EP4601120A1

EP4601120A1 - Beam-steerable antenna arrangement

Info

Publication number: EP4601120A1
Application number: EP24156546.4A
Authority: EP
Inventors: Jonathan DESSY; Modeste BODEHOU; Christophe CRAEYE
Original assignee: Universite Catholique de Louvain UCL
Current assignee: Universite Catholique de Louvain UCL
Priority date: 2024-02-08
Filing date: 2024-02-08
Publication date: 2025-08-13
Also published as: WO2025168830A1

Abstract

A modulated metasurface antenna (302) having an operating wavelength comprises a surface wave propagation medium (304) and an array (308) of surface wave transducers (309) in the surface wave propagation medium (304). The surface wave transducers (309) are spaced from each other by a minimum distance greater than half the operating wavelength. The surface wave transducers (309) are separately couplable with a phased array circuit (303). The surface wave propagation medium (304) has an electromagnetic surface impedance distribution defining respective embedded element patterns for respective surface wave transducers (309) in the array (308) of surface wave transducers. The electromagnetic surface impedance distribution is adapted so that the respective embedded element patterns defined thereby attenuate grating lobes in the radiation pattern of the modulated metasurface antenna (302).

Description

FIELD OF THE INVENTION

An aspect of the invention relates to a beam-steerable antenna arrangement. The beam-steerable antenna arrangement may be used in, for example, radar systems and communication systems. Other aspects of the invention relate to a modulated metasurface antenna, a radio-frequency system and use of a radio-frequency system.

BACKGROUND ART

A beam-steerable antenna arrangement has an antenna pattern with a main lobe that can be steered in different directions. For reception of a signal of interest, the main lobe may thus be steered in a direction where the reception of this signal is optimal. For transmission of a signal, the main lobe may be steered in a direction where a target is located for best transmission of the signal to the target. In radar applications, the main lobe may repetitively be steered in a range or a series of different directions for scanning in these different directions.
A beam-steerable antenna arrangement may be based on a so-called phased array configuration. Basically, such a configuration comprises an array of antennas and a phased array circuit, which may operate in a transmission mode or in a reception mode, or in both these modes. In the transmission mode, the phased array circuit defines phase relationships between respective signals applied to respective antennas in the array. In the reception mode, the phased array circuit defines phase relationships between respective signals coming from respective antennas in the array. In either mode, the phase relationships define the direction of the main lobe in the antenna pattern, which is thus the direction of transmission or reception, respectively. This direction can be changed by changing the phase relationship.
A fundamental constraint of the phased array configuration concerns a spacing between the antennas in the antenna array. The spacing should not exceed a half wavelength of a signal to be transmitted or received to avoid so-called grating lobes. Grating lobes are undesired repetitions of the main lobe, which make that signals are transmitted or received, or both, in directions other than desired ones. In practice, it has been found difficult to suppress grating lobes. Conventional techniques that have been proposed to suppress grating lobes require structures that are prohibitively complex, bulky, and costly for many applications.
The fundamental constraint on the spacing discussed hereinbefore may pose a significant problem in applications where frequencies are relatively high and wavelengths are thus relatively short. In those applications, the fundamental constraint requires electronic components to be relatively densely packed in the phased array circuit. This dense packaging may be relatively costly and, moreover, may pose serious power dissipation problems. This is because, in practice, at least some of the electronic components may produce heat, in particular when operating at relatively high frequencies.
In addition, the fundamental constraint on the spacing may pose a significant problem in applications where relatively high antenna gain is required. The phased array configuration generally needs to be relatively large in size, covering a relatively large surface, to achieve relatively high antenna gain. The fundamental constraint requires the phased array configuration to comprise a minimum number of antennas and a corresponding minimum number of signal channels in the phased array circuit. A relatively large size makes that this required minimum number is relatively high, resulting in the beam-steerable antenna arrangement being relatively heavy and bulky.

SUMMARY OF THE INVENTION

There is a need for a technique for implementing a beam-steerable antenna arrangement that allows at least one of the following improvements: lower power consumption, lower weight, less complex and less expensive.
An aspect of the invention, which is defined in claim 1, relates to a modulated metasurface antenna having an operating wavelength comprising:

a surface wave propagation medium;
an array of surface wave transducers in the surface wave propagation medium, the surface wave transducers being spaced from each other by a minimum distance greater than half the operating wavelength, the surface wave transducers being separately couplable with a circuit adapted to carry out at least one of the following operations: applying an array of drive signals at the operating wavelength to the array of surface wave transducers, causing the modulated metasurface antenna to have a radiation pattern dependent on a phase-relationship between the drive signals, and processing an array of receptions signals at the operating wavelength captured by the array of surface wave transducers signals, wherein
the surface wave propagation medium has an electromagnetic surface impedance distribution defining respective embedded element patterns for respective surface wave transducers in the array of surface wave transducers, an embedded element pattern for a surface wave transducer being a radiation pattern of the modulated metasurface antenna when a drive signal at the operating wavelength is exclusively applied to the surface wave transducer, whereas the other surface wave transducers of the array do not receive a drive signal,

A further aspect of the invention, which is defined in claim 13, relates to a beam-steerable antenna arrangement comprising:

a modulated metasurface antenna as defined hereinbefore; and
a circuit adapted to carry out at least one of the following operations: applying an array of drive signals at the operating wavelength to the array of surface wave transducers in the modulated metasurface antenna, causing the modulated metasurface antenna to have a radiation pattern dependent on a phase-relationship between the drive signals, and processing an array of receptions signals at the operating wavelength captured by the array of surface wave transducers signals in the modulated metasurface antenna.

Yet further aspects of the invention, which are defined in claims 14 and 15, relate to a radio-frequency system comprising a beam-steerable antenna arrangement and use of such a radio-frequency system, respectively.
The invention takes the following aspects into consideration. The array of surface wave transducers in the surface wave propagation medium may functionally be equated with the array of antennas in the phased array configuration discussed hereinbefore. The surface wave propagation medium is common to all the surface wave transducers and thus, by analogy, common to all the antennas in the array. Accordingly, the electromagnetic surface impedance distribution of the surface propagation medium applies to all the surface wave transducers and thus, by analogy, to all the antennas in the array, albeit from different points in this distribution.
The electromagnetic surface impedance distribution may thus define an embedded element pattern for each surface wave transducers and thus, by analogy, for each antenna. These embedded element patterns may be quite similar, or even identical, and shaped such that grating lobes are attenuated to a sufficient degree. The fundamental constraint on the spacing can thus be overcome effectively and efficiently. The spacing can be larger than half a wavelength, even significantly larger. This removes, or at least alleviates the aforementioned problems related to power consumption and dissipation, weight, size, and cost. Added to this are inherent advantages of a modulated metasurface antenna, such as, for example, relatively low losses, low profile, ease of manufacture and relatively light, compact electronics.
For the purpose of illustration, some embodiments of the invention are described in detail with reference to accompanying drawings. In this description, additional features will be presented, some of which are defined in the dependent claims, and advantages will be apparent.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram of an elementary beam-steerable antenna arrangement.
FIG. 2 is a combined graph of an array factor of the elementary beam-steerable antenna arrangement and an embedded element pattern for an elementary antenna in the elementary beam-steerable antenna arrangement.
FIG. 3 is a schematic block diagram of an inventive beam-steerable antenna arrangement.
FIG. 4 is a graph of an embedded element pattern in an embodiment of the inventive beam-steerable antenna arrangement.
FIG. 5 is a graph of various embedded element patterns obtained with various electromagnetic surface impedance distributions that differ in modulation depth.
FIG. 6 is a graph of various embedded element patterns obtained with various electromagnetic surface impedance distributions that differ in average impedance.
FIG. 7 is a graph of an exemplary electromagnetic surface impedance distribution.
FIG. 8 is a graph of an embedded element pattern in an evolved embodiment of the inventive beam-steerable antenna arrangement.
FIG. 9 is a schematic top view of an embodiment of a modulated metasurface antenna in the inventive beam-steerable antenna arrangement.
FIG. 10 is a graph of an electromagnetic surface impedance distribution of the embodiment of the modulated metasurface antenna.

DESCRIPTION OF SOME EMBODIMENTS

FIG. 1 schematically illustrates an elementary beam-steerable antenna arrangement 100. FIG. 1 provides a schematic block diagram of the elementary beam-steerable antenna arrangement 100. The elementary beam-steerable antenna arrangement 100 comprises an array of elementary antennas 101 and a phased array circuit 102. In FIG. 1, six elementary antennas 103-108 are represented for the sake of simplicity and illustration. Embodiments may comprise more or fewer elementary antennas.
The elementary beam-steerable antenna arrangement 100 may operate in a transmission mode, or in a reception mode, or in both these modes. In the transmission mode, the phased array circuit 102 applies an array of drive signals 109-114 to the array of elementary antennas 101. Respective elementary antennas 103-108 may receive respective drive signals 109-114. The drive signals 109-114 may be phase shifted with respect to each other according to a phase shift scheme. The phased array circuit 102 may be controllable so as to adjust the phase shift scheme, or to adjust an amplitude relationship between the respective drive signals 109-114, or to adjust both.
In the reception mode, the phased array circuit 102 receives an array of reception signals 115-120 from the array of elementary antennas 101. In a converse manner, the phased array circuit 102 may phase shift the reception signals 115-120 with respect to each other according to a phase shift scheme, which may be adjustable. Alternatively, or additionally, respective weighting factors may be applied to respective reception signals 115-120. These respective weighting factors may be adjusted.
The elementary beam-steerable antenna arrangement 100 has an array factor. The array factor is a radiation pattern that the array of elementary antennas 101 would have if all the elementary antennas 103-108 radiated isotropically. The array factor depends on the aforementioned phase shift scheme in the transmission mode and in the reception mode. The array factor can thus be controlled by controlling the phase shift scheme. Accordingly, the array of elementary antennas 101 can be made to transmit a signal in a particular direction or to receive a signal coming from a particular direction.
The elementary beam-steerable antenna arrangement 100 further has an embedded element pattern for an elementary antenna in the array of elementary antennas 101. The embedded element pattern is a radiation pattern that the array of elementary antennas 101 would have if a drive signal were exclusively applied to the elementary antenna concerned, whereas the other elementary antennas of the array 101 do not receive a drive signal. The embedded element pattern may be identical for all the elementary antennas 103-108 in the array 101, or at least similar. In that case, the elementary beam-steerable antenna arrangement 100 has a radiation pattern that is a product of the array factor and the embedded element pattern.
FIG. 2 schematically illustrates two array factors 201, 202 of the elementary beam-steerable antenna arrangement 100 and an embedded element pattern 203 for an elementary antenna in the elementary beam-steerable antenna arrangement 100. FIG. 2 provides a combined graph representing the two array factors 201, 202 and the embedded element pattern 203. The combined graph has a horizontal axis representing an angle with respect to a vector normal to the array of elementary antennas 101, and a vertical axis representing a magnitude of radiation in the transmission mode. A curve in broken lines represents a first array factor 201. A curve in dotted lines represents a second array factor 202. A curve in solid lines represents the embedded element pattern 203.
FIG. 2 illustrates beam steering by controlling the array factor as discussed hereinbefore. The first array factor 201 has a main lobe 204 that is centered on a zero angle corresponding with the vector normal to the array of elementary antennas 101. The elementary beam-steerable antenna arrangement 100 will radiate in this direction with the first array factor 201. The second array factor 202 has a corresponding main lobe 205, which is shifted in angle, to the right in FIG. 2. The elementary beam-steerable antenna arrangement 100 will radiate in this different direction with the second array factor 202.
FIG. 2 further illustrates that the two array factors 201, 202 each have grating lobes 206-209 in addition to the main lobe. Grating lobes are undesired repetitions of the main lobe. Grating lobes are undesired because these cause directional ambiguities. In the transmission mode, a signal is also radiated in directions other than that corresponding to the main lobe. In the reception mode, a signal may also be received from directions other than that corresponding to the main lobe.
Grating lobes occur when spacing between the elementary antennas 103-108 is sufficiently large to allow in-phase addition of radiation in more than one direction. Specifically, grating lobes occur when the spacing is greater than a half wavelength. Grating lobes are due to a spatial aliasing effect akin to frequency aliasing in signal processing with subsampled signals.
The embedded element pattern 203 may attenuate the grating lobes 206-209, which transpose from the array factor into the radiation pattern of the elementary beam-steerable antenna. FIG. 2 illustrates this by way of example. The embedded element pattern 203 has an angle of aperture 210, a single lobe 210. As mentioned hereinbefore, the radiation pattern of the elementary beam-steerable antenna is the product of the array factor and the embedded element pattern 203. Since the grating lobes 206-209 are outside of the angle of aperture 210 of the embedded element pattern 203, the grating lobes 206-209 are attenuated. This attenuation of the grating lobes 206-209 by the embedded element pattern 203 comes with a constraint. Namely the beam steering is restricted to a range of directions corresponding with the angle of aperture of the embedded element pattern 203.
In practice, it has been found difficult to achieve attenuation of the grating lobes in the array factor by the embedded element pattern. This is because the embedded element pattern needs to have a sufficiently narrow and sharply defined angle of aperture with a sufficiently flat magnitude distribution. Conventional techniques require relatively complex, bulky, and costly structures in order to achieve that the embedded element pattern has a sufficiently narrow and sharply defined angle of aperture with a sufficiently flat magnitude distribution.
In many cases, it is better to avoid grating lobes in the array factor altogether by spacing the elementary antennas 103-108 sufficiently close to avoid the spatial aliasing effect mentioned hereinbefore. This, however, may pose a problem at an operating wavelength that is relatively small such as, for example, an operating wavelength that is in the order of centimeters, or lower. In practice, the phased array circuit 102 will generally comprise respective signal channels for respective elementary antennas 103-108. A relatively small operating wavelength requires that the respective signal channels be relatively close together. That is, the respective signal channels need to be densely packed. Moreover, at least some of these signal channels may produce a relatively large amount of heat, which may cause heat dissipation problems.
FIG. 3 schematically illustrates an inventive beam-steerable antenna arrangement 300. FIG. 3 provides a schematic block diagram of the inventive beam-steerable antenna arrangement 300. The inventive beam-steerable antenna arrangement 300 may form part of a radiofrequency system 301, which is very schematically indicated in FIG. 3. The inventive beam-steerable antenna arrangement 300 may be used therein for emitting a radiofrequency signal, or receiving a radiofrequency signal, or both. The inventive beam-steerable antenna arrangement 300 may have an operating wavelength that is in order of, for example, centimeters or millimeters. The operating wavelength may correspond to a center frequency of a frequency band in which the inventive beam-steerable antenna arrangement 300 may operate. The center frequency may be anywhere between, for example, 1 GHz and 100 GHz.
The inventive beam-steerable antenna arrangement 300 comprises a modulated metasurface antenna 302 and a phased array circuit 303. The modulated metasurface antenna 302 comprises a surface wave propagation medium 304 having a surface 305 from which an electrical field may radiate. This surface 305 will therefore be referred to hereinafter as the radiating surface 305. An electromagnetic surface impedance distribution extends over the radiating surface 305 of the surface wave propagation medium 304. The electromagnetic surface impedance distribution exhibits variations over the radiating surface 305.
FIG. 3 illustrates an embodiment in which the surface wave propagation medium 304 comprises a dielectric substrate 306. The dielectric substrate 306 has a main surface that is provided with a ground plane 307. An opposite main surface corresponds with the aforementioned radiating surface 305 of the surface wave propagation medium 304. The dielectric substrate 306 may be a commercially available substrate, such as the substrate named ROGERS4350B^®, which is a registered trademark of the ROGERS Corporation (US). This substrate has a relative permittivity ε_r of 3.66 and a thickness of 1.524 mm.
The radiating surface 305 is provided with a multitude of electrically conductive elements, which are subwavelength-sized. The term subwavelength-sized indicates that a largest dimension of an electrically conductive element is about an order of magnitude shorter than the operating wavelength. The electrically conductive elements are distributed over the dielectric substrate 306 in a manner whereby these vary in density, or in size, or in shape, or in orientation, in any combination of these. The electrically conductive elements could therefore also be referred to as electrically conductive patches.
The electromagnetic surface impedance distribution may, at least partially, be defined by the subwavelength-sized conductive elements. Various properties of the subwavelength-sized conductive elements may play a role in this respect, such as, for example, size, shape, orientation, and density of these elements. The variations in the electromagnetic surface impedance distribution may be implemented by, for example, varying the subwavelength-sized conductive elements in density, or in size, or in shape, or in any combination of these.
The modulated metasurface antenna 302 further comprises an array of surface wave transducers 308 in the surface wave propagation medium 304. A surface wave transducer may comprise a single transducer element, which may also be referred to as a feed, or a set of transducer elements, which may be spatially distributed. In this respect, the surface wave transducers are very schematically represented in FIG.3 by dots. For the sake of simplicity and clarity, only a single surface wave transducer represented by a dot is denoted by reference numeral 309. The reference numeral 309 may be used to denote any one of the surface wave transducers wherever appropriate.
The surface wave transducers 309 are separately coupled with the phased array circuit 303. Respective surface wave transducers 309 may receive respective drive signals. In this respect, the surface wave transducers 309 may be equated with the elementary antennas 103-108 in the elementary beam-steerable antenna arrangement 100 illustrated in FIG. 1. In embodiments where a surface wave transducer 309 comprises several transducer elements, these are jointly coupled to a same node of the phased array circuit 303 through different branches. These different branches may apply different weighing factors. The phased array circuit 303 may be basically similar to the phased array circuit 303 discussed hereinbefore with reference to FIG. 1.
The modulated metasurface antenna 302 basically operates as follows in a transmission mode. A surface wave transducer 309 generates a surface wave in the surface wave propagation medium 304 in response to a drive signal at an operating wavelength. The surface wave that is launched, as it were, from the surface wave transducer 309 propagates through the propagation medium. Variations in the electromagnetic surface impedance distribution perturb, as it were, the surface wave that propagates. These variations cause leakage of the surface wave from the surface wave propagation medium 304. This leakage, which occurs at the radiating surface 305, is also referred to as transformation of the surface wave into a leaky wave.
The leakage of the surface wave propagating through the surface wave propagation medium 304 constitutes an electrical field radiating from the radiating surface 305 of the surface wave propagation medium 304. This radiated electrical field has a distribution over the radiating surface 305 that depends on the electromagnetic surface impedance distribution. Accordingly, the electromagnetic surface impedance distribution defines, at least partially, an embedded element pattern for the surface wave transducer in the modulated metasurface antenna 302.
The basic operation described hereinbefore equally applies to all surface wave transducers 309 in the surface wave propagation medium 304. Accordingly, the electromagnetic surface impedance distribution defines respective embedded element patterns for respective surface wave transducers 309 in the surface wave propagation medium 304. For simplicity, it is assumed that the respective embedded element patterns are identical, which is a reasonable assumption, in particular if the array comprises relatively many surface wave transducers. The respective embedded element patterns will therefore jointly be referred to as the embedded element pattern of the modulated metasurface antenna 302.
The surface wave transducers 309 are spaced from each other by a minimum distance greater than half an operating wavelength. For example, the surface wave transducers 309 may be spaced from each other by two times the operating wavelength. The array of surface wave transducers 308 may therefore be qualified as a sparse array. Similar to what was discussed hereinbefore, the phased array circuit 303 will generally comprise respective signal channels for respective surface wave transducers 309.
Since the array of surface wave transducers 308 is sparse, relatively few signal channels are required. This allows the phased array circuit 303 to have a relatively low power consumption, be relatively lightweight, and be relatively inexpensive. Furthermore, this allows less densely packed signal channels, which facilitates power dissipation.
However, the sparse array of surface wave transducers 308 has an array factor that includes grating lobes, as discussed hereinbefore. Beam steering may potentially make that a radiation direction falling within the main lobe may also fall within a grating lobe. This constitutes a lobe ambiguity, which is generally undesirable. This lobe ambiguity can be avoided by restricting the beam steering in a sufficiently narrow range of directions.
The sparser the array of surface wave transducers 308 is, the further apart the surface wave transducers 309 are, and the closer the grating lobes will be to the main lobe. Thus, the sparser the array of surface wave transducers 308 is, the narrower the range of directions that the beam steering may cover. In general, it holds that if the surface wave transducers 309 are spaced from each other by a distance that is p times half the operating wavelength, p being a real number, the beam steering is restricted to a range of angles between -arcsin(1/p) and +arcsin(1/p).
The grating lobes may be attenuated by the embedded element pattern of the modulated metasurface antenna 302. As mentioned hereinbefore, the electromagnetic surface impedance distribution defines, at least partially, the embedded element pattern. The surface impedance distribution, which extends over the radiation surface of the surface wave propagation medium 304, may be designed so that the grating lobes are sufficiently attenuated. For example, the electromagnetic surface impedance distribution may be designed so that the embedded element pattern has an angle of aperture that is narrower than 2 times arcsin(1/p). Attenuation of the grating lobes by the embedded element pattern can thus be achieved efficiently and effectively. In contrast with prior art techniques, there is no need for relatively complex, bulky, and costly structures.
For example, the electromagnetic surface impedance distribution may be designed so that the distribution of the radiated electrical field over the radiating surface 305 approximates a sinc function. The sinc function may have a maximum at the surface wave transducer to which the drive signal at the operating frequency is applied. The sinc function may go through zero where other surface wave transducers are located. This sinc function is schematically represented in FIG. 3.
The sinc function may be regarded as an optimal distribution of the radiated electrical field over the radiating surface 305. Namely, this optimal sinc-like distribution results the embedded element pattern having an angle of aperture with a flat magnitude distribution delimited by sharp, brick-wall-like edges akin to an ideal bandpass filter. The optimal sinc-like distribution may not be achievable in practice, but can be approximated sufficiently closely.
The electromagnetic surface impedance distribution may have a periodicity corresponding with a distance by which the surface wave transducers 309 are spaced from each other divided by a natural number, including the natural number 1. In such embodiments, the electromagnetic surface impedance distribution is, in effect, formed by a seamless array of elementary electromagnetic surface impedance distributions, which may be identical to each other. That is, the electromagnetic surface impedance distribution may be formed by seamless repetitions of an elementary electromagnetic surface impedance distribution. Respective repetitions of the elementary electromagnetic surface impedance distribution may thereby cover respective surface wave transducers 309. Accordingly, each surface wave transducer 309 may be covered by a single repetition of the elementary electromagnetic surface impedance distribution.
Design and analysis of the electromagnetic surface impedance distribution may involve a technique called "method of moments" (MoM). Details of this technique may be found in, for example, the publication by M. Bodehou, et al. entitled "Direct numerical inversion methods for the design of surface wave-based metasurface antennas: Fundamentals, realizations, and perspectives" in IEEE Antennas Propag. Mag., vol. 64, no. 4, pp. 24-36, 2022. The method of moments allows determining a current distribution on the radiating surface 305 for a given electromagnetic surface impedance distribution when a drive signal is applied to a surface wave transducer 309. The radiated electrical field may be computed from the current distribution. Accordingly, the embedded element pattern may be computed from the current distribution.
In essence, the method of moments relies on an entire-domain discretization of an electric field integral equation, which may be generally expressed as follows: $\hat{n} \times [\iint_{S'} \underline{\underline{G}} (r, r') J (r') dS' - {\underline{\underline{Z}}}_{s} (r) J (r)] = - \hat{n} \times E_{i} (r)$ where n̂ is a unit vector perpendicular to the radiating surface 305 S', G is a spatial Green's function on the surface wave propagation medium 304, J is the current distribution, Z _s is the electromagnetic surface impedance distribution, E_i is an incident electrical field at the radiating surface 305, and r and r' refer to a position of observation and of a source, respectively.
The electromagnetic surface impedance distribution may have a spatial frequency that determines a main direction of the radiated electrical field. A continuous range of radiation directions may be obtained by varying the spatial frequency within a range of spatial frequencies. The continuous range of radiation directions defines the angle of aperture of the embedded element pattern of the modulated metasurface antenna 302.
On the one hand, the angle of aperture should be sufficiently narrow to prevent grating lobes from falling therein. On the other hand, the angle of aperture should be sufficiently wide to allow beam steering over a desired range of directions. Namely, as mentioned hereinbefore, the beam steering is restricted to a range corresponding with the angle of aperture of the embedded element pattern. An optimal angle of aperture corresponds to 2 times arcsin(1/p) with infinitely sharp edges, p being a real number corresponding to a ratio between a spacing of the surface wave transducers 309 divided by half the operating wavelength.
The elementary electromagnetic surface impedance distribution may have a varying spatial frequency according to the following equations: $Z_{s} (x) = {\begin{array}{r} {jX}_{0} (1 + M_{0} \sin (2 π (\frac{ƒ_{2} - ƒ_{1}}{a} x^{2} + ƒ_{2} x))) \\ if \frac{- a}{2} \leq x < 0 \\ {jX}_{0} (1 + M_{0} \sin (2 π (\frac{ƒ_{1} - ƒ_{2}}{a} x^{2} + ƒ_{2} x))) \\ if 0 \leq x < \frac{a}{2} \end{array}$ $ƒ_{1,2} = \frac{k_{sw} - k_{0} \sin (θ_{p 1,2})}{2 π}$ where Zs is the electromagnetic surface impedance distribution along an axis x, with x=0 being a center point in the elementary electromagnetic surface impedance distribution, X₀ is an average reactance, M₀ is a modulation depth,f₁ and f₂ are boundaries of a range of spatial frequencies, a is a distance over which the elementary electromagnetic surface impedance distribution extends, k_sw is a wave number of a main surface wave in the absence of modulation (M₀ = 0), k₀ is the wave number in free space, θp₁ and θp₂ define a desired angle of aperture of the embedded element pattern.
The elementary electromagnetic surface impedance distribution Zs presented hereinbefore may be decomposed into a Fourier series with N coefficients, N being a natural number. This number N may be equal to, for example, 31. The Fourier series composition may be used as a basis to further optimize and design the elementary electromagnetic surface impedance distribution.
The aforementioned was applied to an embodiment in which the surface wave transducers 309 were spaced from each other by two times the operating wavelength (2λ). Optimization resulted in an exemplary electromagnetic surface impedance distribution characterized by the following equation: $Zs (x) = {jX}_{0} (1 + M \sin (3 ω_{0} x)) with ω_{0} = 2 π / a$ In this embodiment, the exemplary electromagnetic surface impedance distribution has a sinusoidal periodicity equal to two times the operating wavelength divided by three. The electromagnetic surface impedance distribution is anti-symmetric with respect to the surface wave transducer 309.
FIG. 4 schematically illustrates an embedded element pattern 401 in the aforementioned embodiment of the inventive beam-steerable antenna arrangement 300. FIG. 4 provides a graph having a horizontal axis representing an angular direction in units of degrees, whereby 0° corresponds with the angular direction perpendicular to the radiating surface 305. A vertical axis represents directivity in units of decibel. A curve in solid lines represents the embedded element pattern 401 that was obtained with X₀ = -1200 Ω and M = 1.2. A curve in dashed lines represents an ideal embedded element pattern having an angle of aperture with a flat magnitude distribution delimited by infinitely sharp edges.
FIG. 5 schematically illustrates various embedded element patterns 501, 502, 503 obtained with various electromagnetic surface impedance distributions that differ in modulation depth. FIG. 5 provides a graph similar to that of FIG. 4 with the curve in solid lines again representing the embedded element pattern 401 that was obtained with X₀ = -1200 Ω and M = 1.2. A curve in dotted lines represents an embedded element pattern 501 that was obtained with X₀ = -1200 Ω and M = 0.5. A curve in dashed lines represents an embedded element pattern 502 that was obtained with X₀ = -1200 Ω and M = 0.75. A curve in dash-dotted lines represents an embedded element pattern 503 that was obtained with X₀ = -1200 Ω and M = 1.0.
FIG. 5 shows that the embedded element pattern changes by varying M. Specifically, FIG. 5 illustrates that a relatively high modulation depth, exceeding 1, may provide a satisfactory embedded element pattern, which generally also applies to other embodiments. A relatively high modulation depth, exceeding 1, produces more leakage. This produces an effect of two peaks in the embedded element pattern merging with each other. This merging effect, in turn, allows obtaining a relatively wide angle of aperture with a relatively flat magnitude distribution.
FIG. 6 schematically illustrates various embedded element patterns obtained with various electromagnetic surface impedance distributions that differ in average impedance. FIG. 6 provides a graph similar to that of FIG. 4 with the curve in solid lines again representing the embedded element pattern that was obtained with X₀ = -1200 Ω and M= 1.2. A curve in dash-dotted lines represents an embedded element pattern 601 that was obtained with X₀ = -600 Ω and M = 1.2. A curve in dashed lines represents an embedded element pattern 602 that was obtained with X₀ = -900 Ω and M = 1.2. A curve in dotted lines represents an embedded element pattern 603 that was obtained with X₀ = -1500 Ω and M = 1.2.
FIG. 6 shows that the embedded element pattern changes by varying X₀. FIG. 5 and 6 jointly illustrate that the embedded element pattern can be tuned, as it were, to an optimum by varying X₀, or by varying M, and thus by varying both. FIGS. 4-6 all concern an embodiment of the inventive beam-steerable antenna arrangement 300 in which the surface wave transducers 309 comprise a single transducer element only. A further optimization of the embedded element pattern may be achieved in embodiments where the surface wave transducers 309 comprise a set of spatially distributed transducer elements. This is discussed in what follows.
FIG. 7 schematically illustrates an example 700 of the exemplary electromagnetic surface impedance distribution presented hereinbefore. FIG. 7 provides a graph having a horizontal axis representing a distance in units of wavelength with 0 corresponding with a center point of a surface wave transducer. A vertical axis represents a reactance value of the exemplary electromagnetic impedance distribution. The reactance value sinusoidally varies with the distance with a sinusoidal periodicity whereby one period covers two times the operating wavelength divided by three. This corresponds with the exemplary electromagnetic surface impedance distribution mentioned hereinbefore.
FIG. 7 schematically indicates various locations where transducer elements of the surface wave transducer may be present. These various locations are indicated by means of dots from which relatively short arrows extend upwards. These locations correspond with locations where the periodicity of the electromagnetic surface impedance distribution has a given phase corresponding to a given reactance value, which is -1200 Ω in this example. This value corresponds to an average reactance of the exemplary electromagnetic surface impedance distribution.
Various evolved embodiments are possible in which the surface wave transducers comprise several transducer elements that are spatially distributed. For example, in an evolved embodiment, a surface wave transducer may comprise two transducer elements that, referring to FIG. 7, are located at x = ±λ/3. In another evolved embodiment, these two transducer elements may be located at x = ±2λ/3. In any case, the two transducer elements receive a same drive signal. In yet another evolved embodiment, a surface wave transducer may comprise four transducer elements that are located at x = [-λ;-λ/3; λ/3; λ]. A drive signal for the surface wave transducer may be applied to these four transducer elements with the weighing factors [0.5; 1; 1; 0.5], respectively. A power divider may be used, for example, to apply a weighing factor of 0.5.
The locations x = [-λ; λ] imply that these two transducer elements are at a border between the surface wave transducer and an adjacent surface wave transducer. Accordingly, in this embodiment, two surface wave transducers may share, as it were, a transducer element at the border between these. This, in turn, implies that the embodiment may comprise a combiner for applying a combination of two drive signals to the transducer element at the border. One of these two drive signals is related to one of the two surface wave transducers; the other of the two drive signals is related to the other surface wave transducer.
FIG. 8 schematically illustrates an embedded element pattern 801 in an evolved embodiment of the inventive beam-steerable antenna arrangement 300. FIG. 8 provides a graph similar to that of FIG. 4 with the curve in solid lines again representing the same embedded element pattern 401. This embedded element pattern 401 was thus obtained with surface wave transducers comprising a single transducer element only. The curve in dashed lines again represents an ideal embedded element pattern. A curve in dash-dotted lines represents the embedment element pattern 801 of the evolved embodiment in which surface wave transducers 309 comprise four transducer elements located as discussed hereinbefore.
FIG. 8 shows that the embedded element pattern 801 of the evolved embodiment, with four transducer elements per surface wave transducer 309, better approximates the ideal embedded element pattern than the embedded element pattern 401 of the embodiment with a single transducer element per surface wave transducer. The embedded element pattern 801 of the evolved embodiment has an angle of aperture with a flatter magnitude distribution delimited by sharper edges. Moreover, this embedded element pattern 801 provides greater attenuation of the grating lobes. This shows that using surface wave transducers 309 with several transducer elements, which may be in a number of two or four, or another number, may be advantageous.
FIG. 9 schematically illustrates an embodiment 900 of a modulated metasurface antenna 302 in the inventive beam-steerable antenna arrangement 300. FIG. 9 provides a schematic top view of this embodiment 900 showing the radiating surface 305 of the surface wave propagation medium 304. The radiating surface 305 is provided with a two-dimensional array of elementary patterns of subwavelength-sized conductive elements. In this embodiment, the elementary patterns are identical to each other. That is, the radiating surface 305 is provided with a repetition in two dimensions, horizontally and vertically, of an elementary pattern 901 of subwavelength-sized conductive elements. The elementary pattern of subwavelength-sized conductive elements defines, at least partially, an elementary electromagnetic surface wave impedance distribution, which is thus equally repeated over the radiating surface 305 as discussed hereinbefore.
Respective repetitions of the elementary pattern of subwavelength-sized conductive elements cover respective surface wave transducers. Accordingly, each surface wave transducer is covered by a single repetition of the elementary pattern of subwavelength-sized conductive elements. Accordingly, the surface wave transducers are equally arranged in a two directions, horizontally and vertically. The surface wave transducers are spaced from each other in the horizontal direction by a distance that is p times half the operating wavelength, p being a real number greater than 1. The surface wave transducers are spaced from each other in the vertical direction by a distance that is q times half the operating wavelength, q being a real number greater than 1. In this embodiment, p is equal to q. Moreover, each surface wave transducer comprises four transducer elements 902-905, which are designated by references in the left-bottom most occurrence of the elementary pattern 901 of subwavelength-sized conductive elements.
FIG. 10 schematically illustrates an electromagnetic surface impedance distribution 1000 of the aforementioned embodiment 900 of the modulated metasurface antenna 302. FIG. 10 is a graph that represents the radiating surface of the evolved embodiment. The graph has a horizontal axis and a vertical axis that each indicate a distance from a center point on the radiating surface along the axis concerned. The distance is expressed in units of wavelength. The graph indicates the electromagnetic surface impedance distribution 1000 by means of gray levels. Specifically, the graph indicates an electromagnetic surface reactance distribution by means of gray levels. A grayscale indicates a relationship between gray levels and reactance values.
The elementary electromagnetic surface wave impedance distribution mentioned hereinbefore in connection with FIG. 9 is indicated in FIG. 10 and denoted by reference numeral 1001. FIG. 10 shows that the electromagnetic surface impedance distribution is formed by a repetition in two dimensions of the elementary electromagnetic surface wave impedance distribution 1001, as discussed hereinbefore.

NOTES

The embodiments described hereinbefore with reference to the drawings are presented by way of illustration. The invention may be implemented in numerous different ways. In order to illustrate this, some alternatives are briefly indicated.
There are numerous different ways of implementing a modulated metasurface antenna in accordance with the invention. Specifically, there are numerous different ways of forming an array of surface wave transducers in a modulated metasurface antenna. In the presented embodiments, the surface wave transducers are arranged as a one-dimensional series and as a two-dimensional matrix. In other embodiments, the surface wave transducers may be arranged, for example, along two different lines that need not necessarily be orthogonal to each other. As another example, the surface wave transducers may be circularly arranged. Furthermore, the surface wave transducers need not necessarily be spaced equidistantly.
The term surface wave propagation medium should be interpreted broadly. This term encompasses any type of medium in which a surface wave may propagate while leaking from a surface thereof causing radiation of a field.
The remarks made hereinbefore demonstrate that the embodiments described with reference to the drawings illustrate the invention, rather than limit the invention. The invention can be implemented in numerous alternative ways that are within the scope of the appended claims. All changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope. Any reference sign in a claim should not be construed as limiting the claim. The verb "comprise" in a claim does not exclude the presence of other elements or other steps than those listed in the claim. The same applies to similar verbs such as "include" and "contain". The mention of an element in singular in a claim pertaining to a product, does not exclude that the product may comprise a plurality of such elements. Likewise, the mention of a step in singular in a claim pertaining to a method does not exclude that the method may comprise a plurality of such steps. The mere fact that respective dependent claims define respective additional features, does not exclude combinations of additional features other than those reflected in the claims.

Claims

A modulated metasurface antenna (302) having an operating wavelength comprising:
- a surface wave propagation medium (304);

- an array of surface wave transducers (308) in the surface wave propagation medium, the surface wave transducers being spaced from each other by a minimum distance greater than half the operating wavelength, the surface wave transducers being separately couplable with a circuit (303) adapted to carry out at least one of the following operations: applying an array of drive signals at the operating wavelength to the array of surface wave transducers, causing the modulated metasurface antenna to have a radiation pattern dependent on a phase-relationship between the drive signals, and processing an array of receptions signals at the operating wavelength captured by the array of surface wave transducers signals, wherein

- the surface wave propagation medium has an electromagnetic surface impedance distribution (700, 1000) defining respective embedded element patterns for respective surface wave transducers in the array of surface wave transducers, an embedded element pattern (401, 801) for a surface wave transducer (309) being a radiation pattern of the modulated metasurface antenna when a drive signal at the operating wavelength is exclusively applied to the surface wave transducer, whereas the other surface wave transducers of the array do not receive a drive signal,
wherein the electromagnetic surface impedance distribution is adapted so that the respective embedded element patterns defined thereby attenuate grating lobes (206-209) in the radiation pattern of the modulated metasurface antenna due to the minimum distance by which the surface wave transducers are spaced from each other being greater than half the operating wavelength.
A modulated metasurface antenna according to claim 1, wherein the electromagnetic surface impedance distribution (700, 1000) has a periodicity corresponding with a distance by which the surface wave transducers are spaced from each other divided by a natural number, including the natural number 1.
A modulated metasurface antenna according to claim 2, wherein at least some of the surface wave transducers each comprise multiple surface wave transducer elements (902-905).
A modulated metasurface antenna according to claim 3, wherein the surface wave transducer elements (902-905) are present at locations where the periodicity of the electromagnetic surface impedance distribution (700, 1000) has a given phase corresponding to a given electromagnetic surface impedance.
A modulated metasurface antenna according to claim 4, wherein the given phase of the electromagnetic surface impedance distribution, which defines the locations where the surface wave transducer elements (902-905) are present, corresponds to an average value of the surface impedance distribution.
A modulated metasurface antenna according to any of claims 1 to 5, wherein the electromagnetic surface impedance distribution (700, 1000) is adapted to cause the surface wave propagation medium (304) to produce a radiated electrical field distribution approximating a sinc function in response to a drive signal at the operating frequency being applied to a surface wave transducer.
A modulated metasurface antenna according to claim 6, wherein the sinc function has a maximum at the surface wave transducer to which the drive signal at the operating frequency is applied and goes through zero where other surface wave transducers are located.
A modulated metasurface antenna according to any claims 2 to 7, wherein the distance by which the surface wave transducers are spaced from each other is two times the operating wavelength and the periodicity of the electromagnetic surface impedance distribution (700, 1000) is two times the operating wavelength divided by three.
A modulated metasurface antenna according to any of claims 1 to 8, wherein:
- the surface wave transducers are arranged in a direction, the distance by which the surface wave transducers are spaced from each other being p times half the operating wavelength, p being a real number; and

- the electromagnetic surface impedance distribution (700, 1000).is adapted so that the respective embedded element patterns defined thereby have an angle of aperture comprised within a range between -arcsin(1/p) and +arcsin(1/p) in the direction in which the surface wave transducers are arranged.
A modulated metasurface antenna according to any of claims 1 to 8, wherein
- the surface wave transducers are arranged in a first direction and a second direction that are different from each other, the distance by which the surface wave transducers are spaced from each other in the first direction being p times half the operating wavelength, p being a real number, the distance by which the surface wave transducers are spaced from each other in the second direction being q times half the operating wavelength, q being a real number; and

- the electromagnetic surface impedance distribution (700, 1000).is adapted so that the respective embedded element patterns defined thereby have an angle of aperture comprised within a range between -arcsin(1/p) and +arcsin(1/p) in the first direction and an angle of aperture comprised within a range between -arcsin(1/q) and +arcsin(1/q) in the second direction.
A modulated metasurface antenna according to claim 10, wherein the distance by which the surface wave transducers are spaced from each other in the first direction corresponds to the distance by which the surface wave transducers are spaced from each other in the second direction, making p equal to q.
A modulated metasurface antenna according to any of claims 1 to 11, wherein the surface wave propagation medium (304) comprises a dielectric substrate (306) having one side that is provided with a ground plane (307) and another, opposite side (305) that is provided with a multitude of subwavelength-sized conductive elements.
A beam-steerable antenna arrangement (300) comprising:
- a modulated metasurface antenna (302) according to any of claims 1 to 12; and

- a circuit (303) adapted to carry out at least one of the following operations: applying an array of drive signals at the operating wavelength to the array of surface wave transducers in the modulated metasurface antenna, causing the modulated metasurface antenna to have a radiation pattern dependent on a phase-relationship between the drive signals, and processing an array of receptions signals at the operating wavelength captured by the array of surface wave transducers signals in the modulated metasurface antenna.
A radio-frequency system (301) comprising a beam-steerable antenna arrangement (300) according to claim 13.
Use of a radio-frequency system (301) according to claim 14, wherein the beam-steerable antenna arrangement is controlled to carry out at least one of the following operations: emitting a radio-frequency signal in a particular direction and receiving a radio-frequency signal coming from a particular direction.