent polymer walls. However, because our goal was to explain the operational principle of the investigated in-plane switchable grating structures and not to exactly determine their grating parameters, we feel that the presented theoretical model satisfactory explains the experimental observations.
Fig. 8 Diffraction efficiencies of the 0th, the 1st and the 2nd diffraction orders as a function of rotation angle β obtained by numerical calculation of the electromagnetic field propagation in a one-dimensional grating structure composed of the unit cells shown in Fig. 7. (a) Results obtained for an s-polarized beam and (b) for a p-polarized beam. The definition of β is shown Fig. 3. The value β = 0 corresponds to n pointing along the grating planes, i.e. along the y axis.
5. Discussion and conclusions
We have demonstrated that a combination of recently discovered LC materials, i.e. nano-platelets based ferromagnetic LCs [44–49], with a recently developed new LC alignment principle, i.e. alignment by out-of-plane oriented polymeric ribbons fabricated by a direct laser writing method [51,52,71], enables realization of tunable DOEs that can be manipulated with magnetic fields in the range of a few mT. Such low magnetic fields can readily be obtained by standard portable electromagnets. The corresponding DOEs do not require any fixed electrodes and consequently no electric contacts are needed for their operation. Due to this, the orientation of the magnetic field with respect to the diffractive structure can easily be modified, so that, e.g. either in-plane or out-of-plane LC reorientation can be induced. We investigated in-plane reorientation, because it is quite difficult to realize entirely in-plane reorientation with electrically tunable LC gratings. This is because interdigitated electrodes that are usually used for this type of switching actually produce partially in-plane and partially out-of-plane electric fields [66].
Although magnetic tuning is contactless, it requires a controlling magnet to be placed close to the device, which may sometimes hinder its practical use. In such cases its advantages or disadvantages with respect to other noncontact LC DOE tuning schemes, such as those tunable by heating or optical irradiation [67,68], have to be considered. For instance, magnetic tuning can be advantageous in applications associated with biological systems, where heating or irradiation might damage the sample.
In our experiments the magnetic field was oriented at 45° with respect to the intrinsic LC alignment direction, as this arrangement is very convenient for visualization of the induced effects by optical polarization microscopy. In this configuration the diffraction efficiencies of a selected diffraction order for s and p polarized light, which are usually considerably different from each other at B = 0, became more or less the same at stronger fields (see Fig. 4). To generate even larger modulation, magnetic field should be oriented perpendicular to the alignment direction of the LC, i.e. along the x-axis in Fig. 2(b). In this respect it should be mentioned that there is no threshold effect present in ferromagnetic LCs even if the magnetic field vector B is perpendicular to the initial director orientation n0 [48,49]. Therefore, also in this case very low fields should already cause a significant LC reorientation.
Optimal modulation contrast can be obtained by an appropriate setting of the thickness D of the grating structure, which can be adjusted by the proper selection of the polymer precursor and parameters of the spin coating process. With B⊥n0 and an appropriate value of D, grating configuration can be realized in which at B = 0 one of the two polarizations (s or p) is fully diffracted (mostly into the 1st order diffraction peaks) and the other is fully transmitted, while in sufficiently strong B field the former becomes fully transmitted and the latter fully diffracted. In this way, magnetically tunable polarization switch can be obtained.
Another option to fully switch off or on of the diffraction efficiency by applying magnetic fields of several tens of mT, is to use a LC material whose extraordinary refractive index matches the refractive index of SU-8. Many standard LC mixtures have extraordinary refractive index of around 1.7, which is the value also typical for SU-8 (the exact value depends on additives and on the curing process). In such “index-matched” configuration at B = 0 (regardless the value of D) there should be be no diffraction for s-polarization, while there should appear strong diffraction for this polarization when a magnetic field oriented perpendicular to the grating planes is applied. For p-polarization, the behavior should be vice versa.
The main open problem that needs to be solved before the above-described DOEs can be considered for applications in practical devices, is the long-term stability of the ferromagnetic LC phase. Despite the fact that the ferromagnetic LC material used in our study is known to be stable in assemblies with standard alignment layers [44–48,69], our observations show that its contact with the SU-8 walls stimulates some segregation. For instance, small boojum defects at the surface could attract the BaHF nanoplatelets and cause their aggregation. Therefore, either a suitable surface coating for the platelets has to be developed that reduces their interaction with the SU-8 surface, e.g. such as the one reported in [43], or another photoresist has to be found that is less disposed to interaction with the platelets.
Another issue that needs further optimization, is the switching speed of the gratings. This can be improved by using smaller grating periods and stronger surface anchoring at the polymer-LC interface. The relatively slow DOEs described in this work are predominantly interesting for applications in contactless sensor devices for static or quasi-static low magnetic fields. Another interesting application associated with their ferromagnetic properties are spin-sensitive diffractive elements for cold and ultra-cold neutron beams [70]. However, with increasing switching speed, they might also become interesting for other usages, such as magnetically controllable dynamic beam shaping, for instance, by using polymer scaffolds with q-plate instead of line grating configuration [71].
In summary – our results prove the principle of operation of a new type of LC-based DOEs that are composed of periodic planes of a conventional photoresist polymer and a ferromagnetic liquid crystal. Due to the incorporation of the latter, the LC orientation can be switched by very weak magnetic fields. This feature can be used in diffractive structures with microscale periodicity, which makes them suitable for applications in the spectral region of the visible light. Further investigations need to focus mainly on chemical aspects of the involved materials to improve nanoparticle dispersability and dispersion stability and to optimize other material properties of the ferromagnetic LC phase, such as its temperature range or viscoelastic properties, that are required for specific applications.
Funding
Slovenian research agency (ARRS) (program P1-0192), Ministry of Education, Science and Sport (MIZŠ) & ERDF (project OPTIGRAD), Inter-governmental S&T cooperation program China-Slovenia (BI-CN/17-18-018,11-16), National Key R&D Program of China (2017YFA0303800), National Natural Science Foundation of China (91750204, 11674182), 111 Project (B07013), PCSIRT(IRT_13R29), Tianjin Natural Science Foundation (17JCYBJC16700), and Hundred Young Academic Leaders Program of Nankai University.
References
1. V. A. Soifer, Diffractive optics and nanophotonics, (CRC, 2017).
2. Y. G. Soskind, Field guide to diffractive optics, (SPIE, 2011).
3. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed., (Oxford University, 1993).
4. J. Chen, P. J. Bos, H. Vithana, and D. L. Johnson, “An electrooptically controlled liquid-crystal diffraction grating,” Appl. Phys. Lett. 67(18), 2588–2590 (1995). [CrossRef]
5. I. Drevenšek -Olenik, M. Copic, M. E. Sousa, and G. P. Crawford, “Optical retardation of in-plane switched polymer dispersed liquid crystals,” J. Appl. Phys. 100(3), 033515 (2006). [CrossRef]
6. S. M. Morris, D. J. Gardiner, F. Castles, P. J. W. Hands, T. D. Wilkinson, and H. J. Coles, “Fast-switching phase gratings using in-plane addressed short-pitch polymer stabilized chiral nematic liquid crystals,” Appl. Phys. Lett. 99(25), 253502 (2011). [CrossRef]
7. F. Fan, A. K. Srivastava, V. G. Chigrinov, and H. S. Kwok, “Switchable liquid crystal grating with sub millisecond response,” Appl. Phys. Lett. 100(11), 111105 (2012). [CrossRef]
8. V. Yu. Reshetnyak, V. I. Zadorozhnii, I. P. Pinkevych, T. J. Bunning, and D. R. Evans, “Surface plasmon absorption in MoS2 and graphene-MoS2 micro-gratings and the impact of a liquid crystal substrate,” AIP Adv. 8(4), 045024 (2018). [CrossRef]
9. D. Xu, G. Tan, and S. T. Wu, “Large-angle and high-efficiency tunable phase grating using fringe field switching liquid crystal,” Opt. Express 23(9), 12274–12285 (2015). [CrossRef] [PubMed]
10. Z. Feng and K. Ishikawa, “High-performance switchable grating based on pre-transitional effect of antiferroelectric liquid crystals,” Opt. Express 26(24), 31976–31982 (2018). [CrossRef] [PubMed]
11. D. C. Flanders, D. C. Shaver, and H. I. Smith, “Alignment of liquid-crystals using submicrometer periodicity gratings,” Appl. Phys. Lett. 32(10), 597–598 (1978). [CrossRef]
12. C. M. Titus and P. J. Bos, “Efficient, polarization-independent, reflective liquid crystal phase grating,” Appl. Phys. Lett. 71(16), 2239–2241 (1997). [CrossRef]
13. M. Honma and T. Nose, “Polarization-independent liquid crystal grating fabricated by microrubbing process,” Jpn. J. Appl. Phys. 42(11), 6992–6997 (2003). [CrossRef]
14. V. K. Gupta and N. L. Abbot, “Design of surfaces for patterned alignment of liquid crystals on planar curved substrates,” Science 276(5318), 1533–1536 (1997). [CrossRef]
15. G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005). [CrossRef]
16. C. Provenzano, P. Pagliusi, and G. Cipparrone, “Electrically tunable two-dimensional liquid crystals gratings induced by polarization holography,” Opt. Express 15(9), 5872–5878 (2007). [CrossRef] [PubMed]
17. R. K. Komanduri and M. J. Escuti, “High efficiency reflective liquid crystal polarization gratings,” Appl. Phys. Lett. 95(9), 091106 (2009). [CrossRef]
18. J. Sun, A. K. Srivastava, L. Wang, V. G. Chigrinov, and H. S. Kwok, “Optically tunable and rewritable diffraction grating with photoaligned liquid crystals,” Opt. Lett. 38(13), 2342–2344 (2013). [CrossRef] [PubMed]
19. C. C. Bowley and G. P. Crawford, “Diffusion kinetics of formation of holographic polymer-dispersed liquid crystal display materials,” Appl. Phys. Lett. 76(16), 2235–2237 (2000). [CrossRef]
20. K. Kato, T. Hisaki, and D. Munekazu, “In-Plane Operation of Alignment-Controlled Holographic Polymer-Dispersed Liquid Crystal,” Jpn. J. Appl. Phys. 38(3A), 1466–1469 (1999). [CrossRef]
21. T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L. Sutherland, “Holographic Polymer-Dispersed Liquid Crystals (H-PDLCs),” Annu. Rev. Mater. Sci. 30(1), 83–115 (2000). [CrossRef]
22. M. Jazbinšek, I. Drevensek-Olenik, M. Zgonik, A. K. Fontecchio, and G. P. Crawford, “Characterization of holographic polymer dispersed liquid crystal transmission gratings,” J. Appl. Phys. 90(8), 3831–3837 (2001). [CrossRef]
23. L. V. Natarajan, C. K. Shepherd, D. M. Brandelik, R. L. Sutherland, S. Chandra, V. P. Tondiglia, D. Tomlin, and T. J. Bunning, “Switchable Holographic Polymer-Dispersed Liquid Crystal Reflection Gratings Based on Thiol-Ene Photopolymerization,” Chem. Mater. 15(12), 2477–2484 (2003). [CrossRef]
24. R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, “Development of a new kind of switchable holographic grating made of liquid-crystal films separated by slices of polymeric material,” Opt. Lett. 29(11), 1261–1263 (2004). [CrossRef] [PubMed]
25. M. Castriota, A. Fasanella, E. Cazzanelli, L. De Sio, R. Caputo, and C. Umeton, “In situ polarized micro-Raman investigation of periodic structures realized in liquid-crystalline composite materials,” Opt. Express 19(11), 10494–10500 (2011). [CrossRef] [PubMed]
26. L. De Sio, L. Ricciardi, S. Serak, M. La Deda, N. Tabiryan, and C. Umeton, “Photo-sensitive liquid crystals for optically controlled diffraction gratings,” J. Mater. Chem. 22(14), 6669–6673 (2012). [CrossRef]
27. R. Fernández, S. Gallego, A. Márquez, J. Francés, F. J. Martínez, I. Pascual, and A. Beléndez, “Analysis of holographic polymer-dispersed liquid crystals (HPDLCs) for tunable low frequency diffractive optical elements recording,” Opt. Mater. 76, 295–301 (2018). [CrossRef]
28. C.-Y. Chen, T.-R. Tsai, C.-L. Pan, and R.-P. Pan, “Room temperature terahertz phase shifter based on magnetically controlled birefringence in liquid crystals,” Appl. Phys. Lett. 83(22), 4497–4499 (2003). [CrossRef]
29. C.-Y. Chen, C.-F. Hsieh, Y.-F. Lin, R.-P. Pan, and C.-L. Pan, “Magnetically tunable room-temperature 2 π liquid crystal terahertz phase shifter,” Opt. Express 12(12), 2625–2630 (2004). [CrossRef] [PubMed]
30. C.-J. Lin, Y.-T. Li, C.-F. Hsieh, R.-P. Pan, and C.-L. Pan, “Manipulating terahertz wave by a magnetically tunable liquid crystal phase grating,” Opt. Express 16(5), 2995–3001 (2008). [CrossRef] [PubMed]
31. L. Yang, F. Fan, M. Chen, X. Zhang, J. Bai, and S. Chang, “Magnetically induced birefringence of randomly aligned liquid crystals in the terahertz regime under weak magnetic field,” Opt. Mater. Express 6(9), 2803–2811 (2016). [CrossRef]
32. L. Zhang, Y.-X. Fan, H. Liu, L.-L. Xu, J.-L. Xue, and Z.-Y. Tao, “Hypersensitive and tunable terahertz wave switch based on non-Bragg structure filled with liquid crystal,” J. Lit. Technol. 35(14), 3092–3098 (2017). [CrossRef]
33. L. Zhang, Y.-X. Fan, H. Liu, X. Han, W.-Q. Lu, and Z.-Y. Tao, “A magnetically tunable non-Bragg defect mode in a corrugated waveguide filled with liquid crystals,” Phys. Lett. A 382(14), 1000–1005 (2018). [CrossRef]
34. F. Brochard and P. G. De Gennes, “Theory of magnetic suspensions in liquid crystals,” J. Phys. (Paris) 31(7), 691–708 (1970). [CrossRef]
35. S. H. Chen and N. M. Amer, “Observation of macroscopic collective behavior and new texture in magnetically doped liquid crystals,” Phys. Rev. Lett. 51(25), 2298–2301 (1983). [CrossRef]
36. M. Koneracká, V. Kellnerova, P. Kopčanský, and T. Kuczynski, “Study of magnetic Fredericksz transition in ferronematic,” J. Magn. Mater. 140, 1455–1456 (1995). [CrossRef]
37. Y. L. Raikher and V. I. Stepanov, “Transient field-induced birefringence in a ferronematic,” J. Magn. Mater. 201(1–3), 182–185 (1999). [CrossRef]
38. N. Podoliak, O. Buchnev, D. V. Bavykin, A. N. Kulak, M. Kaczmarek, and T. J. Sluckin, “Magnetite nanorod thermotropic liquid crystal colloids: synthesis, optics and theory,” J. Colloid Interface Sci. 386(1), 158–166 (2012). [CrossRef] [PubMed]
39. N. Podoliak, O. Buchnev, O. Buluy, G. D’Alessandro, M. Kaczmarek, Y. Reznikov, and T. J. Sluckin, “Macroscopic optical effects in low concentration ferronematics,” Soft Matter 7(10), 4742–4749 (2011). [CrossRef]
40. P. Kopčanský, I. Potočová, M. Koneracká, M. Timko, J. Jadzyn, G. Czechowski, and A. M. G. Jansen, “The structural instabilities of ferronematic based on liquid crystal with low negative magnetic susceptibility,” Phys. Status Solidi, B Basic Res. 236(2), 450–453 (2003). [CrossRef]
41. T. Tóth-Katona, P. Salamon, N. Éber, N. Tomašovičová, Z. Mitróová, and P. Kopčanský, “High concentration ferronematics in low magnetic fields,” J. Magn. Mater. 372, 117–121 (2014). [CrossRef]
42. N. Tomašovičová, S. Burylov, V. Gdovinová, A. Tarasov, J. Kovac, N. Burylova, A. Voroshilov, P. Kopčanský, and J. Jadżyn, “Magnetic Freedericksz transition in a ferronematic liquid crystal doped with spindle magnetic particles,” J. Mol. Liq. 267, 390–397 (2018). [CrossRef]
43. M. F. Prodanov, O. G. Buluy, E. V. Popova, S. A. Gamzaeva, Y. O. Reznikov, and V. V. Vashchenko, “Magnetic actuation of a thermodynamically stable colloid of ferromagnetic nanoparticles in a liquid crystal,” Soft Matter 12(31), 6601–6609 (2016). [CrossRef] [PubMed]
44. A. Mertelj, D. Lisjak, M. Drofenik, and M. Copič, “Ferromagnetism in suspensions of magnetic platelets in liquid crystal,” Nature 504(7479), 237–241 (2013). [CrossRef] [PubMed]
45. A. Mertelj and D. Lisjak, “Ferromagnetic nematic liquid crystals,” Liq. Cryst. Rev. 5(1), 1–33 (2017). [CrossRef]
46. Q. Liu, P. J. Ackerman, T. C. Lubensky, and I. I. Smalyukh, “Biaxial ferromagnetic liquid crystal colloids,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10479–10484 (2016). [CrossRef] [PubMed]
47. P. Medle Rupnik, D. Lisjak, M. Čopič, S. Čopar, and A. Mertelj, “Field-controlled structures in ferromagnetic cholesteric liquid crystals,” Sci. Adv. 3(10), e1701336 (2017). [CrossRef] [PubMed]
48. N. Sebastián, N. Osterman, D. Lisjak, M. Čopič, and A. Mertelj, “Director reorientation dynamics of ferromagnetic nematic liquid crystals,” Soft Matter 14(35), 7180–7189 (2018). [CrossRef] [PubMed]
49. T. Potisk, H. Pleiner, D. Svenšek, and H. R. Brand, “Effects of flow on the dynamics of a ferromagnetic nematic liquid crystal,” Phys. Rev. E 97(4), 042705 (2018). [CrossRef] [PubMed]
50. Y. Reznikov, A. Glushchenko, and Y. Garbovskiy, “Ferromagnetic and ferroelectric nanoparticles in liquid crystals”, in Liquid crystals with nano and microparticles ed. J. P. Lagerwall and G. Scalia, (World Scientific, 2017.
51. W. Li, W. Cui, W. Zhang, A. Kastelic, I. Drevensek-Olenik, and X. Zhang, “Characterisation of POLICRYPS structures assembled through a two-step process,” Liq. Cryst. 41(9), 1315–1322 (2014). [CrossRef]
52. Z. Ji, X. Zhang, B. Shi, W. Li, W. Luo, I. Drevensek-Olenik, Q. Wu, and J. Xu, “Compartmentalized liquid crystal alignment induced by sparse polymer ribbons with surface relief gratings,” Opt. Lett. 41(2), 336–339 (2016). [CrossRef] [PubMed]
53. D. W. Berreman, “Alignment of liquid crystals by grooved surfaces,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 23(3–4), 215–231 (1973). [CrossRef]
54. I. Drevenšek -Olenik, M. Fally, and M. A. Ellabban, “Optical anisotropy of holographic polymer-dispersed liquid crystal transmission gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 021707 (2006). [CrossRef] [PubMed]
55. M. Fally, M. Ellabban, and I. Drevensek-Olenik, “Out-of-phase mixed holographic gratings: a quantative analysis,” Opt. Express 16(9), 6528–6536 (2008). [CrossRef] [PubMed]
56. A. E. Costa Pereira and A. Rosato, “Transmission of Nematic Liquid Crystals in Electric Fields,” Revista Brasileira de Fisica. 5(2), 237–241 (1975).
57. P. Nayek and G. Li, “Superior electro-optic response in multiferroic bismuth ferrite nanoparticle doped nematic liquid crystal device,” Sci. Rep. 5, 10845–1-9 (2015). [CrossRef]
58. V. I. Zadorozhnii, I. P. Pinkevich, V. Y. Reshetnyak, S. V. Burylov, and T. J. Sluckin, “Adsorption phenomena and macroscopic properties of ferronematics caused by orientational interactions,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 409(1), 285–292 (2004). [CrossRef]
59. O. Buluy, E. Ouskova, Y. Reznikov, A. Glushchenko, J. West, and V. Reshetnyak, “Magnetically induced alignment of FNS,” J. Magn. Mater. 252, 159–161 (2002). [CrossRef]
60. T. K. Gaylord and M. G. Moharam, “Thin and thick gratings: terminology clarification,” Appl. Opt. 20(19), 3271–3273 (1981). [CrossRef] [PubMed]
61. https://simulation.cloud/electromagnetics, (FlexCompute Inc. 2017).
62. M. Rubin, “Optical properties of soda lime silica glasses,” Sol. Energy Mater. 12(4), 275–288 (1985). [CrossRef]
63. T. A. F. König, P. A. Ledin, J. Kerszulis, M. A. Mahmoud, M. A. El-Sayed, J. R. Reynolds, and V. V. Tsukruk, “Electrically tunable plasmonic behavior of nanocube-polymer nanomaterials induced by a redox-active electrochromic polymer,” ACS Nano 8(6), 6182–6192 (2014). [CrossRef] [PubMed]
64. O. Prakash Parida and N. Bhat, “Characterization of optical properties of SU-8 and fabrication of optical components,” ICOP Int. Conf. on Opt. and Photon. (CSIO) (2009).
65. J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” IEEE J. Display Technol. 1(1), 51–61 (2005). [CrossRef]
66. S. H. Lee, S. L. Lee, and H. Y. Kim, “Electro-optic characteristics and switching principle of a nematic liquid crystal cell controlled by fringe-field switching,” Appl. Phys. Lett. 73(20), 2881–2883 (1998). [CrossRef]
67. C. H. Lin, R. H. Chiang, S. H. Liu, C. T. Kuo, and C. Y. Huang, “Rotatable diffractive gratings based on hybrid-aligned cholesteric liquid crystals,” Opt. Express 20(24), 26837–26844 (2012). [CrossRef] [PubMed]
68. H. Jau, Y. Li, C. Li, C. Chen, C. Wang, H. K. Bisoyi, T. Lin, T. J. Bunning, and Q. Li, “Light‐Driven Wide‐Range Nonmechanical Beam Steering and Spectrum Scanning Based on a Self‐Organized Liquid Crystal Grating Enabled by a Chiral Molecular Switch,” Adv. Opt. Mater. 3(2), 166–170 (2015). [CrossRef]
69. M. Mur, J. A. Sofi, I. Kvasić, A. Mertelj, D. Lisjak, V. Niranjan, I. Muševič, and S. Dhara, “Magnetic-field tuning of whispering gallery mode lasing from ferromagnetic nematic liquid crystal microdroplets,” Opt. Express 25(2), 1073–1083 (2017). [CrossRef] [PubMed]
70. M. Ličen, I. Drevenšek-Olenik, L. Čoga, S. Gyergyek, S. Kralj, M. Fally, C. Pruner, P. Geltenbort, U. Gasser, G. Nagy, and J. Klepp, “Neutron diffraction from superparamagnetic colloidal crystals,” J. Phys. Chem. Solids 110, 234–240 (2017). [CrossRef]
71. Z. Ji, X. Zhang, Y. Zhang, Z. Wang, I. Drevensek-Olenik, R. Rupp, W. Li, Q. Wu, and J. Xu, “Electrically tunable generation of vectorial vortex beams with micro-patterned liquid crystal structures,” Chin. Opt. Lett. 15(7), 070501- (2017).
