Abstract
The emergence of new technological needs in 5 G/6 G networking and broadband satellite internet access amplifies the demand for innovative wireless communication hardware, including highperformance lowprofile transceivers. In this context, antennas based on metasurfaces – artificial surfaces engineered to manipulate electromagnetic waves at will – represent highly promising solutions. In this article, we introduce leakywave metasurface antennas operating at micro/millimeterwave frequencies that are designed using the principles of quasibound states in the continuum, exploiting judiciously tailored spatial symmetries that enable fully customized radiation. Specifically, we unveil additional degrees of control over leakywave radiation by demonstrating pointwise control of the amplitude, phase and polarization state of the metasurface aperture fields by carefully breaking relevant symmetries with tailored perturbations. We design and experimentally demonstrate metasurface antenna prototypes showcasing a variety of functionalities advancing capabilities in wireless communications, including singleinput multioutput and multiinput multioutput nearfield focusing, as well as farfield beam shaping.
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Introduction
Leaky wave antennas (LWAs) are traveling wave transceivers with highly desirable practical features, including high directivity, low profile, simple feeding architecture, and inherent beamscanning capability enabled by frequency dispersion^{1}. They leverage tailored perturbations that partially couple guided electromagnetic modes into directive freespace radiation. Owing to their flexibility, LWAs have found applications not just in wireless communications but also for imaging^{2,3}, radar detection^{4}, and remote sensing^{5} systems. The key design parameters for a traditional LWA are the attenuation and propagation constants, which respectively control, to a limited degree, the effective aperture and scan angle of the radiated beam (typically a simple linearlypolarized plane wave). The polarization is usually fixed to a single state, dictated by the antenna architecture.
The limited set of degrees of freedom (DoFs) offered by conventional LWAs does not meet the great demand from today’s wireless infrastructures for data capacity, channel diversity, and energy efficiency. Hence, recent years have witnessed a proliferation of advanced antenna designs based on electromagnetic metamaterials and metasurfaces^{6,7,8,9,10}. These artificial structures consist of subwavelength building blocks called “metaatoms” or “metaunits” with engineered electromagnetic scattering responses. Their ability to manipulate fields and waves has unlocked a plethora of highperformance radiofrequency wireless devices, including LWAs, with unprecedented capabilities. For example, ultrathin artificial impedance surfaces supporting surface waves can be made radiating via periodic or quasiperiodic perturbations to their effective electric impedance, forming holographic leakywave metasurfaces (LWMs)^{11,12}. With properly engineered anisotropy, the effective impedance takes a tensorial form, leading to radiation with controlled polarization states^{13,14}. To exert simultaneous and independent control over all aspects of the aperture field and, accordingly, the farfield radiation, LWAs incorporating Huygens’ metasurfaces^{15,16,17} or cascaded tensorial impedance sheets have been proposed^{18}. Instead of modeling the metaatoms as continuous sheets of effective electric and magnetic polarization currents, it is also possible to treat them as discrete arrays of noninteracting resonant dipoles^{19,20,21}. This latter approach trades some of the beamforming DoFs of the former for simpler designs that are easier to realize in practice.
Besides the aforementioned metasurfaces exploiting an engineered local response to external fields, the emerging field of “nonlocal” metasurfaces has been showing that it is possible to fully tailor all aspects of electromagnetic wave interactions by harnessing the mutual coupling among metaunits (e.g., mediated by a guided mode). These nonlocal metasurfaces have been receiving intense investigation in the optical regime, particularly in the context of bound states in the continuum (BICs), which are resonant modes that remain confined despite their compatibility in terms of momentum with a continuum of radiating waves (i.e., accessible radiation channels)^{22,23}. One class of BICs, known as symmetryprotected BICs, is of particular interest to the scientific and engineering communities^{23,24}. They arise from certain symmetries in the modal field profile that inhibit coupling to farfield radiation due to mismatched field parity. However, when these modal symmetries are broken through tailored perturbations, they turn into “quasiBICs” (qBICs), which can radiate with fully controlled features^{25,26}. Researchers have utilized this concept to shape the wavefront, polarization, and spectra of coherent as well as thermal emission^{27} with extreme precision. Very recently, this concept has also enabled integrated photonic LWMs leveraging spatially varying perturbations to symmetrybroken photonic crystal slabs to convert guided optical modes into customized freespace emission^{28}.
The qBIC framework is very powerful in terms of added DoFs and waveform control since its underlying principles stem from spatial symmetries^{25}. Hence it is generalizable to any frequency regime, and it is agnostic to details of the physical implementation (to first order in perturbation theory). Furthermore, it enables a completely rational design scheme for highly sophisticated nonlocal metasurfaces by providing a set of simple algebraic relations linking the four DoFs of a monochromatic wave (amplitude, phase, orientation, and ellipticity of polarization) to four independent geometrical DoFs embedded inside the constituent metaunit. This feature represents a significant advantage over conventional metasurface design approaches, which often require cumbersome numerical optimization or the construction of extensive metaatom lookup tables to bridge the gap between idealized analytical models and physical implementations.
In this work, motivated by emerging technological needs in 5 G/6 G networking, satellite internet, autonomous vehicles, and smart/cognitive radio environments^{29,30}, we translate the concept of qBICs from optical frequencies into the micro/millimeterwave spectrum to empower advanced nonlocal LWM antennas with fully controlled radiation features. Although the underlying design principles are consistent with integrated photonic LWMs^{28}, operation at mmwaves enables increased flexibility by the much more versatile and accessible printed circuit board (PCB) manufacturing platform. For example, the incorporation of a conductive ground plane admits unidirectional radiation with significantly higher directivity than attainable at optical frequencies (for which compact and lowloss reflectors near the guided mode are not trivially achieved). Furthermore, we can feed the LWM with sophisticated and compact substrateintegrated wave launchers, opening the opportunity for more advanced modes of operation (e.g., multiport excitations). Moving into radio frequencies also introduces new challenges, such as limitations on the aperture size and the overall device footprint (due to increased wavelength), demanding innovative solutions that take full advantage of the available fabrication technologies.
As proofs of concept, we present three qBICbased LWM antenna prototypes with unprecedented functionalities for leakywave radiation control. The first metasurface antenna is a singleinput multipleoutput (SIMO) LWM lens that generates two distinct orthogonally polarized focal spots placed at arbitrary locations from a single guided mode input. The second design realizes a multipleinput multipleoutput (MIMO) lens that focuses its radiation to different locations within the Fresnel zone, depending on which of its two ports is excited. Lastly, we present a multibeam LWM antenna with dualpolarized farfield beamshaping capabilities. All three implementations are validated through fullwave numerical simulations, as well as experimental measurements.
Results
Working principle
The physical principles governing the radiative behavior of symmetryprotected qBICs are general, and they can be applied to a range of vastly different device platforms. Here, for illustrative purposes, we utilize a parallel plate waveguide (PPWG) with thickness h and relative permittivity \({\epsilon }_{r}\), perforated by a staggered array of rectangular slots (Fig. 1), which supports a qBIC in the form of a quasitransverseelectromagnetic (TEM) mode. The shape and the orientation of the slots have been tailored such that the mode leaks energy in a fully controlled fashion as it propagates. Here, the parameters A and Φ refer to the local field amplitude and phase over the LWM aperture, while 2ψ and 2χ refer to the longitude and latitude of the local polarization state on the Poincaré sphere. The dependence of these parameters on the spatial coordinates (x,y) and a global time convention of \({e }^{j\omega t}\) are left implicit for brevity. In the following subsections, we summarize the design methods employed to rationally pattern the slot array and exert pointwise control over all four DoFs of the aperture field, along with physical insights into the underlying phenomena.
Control of radiation magnitude
We begin by examining the simplest case of an LWM perforated by uniformly sized staggered square slots (with width w), whose primitive unitcell (when considering a rectangular lattice) is pictured in Fig. 2a, marked by the dotted outline and with dimensions \({L}_{x}\times 2{L}_{y}\). Using numerical simulations (see “Methods”), we evaluated the first Brillouin Zone (FBZ) of a typical dispersion diagram for xdirected wave vectors (Fig. 2b), in which the purple dashed line represents the freespace light line. The lowestorder eigenmode is a quasiTEM traveling wave with respect to \(\hat{x}\). At the X highsymmetry point (\({k}_{x}=\pi /{L}_{x}\)) of the FBZ, such a mode (marked by the green star) can be referred to as an “artificial BIC” (aBIC)^{31}: when we artificially double the metasurface periodicity along \(\hat{x}\) by considering two adjacent primitive cells as a collective metaunit, as done in Fig. 2c, the mode is shifted to the Γ point (\({k}_{x}=0\)) of the folded FBZ (Fig. 2d), where it now resides above the light line. Despite artificially coexisting with a continuum of radiating waves, this mode cannot couple to the far field. One interpretation for the lack of energy leakage is provided by the symmetry of the modal field profile: since the aperture electric field over every two adjacent slots have the same magnitude but are in antiphase, they destructively interfere with each other in the far field. As a result, the aBIC possesses an ideally infinite radiative Qfactor. Ultimately, it is important to remember that, in the current configuration, the mode, in fact, resides below the light line. Therefore, its confinement to the waveguide is not surprising, and it is guaranteed by translational symmetry.
The key realization to enable LWMs is that we can revoke the symmetry protection that inhibits the aBIC from radiating by introducing a perioddoubling symmetrybreaking perturbation to the metaunit as depicted in Fig. 2e (and with the corresponding band diagram in Fig. 2f), where the parameter δ quantifies the degree of introduced asymmetry. In this way, one of the two neighboring slots radiates stronger than the other, and the mode is transformed into a leaky qBIC with a finite radiative Qfactor. Hence, the “artificial continuum” is promoted to a “true continuum”. As seen in Fig. 2g, the Qfactor varies approximately as \({\delta }^{2}\), implying that a higher degree of asymmetry leads to more intense radiation^{23,24}. To illustrate this further, Fig. 2h showcases snapshots of the simulated electric field distribution above the waveguide for several values of δ. Larger perturbations evidently produce stronger radiated fields. It is also possible to map the Qfactor to the corresponding attenuation (leakage) constant, more commonly used in the leakywave antenna literature^{32}.
The degree of asymmetry of each metaunit can be individually controlled, allowing us to precisely pattern the amplitude profile of the entire LWM aperture in a pointwise fashion. In this study, we have neglected the tapering of the qBIC power density as it propagates along the LWM. Such an approximation will not cause significant issues for weakly perturbed designs since they generally have low leakage rates. It is also worth noting that, as revealed by Fig. 2g, the resonant frequency of the qBIC, i.e., the eigenfrequency at the Γ point, is only weakly dependent on the perturbation strength. When larger perturbations are considered, it may be necessary to slightly adjust the slot dimensions in order to compensate for the frequency drift, which may otherwise lead to undesirable radiation squinting.
Control of linear polarization state
The polarization of the radiated field can be customized in a pointwise manner by breaking the mirror symmetries of each adjacent pair of slots. For instance, we can introduce a rotation angle α, as shown in the inset of Fig. 3. When \(\alpha \in \left[{0}^{\circ },{90}^{\circ }\right]\), the aperture electric fields of both slots are symmetric across the xzplane. A magnetic wall bisects both slots, leading to purely xpolarized radiation into the far field. Conversely, when \(\alpha \in \left[{45}^{\circ },{135}^{\circ }\right]\), a magnetic wall is formed between the slot pair, giving rise to purely ypolarized radiation. Continuously sweeping \(\alpha\) from \({0}^{\circ }\) to \({180}^{\circ }\) allows us to traverse the equator of the Poincaré sphere twice, covering all possible combinations of linear polarization states and polarity.
Control of aperture phase
To locally control the phase of the radiated fields, we introduce another geometric degree of freedom, imparting different perturbation strengths to the lower and upper rows of the metaunit. At the Γ point, the modal profile of the qBIC includes two rows of radiating apertures that are \({90}^{\circ }\) out of phase, as they are staggered by 1/4 of a guided wavelength. Hence, the perturbation strengths for the lower and upper pairs (\({\delta }_{1}\) and \({\delta }_{2}\)) can independently control the inphase and quadrature components of the radiating part of the aperture field, granting us full \({360}^{\circ }\) phase coverage. In Fig. 4, we demonstrate how to tailor the phase for xpolarized fields (\({\varPhi }_{x}\)). The same scheme can be used for any other linearly polarized radiation if we set \(\alpha \notin \left[{0}^{\circ },{90}^{\circ }\right]\), following Fig. 3.
We can parameterize the perturbation strengths of the two rows as
where Φ is the desired phase. This mapping reveals the geometric nature of the aperture phase, implying that, when patterned with slowly varying profiles, the LWM is robust against performance degradations typically associated with the sharp geometric discontinuities at phase wraps^{33}.
We note that the introduction of this final degree of freedom breaks the translational symmetry between the top and the bottom rows of the metaunits (i.e., they have shifted copies of one another), and such broken symmetry opens a bandgap at the \(\varGamma\) point of the folded FBZ. However, this gap is typically very small, with negligible influence over the performance of a finitesize device.
Full control of leaky wave radiation
Based on these principles, we may exert full control over the four DoFs for the radiated waves from each metaunit by imparting different perturbation strengths \({\delta }_{\{1,2\}}\) and rotation angles \({\alpha }_{\{1,2\}}\) to the lower and upper slot pairs (see inset of Fig. 1). In turn, these DoFs allow us to tailor both the magnitudes and linear polarization states of the inphase and quadrature components of the aperture field. More precisely, the radiated electric field of each metaunit can be described by
The weights \({c}_{x}\) and \({c}_{y}\) account for the unequal coupling strengths of the quasiTEM mode with x and ypolarized radiation (i.e., the Qfactor varies sinusoidally with \(\alpha\)). Here, we have assumed that the radiated field magnitude varies approximately linearly with respect to \(\delta\), which is valid within the small perturbation regime and is consistent with Fig. 2g.
Equating (2) with the most general form of an arbitrarily stipulated aperture field
we obtain deterministic design equations for all geometrical parameters of the metaunit:
Here, \(\delta\) is the maximum perturbation strength, which can be chosen in compliance with design considerations such as overall footprint and fabrication tolerance. Note that the only systemspecific parameters in (4) are the two unknown coupling constants \({c}_{x}\) and \({c}_{y}\), which can be retrieved through fullwave numerical simulations of physical models. Hence, we can use the same set of equations to design LWMs with much more sophisticated slot topologies, e.g., meandered slots, or even one with a totally different physical implementation, e.g., a grounded dielectric slab with metallic patch claddings or additively manufactured metallic pillar arrays^{34}. This is in sharp contrast with conventional metasurface design methods, which heavily rely on phenomenological descriptions, such as equivalent circuits or homogenization theory, which cannot be easily transferred between different technological platforms.
In the following examples, we adopt these rational design principles to synthesize and experimentally validate several LWM antennas with a wide range of functionalities. For simplicity, we restrict our attention to onedimensional designs which are periodic along the ydirection.
Singleinput/multipleoutput focusing
As one remarkable demonstration, we design a SIMO LWM antenna that generates two spatially separated nearfield focused spots with orthogonal circular polarizations from a single input wave (Fig. 5a). We stipulate an aperture electric field distribution consisting of two superimposed converging cylindrical wavefronts centered at \({\vec{{{{{{\bf{r}}}}}}}}_{\left\{R,L\right\}}^{\, \star }\), described by
where \({E}_{\left\{R,L\right\}}\) are the complex amplitudes of the two circularly polarized aperture field components, \({H}_{0}^{\left(1\right)}\) is the 0thorder Hankel function of the first kind, and \({k}_{o}\) is the freespace wavenumber.
We select a design frequency of 20.55 GHz in the mmwave range and focal points \({\vec{{{{{{\bf{r}}}}}}}}_{R}^{\, \star }=\left(2{\lambda }_{o},6{\lambda }_{o}\right)\), \({\vec{{{{{{\bf{r}}}}}}}}_{L}^{\, \star }=\left({\lambda }_{o},4{\lambda }_{o}\right)\), where \({\lambda }_{o}\) is the freespace wavelength. The unperturbed square slots have widths \(w=1.85\) mm, while the maximum perturbation strength \(\delta\) is set to 1.55 mm. The metaunit dimensions are \(2{L}_{x}=8.25{{{{{\rm{mm}}}}}}\) and \(2{L}_{y}=6.25{{{{{\rm{mm}}}}}}\). The yperiodicity is made smaller than the xperiodicity in order to shift all transversely propagating modes up in frequency, thereby suppressing them in the band of interest^{28}. The antenna aperture consists of 16 distinct metaunits, making it approximately \(9{\lambda }_{o}\) long. The substrate is assumed to have a dielectric constant of \({\epsilon }_{r}=3\) and thickness of \(h=1.52{{{{{\rm{mm}}}}}}\). Materials with higher dielectric constants can be used to miniaturize the metaunit dimensions with respect to the freespace wavelength, which serves to reduce the overall device footprint and enable more precise control over the aperture field distribution. For simplicity, we assume that the qBIC can couple to x and ypolarized radiation with equal efficiencies (i.e., \({c}_{x}={c}_{y}\)). Then, inserting (5) into the synthesis equations (4), we directly obtain the required metaunit geometries of our LWM, which have been summarized in Fig. 5b.
To excite the qBIC mode, conventional compact TEMwave launchers can be employed^{35,36,37}. However, they typically suffer from severely restrictive bandwidths or implementation complexity. Considering both factors, we choose to feed our LWM with a fourway substrateintegrated waveguide (SIW) power divider that tapers into a horn array (see Supplementary Fig. S1). A photograph of the fabricated prototype is shown in Fig. 5c. Figure 5d depicts our experimental measurement setup (see Methods for details). To verify the functionality of our design, we first performed preliminary fullwave numerical simulations with a simplified model of the LWM, which is infinitely periodic along the lateral direction (see Methods). The calculated normalized Fresnelzone electric field intensity is plotted at the top of Fig. 5e. There are two clearly observable focal spots centered at \({\vec{{{{{{\bf{r}}}}}}}}_{R}^{\, \star }\) and \({\vec{{{{{{\bf{r}}}}}}}}_{L}^{\, \star }\), marked by the pink and green circles, respectively. Similar results can be observed in the experiment (bottom plot). Due to nonidealities such as lateral truncation, an imperfection in the input wavefront, fabrication tolerances (see Supplementary Fig. S3 for additional discussion), and deviation of the dielectric substrate properties from their nominal values, the optimal operating frequency was upshifted from 20.55 GHz to 21.05 GHz. Hence, we have plotted the measured field intensity at the latter frequency. Despite the slight discrepancy between simulation and measurements, we can observe two highfieldintensity regions near the designated focal spots. The measured −10 dB input reflection bandwidth is approximately 2.3 GHz (see Supplementary Fig. S2), which may be further improved by optimizing the transition between the launcher and the LWM.
To resolve the polarization state of the LWM output, we evaluate the LCP and RCP components at the two designated focal planes, according to^{38}
In Fig. 5f, we plot the normalized simulated (top) and measured (bottom) intensities of RCP (solid lines) and LCP (dotted lines) fields for various input frequencies. As expected, the focal spot can be continuously scanned in the xdirection simply by tuning the operating frequency, owing to the radiation mechanism of the leaky wave. Importantly, except for a single measurement (19.55 GHz, \(z=6{\lambda }_{o}\)), we observe outputs with very high polarization purity, exhibiting at least 15 dB crosspolarization discrimination at the focal spots. This corroborates our ability to independently control the amplitude and phase profiles of the two orthogonally polarized field components. The lateral displacement between the simulated and measured focal spots is again attributed to the nonidealities in the fabricated sample.
We note that the experimentally measured size of our focusing LWM spot is larger than an ideal diffractionlimited spot. This is because the tapered aperture profile, which we have stipulated through (5b), serves to broaden the focal spot. As shown by Fig. S4 in the Supplementary Material, considering this factor, the focusing power of our LWM is very close to the theoretical predictions.
Multiinput multioutput focusing
To further exploit the full aperture customizability offered by our nonlocal LWM, we implement a device that focuses its output to different arbitrary nearfield positions when excited from different ports. This capability enables MIMO nearfield communication via spatialdivision multiple access with scannable focal spots  a desirable feature for highthroughput smart radio environments powered by reconfigurable intelligent surfaces^{39}.
We again stipulate an aperture field distribution consisting of two superimposed orthogonal circularly polarized cylindrical waves. However, we now assign a negative focal length for the LCP component (i.e., \({y}_{L}^{\star } \, < \,0\)), and encode a diverging phase front described by
where \({H}_{0}^{(2)}\) is the Hankel function of the second kind. The RCP component of the aperture field remains the same as that given in (5). Effectively, this means that when the leaky qBIC is excited from port 1 of the LWM, an RCP wave focused at \({\vec{{{{{{\bf{r}}}}}}}}_{R}^{\, \star }\) and a diverging LCP wave emanating from a virtual source at \({\vec{{{{{{\bf{r}}}}}}}}_{L}^{\, \star }\) will be generated. This results in a region of high field intensity in a righthanded CP state and weak background radiation with lefthanded CP (Fig. 6a).
On the other hand, when the LWM is excited from the opposite port, a timereversed copy of the qBIC is excited, leading to two key consequences. First, the radiated LCP and RCP components are exchanged as they are linked to each other by time reversal. In other words, the aperture profile previously encoded for LCP is now responsible for the RCP radiation, and vice versa. Second, the patterned phase profiles are conjugated due to timereversal symmetry, transforming a converging (diverging) wavefront into a diverging (converging) one. The combined result is that the radiation of the LWM again consists of a focused RCP spot and a weak LCP background (Fig. 6b). Notably, the focal points produced by port 1 and port 2 excitations can be independently stipulated, as they are controlled by two completely uncorrelated aperture field profiles. This allows the LWM to be used as a MIMO transceiver which communicates with sources at different locations using different ports.
In contrast with conventional techniques to achieve this effect, such as the physical partitioning of a single shared aperture^{40}, our proposed concept trades efficiency for more effective aperture illumination. Since each output spot fully leverages the entire physically available aperture area, we obtain significantly enhanced spatial resolution while performing nearfield focusing, albeit with reduced polarization purity and power efficiency due to the crosspolarized background radiation.
Interestingly, the physical mechanism by which we achieve MIMO operation is reminiscent of the wellknown phenomenon of spinmomentumlocking, which has been reported in metasurfaces with broken rotational symmetries supporting circularly polarized chiral surface waves with outofplane spin^{41}. In our platform, the momentum (direction of propagation of the guided mode) is not necessarily locked to a circularly polarized state (spin). Instead, the customized symmetrybreaking perturbations allow us to couple the qBIC with any arbitrary polarization state on the Poincaré sphere, such that when its momentum is reversed, the generated output field can still provide useful functionality.
We designed and fabricated a MIMO LWM prototype with the same operating frequency and key geometrical features as the previous example. The focal spots are chosen as \({\vec{{{{{{\bf{r}}}}}}}}_{R}^{\, \star }=\left(2{\lambda }_{o},5{\lambda }_{o}\right)\) and \({\vec{{{{{{\bf{r}}}}}}}}_{L}^{\, \star }=\left(2{\lambda }_{o},6{\lambda }_{o}\right)\). The analytically derived metaunit shapes are presented in Fig. 6c. In Fig. 6d, we plot the simulated and measured nearfield electric field intensities with port 1 and port 2 excitations, respectively. For each input, a distinct, focused spot around the intended location (marked by the green circle) is generated, confirming the MIMO functionality of our LWM. Since the optimal frequency was downshifted by nonidealities in the prototype, we have plotted the measured fields at 20.05 GHz and the simulated fields at 20.55 GHz. Nevertheless, we observe an excellent qualitative agreement between experimental and simulated results, which further confirms the practical viability of our proposed LWM and feeding architecture.
Next, we examine the polarization state of the outputs in the two prescribed focal planes. In Fig. 6e, we plot the RCP (solid) and LCP (dashed) components of the simulated and measured electric field for various input frequencies at the planes \(z=5{\lambda }_{o}\) and \(z=6{\lambda }_{o}\). As predicted by theory, while one of the two ports is excited, we observe a region of high RCP field strength in its corresponding focal plane. The position of the spot can be steered by tuning the frequency. There is a weak LCP background which is at most −5 dB below the peak RCP intensity. The polarization purity is significantly improved at the center of the focal spots where the crosspolarization level is at most −9.3 dB (−9.7 dB) below the copolarized radiation, for port 1 (port 2) excitation, throughout the measured frequency range.
To quantify the isolation between the two channels of our MIMO LWM in halfduplex operation, we define the signaltocrosstalk ratio (SCR) for channel \(i\) as
where \({P}_{i,\, j}\) is the power received (sent) by port \(i\) from (to) an RCP transmitter (receiver) at location \(j\). As indicated in Fig. 6a and Fig. 6b, \(j\in \left[A,B\right]\) denotes one of the two prescribed focal spots of our LWM. The measured and simulated SCR of our LWM for various input frequencies are shown in Fig. 6f. We observe satisfactory interchannel isolation in the measurements (solid lines), with at least 5 dB SCR throughout the entire measured scan range. The simulated SCR (dashed lines) is much better, suggesting that the interchannel interference may be alleviated by considering the effects of the realistic SIW wave launchers, which were not included in the numerical model. Specifically, due to imperfect wave impedance matching, the launcher on the terminating side of the LWM can generate significant unwanted reflections, which act as input from the opposite port. This effect is especially evident in the bottom left plot of Fig. 6d, which shows that port 1 excitation resulted in a weak signature at the focal spot assigned to port 2. Besides improving launchertometasurface transitions, we may increase the aperture size or the leakage rate, ensuring that the qBIC radiates most of its power before reaching the end. This solution may also unlock full duplex operation by isolating the two ports. Finally, the nonideal phase front of the excited qBIC, and the edge effects introduced by the lateral truncation of the sample, both serve to degrade the performance of our practical LWM prototype.
Dualpolarized multibeam LWM antenna
In the final design example, we demonstrate an LWM antenna capable of generating multiple independent, arbitrarily directed highgain beams with custom polarizations. It can be useful for spot beam coverage in satellite communications, especially when paired with reconfigurable elements to facilitate dynamic beamsteering and beamshaping^{21,42}.
A schematic of the proposed antenna layout is shown in Fig. 7a. We consider an illustrative design producing two RCP beams directed at \({\theta }_{R,1}\) and \({\theta }_{R,2}\), as well as a single LCP beam directed at \({\theta }_{L,1}\). For simplicity, we attribute each beam to a uniform aperture with an appropriate linear phase gradient. Furthermore, we assign different weights (\({A}_{R,1}\), \({A}_{R,2}\), \({A}_{L,1}\)) to the three summands of the complete aperture to scale their relative gain in the far field. We assume the parameters \(f=20.55\)GHz, \({\theta }_{R,1}={\theta }_{L}={10}^{\circ }\), \({\theta }_{R,2}={30}^{\circ }\), \({A}_{R,1}={A}_{L}=1\), \({A}_{R,2}=1.14\), for which the synthesis equations yield an antenna design described by Fig. 7b. The experimentally measured radiation patterns match simulation results (see Methods) almost exactly in terms of the realized gains and the directions of the main beams, at a slightly detuned optimal frequency of 20.8 GHz. In both results, we observe two distinctive RCP beams with −10 dB side lobe levels (SLL), as well as a single LCP beam with a \(8{{{{{\rm{dB}}}}}}\) back lobe at around \({30}^{\circ }\), but otherwise low SLL. The back lobe is caused by the counterpropagating wave due to reflections at the transition between the LWM and the SIW power divider. Hence, to suppress it, one can optimize the impedance matching between these two components. It is possible to further enhance the directivity of the main beams by numerically optimizing its aperture field profile, with the objective of suppressing all spurious lobes. In both the simulation and the experiment, a small amount of beam squinting from the prescribed scan angles is observed due to frequency dispersion.
In this work, we limit ourselves to the small perturbation regime for simplicity. Hence the antenna designs may suffer from reduced efficiency. For instance, the numerically simulated radiation efficiency (including dielectric and conduction loss) of the multibeam LWM is 44%. This metric can be significantly improved by: (1) increasing the physical size of the antenna aperture; and (2) utilizing more sophisticated metaunit designs with lower radiative Qfactors, such as a set of four meandered slots^{43}. However, for each given metaatom design, there exists a maximum bound on the leakage rate since the size of the slots and the allowable perturbations are limited by the metaunit footprint. Hence, in order to obtain a certain level of radiation efficiency, the physical size of the LWM aperture must exceed a corresponding lower limit (i.e., it must contain sufficiently many metaatoms). Additionally, it is important to keep in mind the inherent tradeoff between radiation efficiency and aperture efficiency since large leakage rates will lead to lower qBIC power density near the end of the LWM. This issue can be corrected using an analytically derived aperture amplitude envelope to counterbalance the tapered excitation intensity^{1,44}. Finally, we emphasize that our perturbative design framework assumes a primarily dipolarlike element factor for all metaunits, which is most accurate near the broadside. At very large oblique angles (i.e., toward the endfire directions), the presented design formulae lose accuracy in their ability to capture the nature of the radiation. To address this issue, future work can rigorously model higherorder multipole terms in the element factors^{45}.
Discussion
In this work, we introduced a class of LWM antennas empowered by quasibound states in the continuum and associated nonlocal phenomena. By judiciously breaking and tailoring relevant symmetries in the constituent metaunits, we can independently engineer the amplitude, phase, and polarization state of the aperture fields in a pointwise manner, thereby enabling full customization of the radiated fields (see Table S1 in Supplementary Information for comparison with prior arts). The proposed framework admits an almost fully rational design scheme that eschews the cumbersome numerical optimization routines or lookup tables required by conventional approaches. Using this concept, we realized several metasurface prototypes with different functionalities, ranging from nearfield wavefront shaping to farfield beam forming, all of which were validated through numerical simulations and experimental measurements. In contrast to conventional LWA approaches, which judiciously choose the position and periodicity of scattering elements in order to control the output phase profile (i.e., an aperiodic tiling), our approach uses a fixed periodicity with a spatially varying geometric phase. Future work may explore the combination of both approaches in order to create custom aperture fields with dispersion control.
We envision a straightforward application of the presented design principles to facilitate arbitrary twodimensional aperture engineering. The main challenge is the implementation of compact and wideband wave launchers, which can uniformly distribute the input power of a localized feed into a wide aperture. Besides conventional solutions, such as substrateintegrated reflectors, one potential alternative is the utilization of multiple independent inputs^{21}, which also has the added benefit of enabling fixedfrequency beam scanning in the yzplane with the incorporation of phase shifters. It is also worth noting that all the designs discussed in this paper utilize a single guided qBIC mode. We can augment an LWM with a suite of additional functionalities by leveraging multiple orthogonal qBIC modes^{46}. For instance, it is possible to at least double the number of independent channels in our proposed MIMO LWM with just one added mode (along with its timereversed counterpart). Overall, our results demonstrate the power of qBICs in a PCBcompatible radiofrequency platform and encourage further investigation of controlled symmetry as an attractive ingredient for engineering advanced microwave and mmwave wireless devices. The generality and elegance of the symmetrybased principle introduced here also invite exploration into the terahertz regime, in which physicsinformed design principles are particularly welcome due to strict technological limitations.
Methods
Numerical simulations
The band diagrams in Fig. 2 were obtained using the eigenfrequency solver in COMSOL Multiphysics (Electromagnetic Waves, Frequency Domain interface). A single metaunit, consisting of a lossless dielectric substrate sandwiched between two perfect electric conductors (PEC) surfaces, the top one being perforated and both with infinitesimal thickness, is placed between two sets of Floquet periodic boundaries. The bottom side of the simulation domain is terminated by the ground plane, while the top side is implemented as a scattering boundary. Such a setup will occasionally produce spurious eigenmodes that are not supported by the metasurface but rather by the simulation domain itself. These modes can be easily identified by their nonphysical power densities (e.g., growing intensities away from the surface) and have been rejected from our results.
To perform efficient preliminary confirmation of the functionality of the SIMO and MIMOfocusing LWM, we conducted simplified fullwave numerical simulations using the frequency domain solver in COMSOL. In the analysis, the LWMs were made infinitely periodic along the transverse ydirection using the “continuity” boundary condition. The LWM is again implemented as a lossless dielectric slab sandwiched by two PEC sheets, the top one being perforated. The two ends of the LWM were connected to short sections of unperforated PPWG. To excite the surface, the waveguide corresponding to port 1 is fed by an ideal TEM wave (launched by a uniform wave port), while the other side is terminated by a matched uniform wave port.
To accurately predict the realized gain of the multibeam LWM antenna, we use ANSYS High Frequency Structure Simulator (HFSS) to analyze the full prototype, consisting of a laterally truncated LWM (with seven identical columns), as well as the realistic feeding networks and radio frequency (RF) connectors. In the model, the antenna is built on a lossy dielectric substrate (\(h=1.52\,{{{{{\rm{mm}}}}}}\), \({\epsilon }_{r}=3\), \({{\tan }}\delta=0.001\)), with conductive copper claddings (thickness 0.018 mm, conductivity \(5.8\times {10}^{7}S/m\)). The SIW horn arrays were modeled as copper via posts. The radiation efficiency of the antenna was evaluated using the radiation surface integral method.
Device fabrication
All three designs presented in this article were fabricated inhouse using LPKF prototyping systems (Protomat S104, Protolaser S4, Contac S4) on Rogers RO3003 substrates with a thickness of 1.52 mm, dielectric constant \({\epsilon }_{r}=3\), and loss factor \({{\tan }}\delta=0.001\).
For each sample, seven identical columns of metaunits were etched onto the substrate and repeated along the transverse direction to form a quasi1D LWM. Ideally, a sample should contain as many columns as permitted by the device footprint, which would serve to suppress the guided wave components with nonzero transverse wavevectors, thereby minimizing the edge effects associated with the lateral truncation. However, the required SIW wave launcher would be substantially more complex due to the expanded aperture. In our simulations and experiments, we observed that seven columns provided a good compromise between device complexity and performance.
The SIW horn array launchers were fed by flangemount SMA connectors (Amphenol P/N: 2933–6004), whose pins have been trimmed to a length of 1.52 mm to match the substrate thickness.
Measurement
The Fresnelzone field distributions of the SIMO and MIMOfocusing LWMs were measured using a nearfield planar scanner from NSIMI Technologies. The nearfield radiation profiles of the prototypes were sampled with a Kband openended waveguide probe placed 5 cm away from the metasurface aperture. Then, the fields were projected to various planes parallel to the measurement plane, yielding the field intensity holograms reported in Fig. 5 and Fig. 6. The farfield radiation pattern of the multibeam LWM antenna was obtained using the same setup. Then, its gain was evaluated by direct comparison with a Kband standard gain horn antenna (Pasternack PE9852/2F15, 15 dBi gain) in a separate farfield measurement setup.
During measurement, the input port of the prototype is connected to a vector network analyzer, while the opposite port is terminated by a 50\(\Omega\)matched load.
Data availability
Authors can confirm that all relevant data are included in the paper and/or its supplementary information files, and raw data are available upon request from the corresponding author.
Code availability
The codes used to produce these results are available upon request from the corresponding author.
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Acknowledgements
This work acknowledges support from the U.S. Army/ARL via the Collaborative for Hierarchical Agile and Responsive Materials (CHARM) under cooperative agreement W911NF1920119, the Air Force Office of Scientific Research MURI program with grant No. FA95501810379, the National Science Foundation, and the Simons Foundation.
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A.O. developed the theoretical framework. G.X. and Y.K. designed and optimized the prototypes. G.X. performed numerical simulations and fabricated and experimentally characterized the prototypes. G.X. led the writing of the paper with contributions from A.O., Y.K., E.M., S.M., and A.A. A.A. conceived and supervised the project.
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Xu, G., Overvig, A., Kasahara, Y. et al. Arbitrary aperture synthesis with nonlocal leakywave metasurface antennas. Nat Commun 14, 4380 (2023). https://doi.org/10.1038/s41467023398182
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DOI: https://doi.org/10.1038/s41467023398182
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