A Review of Tunable Electromagnetic Metamaterials With Anisotropic Liquid Crystals

The performance of metamaterial is limited to a designed narrow band due to its resonant nature, it is highly desirable to incorporate active inclusions in metamaterials to extend the operation bandwidth. This review summarizes the development in realizing the tunability of electromagnetic response in metamaterials incorporated with nematic liquid crystal (LC). From rigorous comparison, it is found that the anisotropic property of nematic LC is essential in predicting the influence of LC molecular director orientation on the resonant frequency of metamaterials. By carefully designing the metamaterials and properly infiltrating LC, the operation frequency of single/double negative parameters of metamaterials can be dynamically modulated with remarkable red/blue-shift, depending on the LC molecular orientation angle. Moreover, the recent liquid crystal-based developments and novel applications are investigated and highlighted.


INTRODUCTION
In most cases, the electromagnetic parameters of natural materials are positive and larger than unity, while the materials whose optical parameters are less than unity or even negative are only investigated in specific hypotheses. Recently, metamaterials with customizable performance have attracted a great deal of attention in the fields of optics, electronics, physics, and materials, since their optical properties can be arbitrarily tailored by rationally designing their micro/nanostructures. Theoretically, the electromagnetic parameters of metamaterials (including the permittivity, permeability, and refractive index) can be designed with any desired values (even to negative), which provides an ideal platform for the free manipulation of electromagnetic waves.
In 1968, Veselago theoretically proposed a medium with both negative permittivity and permeability for the first time [1]. According to a rigorous analytical investigation, such a medium can exhibit various intriguing properties such as negative index, reversed Doppler effects, and perfect lens, etc. [2][3][4][5]. In natural materials, ferrite can exhibit negative permeability around its resonant frequencies, while metal can exhibit negative permittivity below its electron plasmon frequency [6]. However, research related to negative electromagnetic parameters has seldom been reported for a long time since natural materials rarely exhibit such special properties. To broaden the design strategies of material parameters, in 1996, Pendry proposed a kind of artificial structure with periodic split ring resonators (SRR), to significantly enhance the magnetic resonance and realize negative effective permeability [7]. Moreover, Pendry also designed a thin wire array to lower the plasma frequency and obtain a limited negative permittivity in a microwave frequency band [8]. Inspired by Pendry's works, D. R. Smith combined periodic metallic SRR and a wire array together to promote simultaneous negative permittivity and permeability in a certain frequency band, and thus realized a negative refractive index for the first time in experiment [9]. They found that periodic SRR exhibited an effective negative permeability, and the wire array alone exhibited a negative permittivity below its effective plasma frequency, while with the SRR and wire array together, a passband would appear when both permittivity and permeability were negative. The experimental demonstration of negative index along with a serial confirmation of extraordinary behaviors has attracted increased interest for studies on metamaterials [10][11][12]. During the last few decades, metamaterials with various different structural designs including Omega [13], S type [14], and fishnet [15,16], have been proposed. The rapid development of metamaterials has also stimulated many promising applications such as diffraction-unlimited imaging [17][18][19], invisible cloaks [20,21], subwavelength high-Q cavities [22][23][24][25], polarization manipulation [26], and electromagnetic absorbers [27][28][29][30]. It is significant that the freely designable electromagnetic parameters of metamaterials are important for the implementation of such devices.
Liquid crystal (LC) has emerged as a promising candidate for the manipulation of light waves since its director axis and optical properties are strongly dependent on the surface effect and ambient temperature, and its optical properties are very sensitive to the variation of external fields (such as the electric field, magnetic field, light field, sound field, etc.) [51,52]. The anisotropy of LC covers a wide frequency range from ultraviolet to microwave. Moreover, LC-based devices have many advantages such as small size, light weight, low cost, simple process, and continuous tunability. Therefore, as an excellent tunable functional material, LC is widely used in the optoelectronic fields. Recently, tunable metamaterials incorporated with liquid crystals have been widely reported in microwave, terahertz (THz), and even infrared bands. LC-based tunable metamaterials taking advantage of a large birefringence that can be dynamically controlled by applying external fields, have shown great potential to actively modulate the electromagnetic waves over a broad spectrum [15,16,47,49,50,[53][54][55][56][57][58][59][60].
Tunable LC metamaterials were first demonstrated in a microwave regime by applying external voltage [53,59]. The reorientation of the nematic crystals takes a response time of 300 ms to obtain a frequency shift of 360 MHz with the voltage changing from 0 V to 100 V [59]. Khoo et al. theoretically reported an analysis on tunable metamaterials based on coreshell nanospheres randomly dispersed in LC [47]. Werner et al. presented a reconfigurable metamaterial by sandwiching a nematic LC as a substrate into the conventional negative index metamaterial [50]. Wang et al. numerically investigated the tunability of metamaterials using a rigorous treatment for the LC director reorientation [49]. Compared to the control of microwaves, the manipulation of THz waves can be realized under a lower applied voltage with faster response speed due to the smaller required thickness of LCs. LC metamaterials with real-time control functions, such as polarization controllers [61], absorbers [62], and spatial light modulators [63] are employed in THz communications, imaging, sensing, detection, and other fields [64][65][66][67][68][69]. In 2013, Padilla et al. designed and implemented an LC-based tunable metamaterial absorber in the THz regime for the first time [70]. Subsequently, they also designed a THz spatial light modulation which could be independently controlled by a single pixel, and the overall modulation depth of the device reached 75% [71]. In 2017, Yang et al. used liquid crystals to achieve tunable THz metamaterial-like electromagnetically induced transparency and electromagnetically induced absorption, with modulation depths of 18.3 dB and 10.5 dB, respectively [72]. Vasić et al. realized an electrically adjustable liquid crystal THz metamaterial polarization converter based on a metal dielectric metal cavity structure [61]. Shen and others designed and implemented a multi-functional THz metamaterial device integrated with liquid crystal, which further expanded the application of liquid crystal metamaterial devices in the THz regime [73].
In this context, we will give a brief review for the development of tunable metamaterials incorporating liquid crystals. In Section 2, we will discuss the analytical approach for liquid crystals inside metamaterials in detail. Section 3 presents tunable electromagnetic parameter metamaterials based on liquid crystals. A survey of the recent novel liquid crystal-based developments and application is conducted in Section 4. Finally, we will discuss some of the major limitations of LCs and envision a promising future of tunable metamaterials incorporating liquid crystals. Hopefully this review can promote the research on tunable and reconfigurable metamaterials with various active inclusions for the improvement of the operation bandwidth and smart electromagnetic responses.

ANALYTICAL APPROACH FOR LIQUID CRYSTALS INSIDE METAMATERIALS
During previous analysis for LCs incorporated into an artificial microstructure, an isotropic treatment was found to be effective provided that the EM fields exhibited isotropic field distributions as is the case for most of the 2D photonic crystals. This means that only consideration of the effective permittivity change of anisotropic LC along the incident electric field axis is required. For metamaterial, such an assumption is more doubtful and clearly the anisotropic distribution has to be taken into account.
In this section, we present a comparison of anisotropic and isotropic treatments for a C-type metamaterial. As shown in Figure 1, the SRR design used in the present work is composed of double C-shaped strips with a back-to-back direction ( Figure 1A) to avoid a magneto-electric response. The metal patterns are printed onto the surface of fiberglass slabs made by Teflon with voids, and then permeated with nematic LC [54]. It is assumed that the electric field of the incident beam is polarized along the x direction and the magnetic field of the incident beam is polarized along the y direction to illuminate the structure along z.
The LC layer is treated as a homogenous isotropic material during the first analysis. For aligned nematic liquid crystal, the electric field of the incident beam is polarized along the x direction ( Figure 1), and its dielectric constant is approximately given as [56]: Where ε ⊥ and ε // represent the respective permittivities for the polarized beam perpendicular and parallel to the director axis n, θ denotes the rotation angle of the molecular director with respect to the x axis. On the other hand, a rigorous tensor description for LC is introduced for the anisotropic permittivity of LC. For the LC plate with the initial vector of the molecules in the x direction, the director axis n can take all values {cos θ, sin θ, 0} by applying a magneto/electric field based on the Fréedericksz effect. LC permittivity is described as follows [49,55]: Where Δε ε // − ε ⊥ Figure 1 shows the frequency dependence of the metamaterial transport response on the liquid crystal reorientation angle. For the isotropic treatment ( Figure 1E), when the LC orients from 0°to 90°, the resonance frequency of SRR increases gradually from 10.9 to 11.4 GHz whose change is 0.8 GHz. On the contrary, for an anisotropic treatment as shown in Figure 1F, the resonance frequency of SRR shifts toward a lower frequency with the increase of the liquid crystal orientation angle. Figure 1G shows the electric field distribution in the x-y plane when the SRR is resonated. It is observed that the localized electric field around SRR is mostly concentrated on the space between two C strips and parallel to the y-direction, instead of being polarized along the x-direction where the incident beam is polarized. Therefore, isotropic treatment is no longer so valid for the tunability analysis for the metamaterial [55]. As a matter of fact, the capacitance of the SRR depends on the permittivity component of ε x , ε y , and ε z , of which ε y dominates as shown in Figure 1C. When an external field orientates the liquid crystal director from paralleling x to paralleling y, ε y will grow from ε 0 to ε e , resulting in an increase in the capacitance and a decrease in the resonance frequency.

Tunable Negative Permeability Metamaterial
In this section, we will introduce two types of negative permeability metamaterial with frequency tunability via LC reorientation. In Figure 1, a typical broadside coupling SRR incorporates an LC layer between two reversed C-type metallic patterns. The prototype sample was prepared using printed circuit board technology, as shown in the inset of Figure 2A [54]. The transfer rate of the tunable SRR archetype is measured in the following three conditions; i) the SRR without magnets (in this case the average permittivity is ε 0 (2ε ⊥ + ε // )/3, ii) applying the magnetic field along x (θ 90), and iii) along y (θ 90). The calculated results and experimental shown in Figure 2A indicate that a noticeable decrease occurs at 10.9 GHz for the instance without the external magnetic field. The resonance frequency increases to 11.0 and 10.7 GHz when the magnetic field is then applied parallel to the x and y axes, respectively. It can be seen that the dependency of the resonance frequency to the liquid crystal director reorientation corresponds to the calculating results that involve the description of the permittivity tensor of the nematic substance.
Unlike an SRR operating under grazing incidence with magnetic field perpendicular to its surface, Figure 2B shows an electrically tunable short-wire pair-type of negative permeability metamaterial which can work under normal excitation of electromagnetic waves [59]. The unit cell of tunable metamaterial is made up of a couple of short wires put on the surface of fiberglass slabs made from Teflon with voids in between which were infiltrated with a nematic compound. And by adding an extra couple of narrower inplane bars to connect neighbor unit cells. It can be assessed that such interconnecting bars do not change the magnetic resonance behavior of a short-wire pair. To give a preliminary orientation of LC, on the surface of the Teflon substrate and copper element is covered with a thin layer of polyimide (PI) to compel the nematic liquid crystal parallel to the short-wire surface in an alignment state [57,59].
The transmission spectra for the short-wire metamaterial as a bias voltage function are given in Figure 2C. For zero-bias voltage, an obvious decrease takes place at 9.91 GHz, around that the effective permeability is anticipated to be negative. And the resonant frequency falls to 9.55 GHz as bias voltage gradually grows from 0 to 100 V. Then the saturation was adjusted and even the bias voltage was increased further. Therefore, the total  Figure 2D, it is obvious that when the director of LC is redirected from 0°to 90°, magnetic resonance frequency of the short-wire pair gradually reduces to 9.45 GHz, which results in a 0.42 GHz variation. A slightly narrow frequency variation is most probably due to the existence of a pre-tilted angle of liquid crystal via the PI surface. This means actual LC reorientation will be less than 90°, resulting in less permittivity alteration as well as the changes of resonance frequency.

Negative Index Metamaterial
On the basis of the successful demonstration of a frequency tunable metamaterial with a single negative parameter, we will present a double negative metamaterial with a dynamically varied left-handed passband. The idea is to add negative permittivity via a wire array to the original negative components. In view of tunability requirements, it is necessary to employ unit cells with a combination of negative permittivity and negative permeability parts. Figure 3 shows a tunable omega metamaterial sample with a broadside coupling SRR connected with infinite wire [58]. By utilizing external magnets, it is able to orientate the LC molecular director angle with respect to the x axis from 0°to 90°. Figure 3C shows the experimental transmission spectra of the metamaterial. When applying the magnetic field along the x axis (θ 0), the omega array shows a clear transfer passband, and it has a negative index of refraction as expected, of which the peak is located at 11.72 GHz, whereas a redshift of the passband can be observed with the peak shifts at 11.50 GHz under an orthogonal magnetic field excitation (θ 90). Although this passband deviation of 210 MHz is not wide, it is clearly perceptible with the comparatively broad bandwidth. The frequency shift is in accordance with numerical results calculated using the full tensor description for LC permittivity, as shown in Figure 3C. Experimental broader bandwidth is mainly due to a slight variation of the voids interspacing since the Teflon fiberglass is not so rigid, resulting in different magnetic resonances between layers, causing multi conjoined passbands and consequently a wider transmission window. Figure 3D plots the phase shift for the omega sample with different LC direction angles. From the variation of phase shift, it can be seen that phase difference increases around 10.6 GHz and reaches a peak of 174.5°at 10.93 GHz, corresponding to an approximate index variation of 0.25 for a 5.4-cm-long sample along the propagation path. Figure 4 shows the schematic view of the fishnet type of negative index metamaterial [60]. Due to the intrinsic structural characteristic, one layer of unit cells was connected to the other, therefore designing extra connecting bars for bias voltage is not required. Figure 4 gives the transmission spectra variation of the fishnet sample. As shown in Figure 4B, toward the initial target of liquid crystal director parallel to the fishnet surface, there is a well-resolved and high strength transfer summit around 9.01 GHz. The liquid crystal director redirecting from 0°to 90°shows that the ground transfer summit moves downward to 8.60 GHz. Figure 4C demonstrates the fishnet array's measured transmission spectra under different bias voltages. For zero-bias voltage, the fishnet structure displays a transfer passband around 9.14 GHz and another higher passband starting at 10.60 GHz with a smaller decrease in the gap. Quantitatively, as the bias voltage grows up to 60 V, the first transfer summit moves from 9.14 GHz downward to 8.80 GHz, accounting for a frequency shift of 340 MHz. The frequency shift for the passband is saturated beyond 60 V, indicating that the LC director is nearly perpendicular to the surface of the fishnet pattern.

Tunable Metamaterials With Liquid Crystals
Liquid crystals have the dual properties of crystals and fiuids. As mentioned in Section 3, LC reorientations would result in a dramatic change in the refractive index of LC, which in turn, would further change the response to electromagnetic waves. In nematic LCs, the crystal is in a rod-shape and the external stimulations such as thermal heating, pressure, and the magnetic and electric field, can control its directional order, resulting in good refractive index tunability [42,59,[74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91]. Therefore, LCs are extensive used as the liquid background of solid metamaterials [51,52,92]. The manipulations on the LC background metamaterial are first protested against in the microwave regime. The resonant frequency of the metamaterial is shifted under a DC voltage [93][94][95][96][97]. Compared to the operation under microwave conditions, the control of the THz wave can be obtained with a much faster response at a lower electrical voltage since the needed thickness of LC is much smaller [69,98,99]. For liquid crystals in a particular phase such as NLC, it is necessary to discuss their collective crystal responses. The timescale of collective crystal response is usually in the order of milliseconds-microseconds. The thickness of the liquid crystal will influence its response speed. To achieve certain modulations requires a very thick LC layer, leading to several disadvantages such as high operating voltage, slow response, and poor pre-alignment. A large birefringent liquid crystal material can reduce the thickness of the liquid crystal device, ensure the good orientation of the liquid crystal, and improve the response speed of the device. For a liquid crystal layer of the same thickness, it can increase the modulation range of the liquid crystal device. Compared with the thermal and UV irradiation-induced tunability of optical metamaterials, which have been experimentally tested, showing a slow temporal response, electrical tuning has a faster time response, which is the most attractive due to its easy integration and high reliability. Recently, a nematic liquid crystal-based tunable terahertz metamaterial which has large modulation depth and low insertion loss was designed [82]. The structure of the proposed compositive metamaterial is shown in Figure 5A, which consists of a two-layer sub-wavelength circular air loop array fabricated on a quartz glass substrate and embedded into the liquid crystal. The obtained results show that the amplitude modulation depth and insertion loss for normally incident electromagnetic waves are about 96% and 1.19 dB at 0.4212 THz, respectively, with the bias voltage varying from 0 to 16 V. Meanwhile, the transmission peak frequency gradually decreases from 0.42 to 0.38 THz. Differing from the resonant frequency shifted under a DC voltage, another literature paper about the continuously tunable and fast-response terahertz metamaterial was studied using in-plane switching (IPS) dual-frequency liquid crystal (DFLC) cells, in which dielectric anisotropy could be changed with the variation of applied voltage frequency [79]. When the frequency of an external voltage is switched, the resonance peak of the metamaterial can move to the high frequency or the low frequency, and the response times of the redshift and blueshift are 1.044 and 1.376 ms, respectively. Figure 5C shows the dual-frequency liquid crystal director orientations at the three applied voltages (voltages of 0, 80 V at 1 kHz, and 80 V at 22 kHz). More recently, a THz programmable meta-surface integrated with LC was proposed to manipulate the THz beam dynamically [69]. Figure 5E shows the 3D view of the THz programmable meta-surface. In Figure 5E, a 24-element linear array consists in the meta-surface, and a multichannel amplifier is in connection with each element. The control signal is outputted by the FPGA, and the amplified signals are utilized to control the phase of every element individually.
By further shrinking LC background metamaterials, the realtime control of IR and visible light are realized. Andrei Komar et al. presented an electrically tunable all-dielectric optical metasurface consisting of silicon nanodisks embedded into liquid crystals, as shown at Figure 5D [81]. The reorientation of nematic liquid crystals under an external electric field can change the anisotropic permittivity tensor of the meta-surface, which in turn, alters the response to electromagnetic waves. By controlling voltage "on" and "off" to achieve reorientation of the nematic liquid crystals and obtain 75% modulation depth and a phase change of up to approximately π. Similarly, a new combination of nematic liquid crystals and a binary-grating meta-surface was presented to control the diffraction efficiency by altering the applied voltage in the visible region, as shown in Figure 5B [91]. In addition, the effective tuning of the LC background metamaterial for wavefront manipulation has a wide prospect such as in tunable gradient indexed lenses [78,94]. By introducing a voltage gradient over the fishnet metamaterial based on liquid crystals, the phase distribution over the aperture can be tuned, and thus the radiation direction can be manipulated. Thus, we can develop novel applications for wavefront manipulation based on liquid crystal metamaterials. In a recent study based on fishnet metamaterials, the unit cells of the fishnet were embedded with nematic liquid crystal which provided a continuous tuning of each column of the array [78]. The photograph of a single opened fishnet unit-cell layer is shown in Figure 6A. Figure 6B shows the simulated electric field distribution at 27.4 GHz. By using liquid crystal as a tunable dielectric layer, the authors could achieve a voltage-tunable phase gradient over the aperture array, and obtain a measured continuous maximum beamscanning angle of 5°at 27.5 GHz, as shown in Figure 6C. The meta-surface based on liquid crystals can also be used to achieve tunable transparent displays for visible light [83]. As shown at Figure 6D, an all-dielectric meta-surface composed of silicon nanocylinders integrated into a nematic liquid crystal cell is presented. A switchable dielectric meta-surface display is achieved by varying the applied voltage from 0 V to 20 V in steps of 5 V. Figure 6E shows the real-color images of the proposed meta-surface at 0, 5, 10, and 20 V recorded in transmission. It is worth noting that the demonstrated meta-surface display uses a different operation theory than normal liquid crystal displays.
In addition to the applied voltage, temperature can be also used as an external control parameter [57,76,85,[100][101][102][103][104][105]. Heating of the sample over the liquid crystal transition temperature leads to the phase transition of the liquid crystal between nematic and isotropic, which can be used to realize the tunability of response to electromagnetic waves. In 2009, a thermally tunable optical metamaterial was demonstrated based on aligned nematic liquid crystals in the visible range [57]. Structure of the coupled sample is shown in Figure 7A. By changing the ambient temperature (from 20°to 50°C, which is beyond the phase transition temperature T c , 35°C), the phase Frontiers in Physics | www.frontiersin.org February 2021 | Volume 9 | Article 633104 8 transition of nematic LCs from the ordered phase to the isotropic phase can be realized, which in turn means the magnetic response wavelength can be effectively changed, as shown in Figure 7A. Temperature control of metamaterials with liquid crystals can also work in the terahertz region. The tunability of resonant response is realized due to the orientations of liquid crystals by changing temperature [76]. The two arrangements of liquid crystals lead to different modulations to the terahertz wave. It is illustrated that the resonant frequency decreases when the liquid crystal is aligned in the x-direction, whereas it increases when the liquid crystal is aligned in the y-direction in Figure 7B. In essence, the temperature control of metamaterials with liquid crystal is due to the changes in the refractive index of the liquid crystal. In Figure 7C, the results showed that the shift of the resonance fits the form of the temperature dependence of the liquid crystals' refractive index [102]. Furthermore, dynamic manipulation of electric and magnetic resonances can be both realized based on the temperature-dependent refractive-index tunability of the liquid crystal [100]. As shown in Figure 7D, the very different degrees of tunability of the two resonances modes allows for dynamically adjusting the spectral mode separation. In this experiment, the effect of temperature change on the refractive index of liquid crystal and the influence of phase transition on the resonant mode are both investigated. Besides the realization of dynamic tuning of the electromagnetic response of such metamaterials based on liquid crystals and the dynamic control of the light-emission properties of active liquid crystal meta-surfaces by an external control parameter were also demonstrated by Justus Bohn and coworkers [103]. Figure 7E shows the schematic of a metasurface integrated into a liquid crystal cell. When heating the liquid crystal, its state changes from nematic to isotropic, resulting in a spectral shift of the meta-surface resonances and the enhancement of tuning of the emission.

Liquid Crystals-Based Applications
Liquid crystals have dielectric and optical anisotropy. The directors of liquid crystal molecules can be adjusted through external fields, thereby effectively controlling the intensity, phase, and polarization of light waves and electromagnetic waves in various frequency bands, giving the liquid crystal materials a huge application potential. Using the controllability of liquid crystals and the special properties of metamaterials, meta-devices with real-time control functions can be realized, such as polarization controllers, absorbers, beam scanning, and spatial light modulators for information communication, imaging, and transmission. It can effectively solve the problems of the slow response speed of traditional liquid crystal devices, and has the advantages of small size, light weight, and easy integration. The free control of liquid crystal orientation can promote the development of manipulability of metamaterial-based devices. Based on the tunability of the refractive index of liquid crystal, more latent applications of liquid crystal background metamaterials have been discussed such as the perfect absorber [62,70,106,107], polarization converter [108,109], and modulators [110][111][112][113]. Salvatore Savo et al. have illustrated the ability of functional liquid crystals in a metamaterial absorber array working as a spatial light modulator during THz wavelengths by experiments. The 3D artistic impression of the metamaterial array is shown in Figures 8A and 8B [110]. The narrow band frequency response of the metamaterials can be electronically controlled by the orientation of the liquid crystal molecules. Polarization converters using liquid crystal metamaterials are also demonstrated. The physical underlying principle of efficient polarization converters consists in their operation in the regime in which the radiative losses are larger than the non-radiative ones [108]. The polarization of the incident electric field is linear. Depending on the applied voltage, the linearly polarized incident light is converted to RCP, linear, and LCP light. Moreover, in a recent literature paper, an electrically switchable color tag on account of an active liquidcrystal meta-surface platform was realized [113]. The realization of the proposed active color tags utilized the ability of the tunability of nematic liquid crystal reorientations controlled by an external electric field which would rotate the polarization of incident light. Figure 8C shows the schematic view of the integrated liquid crystal meta-surface device and the working principle to rotate the polarization of incident y-polarized light. Figure 8D shows the transmission pictures of a NEO tag, without an LC layer for x-polarized incident light (ϕ 0°) and for y-polarized incident light (ϕ 90°). Correspondingly, Figure 8E shows the transmission image of the NEO tag, with an LC layer for ϕ 0°and ϕ 90°at 0, 2, and 5 V.

PROSPECTIVE AND CONCLUSION
Incorporating active inclusions into metamaterial structures is of fundamental importance for increasing the operation bandwidth and dynamically manipulating electromagnetic waves. Artificially micro/nano-structured metamaterials with nematic LC provide a novel way to actively modulate the electromagnetic response. Nematic liquid crystals (NLC) dominate strong optical nonlinearities for photonics applications covering the femtoseconds to milliseconds time scales, and across a wide spectral range. The combination of the optical nonlinear behavior of liquid crystals and the peculiar physical properties of metamaterials is also one of the important advances in the field of liquid crystals. Many promising results on the tunability of metamaterials incorporated with nematic liquid crystal are reviewed, and these experimental studies have also reflected the inherent drawbacks of nematic liquid crystals as the active component. The foremost is the immobile layer in the immediate vicinity of the plasmonic structures [51]. This together with local inhomogeneous director axis alignment on the nanostructures all act to diminish the effective birefringence of the NLC for modulation/tuning effects. The theoretical tuning range due to complete realignment of the director axis with orthogonally polarized illuminating light is usually larger than the experimentally measured tuning range. This defect can be taken into account in the design of the metamaterial, and the optimization of the microstructure of the metamaterial may promote the agreement between the experimental value and the theoretical value. It is also very urgent and important to further design and fabricate liquid crystal materials with broadband, greater birefringence, smaller loss, faster response speed, and taking into account the wide liquid crystal phase temperature and other excellent characteristics. Furthermore, recent studies of another phase of chiral nematic liquid crystals, namely, blue-phase liquid crystals (BPLC) have presented promising alternatives. The second question that should be discussed is molecular anchoring. The realization of the LC tunability of metamaterials in the near infrared and optical regime is a much harder task, since the effects of molecular anchoring to the nanostructured surfaces becomes important when the dimensions of the individual meta-atoms become comparable to the size of the LC molecules, which has a significant impact on the tunability of optical metamaterials [114,115]. For example, under hard-anchoring conditions, the LC director axis in the immediate vicinity of the alignment layer remains unchanged while the bulk undergoes reorientation by the applied field. Liquid-crystal tuning of plasmonic resonances crucially rely on the ability to reorient the LC molecules within the near-fields of the plasmonic structure. One promising way of influencing the anchoring energy of the LC and to enhance tunability is the chemical functionalization of the metamaterial surface. In a recent study, it was found that after reducing the contribution of the supporting substrate to the metamaterial surface area it became possible to minimize the anchoring forces in the resulting hybrid and engage in-plane switching of the LC director at a nanoscale dimension [89].
In this paper, we present a brief review for tunable single/ double negative metamaterials based on nematic LC. And we discuss the development of the tunable behavior of metamaterials induced by liquid crystals. By utilizing an LC director controlled by applied voltage and temperature, it is possible to reversely modulate the metamaterials' operation frequency along with the unique value of effective electromagnetic parameters. LC reorientations will result in a change of the LC refractive index, which in turn, changes the response to electromagnetic waves. The ease of incorporation and large birefringence of LC enable it to become an ideal candidate for metamaterial substrates with varied permittivity. It is worth noting that the birefringence of LC increases with frequency. It is demonstrated that LC-based metamaterials are promising for the remarkable improvement of the bandwidth and may facilitate related applications at terahertz or even optical regimes. Hopefully this review can promote research on tunable and reconfigurable metamaterials with various active inclusions for the improvement of the operation bandwidth and smart electromagnetic responses.