Electronically Reconfigurable Reflectarray Antenna Based on Single-Layer Liquid Crystal With Independent Dual-Polarization Control

This article introduces a low-cost, easy-to-manufacture, dual polarization reconfigurable reflectarray antenna based on liquid crystal (LC) that operates at W-band. The antenna is electrically large and is capable of independently steering the beam of two orthogonal polarizations. Two different implementations of single-layer unit cells (single resonant and multiresonant) capable of providing suitable phase range to independently control the two radiofrequency (RF) polarizations with enough isolation have been investigated. The single resonant cell was finally used to design, manufacture, and test a complete reflectarray antenna made of $55\times 55$ elements, for which an accurate and efficient modeling of the cells was implemented. The effect of the LC bias lines is minimized by following a thorough impact study. At a cell level, the measurements validate both the modeling and the capability of the LC to be locally biased at the same cell provided that the biasing network and the resonators of each polarization are properly distributed. At an antenna level, the measurements are predicted by simulations with excellent accuracy, which validates the design and modeling process. The measured antenna shows 35° of 1-D scanning range with 25 dBi gain and a maximum SLL of −9 dB in the entire range for both polarizations at 98 GHz.


I. INTRODUCTION
I N THE recent years, the popularity of mm-wave planar devices using liquid crystal (LC) technology has experienced a rapid growth.Introducing the tunable capabilities of LC in radiofrequency (RF) filters, metasurfaces, reflecting intelligent surfaces (RIS) or reflectarray antennas allows to provide electronic reconfigurability to these devices [1].The LC is a material whose electric permittivity tensor can be changed when a quasi-static (ac) electric field is applied through it, due to the rotation of its anisotropic rod-like molecules.In the case of reflectarray antennas and RIS, the LC allows to electronically modify the radiation pattern and, thus, to dynamically scan a beam or provide adaptive coverage to a blind zone [2].Compared to the different existing reconfigurable technologies, such as PIN and varactor diodes [3] or MEMS [4], LC can be used at the hundreds of GHz range (W-band and above) while being a low-cost solution, especially due to the industry readiness inherited from the optics manufacturers, where its use is widespread.Moreover, among other advantages, LC allows a continuous (not discrete) tuning and its inherent power consumption is close to zero.Although the response time of LC in mm-wave devices is naturally larger than other technologies, different works have demonstrated several strategies to reduce such times down to the millisecond scale at mm-wave frequencies [5], [6], [7], [8].
Numerous LC-based reflectarray unit cells have been introduced in the last decade, with the aim of improving the performance in terms of reconfiguration bandwidth [9], achievable phase shift [10], scan range [11], losses [12], [13], and temporal response [7], [8], [14].While there exist several passive unit cells targeting different static polarization manipulations [15], [16], [17], a very limited number of reconfigurable [18] and LC-based reflectarrays with polarization-sensitive capabilities have been presented.This is mainly due to the difficult unit cell design and LC characterization in that case.Moreover, given the anisotropy nature of the LC, which intrinsically introduces cross-polarization effects, achieving a single-layer design that can effectively work in a polarization-sensitive application with an accurate control and sufficient isolation becomes challenging.In [19], a LC reflectarray capable of converting a 45 • incident linear polarization signal to circular or orthogonal linear polarization was presented by modifying only one electric field component through a dipole-like unit cell pattern oriented along TE.In [20], a cross-shaped patch unit cell allows to scan a beam for both polarizations together in a dependently manner.In [21], a complex 15-layer structure containing two independent LC cavities and polarizers independently manipulates two orthogonal polarizations.However, a simple single-layer reflectarray based on LC with an independent control of each polarization in the same unit cell, and how to efficiently model it, cannot be found in literature.Nevertheless, this would be very valuable in a LC reflectarray antenna, and it is crucial for the operation and reduced cost manufacturing of a LC-based RIS, as it allows to independently control two separate beams for two orthogonal polarizations in a simple manner, enabling a vast increase in the channel link capacity.
In this article, a single-layer and electrically large LC-based reflectarray antenna capable of beam-steering polarization independent beams in W-band, together with a proper modeling and design process are presented for first time.To achieve such behavior, two LC unit cells sensitive to both polarizations, which in turn minimize the cross polarization, have been designed and evaluated.The first cell (single resonant) exhibits a phase range of 200 • at 98 GHz and its structure enables introducing a simple polarization bias network, provided that it is conveniently designed.The other cell (multiresonant) shows a complete cycle of phase-range (>360 • ) in a wider bandwidth, but at the expense of requiring another type of technology to implement the biasing.An accurate modeling of the LC cells, that includes the bias network to control the phase shift of the two RF polarizations in the same cell, has been proposed and experimentally validated at cell level.The modeling has been used in an efficient element-byelement design strategy that considers the angle of incidence to synthesize the proper biasing voltages at each cell, thus predicting its behavior.This allows analyzing an electrically large surface (composed of 55 × 55 elements) efficiently, as compared to entire device full-wave simulations.Then, a complete LC reflectarray antenna is designed, manufactured, and measured, validating the expected results.The antenna is capable of independently beam-steering and focusing each polarization in one plane at least 35 • with a gain of 25 dBi and a sidelobe level (SLL) as low as −9 dB in the entire scanning range.Due to the simplicity of the cell and the specific unit cell modeling, the agreement between expected results and the measurements is excellent.

II. SINGLE-LAYER DUAL POLARIZATION LC UNIT CELL
Reflectarray unit cells contain certain patterned elements which introduce resonances to the reflection coefficient of the RF electric field which spatially feeds the array, and consequently, this causes the phase of the reflection coefficient to abruptly vary.When the state of the LC molecules is changed through an ac electric bias field, the resonances shift in frequency due to the varying permittivity, and therefore different phase-shifts are introduced in the reflected RF electric field.In this section, two implementations of a unit cell for independent dual-polarization control are studied.

A. Unit Cell Design
In LC-based reflectarray unit cells, the structure consists on a stack of layers, typically one of them being the LC cavity.A common structure, from bottom to top, is the following one: a substrate supporting a metallic ground plane, the LC cavity, and a top superstrate electrode from which resonant elements protrude.Cavity spacers and a LC orienting layer, such as polyimide, are usually included (see Fig. 1).
The most straightforward way to independently control different polarizations in a LC-based reflectarray element is to bias with different voltages the cavity volume beneath the resonant elements sensitive to each polarization, within the same unit cell.Since the rotation of the LC molecules is a local property throughout the cavity, this allows different regions of the same unit cell to be biased independently to achieve separate reflection coefficients for each polarization.However, that introduces a strong inhomogeneity across the transversal direction (parallel to the surface), which must be accurately modeled in a polarization-sensitive design.Nevertheless, besides difficult to achieve, a very fine-grained model of these structures is excessively computationally expensive [22], and an efficient model point which considers the trade-off between computation and accuracy must be found.
Apart from the modeling, designing a unit cell sensitive to two independent polarizations which includes a LC cavity is challenging in different aspects.In a reflectarray antenna, the different cells will have different incident angles from the feed, which can vary their reflection coefficient.To reduce this effect, the size of the period should be minimized to achieve small sensitivities with the angle of incidence.However, when including resonant elements for each polarization, the required area to fit them increases.Another option is to reduce the size of the resonant elements (e.g., their width), which allows reducing the cell period while successfully limiting the coupling between polarization elements.However, this generates other unwanted effects such as sharp resonances and increase on the specular behavior as the electrically smaller cell yields a structure which begins to resemble a ground metallic plane.Some passive reflectarray works rely on a multilayer structure [16], which is undesired in LC designs since it would heavily increase the cost and manufacturing complexity.Moreover, biasing the LC requires adding conductive lines, typically metallic, to bring the correct voltage at determined unit cell areas.This forces the cell period to be large, which entails the need to have an accurate control of the reflection coefficient.
Another handicap appears when trying to minimize the cross-polarization effects of the cell.Together with the sensitivity to the angle of incidence, the anisotropic nature of the LC makes it difficult to maintain the cell symmetry, which further contributes to the cross-polarization.In a cell aiming at manipulating a single polarization, reducing the cross-polarization is useful to reduce the losses.However, in a cell aiming at manipulating both polarizations, these effects not only represent losses in each polarization but also affect substantially to the phase profile of the counter orthogonal polarization, which can lead to aberrant errors and important degradation of the radiation pattern.In [23], these effects are studied, and a rotation of elements is proposed for passive devices.Another possible strategy to reduce the coupling between polarization consists on maximizing the distance between the resonant elements of each polarization in the unit cell, which again has repercussions on the period size.Therefore, a trade-off between period size, sensitivity to angle of incidence, and cross-polarization levels must be found.
Another important aspect to consider when designing the unit cell geometry is the area of the superstrate containing resonant elements, as it has several effects.First, since this area (e.g., metallic patches) has both purposes of generating RF resonances and acting as a bias electrode for the LC, the larger the area the more LC material will be biased.This has an impact on the effective tunability of the cell.Second, the biasing of the LC results in an inhomogeneous molecule rotation both in the longitudinal and transversal directions of the cavity.The inhomogeneity in the transversal direction (parallel to the surface) comes directly from the resonant elements area.Since there is inhomogeneity on the metallic regions along this direction, the electric field will vary across it and therefore LC molecules will align differently.The inhomogeneity in the longitudinal direction (perpendicular to the surface) comes from the molecule anchoring forces in the cavity enclosing plates.These impose a pretilt angle which is independent of the driving voltage.Thus, when nonzero voltages are used, inhomogeneity appears along the longitudinal direction.Finally, it can also have an impact on the reconfiguration time.
Considering all the aforementioned effects, two different dual-polarization LC reflectarray unit cells have been designed: one containing a single resonant element per polarization (Fig. 1), and another one containing multiple resonant elements per polarization (Fig. 2).In both cases, the chosen LC is GT7-29001 (by Merck [24]), since it is specifically designed for mm-wave devices.Since the manufacturer specifications do not detail its electromagnetic properties at W-band, these have been extracted a priori, as detailed in Appendix A.
The unit cells consist of dipole-shaped metallic elements orthogonally oriented (along x and y considering the coordinate systems of Figs. 1 and 2).The geometry of the cell is such that the cross-polarization is minimized as much as possible.Specifically, the position, width, and length of the dipoles, together with the cell period are optimized and fine-tuned under different incidence angles and LC pairs of states.Among other aspects, it is important to keep certain symmetry in the cell so that both polarizations behave similar.Note that due to the LC anisotropy, the resonances for each polarization will vary.This variation is stronger in the multiresonant case, given the couplings between dipoles.Since the correct spectral concatenation of resonances in this case is essential, the set of dipoles are designed independently and finally combined and fine-tuned in a single cell.The design of the LC thickness considers a trade-off between losses and phase range.Whereas a thinner cavity increases the phase range and diminishes response time, it comes at the cost of increased losses.
Fig. 3 shows the reflection coefficient as a function of the frequency for the two polarizations (S X X and S Y Y ) at incidence angle φ inc = 0 • , θ inc = 25 • .As can be seen, the multiresonant cell exhibits a larger instantaneous bandwidth and phase range than the single-resonant cell, but since it must fit a larger number of dipoles, its period is larger and thus its tolerance to different incidence angles is much lower.Note that in the single-resonant case a relatively thick cavity (h LC = 80 µm) is chosen, since a single dipole resonance cannot achieve 360 • phase range anyway, and this way losses are reduced and critically coupled resonances are avoided.

B. LC Bias Lines
Finally, after the RF design of the cell topology and dimensions is finished, the metallic bias lines necessary to polarize the LC are added.This must be done carefully, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
as an improper placing of these lines could introduce in-band resonances and unwanted effects.In fact, in the multiresonant cell topology, adding the LC bias lines has a very strong effect on the response, and an alternative solution (e.g., using a material which is conductive for ac signals but transparent to RF) should be used.Moreover, the complexity of this cell would also add a lot of manufacturing difficulties.Considering this and the aforementioned reasons, the focus of this work (including the manufacturing) is the single-resonance unit cell reflectarray, which is enough to prove the dual polarization concept and allows to successfully scan independent beams.
In order to minimize the effect of introducing such lines in the single-resonant cell [Fig.4(a)], a thorough study has been carried out.Since the antenna should be able to perform scanning and focusing in a single plane, a column-like (along y) bias addressing will be used, where all the unit cells of the same column are interconnected.Three different kind of bias geometries (A, B, and C) have been analyzed and compared to the nonbiased (ideal) geometry.Note that in the ideal geometry of Fig. 4(a) the response of each polarization differs moderately.This lack of symmetry is due to the LC anisotropy and the oblique incidence.
In geometry A [Fig. 4(b)], the bias lines are added continuously (along y) for both dipoles.Given that the lines are orthogonal to the x-oriented dipole, the effect on S X X is almost unnoticeable, but S Y Y is significantly altered.In fact, in this case the resonance is completely out of band and, as a consequence, the phase is distorted by more than 200 • .
Geometry B [Fig. 4(c)] performs the column addressing at the bottom plane instead of the top plane.Since the bias signals are ac, and the LC molecules only react to the absolute magnitude of the ac electric field, in LC terms, it is not relevant whether the addressing of the columns is performed at the top electrode (each dipole of a different column is connected to a different voltage and the RF ground plane acts as ac ground plane) or at the bottom electrode (the bottom metallic plane is segmented in columns and each of those is connected to a different voltage, and all the dipoles are short-circuited in ac acting as ground plane).This is, in fact, how the different pixels in LC displays (LCDs) and other optical devices are addressed.However, the study reveals that it has important implications in RF, as segmenting the bottom electrode introduces unwanted resonances in the RF ground plane, mostly on S X X , which can fall in band.As can be observed, the S X X resonance is amplified by more than 4 dB and the phase slope becomes less linear.It should be mentioned that this architecture should be used if a full 2-D beam scanning is desired, provided that two isolated back-plane segments are considered with proper via-holes and at the expense of the spurious resonances that this type of segmentation introduces, thus requiring a proper and complex design of the electrodes.
The bias lines of geometry C [Fig.4(d)] connect to the dipoles orthogonally in a region where the electric field tends to be small, close to the center of the dipole.This introduces an elbow-like turn on the bias line of the y-oriented dipole, which slightly breaks the symmetry of the cell and marginally modifies S X X .Nevertheless, the effects of this addressing on both S X X and S Y Y are very limited [Fig.4(d)], due to the continuous bottom plane and an optimal position of the bias connection.In fact, any other connection point enhances the superficial currents in the bias lines, which generates noticeable effects in the reflection coefficients and degrades cross-polarization.Therefore, given that the segmented ground plane (Geometry B) introduces spurious resonances, among the geometries using a continuous ground plane (Geometries A and C), the Geometry C is finally chosen because its bias lines layout, perpendicularly connecting the dipoles at their center, yields the best results.The study also revealed that a width of the lines (W B ) as thin as 20 µm is a reasonable trade-off between RF impact and manufacture complexity.

C. Unit Cell Modeling
As previously mentioned, the modeling of these structures must be done carefully.On the one hand, the LC cavity is electrically very thin, and a number of high order nonevanescent modes are excited.This makes difficult to perform an equivalent circuital analysis and forces full-wave simulations of the unit cell.Moreover, due to the presence of two different potentials in the same unit cell (one per each dipole), not only the z inhomogeneity must be accounted for, but also the x − y inhomogeneity.On the other hand, using exhaustive volumetric models for the LC cavity, which can result very accurate since the LC director (i.e., the unit vector indicating the LC molecules orientation) is precisely determined in the whole cavity, results prohibitive in a design stage due to their computation cost.To tackle the z inhomogeneity, the community has successfully used an averaging strategy of the director tilt angle in the past, which reduces tremendously the computation while assuming a very limited error [22], [25].However, the x − y inhomogeneity problem has not been properly examined to its full extent, as the previous LC unit cells did not have to face this variation.Most of the cells in the literature do have an x − y variation, since the top electrode is not continuous [9].However, in those cases by assuming that the LC of the whole cavity is equally polarized results in negligible errors.This is because the regions where this assumption does not hold do not have a strong RF relevance, as the RF electric field is confined only below the metallic elements.
However, in the unit cells proposed in this work, the RF electric field of both polarizations must be considered, and the volumes underneath the dipoles will, in general, have different LC states.Therefore, to consider an accurate LC state in those regions, a strategy to account for x − y inhomogeneity in an efficient way must be introduced.The proposed solution consists on splitting the LC region in two sub-volumes, one per each polarization, and considering two different permittivity tensors.However, defining the boundary of each volume requires to look at the ac electric field of the cavity in different biasing scenarios, especially where the interactions between the different LC states are greater.The methodology to determine these two LC subvolumes is shown in Fig. 5.The ac electric field of the region of interest, in which a boundary of the subvolume must be defined, is shown in Fig. 5(a) for several pairs of biasing voltages (bottom: surface plot; top: cut plane at y = 1.2 mm).For the sake of brevity, only the ac field in one of the boundaries [red region of bottom Fig. 5(a)] is shown in the top Fig. 5(a).Considering such ac electric field, the boundary is placed where the interaction between both metallizations is lowest (x = 0.972 mm).Similarly, the other region where the interaction can be strong, between the x-oriented dipole and y-oriented dipole, is also analyzed, resulting in a boundary in x = 0.085 mm, thus defining the X-polarization LC subvolume block.The Y-polarization block is then defined as the subtraction between the defined block (X-pol) and the period.The resulting LC blocks are shown in Fig. 5(b).Once the two blocks are defined, the averaged E-field is used to solve the Ericksen-Leslie Equation [25] in each one, so the average orientation of the molecules and therefore the corresponding effective homogeneous tensor are computed.This enables a fast but accurate simulation of the unit cells in all the voltage state pairs in periodic environment.The phase shift resulting from this partition strategy has been compared with a finer grained partitioning where only the regions below the metallic elements are switchable, with very little discrepancy between both but resulting in a lower computation time.Note that by independently controlling different LC volume regions within the same cavity and unit cell, not only it is possible to control two independent polarizations but it also opens the door to future unit cell designs in which local knowledge of the LC is needed, such as dual-band LC unit cells.This modeling strategy is experimentally validated in Section IV.

III. DUAL POLARIZATION LC ANTENNA DESIGN
With the previously proposed unit cell, an electrically large reflectarray antenna capable of beam steering in two orthogonal linear polarizations is designed (Fig. 6).The reflectarray surface contains a quasi-periodic array of 55 × 55 elements whose structure can be seen in Fig. 1, and the focal points for the two polarizations are chosen to be at (x f , y f , z f ) = (31.3,0, 136) mm, which will drastically simplify the setup for measuring the radiation patterns of the two RF polarizations using a single polarization horn conveniently rotated, as explained below.The corresponding f/D ratio is 1.98, which is relatively large as this reduces the impact of a limited phase range.However, the illumination taper is kept at −10 dB, with Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.minimum differences between polarizations.Since analyzing the behavior of such electrically large surface in a full-wave simulation would be computationally prohibitive, an elementby-element analysis is performed assuming a local periodicity approach.To do so, the unit cells are simulated in a periodic environment using CST Studio [26] (∼5 min per simulation).A simulation is carried out for each of the different incident angles and pairs of biasing voltages, in order to obtain the S-parameter matrix in each case.Then, considering the impinging electric field from the feed, and the desired S-parameters for a specific radiation pattern, the reflected field on the aperture is computed in each unit cell.This way, the different configurations can be computed just by choosing the convenient S-parameter in each element and performing simple matrix multiplications, instead of having to perform all simulations in the entire surface (several hours per simulation) per each pair of states in each cell.
In order to synthesize the radiation patterns, a phase-only algorithm is used initially.An in-house tool [25] allows calculating the appropriate biasing voltage for each polarization at each angle of incidence from the required phase shift.However, considering that the single-resonant unit cell does not have a complete 360 • phase cycle (the phase range is 200 • but continuous), and that there might be substantial amplitude variations along the surface, several phase constants are added to the chosen S-parameters to obtain a set of valid radiation patterns.Then, the best performing ones in terms of directivity and SLL are chosen, which mostly leaves the strong amplitude and phase variations far from the array center.

A. Manufacturing Process
The reflectarray antenna has been manufactured in a clean room facility at UPM.First, a 1 − µm-thick gold layer is deposited on a 400 − µm 4-in quartz and patterned with the top electrode mask.The mask contains two connector regions where the 55 voltages of each polarization can be coupled to external flex connectors.Then, a glass is continuously covered in gold to create the ground plane.Next, polyimide is deposited and rubbed in both top and bottom electrodes to define the rotation plane of the LC molecules.On top of this layer, a SU-8 photoresist deposition and posterior patterning is performed to grow the LC cavity spacers.Note that these spacers are placed far from the dipoles to diminish their effect in RF [see Fig. 7(a)].Finally, the cavity is closed, filled with the LC, and sealed with adhesive, and the entire antenna is fixed on a methacrylate plate to provide robustness.A ground connector and a couple of flex cables interconnect the electrodes with pulsewidth-modulation (PWM) drivers [27], which are capable of controlling the 110 bias lines simultaneously with the desired root mean square voltage [Fig.7(b)].

B. Unit Cell Measurement
Once the reflectarray surface is manufactured, a macroscopic unit-cell measurement in periodic environment is necessary to validate cell level simulations.A VNA connected to a pair of horn antennas is first calibrated (thru calibration procedure) and then used to measure the reflection coefficient at a certain incidence angle (φ inc = 0 • , θ inc = 30 • ) of the reflecting surface.The surface has been measured in the setup of Fig. 7(c).These horn antennas (Anteral LHA-30-WR10) have lenses embedded, which contributes generating a plane wavefront to illuminate the sample.
In order to obtain a macroscopic measurement of the unit cell reflection coefficient, all unit cells are short-circuited to the same voltage (ac square waveform).This way, the LC is equally excited in each unit cell along the surface, obtaining a periodical surface with specular reflection.Note that the voltages of X-polarization (V x ) and Y-polarization (V y ) can be different.Fig. 8 shows the measured and simulated unit cell reflection coefficient for different pairs of LC states.Specifically, Fig. 8(a) shows S X X when varying the voltage for the x-oriented dipole, V x , and keeping V y = 0. Similarly, Fig. 8(b) shows S Y Y when varying the voltage for the y-oriented dipole, V y , and keeping V x = 0.As can be seen, the previously proposed efficient model allows an excellent prediction of the reflection coefficient in every state.Moreover, thanks to the final dimensional fine tuning in the unit cell design, the maximum measured cross-polarization levels of the unit cell reflection coefficient (S X Y and S Y X ) across all the bias states is −12 dB.
In order to test the independence between polarizations at the unit cell level, the reflection coefficients have also been measured while varying the states of the opposite polarization.In Fig. 9, S Y Y remains almost unchanged when varying V x from 0 to 5 V, both in simulation and measurement.
Finally, the unit cell tolerance to different incidence angles is also tested (Fig. 10).As expected, due to the small period and high symmetry of the unit cell, changing the incidence angle has very limited effect on the reflection coefficient.In the Measured and simulated S Y Y phase for different X-polarization biasing states (V x ), keeping V y = 0.

C. Antenna Measurement
The antenna has been measured in an anechoic chamber under different beam configurations for each polarization.The measurements for each polarization have been carried out individually, using a single polarization horn antenna (Flann 27 240) as feed and rotating it 90 • , leveraging the same focal point.This facilitates a simpler measurement setup and the results are equivalent to using a dual-polarization feed, due to the electric field superposition principle.Fig. 11 shows the antenna measurement setup in the anechoic chamber.As can be seen, a 3-D-printed plastic holder helps setting the feed in place.
The measured and simulated cuts of the gain radiation patterns in the scanning plane can be observed in Fig. 12.As can be seen, each polarization behaves very similarly when pointing toward different directions between 5 • and 40 • .The maximum gain is 25 dBi and the corresponding efficiency is of 24%.The achieved gain is consistent with this kind of antenna, considering that an ideal reflectarray aperture would provide 36 dB gain (including spillover and illumination efficiency), and that the ohmic losses, one-plane focusing, limited phase range (continuous 200 • ), and phase errors have been estimated to approximately represent 1.5, 6, 1.4, and 2.1 dB gain reduction, respectively (see Table I).Note that these estimated gain losses are obtained for the maximum beam direction.For other directions, not only these gain losses should be  considered, but also the additional scanning losses.It is worth noting that additional simulations show that the antenna can further beam-steer to 60 • at the expense of assuming the inherent scanning losses, although no experimental data are available.Moreover, it must be mentioned that the scanning region from 5 • to negative angles was not measured due to the blockage of the feeding chain and holder.However, if the distortion and gain reduction due to the scattering on these elements are assumed, the scanning range could be drastically increased.
Even though the agreement is very close, there exist small mismatches between measurements and simulations (for instance, 40 • beam at X-polarization), which are due to different sources of errors.First, inevitable manufacturing tolerances are present (∼5µm in gold photolithography, ∼3µm in SU8 spacers, ±20µm in quartz thickness, and so on).During the final checks, it was detected that one bias line was cut due to the photolithography process, introducing a small error.Second, there might be a small inaccuracy on the feed location, due to the 3-D-printed plastic holder.It is worth noting that, close to 100 GHz, any mismatch can result in several wavelengths displacement.Third, the fact that the cell is limited to a 200 • quantization.Fourth, inherent measurement errors such as alignment (near-field measurement in planar range), and unwanted reflections on the flex connectors, are also present.In order to better quantify the impact of those factors, a tolerance analysis has been carried out, which consisted on computing the cell response considering all the different sources of errors.The worst case scenarios for the phase deviation have been used to recompute the far-field radiation patterns.The results indicate that all the measured mismatches are consistent with the tolerances.Moreover, the tolerance analysis for the scanning angle of 40 • also shows  that the X-polarization is more sensitive to tolerances than the Y-polarization.However, even so, the differences between simulations and measurements for 40 • X-polarization are not completely explained by the tolerances.Thus, we attribute this to a misalignment of the feeder that was detected when measuring this particular scanning angle, which could degrade the illumination to the reflectarray surface.
The independence between polarizations has also been measured at the antenna level in the anechoic chamber.Fig. 13 shows the measured U-V radiation pattern for two different beam directions in X-polarization.As can be observed, when varying V y to point the Y-polarization beam toward other directions, the X-polarization remains unchanged.Note that, due to the 1-D scanning (LC bias addressing made by columns), as expected only one plane is collimated.a low complexity, both in terms of manufacturing and analysis design process.Compared to most of the literature, antenna is electrically larger and achieves a lower SLL (maximum SLL of −9 dB in the entire scanning range and both polarizations).Close to the specular direction, this SLL is improved to −13.5 dB, and it worsens with increasing scanning angle due to the abrupt phase variations leading to greater phase errors.Note that for a fixed illumination, the measured SLL level is closely related with the phase errors committed on the antenna surface, which can be produced by the phase quantization (if assumed), the manufacturing tolerances, the accuracy of the electromagnetic modeling used to design the structure and/or the design process itself.Therefore, even when the phase-range of the cell does not cover 360 • , these results highlight that both the modeling and the design process described here are suitable to develop this type of antennas with excellent accuracy.

V. CONCLUSION
A dual-polarization LC-based reconfigurable reflectarray antenna operating at W-band is proposed in this work.Two novel unit cells, a single-resonant one and a multiresonant one, have been designed such that different LC states can control independent polarizations within the same cell and single LC cavity, which represents a considerable complexity reduction with respect to the state of the art.It has been shown that the LC can be locally tuned while maintaining low the coupling between polarizations, which is not evident in anisotropic materials.A study is carried out to minimize the impact of introducing the LC bias lines in the cells, after which the single-resonant cell has been chosen for manufacturing.To aim at higher phase range and bandwidth using the multiresonant cell, other addressing technologies are needed.Together with the proposed cell, an analysis strategy has been developed to model it accurately.It is confirmed by experimental validation that partitioning the LC volume in subvolumes to account for x − y inhomogeneity allows a precise and computationally efficient analysis.The complete reflectarray antenna has been designed, manufactured and measured, achieving significant agreement with simulations, due to the element-by-element design process and a precise cell modeling.The antenna is capable of beam-steering over one plane from 5 • to 40 • , with a maximum gain of 25 dBi and an SLL as low as −9 dB.

APPENDIX A W-BAND LC CHARACTERIZATION
Prior to perform any LC unit cell design, the characteristics of the LC under use at the operating band must be known, i.e., the parallel and perpendicular complex permittivities (ε || and ε ⊥ , respectively).In this work, the LC mixture GT7-29001 (by Merck [24]) is used.Nevertheless, the permittivities at W-band are unknown, as the manufacturer data only provides those values at 19 GHz.In order to obtain such information, an experimental extraction process is performed, in which the measured unit cell reflection coefficient of a manufactured device is iteratively compared to the simulated one, in the whole band, varying the complex permittivity.This process has been validated by several works [6], [7], [29].First, two sample reflectarray surfaces have been manufactured containing the studied LC.The unit cell used for this characterization, shown in Fig. 14(a), is a well-known multiresonant single polarization cell.Its detailed geometry can be found in [9].
The samples are identical apart from the LC cavity thickness, which is 42 µm in one case and 50 µm in the other.The Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
samples consist of 50 × 50 cells, and their unit cell reflection coefficients are measured in the same setup of Fig. 7(a).For redundancy purposes, the reflection coefficient is extracted, for both samples, at two different voltage states (V = 0 V and V = 10 V) and throughout the entire band.Finally, the simulated complex permittivity values that best match those measurements, as shown in Fig. 14, are the extracted values.In this case, the extracted W-band permittivities are ε || = 3.5, tanδ || = 0.015 and ε ⊥ = 2.47, tanδ ⊥ = 0.02, which slightly differ from those provided at 19 GHz.

Fig. 3 .
Fig. 3. Simulated amplitude and phase of the S X X and S Y Y reflection coefficients of the (a) single-resonant and (b) multiresonant unit cells for OFF (V=0) and ON (V≫10V) states.

Fig. 4 .
Fig. 4. Main conclusions of the analysis on the addressing bias geometry.The amplitude and phase of S X X and S Y Y are compared to the original unit cell for each geometry (Vx=Vy=0 V state) under oblique incidence (φ inc = 0 • , θ inc = 25 • ).(a) Original unit cell without bias lines.(b) Addressing geometry A. (c) Addressing geometry B. (d) Addressing geometry C (D = 0.06 mm, W b = 0.02 mm).

Fig. 5 .
Fig. 5. (a) AC electric field in the unit cell region where the bias fields of the different polarizations interact the most (top).As indicated by the surface plot of the field (2×2 unit cells, bottom), the E-field data is from the y = 1.2 mm cut (where the x bias and y bias metallization are the closest) and averaged across z.(b) Resulting LC blocks for an accurate but efficient simulation.

Fig. 6 .
Fig. 6.Sketch of the proposed LC reflectarray antenna, including the horn antenna feed and the flex connectors.

Fig. 7 .
Fig. 7. (a) Microscope view of a unit cell with an SU-8 spacer.(b) PWM-based drivers.(c) Manufactured reflectarray surface and unit cell measurement setup.

Fig. 9 .
Fig. 9.Measured and simulated S Y Y phase for different X-polarization biasing states (V x ), keeping V y = 0.

Fig. 10 .
Fig. 10.Measured and simulated S Y Y phase under different incidence angles for two LC biasing states.

TABLE I BREAKDOWN
OF ESTIMATED GAIN LOSSES

TABLE II LC
REFLECTARRAY ANTENNAS COMPARISON

Table
II compares this work to different LC reflectarray antenna references.As can be observed, it is the first antenna capable of independently controlling dual polarization while