Time-Modulated Patch Antennas With Tunable and Nonreciprocal Polarization Response

In this paper, we propose and demonstrate time-modulated patch antennas able to exhibit opposite polarization ellipticity when operated in transmission or reception, effectively leading to nonreciprocal polarization responses. To this purpose, we merge a patch antenna fed from four symmetrical sides with a low-frequency time-modulation scheme. This configuration exploits the photonic Aharonov Bohm effect to individually manipulate the phase of surface currents flowing along orthogonal directions on the antenna with the phase of the modulation signals. The polarization states of the radiated/received waves can easily be calculated using diagrams in the Poincaré sphere together with the phase difference of the modulating signals. Experimental results at 2.2 GHz demonstrate high conversion efficiency in the time-modulation process, isolation levels over 40 dB in transmission/reception mode, and tunability to generate/receive electromagnetic waves with arbitrary polarization ellipticity. Our findings may enable exciting applications in full-duplex communications as well as in polarimetric radar, sensing and imaging systems.


I. INTRODUCTION
Recent years have witnessed the quick emergence of magnetless nonreciprocity [1], [2] and the development of a wide variety of integrated, CMOS-compatible microwave devices such as circulators [3]- [7], isolators [8], [9], and nonreciprocal filtering structures [10]- [13]. Additionally, ultrathin metasurfaces have recently been put forward to manipulate the refraction and transmission properties of free-space propagating beams in a nonreciprocal manner [14]- [29]. For instance, they have been demonstrated to behave as serrodyne frequency translators employing a sawtooth waveform as modulation signal [14]. Space-time coding metasurfaces have recently enabled simultaneous control of electromagnetic waves in both spatial direction and harmonic power distribution [15]- [18]. Similar responses The associate editor coordinating the review of this manuscript and approving it for publication was Shah Nawaz Burokur .
have been obtained using time-modulated Huygens metasurfaces by independently tailoring in time and space the magnetic and electric dipoles that compose each unit-cell of the structure [19]. Nonreciprocal beam scanning for fixed directions in space has theoretically been investigated by inducing space-time photonic transitions in spatiotemporally modulated surfaces [20] and a more general form of the classical Snell's relation not bounded by Lorentz reciprocity was also derived [21]. Time-modulated gradient metasurfaces [22]- [28] provide nonreciprocal beam steering, focusing, and polarization functionalities. A recent review on this topic can be found in [29].
In the context of antennas [30], [31], nonreciprocal responses able to provide large isolation between reception and transmission at desired directions in space have the potential to significantly impact radar, sensing and wireless communication systems, handle unwanted interferences or jamming signals, and enhance the performance of certain class of sensors. Early attempts employed ferrites to break reciprocity [32], [33], leading to antennas with limited efficiency and whose tunable responses required the presence of bulky and lossy magnets that are not compatible with integrated circuits. Magnetless spatiotemporal modulation techniques [2], [34] have been applied to realize nonreciprocal leaky-wave antennas by exploiting space-time transitions between guided and leaky modes [35]- [37]. Unfortunately, leaky-wave antennas may suffer from challenges in terms of size, complexity, efficiency, and dispersive beam scanning behavior that limit their use in practical applications. Recently, time-modulated phased-array antennas were demonstrated to exhibit drastically different radiation patterns in transmission and reception [38]. There, each antenna element is time-modulated with a low-frequency signal f m enabling controllable nonreciprocity: the phase of transmitted signals follows the phase of the modulating signal ϕ m whereas the phase of the received signal follows the opposite one, i.e., −ϕ m . Even though the magnitude of the radiation pattern of each element is reciprocal, this approach permits to impose different phase profiles for the overall antenna array when transmitting or receiving. As a result, isolation levels over 40 dB were demonstrated at desired directions in space [38]. Other approaches to construct nonreciprocal antennas rely on connecting nonreciprocal components -such as filters or phase-shifters -with the radiating elements [39]- [42].
To date, nonreciprocal antennas have been mostly focused on controlling the magnitude of transmitted/receiving fields with a fixed polarization state. Antennas with nonreciprocal response at the polarization level may pave the way to a new set of polarimetric functionalities [43]- [45] and applications in radar, sensing, and imaging, as well as in communication systems. It should be stressed that these antennas would be quite different than polarization reconfigurable antennas widely explored in recent years [46]- [51]. Even though these structures are tunable and thus can change their polarization state (using switches, diodes, MEMS, etc.), they are always reciprocal because the polarization of transmitted and received waves at any instant are identical. For instance, consider the case of an antenna continuously radiating right-handed elliptically polarized waves. Upon reflection on a metallic screen, the wave handedness changes and thus it cannot be received by the same antenna. This challenge has led to an increased complexity in polarimetric systems.
In this contribution, we propose and experimentally demonstrate time-modulated patch antennas able to exhibit nonreciprocal polarization ellipticity when operating in reception or transmission, as illustrated in Fig. 1. A very preliminary theoretical study on this subject by the authors appeared in a recent conference [52]. The antenna relies on time-modulating orthogonal surface currents induced in a patch using low frequency signals with controllable phases. Measured data confirms isolation over 40 dB at the broadside direction and tunability to generate and receive electromagnetic waves with arbitrary ellipticity. The proposed time-modulation approach is general, as it can be applied to any resonant antenna element able to support surface currents in orthogonal directions.

FIGURE 1.
Time-modulated antenna with nonreciprocal polarization ellipticity in transmission and reception. The antenna is time-modulated with two low-frequency (f m ) signals with phases ϕ x and ϕ y that interact with x-and y-directed surface currents, respectively. Manipulating the phase difference between the modulation signals permits to control the polarization state of the transmitted/receiving fields in a nonreciprocal manner. In the left column, the phase shift is set to ϕ t = ϕ x − ϕ y = −90 • and the antenna radiates LHCP waves and simultaneously receives RHCP waves. In the right column, the phase shift is set to ϕ t = ϕ x − ϕ y = +90 • and the antenna radiates RHCP waves and receives LHCP waves. This paper is organized as follows. Section II describes the operation principle of time-modulated antennas with nonreciprocal polarization ellipticity. Section III proposes a specific implementation of these structures based on a modified patch antenna controlled with low-frequency modulation signals. Sections IV and V describe the simulation and experimental set-up, respectively. Section VI presents numerical and measured data to validate the nonreciprocal and tunable response of the proposed antennas. Finally, Section VII concludes the paper.

II. OPERATION PRINCIPLE
The operation principle of time-modulated antennas with nonreciprocal polarization ellipticity is illustrated in Fig. 1. The approach relies on the photonic Aharanov-Bohm effect [38] to impose opposite phase profiles on orthogonal surface currents induced on the antenna when it is operated in transmission and reception. Let us consider an antenna that resonates at f 0 + f m and that supports orthogonal and symmetric surface currents along the x-and y-directions (Fig. 1). The antenna is time-modulated along these directions with signals exhibiting identical low-frequency f m but different phases ϕ x and ϕ y , respectively. Exploiting certain design considerations in the antenna structure (see Section III), it can be enforced that the time-modulation process yields perfect frequency conversion between an incoming RF signal with frequency f 0 and any desired harmonic (f 0 ± nf m ). For simplicity, we will consider here conversion with the upper side first harmonic n = +1 [38]. In this scenario, the antenna will up-convert a signal at f 0 to the frequency f 0 + f m (i.e., f 0 → f 0 + f m ) that will then be radiated to free space. The fields radiated along the x-and y-directions will exhibit identical amplitude but different phases. Such phases are given by where E t p denotes the phase of the electric fields transmitted at f 0 + f m along the p = {x, y}-direction and ϕ RF is the phase of the RF signal at f 0 . The phase difference between the x-and y-directed radiated fields is given by ϕ t = ϕ x − ϕ y . As a result, the radiated wave will have a polarization state determined by an ellipticity 2χ t = ϕ t and an azimuthal angle ψ = 45 • [30], [31]. The latter appears because this antenna configuration always radiates both x and y components of the electric field with identical amplitude.
In reception mode, the antenna will receive fields oscillating at f 0 + f m along the x-and y-directions and will downconvert them to the frequency f 0 (i.e., f 0 + f m → f 0 ). The phases of the received signals are where E r p denotes the phase of the fields down-converted to f 0 along the p-direction, and ϕ FS p is the phase of the impinging free-space wave at f 0 + f m along p. The received fields E r x and E r y interfere within the antenna, leading to a maximum reception when they are in phase, i.e., E r x = E r y , and minimum reception when they are out of phase, i.e, E r x = E r y + π. The phase difference between the x-and y-directed fields imparted by the time-modulated antenna is given by ϕ r = ϕ y − ϕ x = − ϕ t . As a result, the antenna will optimally receive waves with a polarization state determined by an ellipticity 2χ r = ϕ r and an azimuthal angle ψ = 45 • [30], [31]. It is thus evident that χ t = −χ r , which highlights the nonreciprocal polarization ellipticity between reception/ transmission responses of this type of antennas.
It is instructive to employ the Poincaré sphere to explore the polarization response of antennas [30], [31]. The Poincaré sphere, illustrated in Fig. 2, represents polarized electromagnetic waves using the Stokes parameters (S 1 , S 2 , S 3 ) [30], [31] as the Cartesian coordinates, i.e., where S 1 is associated to horizontal/vertical linearly polarized (LP) light, S 2 is related to ±45 • LP light, and S 3 correlates to circularly polarized (CP) light [30], [31]. Any polarized light represents a point on the surface of the sphere. Let us now consider the proposed antenna operating in transmission. By manipulating the relative phase ϕ t with a phase shifter, the proposed antenna is capable of radiating waves with any desired ellipticity-as highlighted in the green circle plotted over the Poincaré sphere in Fig. 2. For instance, a phase shifter operated in a state Q will lead to a specific relative phase ϕ t q and thus the antenna will radiate waves with an ellipticity χ t q . The same antenna operated in reception will optimally receive waves with an opposite ellipticity  Fig. 2 illustrates such behavior for four different phase shifts ϕ t between the low-frequency signals that modulate the patch antenna. Changing the state of the phase shifter to obtain a relative phase ϕ t = {0, π 2 , π, − π 2 }, will lead to a nonreciprocal antenna that radiates electromagnetic waves with a polarization state {+45 • LP, right-handed CP (RHCP), −45 • LP, left-handed CP (RHCP)} and receive waves with opposite ellipticity, i.e., {+45 • LP, LHCP, It should be noted that manipulating the relative phases of the low-frequency modulation signals does not suffice to cover all possible states of the Poincaré sphere. To obtain such response, the amplitude of the surface currents induced along orthogonal directions within the antenna should simultaneously be controlled upon time-modulation.

III. TIME MODULATED PATCH ANTENNA WITH NONRECIPROCAL POLARIZATION CONTROL
In this section, we propose a specific implementation to realize time-modulated patch antennas with nonreciprocal polarization ellipticity. The antenna details are shown in Fig. 3. Specifically, an RF signal (f 0 ) is input from port 1 (P 1 ) and flows along the microstrip lines on the top layer to feed a square patch from four sides. Quarter-lambda transformers are implemented in the microstrip lines to guarantee impedance matching between the power divided t-lines and the patch antenna. Additionally, four coplanar waveguides (CPWs) are located in the bottom ground plane. Each CPW is loaded with a varactor (SMV1235 from Skyworks Solutions Inc.) and is connected to the microstrip line on the top layer through a metallic via. All varactors are reversely biased by DC voltage. Low frequency (f m ) modulation signals and DC bias voltages are carried simultaneously within each CPW. For each modulation path, an inductor is employed as an RF choke to improve the isolation between the RF and modulation signals. Details of the configuration are shown in Fig. 3(c) and Fig. 3

(d).
Even though all modulation signals oscillate at the same frequency f m , their phase distribution may vary across the different CPW. Specifically, ports located across the x-axis, P x and P x , are fed with f m signals with phases ϕ x and ϕ x + π, respectively. A phase difference of 180 • is imposed between these modulation signals to enforce efficient frequency conversion in the nonlinear process by exploiting the even and odd modes of the antenna at f 0 and f 0 + f m , respectively. This process is described in detail in [38]. Similarly, ports located along the y-axis, P y and P y , are fed with f m signals with phases ϕ y and ϕ y + π, respectively. The final optimal dimensions of the proposed time modulated patch antenna are given in the caption of Fig. 3.
The polarization characteristics of the fields radiated and received by this antenna can be controlled through the phases ϕ x and ϕ y exploiting the orthogonality of the surface currents induced on the patch. This process is illustrated in Fig. 4. Let us first consider that the modulation signals are applied only along the x-oriented CPWs located in the ground plane, as shown in Fig. 4(a). In the transmission mode, the antenna will radiate purely x-polarized electric fields oscillating at f 0 + f m with a phase proportional to ϕ x + ϕ RF . In this process, symmetrical RF signals fed the patch from opposite directions in the x-axis, exciting the patch even mode and generating a surface current null at the center of the structure [38]. The reflected signals are then up-converted to two out-of-phase signals at frequency f 0 + f m that excite the common odd mode of the patch, leading to the efficient radiation of x-polarized fields. Note that even mode harmonics cannot be radiated for the patch, as the antenna effectively impose a virtual open circuit for even harmonics generated by the varactors, i.e., f 0 + pf m with p = ±2, 4, 6 . . . We remark that y-polarized fields cannot be radiated in this case as the lack of time modulation leaves an even mode (virtual open circuit) along that direction. In reception, an incoming wave with frequency f 0 + f m and phase ϕ FS x impinges on the antenna and excites the resonant odd mode of the patch. Then, time-modulation along the x-axis down converts the signal to the guided even mode, with frequency f 0 and phase ϕ FS x − ϕ x , that is routed to the exit port. Similar considerations can be made when the antenna is modulated along the y-axis and no modulation is applied along the x-direction, as illustrated in Fig. 4(b). In the case that the antenna is simultaneously time-modulated along the x and y axis, the low cross-coupling between orthogonal directions in a patch structure (<−25 dB) guarantees an independent control of the x-and y-polarized generated and received fields.

IV. SIMULATION SETUP
The proposed antenna is first designed and simulated in the linear regime using ANSYS HFSS (bottom-left inset of Fig. 5). In the model, lumped ports normalized to 50 are employed in the position in which the varactor diodes and lumped inductors will be placed. In this 3D simulation, the antenna is placed in a periodic environment using two Floquet ports associated to the fundamental TE and TM modes at the broadside direction. This approach permits to obtain the amplitude and phase of the fields radiated 59060 VOLUME 10, 2022 FIGURE 5. Nonlinear circuit simulation of the transmission/reception of electromagnetic waves at broadside between the proposed time-modulated antenna (inset bottom left) and a reference antenna (inset top left) described in Appendix I. The response of the antennas has been first obtained using numerical simulation assuming that the structures are placed in a periodic environment. Their linear response has then been imported into the circuit simulator and are shown in the figure as the box S15P for the time-modulated antenna and box S4P for the reference antenna. The two antennas are connected through transmission lines (characteristic impedance of 120π) that models the propagation of electromagnetic waves for the fundamental TE and TM Floquet modes [53]. The circuit is simulated using large signal scattering parameters.
by antenna, as detailed elsewhere [53]. Even though this simulation accounts for an infinite two-dimensional array of patch antennas, the dimensions of the unit-cells ensure a negligible cross-coupling at the targeted broadside direction. The linear S-parameters of the 3D model are then exported to the circuit simulator Keysight ADS to perform large signal S-parameter (LSSP) simulations. In the nonlinear circuit, the varactor diode and lumped inductor models are imported from the vendors and connected to the lumped ports of the antenna. The model is then explored to maximize the radiation efficiency, optimizing the modulation frequency (f m = 320 MHz), modulation amplitude M = 0.36, and DC bias applied to the varactors (V = 1.53 volts) as described in [38].
To explore the response of the proposed time-modulated antenna, three different reference antennas will be employed. First, a common patch antenna is employed to calibrate the system and extract the overall loss in the radiation process [38]. Second, a linearly polarized horn-antenna is employed to explore the phase variations of the different field components radiated by the time-modulated antenna. And third, a reference patch antenna has been designed in HFSS and fabricated integrating a 90 • hybrid coupler to independently control the LHCP and RHCP components of the radiated/received waves. This antenna, described in detail in Appendix I, will permit exploring the polarization response of the proposed time-modulated device. Fig. 5 illustrates the ADS circuit model employed to interconnect the time-modulated antenna with the reference antenna described in Appendix I. Interchanging such reference antenna with another one (i.e., a patch or a horn antenna) simply requires updating the S parameters that describe the reference device. To simulate free-space propagation along the broadside direction that connect both antennas-assuming they are perfectly aligned-the orthogonal TE and TM Floquet modes from both linear antenna models are connected using transmission lines with a characteristic impedance of Z 0 = 120π . In the model, port 1 is assigned to the RF signal that feeds the time-modulated antenna whereas ports 2 and 3 are related to the LHCP and RHCP components of waves radiated/received by the linear reference antenna. The entire set-up is then simulated using LSSP, which measures nonlinear transmission/reception of fields between the time-modulated and reference antennas in a similar fashion as the frequency offset mode of a performance network analyzer (PNA). This setup permits to analyze the amplitude and phase of all field components radiated and received by the antennas under test.  Fig. 6 shows an overview of the proposed experimental set-up. In all cases, microwave absorbers (not shown) are located around the antenna to minimize unwanted scattering. In the proposed set-up, a 4-port Keysight PNAX N5247A is used to simultaneously control the proposed time-modulated patch antenna as well as the reference antenna, providing quantitative information in amplitude and phase of the radiated fields. In this work, we will focus on the broadside radiation to explore the antenna polarization response. Note that a single time-modulated antenna element provides a reciprocal radiation pattern in amplitude [38] and therefore, obtaining radiation pattern is not an objective of this work. Prior to measurements, a standard short-open-load-through (SOLT) calibration is applied [30], [31]. Time-modulation signals oscillating at f m = 320 MHz are obtained with a Hewlett Packard E4433B signal generator and fed to the antenna CPWs. Varactors are biased with 1.53 volts obtained from a standard DC voltage source. Power amplifiers and VOLUME 10, 2022

V. EXPERIMENTAL SETUP
Mini-Circuits ZXPHS-431 phase shifters are employed to obtain the desired amplitude and to impart phase shifts ϕ x and ϕ y to the modulation signals, respectively. Along each direction, Mini-circuits TCM2-33WX baluns impose the 180 • phase different to the modulation signals.
In transmission mode, the PNAX is configured using the frequency offset mode so that the receivers (P2 and P3 in Fig. 6) are set to measure a swept signal with frequency f 0 +f m (2.1-2.3 GHz) while the transmit port (P1) frequency is swept at f 0 (1.781-1.981 GHz). The 10 MHz reference oscillators of the PNAX and signal generator are coupled together to phase lock the signals of the instruments. In reception, the PNAX is also configured in the offset mode but feeding now the reference antenna with a signal frequency f 0 + f m (2.1-2.3 GHz) through ports 2 and 3 and setting the receiver in port 1 to measure signals at f 0 ∼ 1.781-1.981 GHz.

VI. TUNABLE NONRECIPROCAL RESPONSE OF TIME-MODULATED ANTENNAS
This section explores the performance of the proposed antenna and its use in a simple communication system. The antenna is first characterized in terms of matching, efficiency, and ability to independently control the polarization of radiated fields along orthogonal directions. Then, nonreciprocal polarization in transmission/reception is demonstrated versus frequency, obtaining isolation levels >40 dB. Finally, we will show how the antenna radiates and receives fields with any desired ellipticity while maintaining its nonreciprocal behavior. At that frequency, the input signal is up-converted to 2.21 GHz and radiated to free-space. To verify that this is indeed the case, we employed a standard patch antenna as reference antenna in the experimental schematic shown in Fig. 6 -see [38] for additional details. Strong radiation toward broadside direction is confirmed at 2.21 GHz with a total of ∼3 dB of loss with respect to a common patch [30], [31]. Such losses arise due to (i) presence of non-ideal varactors, capacitors, and power dividers; and (ii) frequency conversion to unwanted harmonics. The amount of loss and associated loss mechanisms are comparable to those found in time-modulated antennas that do not exhibit polarization control [38].
To explore the polarization response of the antenna, we employed a linearly polarized horn as a reference antenna in our experimental set-up. The antenna is aligned with respect to the time-modulated patch and carefully rotated to only receive x-or y-directed fields. Fig. 7(b) [Fig. 7(c)] shows measured and simulated phases of the x-component [y-component] of the received electric fields when the phase φ x [φ y ] of the modulating signals is varied using the phase-shifter and the orthogonal one is set to zero. For simplicity, the phase reference of all signals transmitted in this simple channel has been set to zero for a zero value of the phase shift. Measured data confirm that the phase response of the y polarized electric field component changes linearly with the phase ϕ y of the time-modulated signal directed along the y-axis, while it remains unchanged versus the phase of the low-modulation signal along the xaxis, ϕ x . Similar response can be obtained for x-polarized radiated fields with respect to the ϕ x and ϕ y phases, respectively. This study demonstrates that the phase of each field component can be controlled in an independent manner with the phase of the corresponding time-modulating signal. Fig. 8 explores the nonreciprocal polarization response of time-modulated antennas versus frequency when transmitting and receiving CP waves. This scenario is explored experimentally using the schematic shown in Fig. 6, employing the patch antenna combined with the 90 • hybrid coupler as reference device (see Appendix). This structure is particularly useful to isolate the LHCP and RHCP components of the fields, and it is applied here to experimentally explore the transmission and reception of RHCP and LHCP radiation and to demonstrate isolation at the polarization level.

B. NONRECIPROCAL RESPONSES IN POLARIZATION
The top row of Fig. 8 plots the normalized response of the time-modulated antenna in transmission. In the left (right) panel, the antenna is configured to radiate a RHCP (LHCP) wave by setting the phase difference between the time-modulating signals to ϕ t = +90 • ( ϕ t = −90 • ). The radiated signal is received by the reference antenna, where the LHCP and RHCP components of the  Fig. 8. In the measurements, the reference antenna alternatively radiates RHCP and LHCP waves at f 0 + f m . The antenna receives the waves and down converts them to guided waves at f 0 . In the left (right) panel, the time-modulated antenna maintains a phase difference between time-modulating signals of ϕ t = +90 • ( ϕ t = −90 • ), and therefore is tuned to receive LHCP (RHCP). Both simulated and measured results confirm that this is indeed the case, and that the antenna reception is maximum for LHCP (RHCP) waves, whereas orthogonal RHCP (LHCP) waves are received with over −40 dB of amplitude difference.
Nonreciprocity in polarization immediately follows from Fig. 8: setting ϕ t = +90 • , the antenna radiates RHCP waves and receives waves with the opposite ellipticity, i.e., LHCP; on the other hand, when ϕ t = −90 • , the antenna radiates LHCP waves and receives RHCP. Polarization isolation over 40 dB is obtained in all cases. Another remarkable feature is the high polarization purity exhibited by the antenna when configured to operate either in transmission or reception.

C. POLARIZATION CONTROL
In this subsection, we demonstrate the possibility of radiating and receiving fields with arbitrary polarization ellipticity (see highlighted green circle in Fig. 2) while keeping the nonreciprocal response. Such functionality can be obtained by manipulating the phases of the modulating signals, ϕ x and ϕ y . Let us first consider the transmission mode. The PNAX is used to excite port 1 of the proposed antenna with a fixed frequency of f 0 = 1.89 GHz. The signal generator provides time modulated signals with frequency f m = 320MHz to the antenna CPW ports. In Fig. 9(a), the phase shifter applied to the x-directed time-modulated signals is DC biased (Fig. 6) to provide an increasing phase shift ϕ x while keeping ϕ y = 0. This corresponds to moving counterclockwise in the highlighted states shown in the Poincaré sphere [see inset in Fig. 9(a)] that are radiated to free space. The RHCP and LHCP components of the signal received by the reference antenna are then routed to port 2 and 3 of the PNAX. When ϕ x = 0 • , the antenna is set to radiate +45 • linearly polarized waves and thus the receiver collects an equal amount of LHCP and RHCP component -each with a magnitude of −3 dB. As the phase shift ϕ x increases, the transmitted RHCP component increases whereas the LHCP decreases. At exactly ϕ x = +90 • , the radiated signal acquires an almost pure RHCP state with an orthogonal LHCP component over −50dB lower. Increasing the phase ϕ x further has the opposite effect, as the LHCP component gets larger while the RHCP decreases. Both components intersect again with an amplitude of −3dB when ϕ x = +180 • . At that point, the antenna radiates a +45 • linearly polarized state. Larger ϕ x will decrease further the RHCP component and increase the LHCP, which will be maximum when ϕ x = +270 • . This state reveals that the orthogonal RHCP components is over −45 dB weaker and confirms the high polarization purity of the radiated signal. Greater ϕ x phase shifts complete the circle along the Poincaré sphere. In all cases, excellent agreement has been found between simulations and measurements. Fig. 9(b) repeats this experiment but increasing the ϕ y phase shift while keeping ϕ x = 0 • . In this scenario, the antenna again radiates electromagnetic states with all possible ellipticity values. The main difference is that the rotation over the radiated states in the Poincaré sphere is now clockwise [see inset in Fig. 9(b)] with respect to the phase ϕ y .
In reception mode, the PNAX is first configured to feed the port 2 of the reference antenna with a frequency f 0 + f m = 2.21 GHz while keeping port 3 terminated with a 50 load. Therefore, the antenna radiates a LHCP signal. In the experiment, we monitor the signal that has been received by the time-modulated antenna, down-converted to f 0 = 1.89 GHz and routed to port 1 of the PNAX. In Fig. 9(c) (solid blue line), we explore this situation versus the phase ϕ x while keeping ϕ y = 0. Due to the opposite ellipticity during transmission and reception, the antenna receives now electromagnetic waves with an ellipticity that is moving clockwise with respect to ϕ x [see inset of Fig. 9(c)]. When the phase is set to ϕ x = {0 • , 180 • }, the antenna receives the {+45 • , −45 • } linearly polarized wave component of the transmitted RHCP wave that corresponds to a −3 dB amplitude. When ϕ x = 270 • , the received signal is maximum as the antenna is tuned to received LHCP waves. On the contrary, the received signal is over −40dB weaker when the antenna is configured to receive RHCP signals (by setting the phase ϕ x = 90 • ) that are orthogonal to the radiated LHCP ones.
Next, the reference antenna is configured to radiate RHCP waves [solid red line in Fig. 9(c)]. To this purpose, its port 2 is loaded with 50 while its port 3 is fed by the PNAX with a frequency f 0 + f m = 2.21 GHz. Simulated and measured data follow a similar pattern as described above: maximum (minimum) reception appears when the antenna is tuned to received RHCP (LHCP) with ϕ x = 270 • (ϕ x = 0 • ) whereas the +45 • (−45 • ) linearly polarized component of the transmitted RHCP is received when ϕ x is set to 0 • (180 • ). The experiment is repeated in Fig. 9(d) by varying now the phase ϕ y while keeping ϕ x = 0 • . In such configuration, the antenna receives waves with an ellipticity moving counterclockwise with respect to ϕ y (see inset). Experimental and simulated data show again an excellent agreement, demonstrating the ability of the antenna to receive waves with any polarization state and minimal cross-coupling while maintaining its nonreciprocal nature.

VII. CONCLUSION
This paper has introduced and experimentally demonstrated the concept of antennas exhibiting nonreciprocal polarization response when operated in transmission or reception. These structures support surface currents along orthogonal directions that exhibit opposite phase profile in transmission/reception upon time-modulation. As a result, the antenna is capable of radiating waves with any polarization ellipticity while simultaneously receiving waves with opposite ellipticity. This process is tunable by changing the phase shift applied to the low-frequency modulation signals. The proposed concept has been implemented using a time-modulated square patch antenna that exploits even/odd symmetries to maximize frequency conversion. Simulated and measured results confirm isolation levels over 40 dB in transmission and reception, as well as the ability to generate/receive waves with desired ellipticity and high polarization purity. We expect this antenna to find a wide variety of polarimetric applications, including material analysis, radar, sensing, imaging, and communication systems.
It should be noted that the main goal of this paper was to demonstrate nonreciprocal polarization control, and thus the devices were not fully optimized for other applications. Future antennas will benefit from available techniques based on time-modulation [54], [55] or switched networks [56], [57] to enhance their operational bandwidth and reduce loss while keeping their nonreciprocal nature. Additionally, the proposed concept can be extended to account for any polarization state of the Poincaré sphere. To this purpose, the time-modulated antenna requires the ability to arbitrarily modify the amplitude of each orthogonal surface currents induced in its surface. In the proposed prototype, this can be accomplished by manipulating the 180 • phase difference between time-modulated signals aligned along the same direction (x, y). Indeed, it has been demonstrated that controlling such phase permits to manipulate the intensity of the received/radiated fields [38]. However, this solution increases the prototype complexity by requiring two additional phase shifters and additional control signals. Moving beyond, we envision that future array systems may integrate nonreciprocal antenna elements to obtain fully tailored radiation patterns able to exhibit drastically different responses in both amplitude and polarization while transmitting and receiving electromagnetic waves. Fig. 10 describes a dual-fed microstrip patch antenna combined with a 90 • hybrid coupler able to achieve circular polarization and to split LHCP and RHCP components [30]- [31]. Figs. 10a-b show the dimensions of the structure and a picture of a prototype, respectively. Port 2 and 3 are associated with the LHCP and RHCP components of the fields, respectively. Fig. 10c shows the measured scattering parameters, confirming excellent matching to free-space and very low cross coupling, whereas Fig. 10d shows the numerically simulated axial ratio.