Characterization and Application of Dual-Frequency Liquid-Crystal Mixtures in mm-Wave Reflectarray Cells to Improve Their Temporal Response

Liquid-crystal (LC)-based mm-wave spatially fed antennas with electronic reconfiguration are a promising solution at the higher frequencies required in next-generation networks. However, one of the main drawbacks of the technology in these bands stems from the high reconfigurability times they present. Through this work, a relevant step toward overcoming the temporal problem by using dual-frequency LCs (DFLCs) is presented. This article details, for the first time, both the electromagnetic and temporal characterization of four commercially available DFLC mixtures in W-band, enabling their use in designing faster devices. To evaluate the experimental characterization, a reflectarray surface (made of 50 × 50 cells) specifically designed to achieve fast switching times with a sufficient phase range has been manufactured and measured. For this cell, a preliminary addressing technique based on overdriving has been used, exhibiting reconfigurability (rise and decay) times of 20 ms, one order of magnitude faster than the current state of the art of LC-based mm-wave planar devices. The measured results match the simulations and reveal that a precisely designed biasing technique using overdrive (OD) must be used for DFLC-cells to achieve time reduction. Additionally, the benefits of this technology compared with other LC acceleration strategies in mm-wave are discussed.


I. INTRODUCTION
L IQUID-crystal (LC)-based mm-wave devices, such as reconfigurable intelligent surfaces (RISs), metasurfaces, reflectarray antennas, and other tunable microwave components, rely on the ability to tune the electromagnetic properties of LC materials. Although originally used in optical devices, to date, LCs have been used in RF to manufacture tunable antennas [1], [2], [3], [4], filters [5], [6], delay lines [7], [8], [9], [10] and frequency selective surfaces [11], [12], [13], among other reconfigurable devices [14]. These devices usually contain a cavity filled with an LC material whose dielectric permittivity can be tuned by means of varying an applied electric field. This biasing ac electric field polarizes the anisotropic molecules of the LC, which rotate according to the field, thus exhibiting a varying dielectric permittivity tensor in RF. Compared to other reconfiguration technologies, such as active elements (e.g., p-i-n diodes, MEMS) or novel materials (e.g., graphene, VO 2 ), LC allows for continuous tuning, performs well at higher frequencies (from dc to visible), and given the wide industrialization of LC-based optical devices, is low cost and of immediate availability. Therefore, they are a promising solution to enable the next generation of RIS, expected to be required by the upcoming high-frequency networks to mitigate the massive use of base stations and repeaters, and other next-generation devices.
However, one of the primary drawbacks of LCs is their slow response time in mm-wave [15]. When modifying the biasing electric field, molecules can take from seconds to minutes, to rotate toward their new permanent position, which makes all the previously mentioned devices excessively slow for certain applications.
Delving into the problem, the slowest transition (or switching between states) of LC molecules occurs when the bias voltage is brought down, due to the molecules relaxing only by the effect of viscosity and the weak molecule anchoring forces at the enclosing surfaces. On the contrary, when the bias voltage is increased, a fast response is obtained as a result of the molecules being actively forced to rotate by the applied electric field, which is converted into elastic energy. Conventional nematic LCs exhibit asymmetric temporal behavior with rising times in the range of milliseconds (with appropriate biasing) but decay times, at best, in the range of seconds. This problem does not arise in optical devices due to the reduced thickness of the LC cavity, which is related to the wavelength of the incoming signal. Since the response time increases quadratically with the thickness, reducing it could be an initial strategy to reduce reconfigurability times. However, by doing so one of the main design variables is no longer available for optimization, and for instance, in resonant devices such as reflectarrays, the risk of getting undesired critically coupled resonances greatly increases [16]. Therefore, in RF, novel strategies are required for this technology to overcome the temporal constraints.
Different strategies, summarized in Table I, have been proposed to tackle the decay time limitation. For instance, polymer network LC (PNLC) mixtures have been shown to reduce the decay time of LC molecules up to a 50× factor, achieving decay times in the order of 200 ms in these frequencies [17], and in optical devices, this factor can be even higher [18], [19].
However, the dielectric tunability of PNLCs is dramatically reduced with respect to conventional LCs, given that the polymer network cannot be tuned, which in practice seriously diminishes the achievable phase shift range. Moreover, the required voltage to fully rotate the molecules, rapidly increases with polymer concentration. This is disadvantageous, as the response acceleration also increases with polymer concentration [20].
Another mechanism to reduce the reconfigurability times of LC-based mm-wave devices is using sophisticated biasing signals that leverage the LC dynamics, sometimes referred to as overdrive (OD) and underdrive (UD). By using this approach, a fast-rising transition (from a lower voltage state to a higher voltage state) can be achieved. This is done by applying a timed high-voltage signal that quickly rotates the molecules toward the desired state and then reducing it to the voltage level related to the desired intermediate state. This can accelerate the rising transition by several hundred times. However, in the opposite case of accelerating a decaying transition from a higher voltage to a lower voltage (UD), the benefit is limited to 2×-3× for conventional nematic mixtures, as the minimum elastic energy that can be provided is at 0 V [21]. With the aforementioned decay times, it is clear that research in other technologies must be done to accelerate the decay time into the range of milliseconds.
A third possible solution is to use dual-frequency LCs (DFLCs), a specific type of LC that shows a sign inversion of its dielectric anisotropy at a few kHz (ac bias frequency). Biasing the LC in a positive dielectric anisotropy frequency makes molecules rotate parallelly to the electric field while doing so in a negative dielectric anisotropy frequency will rotate the molecules perpendicularly to the electric field. Therefore, the rising (excitation) and decaying (relaxation) transitions of molecules can be controlled independently and through an active force induced by the applied electric field, which can greatly reduce the response times [22]. The operating principle of DFLC is completely different from the previous strategies, and it does not intrinsically entail a tunability reduction.
Recently, they have also been tested in microwave devices such as filters and phase shifters [6], [7], [9]. However, in such works the device is manufactured blindly, that is, without a priori information of the DFLC material. Since the dielectric permittivity and losses of the DFLC materials are unknown, they have not been considered during the design stage of the devices, which limits repeatability. This also complicates the extrapolation of the technology to other devices. For instance, in [18], DFLCs are not considered assuming that their dielectric permittivity is too small, whereas through this work it will be shown that there exist specific mixtures with enough dielectric permittivity. Therefore, a rigorous electromagnetic and temporal characterization of these mixtures in mm-wave bands is necessary and currently non-existing. In the case of resonant planar structures such as RIS and reflectarray antennas, DFLCs have not been implemented yet, and it is unknown whether their tunability is sufficient to achieve enough phase range (e.g., 360 • ). In some applications, these devices require reconfigurability times of a few milliseconds [15], which have not been achieved with current technologies, as it has been previously introduced. Moreover, in those structures, DFLCs could help reduce the losses since one of the main reasons for the losses is the small thickness of the LC cavities necessary to reduce reconfiguration times. By using DFLCs, thicker cavities can be designed without sacrificing the response times.
In this work, the use of DFLC to reduce the reconfigurability time of planar cells for spatially fed antennas is proven for the first time in multi-resonant mm-wave surfaces, for which four different commercially available DFLC mixtures have been first characterized at W-band. The characterization is made both in electromagnetic (permittivity tensor, dielectric anisotropy, and losses) and temporal terms, thus enabling its use for future designs. It has been experimentally demonstrated that these mixtures provide enough dielectric anisotropy ( ε = 0.2-0.6) in W-band, suitable to design functional devices, although at the expense of having higher losses than devices using conventional LCs. A reflectarray surface specifically designed to exhibit a fast response time has been manufactured and measured using one of the four mixtures. The designed cell validates the characterization of the mixtures and exhibits a complete cycle of phase range (360 • ) and switching times between extreme states under 20 ms, thus improving the response times reported in the literature. The study also reveals the need for using both overdriving techniques, to reduce the times of DFLC cells in RF to achieve times in the millisecond range [21], and accepting a tolerable phase-error because of the undesired inertial effects produced in this type of cells, which are also evaluated in the article.

II. BACKGROUND: DFLCS
Given the anisotropic nature of LCs, its permittivity must be expressed as a tensor. Due to the uniaxial nature of nematic LC molecules, this tensor has the form of the following equation: Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. where O F F and O N refer to the totally unbiased and totally biased extreme LC states, and ε ⊥ and ε || are the parallel and perpendicular dielectric permittivities of the LC. DFLCs are the result of a mixture between an LC that shows a positive dielectric anisotropy, ε q = ε || − ε ⊥ , at low ac frequencies which decreases with frequency, and another LC showing negative dielectric anisotropy in the whole ac biasing band [28]. Consequently, an LC with positive anisotropy at low frequencies and negative anisotropy at higher frequencies, typically within the kHz range, is obtained. The frequency at which ε q = 0 is called the crossover frequency f c (see Fig. 1). Note that we use the nomenclature ε q for the dielectric anisotropy at quasi-static frequencies (ac), while ε refers to the dielectric anisotropy at the RF frequencies. Additionally, it is important to note that the use of dc components when biasing the LC should be avoided, as it can have long-term damaging effects to the mixtures, and only pure ac biasing signals should be used [29]. This change in the sign of the dielectric anisotropy is exploited to make the LC molecules react differently to the bias electric field. The induced polarization on the molecules created by a low-frequency bias field (positive anisotropy) makes them orient parallel to the field, whereas the one induced by a high-frequency bias field (negative anisotropy) orients them perpendicular to the field. This can be seen by looking at the electric energy density of the following equation (2), which is minimum for E ∥ n when ε q > 0, and for E ⊥ n when ε q < 0 [29], being n the unity vector that defines the macroscopic orientation of the molecules: where P is the induced polarization, E represents the ac biasing electric field and ε o is the free-space permittivity constant. Therefore, using DFLCs is a promising solution to reduce the slow decay time of thick mm-wave devices based on LC, since molecule rotation can be actively forced toward both perpendicular and parallel states. As compared to underdriving a conventional LC, which only reduces decay transitions reconfigurability times by 2×, DFLCs can theoretically reduce this time by several orders of magnitude. As compared to PNLCs, DFLC does not necessarily imply tunability reduction, nor requires large biasing voltages. However, DFLCs at 100 GHz have not been properly characterized, so their Additionally, the reduced dielectric anisotropy range that LCs provide in general in mm-wave bands, as opposed to in optic devices, makes the electromagnetic knowledge of the mixture critical for designing. The reduced anisotropy range in these bands makes the different design variables on the edge of viability (e.g., the LC cavity thickness), considering the tight trade-offs between losses, operating voltage, and reconfigurability capabilities and speed. In the case of using a novel mixture, not only a proper characterization is needed, but also an audition of whether it provides a set of favorable design points to tune the different trade-offs must be done. The rest of the article will cover this matter in more depth.

A. Electromagnetic Characterization
In order to obtain the parallel and perpendicular complex permittivities, as well as the temporal performance of different DFLCs, resonant planar surfaces (made of 50 × 50 cells) containing four different commercially available DFLCs have been manufactured and measured. The measurements have been used to extract the complex permittivities of the four mixtures, which allows for identifying their potential suitability in W-band devices. The studied mixtures are MLC-2048 (Merck [30]), MLC-2177 (Merck), W-1978C (MUT [31]) and P00-026 (HCCH [32]). These were designed to operate at optical frequencies and have never been characterized in RF, where the use of this technology is novel.
The electromagnetic measurements have been compared to full-wave electromagnetic simulations (CST Studio [33] under a periodic unit cell configuration in order to consider mutual coupling) with different complex permittivities to extract, through an iterative process, the ε || and ε ⊥ permittivities and the tanδ || and tanδ ⊥ losses, similar to [17]. More specifically, the co-polar reflection coefficient (S 11 parameter) of such structures has been measured in a free-space quasi-optical bench setup. The setup (see Fig. 2) consists of a vector network analyzer (VNA, Anritsu MS4647B), previously calibrated using a metallic plate at the top plane of the reflectarray to consider and normalize all the free-space effects of the setup (through calibration). The VNA, which is equipped with 70-110 GHz extenders to reach the W-band, measures the transmission between a pair of horn antennas (Flann 27240-20 WR10) illuminating the (periodical) cells at an incidence angle of 30 • , which provides the reflection coefficient. The choice of incidence angle corresponds to the optimal angle for the unit cell behavior, although a different angle could also have been used for characterization, granted that the same angle is used in both simulation and measurements. An arbitrary waveform generator, together with a 15× voltage amplifier, is used to bias the LC cells. The temporal characterization of each material has been carried out in the same setup by measuring the temporal evolution of the S 11 phase after changing the LC biasing electric field, following the same procedure as in [21], as further explained in Section III-B.
The structure and dimensions of the manufactured cells are shown in Fig. 3. A top 0.7 mm-thick glass superstrate containing a pattern of metallic resonant dipoles, together with a bottom glass substrate covered with gold to act as a ground backplane, create a 45 µm thick cavity for the DFLCs. The inner surfaces of both the substrate and superstrate are treated with a polyimide layer to anchor the LC molecules, which are rubbed to define their rotation plane. The cavity is sealed at the edges using UV-curing adhesive (NOA 81). The metallic pattern of the top electrode, composed of a periodical unit cell of three dipoles of different lengths, has been chosen such that the S 11 parameter shows different resonances at the W-band, which provides sufficient spectral accuracy for the resonances to be fit by testing different permittivity values. During the unit cell design, the choice of L xi will affect the width of the resonances, L yi affects their spectral location, and D i plays a role in the coupling between them. In order to allow for macroscopic measurement of the unit cell S 11 , the entire patterned array is short-circuited and connected to the same biasing signal [ac square shown in Fig. 4(a) and (b)], which ensures a specular reflection due to the periodic environment. For each device, the S 11 parameter curve has been measured at the OFF (V = 0 V) and ON (V = 45 V) states in the stationary regime and in the entire frequency band ([75, 110] GHz) for redundancy purposes. In the aforementioned iterative process followed to obtain the complex permittivities, the chosen parameter values of ε || , ε ⊥ , tanδ || and tanδ ⊥ are the ones that best fit the S 11 both ON and OFF states in the entire band. The amplitudes of S 11 have been used for the fitting, rather than the phase since it provides a higher level of distinction. In fact, the cells used for the characterization do not show a significant phase range performance since they could not be designed (the mixture parameters were unknown) and they are manufactured in glass superstrate, which has a very reduced cost and is much easier to manufacture with than quartz. However, the phase of the characterization samples is useful for response time characterization. During the extraction process, the pole-zero dispersion model of CST centered at 100 GHz is considered. This allows an accurate extraction, especially for the permittivity. Even though the losses are more complicated to extract from these thin structures, a reasonable approximation, adjusted to the measurements, has been found. In [17], this procedure provided effective values for ε || and ε ⊥ given the unknown real molecular distribution of the LC stemming from their imbrication with the polymer network. However, in this case, the extracted ε || and ε ⊥ are the true permittivities of the DFLC molecules given its uniaxial nature and therefore can be used in any DFLC design, not only reflectarrays. Table II summarizes the values of the complex permittivity of each studied mixture at W-band obtained after the iterative fitting process. Fig. 4 shows the amplitude of the S 11 parameter measured from each device at W-band, compared to the simulation using the values of Table II. As it can be seen, the simulation curves match the measurements throughout the whole band, which validates the obtained permittivities and losses  for each DFLC material. Additionally, it can be observed that the 100 GHz complex permittivities allow predicting accurately the S 11 parameter in the whole W-band using the previously mentioned dispersion model. It is worth mentioning that for this unit cell under this incidence angle (φ = 0 • ) the reflection coefficient in the orthogonal polarization is very close to 1 and the cross-polarization components are very reduced (−60 dB) regardless of the DFLC mixture.  Table II, it can be further seen that the dielectric anisotropy of the studied DFLC materials is reduced compared to mm-wave optimized mixtures (e.g., GT7-29001 by Merck), but can be sufficient to design devices with the required phase range (360 • ). Note that P00-026 shows the greatest dielectric permittivity. In terms of losses, the four mixtures are very lossy, even more than PNLCs [17], given that they were not optimized to be used in this band. This is similar to early LC-based reflectarray works, which used mixtures optimized for optical devices such as K15, BL006, and BL037 [34], [35], [36]. Therefore, as the technology advances, it is expected that the LC manufacturers will further optimize both the dielectric permittivity and especially the losses, at the mm-wave bands.

B. Temporal Characterization
In order to evaluate the temporal behavior to be expected for DFLC-cells that are filled with the different mixtures, the biasing sequences of Fig. 5 have been used, where a qualitative phase evolution is also shown for each state switching. The waveform sequence of Fig. 5(a) is used to measure the time of an induced rise transition (T I R ) from OFF to ON states. Similarly, the sequence of Fig. 5(b) is used to measure the time of a relaxation decay transition (T R D ) from ON to OFF, and the sequence of Fig. 5(c) is used to measure the time of an induced decay transition (T I D ) from on to off. These biasing waveforms are the simplest ones that allow a characterization of the different transitions to demonstrate that both rise and decay times can be controlled independently, while at Section IV more complex waveforms will be proposed and evaluated in order to leverage DFLC properties and engineer a reduction of the LC temporal response.
The temporal characterization results of each DFLC mixture are summarized in Table III. The details of each switching and state are summarized in Table IV, and explained more in depth in the Section IV. As expected, induced decay transitions are significantly faster than relaxation decay transitions since the extra torque induced by the biasing field accelerates the rotation of the molecules toward the relaxed state. In this article, the chosen frequencies f 1 and f 2 were the ones recommended in the manufacturer datasheet. However, note that these could be further optimized to achieve a higher ε q (as it can be seen in Fig. 1). To do so, a fine sweeping of frequencies would reveal the ones for which the mixture shows higher ε q . This would entail lower reconfiguration times since the force induced by the biasing field would increase. This effect can be seen in Table III, for columns T I R (induced rising transition) and T I D (induced decaying transition), where the reconfigurability times differ for the same applied voltage, as this represents different modules of ε q (between positive and negative dielectric anisotropy) being used. Since the times are measured for 45 µm thick LC layers, which is within the typical range of thicknesses of mm-wave planar cells, these times can be used as a reference to know what to expect for these devices. Dynamically modeling the state switching of the LC, that is, predicting the permittivity tensor ε r (r, t) even during transitions, is possible in DFLCs as it is in any nematic LC [21]. However, that would require knowing both the elastic constants of the mixtures and their rotational viscosity. If only the static permittivity tensor is required, it can be predicted by considering the elastic constants alone [37]. In practice, and although it could be extracted by experimental measurements [38] this information is unknown in most LC mixtures. However, the relation between the biasing voltages and the phase shift, and their temporal behavior, can be directly measured in a manufactured device.
Depending on the final application of the LC-based device, it is usual that only the extreme states (on and off) of the LC are used. This is the case of 1-bit reflectarray antennas or RIS. However, other applications can require a fine-tuning of the voltage to intermediate states of the LC biasing. For these cases, relating the required biasing voltage to the molecule tilt angle, and finally to its related exact permittivity tensor, is a previous necessary step to operate the device. In reflectarray antennas, this means relating the applied voltage to the phase shift introduced in each unit cell.

IV. DESIGNING THE BIAS OF DFLC REFLECTARRAYS
In this section, using the characterization from the previous basic bias signals, we design the proper waveforms to reduce reconfigurability times in DFLC devices.  It should be remembered that the biasing techniques used for conventional nematic LCs are based on using their dielectric anisotropy and a biasing field to induce rotation of the molecules on one direction (defined by the sign of ε q , explained in Section II), and rely on the relaxation of the molecules due to anchoring forces and viscosity of the material (in absence of biasing field) to rotate them in the opposite direction. These two rotations are referred to as rising transition for the rotation induced by the biasing field, and decay transition for the relaxation of the molecules (see Fig. 5(a) and (b), Table IV). Note that rise and decay transitions refer to the molecule variation rather than the phase variation.
As previously mentioned, the transitions induced by the biasing field are significantly faster than the relaxation transitions. Additionally, two main extreme states can be defined, these being when the molecules are in a fully relaxed state (off), and when they have rotated fully induced by the biasing field (on), as explained in Section II and Table IV. Any other in-between state is referred to as an intermediate state.
To sustain an intermediate step for a long period of time, the biasing field has to be kept at an intermediate voltage (lower than that which fully rotates the molecules), since the induced elastic forces oppose the anchoring torque. However, when using DFLC, an improvement in reconfiguration times can be achieved by making use of the opposite sign dielectric anisotropies they show at different frequencies of the biasing field. This allows to have induced transitions both rising and decaying (see Fig. 5(a) and (c)), and thus achieve the time reduction, although the decay relaxation can still be used as with conventional LCs [see Fig. 5(b)]. An advantage of being able to induce both rise and decay transitions is that overdrive biasing techniques [21] can be used to further speed up the reconfiguration. This, nonetheless, comes with a more complex biasing technique, due to the signals that need to be used. In the case of overdriven rise transitions to an intermediate state, a short high-voltage pulse with f 1 (e.g.: {±45 V, f 1 }), followed by a lower voltage signal with f 1 (e.g.: {±5 V, f 1 }) has to be applied as shown in Fig. 6(a) under the label Rise O D . In the case of overdriven decay transitions to an intermediate state, a short high-voltage pulse with f 2 (e.g.: {±45 V, f 2 }), followed by a lower voltage signal with f 1 (e.g.: {±5 V, f 1 }) has to be applied as shown in Fig. 6(b) under the label of Decay O D . This is a result of the torques at play, since signals with f 2 induce an elastic force in the same direction of the anchoring torque, and thus an intermediate state cannot be sustained with such frequency. As explained in [21], to use OD techniques requires an accurate design of the bias waveforms. This means that the dynamics of the rotation of the LC molecules, and its effect on the phase, must be known for each transition. This will allow to properly define the duration of the high voltage pulses (labeled T over drive in Fig. 6), of both the induced rising and decaying transitions. Note that, even though OD requires high voltages, the power consumption of the LC cells is very close to zero as the ac current flow is very small.
With these capabilities, two biasing techniques to reduce the reconfigurability time are proposed (see Table V). The first biasing technique makes use of overdriven induced rise and decay transitions to change in between any state (both extreme and intermediate). This technique can have the best temporal performance if optimized, since the molecules only rotate between the desired states, directly, and its rotation is accelerated via overdriving. However, the circuitry is very complex, since each unit cell has to be driven independently at all times (as opposed to the second technique) and must work both with low and high frequencies of the biasing signal ( f 1 and f 2 ). This strategy is implemented in Section V, having short-circuited all unit cells (no independent unit cell biasing).
The second strategy makes use of overdriven induced rise transitions to achieve any intermediate or extreme states but introduces an overdriven decay transition to the OFF state in between any reconfiguration, termed as reset. As it will be explained later, this implies a reduced complexity of the circuitry, since the reset can be easily applied simultaneously to all unit cells, although the reconfigurability time increases, since for every reconfiguration the molecules rotate to the OFF state before reaching the desired state. Fig. 7 shows an example of a complete antenna implementation with independent unit cell addressing (2-D) using the second biasing technique (reset between states). Rise transitions can be achieved by applying the signal ({V i , f 1 }) to each pixel of the bottom electrode and using the top electrode as ground for the biasing field (as shown in Fig. 7). Whereas the reset is easily achieved for all unit cells at once by applying the signal ({V T O P , f 2 }) to the short-circuited top electrode. The resulting voltage across each unit cell of the cavity is A first approach to the specific circuitry needed to drive an electrically large DFLC-based reflectarray, with thousands of pixels, would be implementing an active matrix (AM) similar to the ones used in liquid-crystal displays (LCDs) [39]. It is thus understandable that the first biasing technique would increase the complexity since the transistors and capacitors included in each pixel of the AM should be capable of reaching biasing signals of higher frequencies (e.g., 50 kHz). Instead, the reset technique would allow a fast reconfiguration (compared to conventional driving) with simpler circuitry.

V. FAST LC REFLECTARRAY UNIT CELL
After characterizing and studying both the temporal behavior and driving techniques of the different DFLC mixtures, a reflectarray unit cell fulfilling phase range (>360 • ) and temporal response specifications (<20 ms) has been designed, manufactured and tested. Given the electromagnetic performance of the studied mixtures, the chosen commercial DFLC is P00-026. The unit cell consists of the previously used metallic dipoles but patterned in a 400 µm-thick quartz superstrate, and an LC cavity thickness of 50 µm, as opposed to the 700 µm-thick glass superstrate and 45 µm LC cavity thickness of the characterization samples.
The reflectarray has been measured in the same setup as the previous cells in order to obtain the S 11 parameter and temporal response. Fig. 8 shows, at the two extreme biasing states (on and off) in stationary regime, the measured and simulated amplitude of the S 11 , with an adequate agreement between both. This further validates the extracted permittivity values of Table II, since the model allows a proper prediction of the measured behavior when manufacturing a different device (different LC cavity thickness and superstrate material).
Contrary to the cells used for characterization in Section III, this manufactured reflectarray cell has been designed with the complete mixture electromagnetic information, which allowed optimizing the structure to show enough phase range. The reflectarray shows a reconfiguration bandwidth of 10% (>300 • phase range), as depicted in the measured S 11 phase of Fig. 9 for different biasing states. As can be seen, most of the phase change occurs between 2 and 5 V.
In order to quantify the temporal response of the device, transitions between both extreme (on and off) and intermediate states have been evaluated. Regarding the extreme state switchings, Fig. 10 shows the evolution of the S 11 phase measured after a change in the bias conditions between extreme states, where the phase state at 0 V has been normalized to 0 • . This figure represents the actual measurements of the previously sketched switchings of Fig. 5. The actual biasing signal of each transition is also shown. As can be observed, induced rise (red solid) and relaxation decay (blue solid) transitions without OD take more than 5 s to converge to the final state. However, when using OD, the induced rise transition (red dashed) takes 20 ms, and the induced decay transition (blue dashed) takes 10 ms to converge. Interestingly, the final phase state of the overdriven induced transitions does not perfectly match the non-overdriven states. In the induced decay transition, this is due to the presence of a strong force pushing the molecules parallel to the reflectarray plane (beyond the unbiased position, where they are not perfectly parallel). In the rise transition, this is due to different states being reached (5 V is considered for non-overdriven and 45 V for overdriven), which are very similar (both can be assumed to be beyond the saturation voltage) since most of the phase change occurs from 2 to 5 V. Regarding the switching between intermediate states, Fig. 11(a) illustrates the phase change in an induced rise transition from 0 to 5 V. A transition without OD and two overdriven transitions are shown. The overdriven switchings have been carried out using the induced transition technique rather than the reset technique (see Table V), in order to minimize the response time. Similar to the previous case, the use of OD allows a considerable temporal reduction, although in this case the requirement to keep a 5 V phase state reveals interesting effects on the resulting phase. The biasing of the first overdriven transition (red) consists of a 60 ms 45 V pulse preceding a 5 V sustained state. This creates a rebound on the phase, attributable to backflow and inertia effects of the LC [21]. This introduces a transient 70 • phase error, although the final phase state is error-free. Considering this transient error tolerable, the switching time is 40 ms, while the non-overdriven switching time is 5 s. Similarly, the second overdriven transition (blue), consisting of an 80 ms 45 V pulse preceding a 5 V sustained state, reaches the desired state in 300 ms considering a 20 • transient phase error. These 70 • and 20 • errors, shaded in yellow and red in the figure, represent smaller errors than a 2-and 4-bit quantization errors, respectively, which in the case of a pencil beam only compromise the gain by 0.6 and <0.2 dB and slightly increase the SLL [40].
Finally, Fig. 11(b) details the phase change in a decay transition from 45 to 5 V, where both relaxation and overdriven induced decays are shown. In this case, the overdriven induced transition, whose bias includes a 10 ms 45 V pulse at 50 kHz, converges in 10 ms, while the relaxation transition takes around 1 s (20 • error). The intermediate state switchings shown in Fig. 11 can be considered as the worst case scenarios, due to the presence of LC inertial effects, which are nonexistent in transitions to extreme states, and due to the small difference in bias voltage between states. Table VI shows a comparison of the different LC acceleration techniques in reflectarrays. As can be seen, the acceleration in the decay transitions is the main benefit of DFLC in combination of OD. This is the technique that allows reducing the most decay time   while maintaining a large phase range at a reduced driving voltage.

VI. CONCLUSION
The ability of DFLCs to reduce the reconfiguration time of LC-based mm-wave spatially-fed planar antennas has been studied in this article. The complex permittivities of four different DFLC mixtures have been characterized using reflectarray cells, which enables their use in future designs. Their temporal behavior has been also measured. The dielectric permittivities of the studied mixtures are relatively low but sufficient to design devices with enough phase range. The time response, for 45 µm thick cavities and under different transitions, has been characterized, resulting in several orders of magnitude reduction with respect to conventional LC-based devices for the same thickness. However, they present large losses, given that they have not been optimized to be used in mm-wave. A reflectarray cell designed using one of the characterized mixtures (commercial) exhibits a complete phase range (360 • ), and temporal responses (rise and decay times) in the order of 20 ms, although at the expense of using overdriving techniques for both modes of operation of the DFLC. The use of these techniques is necessary in mm-wave cells, as the thicknesses are relatively large. Therefore, the applied voltage must be in the order of tens of volts, and inertia effects must be also assumed, which produces transient rebound in the phase that makes necessary a previous definition of tolerable phase errors to define the transition times. In any case, the DFLC has demonstrated to be at present the best solution to improve the switching times of LC-based mmwave planar devices. Although the manufactured reflectarray cell has revealed middle cell losses of about 12 dB, these can be improved by manufacturing novel DFLC to specifically operate at mm-waves. Moreover, these response times can be further reduced at the cost of increasing the maximum OD voltage, which requires specific circuitry handling large voltages. However, the power consumption can be kept very low, given that LCs and associated devices show a very small ac current flow. Since 2008, he has been a Researcher with the Applied Electromagnetism Group (GEA), UPM. In 2019, he joined the Department of Signals, Systems, and Radio Communications, where he is currently an Associate Professor. He is involved in the development of reconfigurable antennas in millimeter and submillimeter wavelengths using liquid crystals and the design of devices based on planar periodic structures, including reflectarrays and transmitarrays. His research interests include analysis, characterization, modeling, and the design of antennas and microwave systems, and both the electromagnetic and circuit theory. He has been involved three European projects and four Spanish national projects. He did a two-year post-doctoral stay at the International Iberian Nanotechnology Laboratory, Braga, Portugal, with the Marie Skłodowska-Curie Actions Scholarship and currently has a Distinguished Researcher Contract at the CEMDATIC Center, UPM, with the Beatriz Galindo Grant. His research revolves around the development of active photonics integrated circuits (PICs) with metamaterials or photonics crystals technologies for bio-sensing. Switzerland, from January 2015 to September 2017, as an Electromagnetic (EM), Dosimetry, and Antenna Researcher. Since October 2017, he has been with the Information Processing and Telecommunications Center, UPM, where he is currently an Associate Professor. He has participated in various projects supported by the Spanish Government; the Mexican Council of Science and Technology (CONACYT); the European Union's Sixth, Seventh, and H2020 Framework Programs; the European Space Agency (ESA); and industry (Metawave, Huawei, and Schmid and Partner). His main research interests include the design of reconfigurable antenna arrays, including reflect-and transmit-arrays, from microwave to terahertz frequencies, and EMF exposure, hyperthermia treatment planning, and other bioelectromagnetics topics.
Xabier Quintana is currently a Professor with the Technical University of Madrid (UPM), Madrid, Spain. He has been developing his activity at the Escuela Técnica Superior de Ingenieros (ETSI) de Telecomunicación, UPM, since 1993. He is the coauthor of more than 50 international publications in scientific journals with an impact index. He has made more than 150 communications to international conferences. He is also the coauthor of eight patents. His research interests include guided optical communications (anisotropic waveguides and unconventional fibers), unguided optical communications (atmospheric transmission and space), photonic applications of liquid crystals (displays, micro-displays, phase devices, tunable filters, and modal lenses), and organic electronics (OLEDs and organic photodetectors).