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Title:
VARIABLE METASURFACE ANTENNA STRUCTURES
Document Type and Number:
WIPO Patent Application WO/2020/244743
Kind Code:
A1
Abstract:
This application relates to a metasurface antenna for radiating first electromagnetic field radiation. The metasurface antenna comprises a patterned impedance surface with a position-dependent impedance across the surface, at least one feeding element for irradiating the impedance surface with second electromagnetic field radiation, a conductive ground plane being spaced apart from the impedance surface, 5 so that a respective equivalent transverse transmission line is formed between the impedance surface and the ground plane for each position on the impedance surface, and an engageable structure with a plurality of states that is engageable to transition between states, wherein a transition from one state to another is associated with an alteration of an electric length of the equivalent transverse transmission line for at least one position on the impedance surface. The plurality of states correspond to respective beam patterns of the 10 first electromagnetic field radiation that is radiated by the impedance surface in reaction to being irradiated with the second electromagnetic field radiation by the at least one feeding element. The application further relates to a method of designing a metasurface antenna that radiates first electromagnetic field radiation.

Inventors:
SABBADINI MARCO (NL)
MINATTI GABRIELE (IT)
MACI STEFANO (IT)
CAMINITA FRANCESCO (IT)
Application Number:
PCT/EP2019/064485
Publication Date:
December 10, 2020
Filing Date:
June 04, 2019
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
ESA (FR)
UNIV DEGLI STUDI DI SIENA (IT)
International Classes:
H01Q3/01; H01Q13/20; H01Q15/00
Foreign References:
US20160294054A12016-10-06
US20170018855A12017-01-19
EP3084882A12016-10-26
Other References:
LIU LI ET AL: "Beam Reconfigurable Antenna Based on Liquid Crystal Metasurface", 2018 IEEE 4TH INTERNATIONAL CONFERENCE ON COMPUTER AND COMMUNICATIONS (ICCC), IEEE, 7 December 2018 (2018-12-07), pages 1037 - 1041, XP033586415, DOI: 10.1109/COMPCOMM.2018.8780804
LI WEIWEI ET AL: "A temperature-activated nanocomposite metamaterial absorber with a wide tunability", NANO RESEARCH, TSINGHUA UNIVERSITY PRESS, CN, vol. 11, no. 7, 19 January 2018 (2018-01-19), pages 3931 - 3942, XP036558375, ISSN: 1998-0124, [retrieved on 20180119], DOI: 10.1007/S12274-018-1973-4
CAMINITA F ET AL: "Electronically scanning antennas based on reconfigurable metasurfaces", 2016 IEEE INTERNATIONAL SYMPOSIUM ON PHASED ARRAY SYSTEMS AND TECHNOLOGY (PAST), IEEE, 18 October 2016 (2016-10-18), pages 1 - 2, XP033052024, DOI: 10.1109/ARRAY.2016.7832579
GABRIELE MINATTI ET AL: "Spiral Leaky-Wave Antennas Based on Modulated Surface Impedance", IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, IEEE SERVICE CENTER, PISCATAWAY, NJ, US, vol. 59, no. 12, 1 December 2011 (2011-12-01), pages 4436 - 4444, XP011379565, ISSN: 0018-926X, DOI: 10.1109/TAP.2011.2165691
LOO R Y ET AL: "Two-dimensional beam steering using an electrically tunable impedance surface", IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, IEEE SERVICE CENTER, PISCATAWAY, NJ, US, vol. 51, no. 10, 1 October 2003 (2003-10-01), pages 2713 - 2722, XP011102159, ISSN: 0018-926X, DOI: 10.1109/TAP.2003.817558
G. MINATTI ET AL: "Flat leaky-wave lenses", 2012 6TH EUROPEAN CONFERENCE ON ANTENNAS AND PROPAGATION (EUCAP), 1 March 2012 (2012-03-01), pages 243 - 246, XP055379304, ISBN: 978-1-4577-0919-7, DOI: 10.1109/EuCAP.2012.6206132
Attorney, Agent or Firm:
MERH-IP MATIAS ERNY REICHL HOFFMANN PATENTANWÄLTE PARTG MBB (DE)
Download PDF:
Claims:
Claims

1. A metasurface antenna for radiating first electromagnetic field radiation, comprising:

a patterned impedance surface with a position-dependent impedance across the surface;

at least one feeding element for irradiating the impedance surface with second electromagnetic field radiation;

a conductive ground plane being spaced apart from the impedance surface, so that a respective equivalent transverse transmission line is formed between the impedance surface and the ground plane for each position on the impedance surface; and

an engageable structure with a plurality of states that is engageable to transition between states, wherein a transition from one state to another is associated with an alteration of an electric length of the equivalent transverse transmission line for at least one position on the impedance surface,

wherein the plurality of states correspond to respective beam patterns of the first electromagnetic field radiation that is radiated by the impedance surface in reaction to being irradiated with the second electromagnetic field radiation by the at least one feeding element.

2. The metasurface antenna according to claim 1, wherein the beam patterns to which the plurality of states correspond relate to snapshots of a continuous change of the beam shape and/or beam pointing direction of the first electromagnetic field radiation from an initial state of the beam shape and/or beam pointing direction to a final state of the beam shape and/or beam pointing direction.

3. The metasurface antenna according to claim 1 or 2,

wherein the plurality of states are defined by a finite number of control parameters, with each state being associated with a respective set of values of the control parameters.

4. The metasurface antenna according to claim 3, wherein the number of the control parameters is smaller than a number of degrees of freedom in a subset of degrees of freedoms of elements of a surface pattern of the impedance surface, wherein the subset of degrees of freedom includes those degrees of freedom for which parameters differ from one element to the next.

5. The metasurface antenna according to any one of claims 1 to 4, further comprising a dielectric support structure,

wherein the impedance surface is provided on one side of the dielectric support structure and the ground plane is arranged on the other side of the dielectric support structure, opposite the impedance surface; wherein the engageable structure is coupled to the dielectric support structure; and wherein the dielectric support structure is configured so that a dielectric permittivity between the impedance surface and the ground plane changes for at least one position on the impedance surface when the engageable structure transitions between states.

6. The metasurface antenna according to claim 5, wherein the dielectric support structure is deformable or movable; and

wherein the engageable structure comprises:

one or more movable portions contacting the dielectric support structure for deforming or moving the dielectric support structure; and

an actuating part for inducing movement of the one or more movable portions.

7. The metasurface antenna according to claim 6, wherein the dielectric support structure is deformable;

wherein the one or more movable portions are arranged in such manner that movement thereof causes alteration of a density and/or thickness of the dielectric support structure between the conductive ground plane and the impedance surface for at least one position on the impedance surface.

8. The metasurface antenna according to claim 5, wherein the engageable structure comprises one or more actuatable elements coupled to or embedded into the dielectric support structure.

9. The metasurface antenna according to any one of claims 1 to 4, wherein the engageable structure is coupled to the ground plane; and

wherein the ground plane is deformable or movable so that a distance between the impedance surface and the ground plane changes for at least one position on the impedance surface when the engageable structure transitions between states.

10. The metasurface antenna according to claim 9,

wherein the engageable structure comprises or is formed by a plurality of electrically

interconnected shape-memory alloy cells.

11. The metasurface antenna according to claim 9, wherein the engageable structure comprises: one or more movable portions contacting the conductive ground plane for deforming or moving the conductive ground plane; and

an actuating part for inducing movement of the one or more movable portions.

12. The metasurface antenna according to claim 11, further comprising a dielectric support structure,

wherein the impedance surface is provided on one side of the dielectric support structure and the ground plane is arranged on the other side of the dielectric support structure, opposite the impedance surface;

wherein the dielectric support structure comprises a dielectric layer and a spacer layer between the dielectric layer and the conductive ground plane;

wherein the conductive ground plane is deformable; and

wherein the one or more movable portions are arranged to contact the conductive ground plane and, when moved, to deform the conductive ground plane in a direction perpendicular to the impedance surface.

13. The metasurface antenna according to claim 11, further comprising a dielectric support structure,

wherein the impedance surface is provided on one side of the dielectric support structure and the ground plane is arranged on the other side of the dielectric support structure, opposite the impedance surface;

wherein the conductive ground plane and the dielectric support structure are each deformable and in laminar contact with each other; and

wherein the one or more movable portions are arranged to contact the conductive ground plane and, when moved, to deform the conductive ground plane in a direction perpendicular to the impedance surface.

14. The metasurface antenna according to any one of claims 1 to 4, wherein the engageable structure is part of or forms an active conductive layer arranged between the impedance surface and the ground plane.

15. The metasurface antenna according to claim 14, wherein the engageable structure comprises a plurality of conductive elements that are selectively interconnectable, to thereby alter a dielectric permittivity between the impedance surface and the ground plane for at least one position on the impedance surface.

16. The metasurface antenna according to any one of claims 1 to 15, wherein the impedance surface comprises a surface pattern to produce the position-dependent impedance.

17. A method of designing a metasurface antenna that radiates first electromagnetic field radiation, the metasurface antenna comprising:

a patterned impedance surface with a position-dependent impedance across the surface;

at least one feeding element for irradiating the impedance surface with second electromagnetic field radiation;

a conductive ground plane being spaced apart from the impedance surface, so that a respective equivalent transverse transmission line is formed between the impedance surface and the ground plane for each position on the impedance surface; and

an engageable structure with a plurality of states that is engageable to transition between states, wherein a transition from one state to another is associated with an alteration of an electric length of the equivalent transverse transmission line for at least one position on the impedance surface,

the method comprising:

for a desired sequence of beam patterns of the first electromagnetic field radiation, determining a plurality of snapshots, each snapshot corresponding to a respective beam pattern in the sequence;

for one of the snapshots, determining a first position-dependent target impedance for the impedance surface based on the beam pattern indicated by the snapshot and characteristics of the second electromagnetic field radiation, so that irradiation of the impedance surface having the first position- dependent target impedance with the second electromagnetic field radiation would result in the metasurface antenna radiating the first electromagnetic field radiation with the beam pattern indicated by the snapshot;

determining, based on the first position-dependent target impedance, a surface pattern for the impedance surface, so that the impedance surface provided with the surface pattern would have the first position-dependent target impedance when the engageable structure is in a first state; and

for each of the remaining snapshots:

determining a respective second position-dependent target impedance for the impedance surface based on the beam pattern indicated by the respective one of the remaining snapshots and characteristics of the second electromagnetic field radiation, so that irradiation of the impedance surface having the second position-dependent target impedance with the second electromagnetic field radiation would result in the metasurface antenna radiating the first electromagnetic field radiation with the beam pattern indicated by the respective one of the remaining snapshots;

determining, based on the respective second position-dependent target impedance and the first position-dependent target impedance, a position-dependent alteration amount in the electric length of the equivalent transverse transmission line, so that the impedance surface provided with the surface pattern would have the second position-dependent target impedance when the position-dependent change amount in the electric length of the equivalent transverse transmission line is applied; and

determining, based on characteristics of the engageable structure, a respective state of the engageable structure that would implement the respective position-dependent alteration amount in the electric length of the equivalent transverse transmission line.

18. The method according to claim 17, wherein the desired sequence of beam patterns of the first electromagnetic field radiation relates to a continuous change of the beam shape and/or beam pointing direction of the first electromagnetic field radiation from an initial state of the beam shape and/or beam pointing direction to a final state of the beam shape and/or beam pointing direction.

19. The method according to claim 17 or 18,

wherein the states of the engageable structure are defined by a finite number of control parameters, with each state being associated with a respective set of values of the control parameters.

20. The method according to claim 19, further comprising, for each of the remaining snapshots: performing a modal decomposition of the position-dependent alteration amount in terms of a set of base modes that are chosen in accordance with a geometric characteristic of the engageable structure and the control parameters for the engageable structure.

21. The method according to claim 19 or 20, wherein the number of the control parameters is smaller than a number of degrees of freedom in a subset of degrees of freedoms of elements of a surface pattern of the impedance surface, wherein the subset of degrees of freedom includes those degrees of freedom for which parameters differ from one element to the next.

22. The method according to any one of claims 17 to 21, wherein determining the first position- dependent target impedance for the impedance surface based on the beam pattern indicated by the snapshot and the characteristics of the second electromagnetic field radiation involves:

determining a first modal representation on the basis of the beam pattern indicated by the snapshot in terms of a set of base modes that are chosen in accordance with a model function of the first position-dependent target impedance;

determining a second modal representation on the basis of the second electromagnetic field radiation and the model function in terms of the set of base modes; and

obtaining the first position-dependent target impedance on the basis of the first modal

representation and the second modal representation by determining values for a plurality of parameters of the model function for maximizing an overlap between the first modal representation and the second modal representation.

23. The method according to any one of claims 17 to 22, wherein determining the surface pattern involves:

determining, as the surface pattern, a position-dependent quantity indicative of geometric characteristics of the impedance surface on the basis of the first position-dependent target impedance and a relationship between geometric characteristics of the impedance surface and corresponding impedance values.

24. The method according to any one of claims 17 to 23, wherein determining the second position- dependent target impedance for the impedance surface based on the beam pattern indicated by the respective one among the remaining snapshots and the characteristics of the second electromagnetic field radiation involves:

determining a third modal representation on the basis of the beam pattern indicated by the respective one of the remaining snapshots in terms of a set of base modes that are chosen in accordance with a model function of the first position-dependent target impedance;

determining a fourth modal representation on the basis of the second electromagnetic field radiation and the model function in terms of the set of base modes; and

obtaining the second position-dependent target impedance on the basis of the third modal representation and the fourth modal representation by determining values for a plurality of parameters of the model function for maximizing an overlap between the third modal representation and the fourth modal representation.

25. The method according to any one of claims 17 to 24, wherein determining the position- dependent alteration amount involves:

determining the position-dependent alteration amount on the basis of the second position- dependent target impedance and a relationship between geometric characteristics of the impedance surface, values of electric length of the equivalent transverse transmission line, and corresponding impedance values.

26. The method according to claim 22 or any claim dependent on claim 22, wherein obtaining the first position-dependent target impedance comprises:

calculating a reaction integral of the beam pattern indicated by the snapshot and a third electromagnetic field radiation that would be radiated by an impedance surface having a position- dependent impedance in accordance with the model function and being irradiated by the second electromagnetic field radiation; and

maximizing the reaction integral.

27. The method according to claim 23 or any claim dependent on claim 23, further comprising a step of partitioning the impedance surface into a plurality of elements of area,

wherein the relationship between geometric characteristics of the impedance surface and corresponding impedance values is a relationship between geometric characteristics of the elements of area and corresponding impedance values; and

wherein obtaining the surface pattern comprises, for each of the plurality of elements of area, obtaining geometric characteristics of the element of area on the basis of the first position-dependent target impedance and the relationship between geometric characteristics of the elements of area and the corresponding impedance values.

28. The method according to claim 22 or any claim dependent on claim 22, further comprising: determining the set of base modes so that each of the base modes may propagate on the impedance surface if the impedance surface were provided with a position-dependent impedance in accordance with the model function.

29. The method according to claim 22 or any claim dependent on claim 22, wherein obtaining the first modal representation includes decomposing the beam pattern indicated by the snapshot into a plurality of first modes, wherein each of the plurality of first modes corresponds to a respective one of the set of base modes; and

obtaining the second modal representation includes decomposing the second electromagnetic field radiation into a plurality of second modes, wherein each of the plurality of second modes corresponds to a respective one of the set of base modes.

30. The method according to claim 29, wherein obtaining the first position-dependent target impedance comprises, for each of the set of base modes for which a corresponding first mode in the plurality of first modes and a corresponding second mode in the plurality of second modes exists, calculating an outer product between the corresponding first mode and the corresponding second mode.

31. The method according to claim 22 or any claim dependent on claim 22, wherein one of the plurality of parameters of the model function relates to a period of spatial modulation of the first position- dependent target impedance on the impedance surface.

32. The method according to claim 22 or any claim dependent on claim 22, wherein the model function of the first position-dependent target impedance relates to a decomposition of the first position- dependent target impedance into a plurality of terms, each relating to a spline wavelet.

33. The method according to claim 32, wherein the model function of the first position-dependent target impedance relates to a decomposition of the first position-dependent target impedance into a plurality of products of spline wavelets and phase factors. 34. The method according to claim 23 or any claim dependent on claim 23, further comprising: comparing the beam pattern indicated by the snapshot to a fourth electromagnetic field radiation that would be radiated by the impedance surface provided with the determined surface pattern in reaction to being irradiated by the second electromagnetic field radiation;

adjusting at least one of the model function of the first position-dependent target impedance and the second electromagnetic field radiation; and

repeating the steps according to said claim 23 or said claim dependent on claim 23 to obtain an adjusted surface pattern.

Description:
VARIABLE METASURFACE ANTENNA STRUCTURES

Technical Field

This application relates to metasurface antennas and to methods of designing metasurface antennas. The application particularly relates to variable metasurface antennas that allow to change a beam pattern of the radiated field of the metasurface antenna, and to corresponding methods of designing such metasurface antennas.

Background

Antennas that are based on an artificial electromagnetic surface (metasurface) having a modulated impedance tensor with sub-wavelength variations are known from, for example, EP 3084882 Al. The main goal of such metasurface antennas is to provide an electromagnetic guiding and scattering structure to obtain a desired radiation pattern over a given bandwidth. One drawback of such metasurface antennas is that the guiding and scattering properties of the materials used are generally a fixed input, so that active devices, electrical or mechanical, are required to change the electrical path-length and wave amplitude to obtain changes in the shape of the radiation pattern, if desired. As a result, the range of antenna beam configurations and achievable performances for a single antenna design is limited.

Array-based antennas which are typically used to produce beam pattern changes (e.g., changes of beam shape and/or beam pointing direction) are inherently limited by the segmentation of the aperture and size of their elements, which typically results in a complex and expensive implementation. Also reconfigurable reflectors and the like have a significantly increased level of complexity that makes them difficult and/or expensive to implement.

Attempts to provide for some flexibility in the radiation pattern based on leaky wave antennas, in which some surface impedance modification mechanisms are applied, offer only a single degree of freedom for the radiation pattern, such as elevation scanning. Also metasurface antennas with one or more active elements for each cell of the artificial surface are difficult to implement due to their extreme complexity.

Thus, there is a need for an improved metasurface antenna and a corresponding method of designing such metasurface antenna. There is particular need for such metasurface antenna that allows for a flexible radiation pattern at acceptable levels of complexity. Summary

In view of some or all of these needs, the present disclosure proposes a metasurface antenna and a method of designing a metasurface antenna, having the features of the respective independent claims.

An aspect of the disclosure relates to a metasurface antenna for radiating first electromagnetic field radiation. The metasurface antenna may include a patterned impedance surface with a position-dependent impedance across the surface. The impedance surface may be referred to as a metasurface. The position- dependent impedance may refer to a position-dependent impedance tensor, and thereby, to a position- dependent scattering tensor. That is, the position-dependent impedance may be of tensorial type. The impedance surface may be said to have a surface pattern. The metasurface antenna may further include at least one feeding element for irradiating the impedance surface with second electromagnetic field radiation. The first electromagnetic field radiation may be radiated to the same side of the impedance surface from which the second electromagnetic field radiation impinges on the impedance surface, or to the opposite side, depending on the implementation. Further, the irradiated second electromagnetic field radiation may be anisotropic with respect to a center of the impedance surface. The metasurface antenna may further include a conductive ground that is spaced apart from the impedance surface, so that a respective equivalent transverse transmission line is formed between the impedance surface and the ground plane for each position on the impedance surface. The conductive ground plane may be a metallic ground plane, for example, such as a metal sheet or a metal layer. The metasurface antenna may yet further include an engageable structure with a plurality of states. The engageable structure may be engageable to transition between states. The engageable structure may be engageable by a control signal. The states of the engageable structure may be mechanical or electrical states, for example. A transition from one state to another state may be associated with an alteration of an electric length of the equivalent transverse transmission line for at least one position (possibly, for a plurality of positions) on the impedance surface. The plurality of states may correspond to respective beam patterns of the first electromagnetic field radiation that is radiated by the impedance surface in reaction to being irradiated with the second electromagnetic field radiation by the at least one feeding element. In addition to the elements mentioned above, the metasurface antenna may include a dielectric layer between the patterned impedance surface and the conductive ground plane. Also, the metasurface antenna may include a multi-layer structure with multiple dielectric or active layers.

Configured as described above, metasurface antennas according to the present invention allow to change a surface impedance across the antenna surface without modifying the impedance surface (metasurface) as such. This is achieved by modifying the electric length of the transverse transmission line by the engageable structure transitioning between states. By appropriate choice of the variation of the electric length of the transverse transmission line, the beam pattern (e.g., beam shape and/or beam pointing direction) can be modified in a controlled fashion, with a limited number of control points. Thereby, beam scanning and/or beam widening/narrowing, for example, can be achieved in a simple manner. The use of a limited number of control points enables implementations of the inventive metasurface antenna at reduced complexity, mass, envelope, and/or cost or allows to improve performance of the metasurface antenna at a given complexity, mass, envelope, and/or cost.

In some embodiments, the beam patterns to which the plurality of states correspond may relate to snapshots of a continuous change of the beam shape and/or beam pointing direction of the first electromagnetic field radiation from an initial state of the beam shape and/or beam pointing direction to a final state of the beam shape and/or beam pointing direction. Thereby, the beam shape and/or beam pointing direction can be smooth ly modified with a very simple implementation.

In some embodiments, the plurality of states of the engageable structure may be defined by a finite number of control parameters. Each state may be associated with a respective set of values of the control parameters. The control parameters may be referred to as control points. A finite (limited) number of control points allows for very simple mechanical or electrical implementations of the engageable structure.

In some embodiments, the number of the control parameters may be smaller than a number of degrees of freedom in a subset of degrees of freedoms of elements of a surface pattern of the impedance surface. The subset of degrees of freedom may include (only) those degrees of freedom for which parameters differ from one element to the next. The degrees of freedom in the subset of degrees of freedom may be referred to as available degrees of freedom. In one example, the number of the control parameters may be smaller than the number of degrees of freedom in the subset of degrees of freedom of the elements of the surface pattern of the impedance surface by at least a factor of 2. The elements may correspond to elements of area (cells, or metasurface cells) into which the impedance surface is partitioned. In alternative implementations, the number of the control parameters may be smaller than a number of degrees of freedom of a far field of the first electromagnetic field radiation. The number of the control parameters may be smaller than the number of degrees of freedom of the far field of the first electromagnetic field radiation by at least a factor of 2.

In some embodiments, the metasurface antenna may further include a dielectric support structure. The impedance surface may be provided on one side of the dielectric support structure and the ground plane may be arranged on the other side of the dielectric support structure, opposite the impedance surface. The engageable structure may be coupled (e.g., mechanically coupled) to the dielectric support structure. The dielectric support structure may be configured so that a dielectric permittivity between the impedance surface and the ground plane changes for at least one position (possibly, for a plurality of positions) on the impedance surface when the engageable structure transitions between states. At least one property or characteristic of the dielectric support structure may be altered by the engageable structure so that the dielectric permittivity between the impedance surface and the ground plane changes for at least one position (possibly, for a plurality of positions) on the impedance surface when the engageable structure transitions between states. For example, the dielectric support structure may be deformable or movable by the engageable structure. A change in the dielectric permittivity between the impedance surface and the ground plane may correspond to a change of electric length of the equivalent transverse transmission line for at least one position (possibly, for a plurality of positions) on the impedance surface. These embodiments are understood to also cover the case of powders, which can flow from one position to another, even outside the “RF-active” portion of the metasurface antenna, as well as the case of a so-called e-ink panel in which small spheres filled with dielectrics of different permittivity, one hemisphere each, are rotated in such a way to move the one half toward or away from the ground plane.

In some embodiments, the dielectric support structure may be deformable or movable. In this case, the engageable structure may include one or more movable portions contacting the dielectric support structure for deforming or moving the dielectric support structure. The engageable structure may further include an actuating part for inducing movement of the one or more movable portions. Movement of the movable portions can be linear motion or rotary motion, for example. The actuating part may operate under control of a control signal/unit. Deforming or moving the dielectric support structure may result in a change of the dielectric permittivity between the impedance surface and the ground plane.

In some embodiments, the dielectric support structure may be deformable. In this case, the one or more movable portions may be arranged in such manner that movement thereof causes alteration of a density and/or thickness of the dielectric support structure between the conductive ground plane and the impedance surface for at least one position (possibly, for a plurality of positions) on the impedance surface. Deformable may mean flexible and/or elastic. In one example, the movable portions may relate to microcells with flat/elongated conductive elements that can be alternatively oriented in parallel or in perpendicular to the conductive ground plane. In this configuration, the one or more movable portions may be arranged between the conductive ground plane and the dielectric support structure. As another example, the one or more movable elements may relate to pins slidably arranged in respective opening in the conductive ground plane, to be selectively extended from and retracted through their respective opening. The pins may be conductive/metallic or made from a dielectric. The pins may be arranged in a regular lattice, for example.

In some embodiments, the engageable structure may include one or more actuatable elements coupled to or embedded into the dielectric support structure. The actuatable elements may be (micro-)structures, for example. They may be actuated by mechanical, electromechanical, and/or electrical means. The actuatable elements may form an active layer that is in laminar contact with the dielectric support structure. The actuatable elements may be piezoelectric crystals or nematic crystals, for example. The actuatable elements may be configured to deform or move the dielectric support structure. Further, the actuatable elements may cause an alteration of the density and/or thickness of the dielectric support structure for at least one position (possibly, for a plurality of positions) on the impedance surface.

In some embodiments, the engageable structure may be coupled to the ground plane. The ground plane may be deformable (e.g., flexible) or movable so that a distance between the impedance surface and the ground plane changes for at least one position (possibly, for a plurality of positions) on the impedance surface when the engageable structure transitions between states. That is, the distance can be altered/modified in a position-dependent manner.

In some embodiments, the engageable structure may include or may be formed by a plurality of electrically interconnected shape-memory alloy cells.

In some embodiments, the engageable structure may include one or more movable portions contacting the conductive ground plane for deforming or moving the conductive ground plane. The engageable structure may further include an actuating part for inducing movement of the one or more movable portions. Movement of the movable portions may be linear motion or rotary motion, for example. The actuating part may operate under control of a control signal/unit.

In some embodiments, the metasurface antenna may further include a dielectric support structure. The impedance surface may be provided on one side of the dielectric support structure and the ground plane may be arranged on the other side of the dielectric support structure, opposite the impedance surface. The dielectric support structure may include a dielectric layer and a spacer layer between the dielectric layer and the conductive ground plane. The spacer layer may be air-filled, gas-filled, or empty (vacuum). The conductive ground plane may be deformable. Further, the one or more movable portions may be arranged to contact the conductive ground plane and, when moved, to deform the conductive ground plane in a direction perpendicular to the impedance surface. Deformation of the conductive ground plane may locally alter the distance between the conductive ground plane and the impedance surface.

In some embodiments, the metasurface antenna may further include a dielectric support structure. The impedance surface may be provided on one side of the dielectric support structure and the ground plane may be arranged on the other side of the dielectric support structure, opposite the impedance surface. The conductive ground plane and the dielectric support structure may be each deformable and in laminar contact with each other. Further, the one or more movable portions may be arranged to contact the conductive ground plane and, when moved, to deform the conductive ground plane in a direction perpendicular to the impedance surface. Deformation of the conductive ground plane may locally alter the distance between the conductive ground plane and the impedance surface.

In some embodiments, the engageable structure may be part of or may form an active conductive layer arranged between the impedance surface and the ground plane. In some embodiments, the engageable structure may include a plurality of conductive elements that are selectively interconnectable, to thereby alter a dielectric permittivity between the impedance surface and the ground plane for at least one position (possibly, for a plurality of positions) on the impedance surface. Each of the conductive elements may present a reactive load. Individual conductive elements or groups of conductive elements may be associated with respective cells of the impedance surface. The individual reactive loads may themselves be variable. Further, a variable load may be obtained by changing a connectivity within groups of conductive elements.

In some embodiments, the impedance surface may include a surface pattern to produce the position- dependent impedance. In one example, the impedance surface may be partitioned into a plurality of area elements (cells) and at least one subgroup of the area elements may have a respective conductive structure provided on the dielectric support structure. Alternatively, for at least one subgroup of the area elements, a thickness of the dielectric substrate may be different from a thickness of the dielectric support structure for another subgroup of area elements. Alternatively, the impedance surface may be formed by a metal layer with, for each area element, an opening in the metal layer. A size of the openings in the metal layer may be position-dependent. Different types of area elements may be mixed with each other on the impedance surface.

Another aspect of the disclosure relates to a method of designing a metasurface antenna that radiates first electromagnetic field radiation. The metasurface antenna may include a patterned impedance surface with a position-dependent impedance across the surface. The metasurface antenna may further include at least one feeding element for irradiating the impedance surface with second electromagnetic field radiation. The metasurface antenna may further include a conductive ground plane that is spaced apart from the impedance surface, so that a respective equivalent transverse transmission line is formed between the impedance surface and the ground plane for each position on the impedance surface. The metasurface antenna may further include an engageable structure with a plurality of states that is engageable to transition between states, wherein a transition from one state to another is associated with an alteration of an electric length of the equivalent transverse transmission line for at least one position (possibly, for a plurality of positions) on the impedance surface. The method may include, for a desired sequence of beam patterns of the first electromagnetic field radiation, determining a plurality of snapshots. Each snapshot may correspond to a respective beam pattern in the sequence. The method may further include, for one of the snapshots, determining a first position-dependent target impedance for the impedance surface based on the beam pattern indicated by the snapshot and characteristics of the second electromagnetic field radiation, so that irradiation of the impedance surface having the first position-dependent target impedance with the second electromagnetic field radiation would result in the metasurface antenna radiating the first electromagnetic field radiation with the beam pattern indicated by the snapshot. The method may further include determining, based on the first position-dependent target impedance, a surface pattern for the impedance surface. The surface pattern may be determined so that the impedance surface provided with the surface pattern would have the first position-dependent target impedance when the engageable structure is in a first state. The method may further include, for each of the remaining snapshots, determining a respective second position- dependent target impedance for the impedance surface based on the beam pattern indicated by the respective one of the remaining snapshots and characteristics of the second electromagnetic field radiation, so that irradiation of the impedance surface having the second position-dependent target impedance with the second electromagnetic field radiation would result in the metasurface antenna radiating the first electromagnetic field radiation with the beam pattern indicated by the respective one of the remaining snapshots. The method may further include, for each of the remaining snapshots, determining, based on the respective second position-dependent target impedance and the first position-dependent target impedance, a position-dependent alteration amount in the electric length of the equivalent transverse transmission line, so that the impedance surface provided with the surface pattern would have the second position-dependent target impedance when the position-dependent change amount in the electric length of the equivalent transverse transmission line is applied. The method may yet further include, for each of the remaining snapshots, determining, based on characteristics of the engageable structure, a respective state of the engageable structure that would implement the respective position-dependent alteration amount in the electric length of the equivalent transverse transmission line.

By such a design method, complexity of the metasurface antenna is to large extent relegated into the design phase, which allows for very simple and efficient implementations of the resulting metasurface antenna metasurface antennas designed in line with the proposed design method can achieve operations such as beam scanning and beam widening/narrowing in a very simple, yet controlled manner. Notably, this can be achieved without modifying the structure of the impedance surface (metasurface) during operation of the metasurface antenna.

In some embodiments, the desired sequence of beam patterns of the first electromagnetic field radiation may relate to a continuous change of the beam shape and/or beam pointing direction of the first electromagnetic field radiation from an initial state of the beam shape and/or beam pointing direction to a final state of the beam shape and/or beam pointing direction.

In some embodiments, the states of the engageable structure may be defined by a finite number of control parameters, with each state being associated with a respective set of values of the control parameters.

In some embodiments, the method may further include, for each of the remaining snapshots, performing a modal decomposition of the position-dependent alteration amount in terms of a set of base modes. The base modes may be chosen in accordance with a geometric characteristic of the engageable structure and the control parameters for the engageable structure. In some embodiments, the number of the control parameters may be smaller than a number of degrees of freedom in a subset of degrees of freedoms of elements of a surface pattern of the impedance surface. The subset of degrees of freedom may include (only) those degrees of freedom for which parameters differ from one element to the next. The degrees of freedom in the subset of degrees of freedom may be referred to as available degrees of freedom.

In some embodiments, determining the first position-dependent target impedance for the impedance surface based on the beam pattern indicated by the snapshot and the characteristics of the second electromagnetic field radiation may involve: determining a first modal representation on the basis of the beam pattern indicated by the snapshot in terms of a set of base modes that are chosen in accordance with a model function of the first position-dependent target impedance. Said determining may further involve: determining a second modal representation on the basis of the second electromagnetic field radiation and the model function in terms of the set of base modes. Said determining may yet further involve: obtaining the first position-dependent target impedance on the basis of the first modal representation and the second modal representation by determining values for a plurality of parameters of the model function for maximizing an overlap between the first modal representation and the second modal representation.

In some embodiments, determining the surface pattern may involve determining, as the surface pattern, a position-dependent quantity indicative of geometric characteristics of the impedance surface on the basis of the first position-dependent target impedance and a relationship between geometric characteristics of the impedance surface and corresponding impedance values.

In some embodiments, determining the second position-dependent target impedance for the impedance surface based on the beam pattern indicated by the respective one among the remaining snapshots and the characteristics of the second electromagnetic field radiation may involve: determining a third modal representation on the basis of the beam pattern indicated by the respective one of the remaining snapshots in terms of a set of base modes that are chosen in accordance with a model function of the first position- dependent target impedance. Said determining may further involve determining a fourth modal representation on the basis of the second electromagnetic field radiation and the model function in terms of the set of base modes. Said determining may yet further involve obtaining the second position-dependent target impedance on the basis of the third modal representation and the fourth modal representation by determining values for a plurality of parameters of the model function for maximizing an overlap between the third modal representation and the fourth modal representation. That is, the second position-dependent target impedance may be determined in analogous manner to the first position-dependent target impedance.

In some embodiments, determining the position-dependent alteration amount may involve: determining the position-dependent alteration amount on the basis of the second position-dependent target impedance and a relationship between geometric characteristics of the impedance surface, values of electric length of the equivalent transverse transmission line, and corresponding impedance values.

In some embodiments, obtaining the first position-dependent target impedance may include: calculating a reaction integral of the beam pattern indicated by the snapshot and a third electromagnetic field radiation that would be radiated by an impedance surface having a position-dependent impedance in accordance with the model function and being irradiated by the second electromagnetic field radiation. Said obtaining may further include maximizing the reaction integral. The second position-dependent target impedance may be determined in analogous manner.

In some embodiments, the method may further include a step of partitioning the impedance surface into a plurality of elements of area (cells). The relationship between geometric characteristics of the impedance surface and corresponding impedance values may be a relationship between geometric characteristics of the elements of area and corresponding impedance values. Further, obtaining the surface pattern may include, for each of the plurality of elements of area, obtaining geometric characteristics of the element of area on the basis of the first position-dependent target impedance and the relationship between geometric characteristics of the elements of area and the corresponding impedance values.

In some embodiments, the method may further include determining the set of base modes so that each of the base modes may propagate on the impedance surface if the impedance surface were provided with a position-dependent impedance in accordance with the model function.

In some embodiments, obtaining the first modal representation may include decomposing the beam pattern indicated by the snapshot into a plurality of first modes. Each of the plurality of first modes may correspond to a respective one of the set of base modes. Obtaining the second modal representation may include decomposing the second electromagnetic field radiation into a plurality of second modes. Each of the plurality of second modes may correspond to a respective one of the set of base modes. Analogous steps may be involved in determining the second position-dependent target impedance.

In some embodiments, obtaining the first position-dependent target impedance may include, for each of the set of base modes for which a corresponding first mode in the plurality of first modes and a corresponding second mode in the plurality of second modes exists, calculating an outer product between the corresponding first mode and the corresponding second mode.

In some embodiments, one of the plurality of parameters of the model function may relate to a period of spatial modulation of the first position-dependent target impedance on the impedance surface.

In some embodiments, the model function of the first position-dependent target impedance may relate to a decomposition of the first position-dependent target impedance into a plurality of terms, each relating to a spline wavelet. In some embodiments, the model function of the first position-dependent target impedance may relate to a decomposition of the first position-dependent target impedance into a plurality of products of spline wavelets and phase factors.

In some embodiments, the method may further include comparing the beam pattern indicated by the snapshot to a fourth electromagnetic field radiation that would be radiated by the impedance surface provided with the determined surface pattern in reaction to being irradiated by the second electromagnetic field radiation. The method may further include adjusting at least one of the model function of the first position-dependent target impedance and the second electromagnetic field radiation. The method may yet further include repeating the steps of determining the first position-dependent target impedance for the impedance surface based on the beam pattern indicated by the snapshot and the characteristics of the second electromagnetic field radiation to obtain an adjusted surface pattern.

Another aspect of the disclosure relates to an apparatus comprising a processor and a memory coupled to the processor. The processor may be configured to perform the method of any of the above aspects and their embodiments.

Another aspect of the disclosure relates to a computer-readable storage medium containing instructions for execution by a processor that cause the processor to perform the method of any of the above aspects and their embodiments.

It will be appreciated that method steps and metasurface antenna features may be interchanged in many ways. In particular, the disclosed method is understood to be a method of designing the disclosed metasurface antenna, such that a product of the method will have features disclosed in connection with the metasurface antenna, and vice versa, as the skilled person will appreciate. Moreover, any of the above statements made with respect to the metasurface antenna are understood to likewise apply to the corresponding method, and vice versa.

Brief Description of the Figures

Example embodiments of the disclosure are explained below with reference to the accompanying drawings, wherein

Fig. 1A and Fig. 1B schematically illustrate a perspective view and a sectional side view, respectively, of an example of a metasurface antenna according to embodiments of the disclosure,

Fig. 2 schematically illustrates a sectional side view of another example of a metasurface antenna according to embodiments of the disclosure, Fig. 3 schematically illustrates a sectional side view of another example of a metasurface antenna according to embodiments of the disclosure,

Fig. 4A and Fig. 4B schematically illustrate sectional side views of further examples of metasurface antennas according to embodiments of the disclosure,

Fig. 5A and Fig. 5B schematically illustrate a perspective view and a sectional side view, respectively, of another example of a metasurface antenna according to embodiments of the disclosure,

Fig. 6 schematically illustrates an example of an area element of a metasurface according to embodiments of the disclosure,

Fig. 7A, Fig. 7B, and Fig. 7C are graphs illustrating examples of quantities in a design process leading from a surface impedance to an inductive load for a metasurface,

Fig. 8A, Fig. 8B, and Fig. 8C are graphs illustrating a required surface impedance for different scan angles of a beam,

Fig. 9 schematically illustrates a change in capacitance required to achieve desired impedance maps for different scan angles,

Fig. 10A, Fig. 10B, and Fig. 10C schematically illustrate the beams at the different scan angles,

Fig. 11A, Fig. 11B, and Fig. 11C illustrate examples of variations in capacitance required for scanning a beam,

Fig. 12A, Fig. 12B, and Fig. 12C illustrate examples of ground plane deformations for different scan angles,

Fig. 13A, Fig. 13B, and Fig. 13C illustrate examples of variations in air gap thickness required for scanning a beam,

Fig. 14 illustrates, in flowchart form, an example of a method of designing a metasurface antenna according to embodiments of the disclosure, and

Fig. 15 and Fig. 16 illustrate, in flowchart form, details of respective steps of the method of Fig. 14.

Detailed Description

In the following, example embodiments of the disclosure will be described with reference to the appended figures. Identical elements in the figures may be indicated by identical reference numbers, and repeated description thereof may be omitted. Overview

Broadly speaking, the present invention relates to variable modulated impedance surfaces (variable metasurfaces). In particular, the invention relates to artificial electromagnetic surfaces having a variable modulated impedance tensor with controlled sub-wavelength variations. The sub-wavelength variations may be determined using the design procedure described in EP 3084882 Al. Variable metasurfaces according to the present invention allow for flexible control of the radiation pattern by providing extensive dynamic control of the impedance or scattering characteristics of the surface. Implementing such metasurface antennas requires a rather complex but effective design procedure that eventually results in limited complexity in the metasurface antenna itself. In particular, the number of active control points required to modify the impedance surface for modifications of the beam pattern (e.g., beam shape and/or beam pointing direction, such as scanning within a limited range, zooming, or small changes in beam shape, etc.) is comparatively small. This enables to reduce the envelope and mass of the metasurface antenna and/or to improve performance at a given envelope and mass, in addition to achieving variable beam patterns at extremely low complexity and cost compared to conventional approaches.

The main difference with respect to other variable-beam antenna configurations may be seen to lie in the use of variable boundary conditions that enable obtaining flexible and dynamic beam shaping. This is opposed to variable components or variable shapes of metasurfaces. Among others, direct modification of the boundary conditions allows for a much broader spectrum of pattern modifications on a single antenna configuration, with just a few control points for a suitably limited range of variation. Thereby, the present invention achieves to obtain very complex changes in the surface impedance distribution across the surface with very few control points and simple means. Thus, contrary to conventional solutions aimed at the same goal, metasurface antennas according to the present invention can be implemented in very simple manner using low-cost technologies, such as standard printed circuit manufacturing and simple mechanical controls.

Depending on the particular metasurface antenna configuration, the surface impedance control according to the present invention can be obtained with a variety of means, including mechanical, electro-mechanical, mechatronic, electrical, electronic, or optical means, or a combination thereof. In particular, controlled changes in shape or physical properties in the (bulk or sheet) materials constituting the metasurface can be applied to achieve essentially the same result. Once the law of variation required for the local surface impedance is determined, any means to obtain the variation is equivalent, apart from implementation limitations. Also the same surface impedance variation can be obtained resorting to different designs of the metasurface thus enabling to match the latter to different modification mechanisms.

What is common to all implementations according to the present invention is that the added degrees of freedom and the simplicity of the basic mechanism for obtaining the variation can be used to reduce cost, mass, and/or envelope of the antenna and/or improve performance of the antenna. Metasurface antennas according to the present invention can be used for a wide range of technical applications, including space RF payloads and instruments, and satellite ground terminals. In particular, metasurface antennas according to the present invention can be applied to the payload data-down link from low earth orbit (LEO) and to high-gain links for deep-space mission telemetry/telecommand (TM/TC) systems, high earth orbit (HEO) missions, and terrestrial telecommunications (e.g., for user terminals).

Metasurface Antennas

In general, (variable) metasurface antennas according to embodiments of this disclosure are based on the use of a special type of scattering surfaces characterized by a modulation of their scattering or impedance tensor. These scattering surfaces are referred to as metasurfaces. The antenna’s metasurface, which can be flat or curved or faceted, is illuminated by one or more feeding elements. These feeding elements can be embedded in the antenna (e.g., in the metasurface), or they can be external. While the present disclosure describes changes in the local impedance of a single surface, it is understood that several surfaces can be combined to achieve the desired result, and that changes in the local impedance can be applied to more than one (possibly all) of these surfaces.

Metasurfaces exploit the interaction of electromagnetic waves with conductors, dielectrics and their combinations shaped and arranged in such a way to obtain discrete or continuous patterns across the surface, with variations starting at sub-wavelength scale. The local interaction of an incident wave with the structured material controls its scattering. The field emerging after interaction is the result of the Huygens- like recombination of the local contributions. All Stokes parameters can be controlled within a wide range across the emerging wave front. Thus amplitude, phase, and polarization of the radiated/emerging field (or wave) can be changed according to needs and within boundaries related to the specific implementation of the metasurface antenna. Notably, the emerging wave may travel in the positive (forward) of negative (backward) direction compared with the incident wave, as seen from the local tangent plane.

Moreover, metasurfaces can be realized in a number of ways. Both reflective and translucent metasurfaces can be used in metasurface antennas according to embodiments of the disclosure. A reflective metasurface may be backed by a metal plate conformal to it or may have a metallized back surface.

A first way or realizing a metasurface is by modulating the thickness of a dielectric slab. A second option is by embedding one or more metal layers within the dielectric, each characterized by a pattern obtained by the repetition (tiling) of a basic sub-wavelength cell, according to a selected reference geometry (e.g., square, triangular, hexagonal, circular, etc.) with dimensions and orientation changing smoothly across the surface. The grid underlying the pattern may also be non-uniform across the surface. For example, the grid underlying the pattern can be a circular grid with growing spacing towards the edge. One layer (possibly the only layer) can be on the front dielectric surface.

Further implementations of a metasurface may include metallic elements perpendicular to the surface, a modulation (e.g., discrete modulation) of the dielectric constant across the surface (e.g., by using interwoven patterns of dielectrics with different constants or by filling honeycomb cells with powders of different dielectric constant), a metal-only structure with 3D sub-wavelength features, etc., including combinations of the individual solutions.

In accordance with the above implementations of metasurfaces in the context of the present invention, various manufacturing technologies can be applied, for example molding, forming, milling, or drilling of bulk dielectric, etching or deposition of metal on dielectric substrates, 3D manufacturing, ink-jet printing with conductive inks (e.g., when losses are of lesser concern). In general, any process suitable to produce the desired pattern of interwoven materials with the required accuracy and repeatability can be used.

Implementation Examples of Variable Metasurface Antennas

The present invention is based on applying local modifications to the surface impedance without modifying the metasurface as such (i.e., without changing the metasurface in terms of its surface elements, etc.). The local modifications required to change the surface impedance can be of quite different nature. The most basic solution applicable to, for example, a ground-plane backed dielectric slab loaded with small metallic patches on the opposite face implies changing the local thickness of the dielectric substrate. This can be achieved by air or a soft material as dielectric and mechanically changing the distance between the ground- plane and the metallic patches. When the distance is changed uniformly in a structure fed from one edge, it is possible to obtain an elevation-scan of the beam radiated by the metasurface antenna. To achieve full control of the beam pattern (e.g., beam shape and/or beam pointing direction) it is necessary to modify the distance in a different way at different positions across the antenna surface. In other words, the modification of the distance needs to be position-dependent. However, it is important to note that the local change does not necessarily require active local control. For instance, in some configurations, bi-dimensional beam scanning may only require the movement of one part of the antenna with respect to the other. Solutions for both rotary and linear motion as well as combinations thereof are in principle feasible as well. Simulations and prototypes have confirmed that the desired results can be achieved by configurations according to embodiments of the disclosure.

Fig. 1A schematically illustrates a perspective view of an example of a (variable) metasurface antenna 100 according to embodiments of the disclosure, and Fig. IB is a sectional side view thereof. The dimensions (e.g., thickness) of the elements of the metasurface antenna 100 may not be to scale. The metasurface antenna 100 is a metasurface antenna for radiating first electromagnetic field radiation. Therein, the first electromagnetic field radiation corresponds to a beam pattern (e.g., beam shape and/or beam pointing direction) that is radiated by the metasurface antenna 100. The metasurface antenna 100 comprises a patterned impedance surface (metasurface) 10. The patterned impedance surface 10 has a position- dependent impedance across the surface. Therein, the position-dependent impedance may refer to a position-dependent impedance tensor, and thereby, to a position-dependent scattering tensor. In other words, the position-dependent impedance may be of tensorial type.

The impedance surface 10 may have a surface pattern that is suitable for producing the position-dependent impedance. Accordingly, the impedance surface 10 may be partitioned into a plurality of area elements (cells). Smoothly varying properties or parameters of these area elements across the impedance surface 10 can produce the position-dependent impedance. These area elements can be implemented in a plurality of different ways and a method for designing appropriate area elements in accordance with desired first electromagnetic field radiation is described for example in EP 3084882 Al. For instance, at least one subgroup of the area elements (possibly, all area elements) may have a respective conductive structure provided on a dielectric substrate. Alternatively, for at least one subgroup of the area elements, a thickness of the dielectric substrate may be different from a thickness of the dielectric substrate for another subgroup of area elements. Alternatively, the impedance surface may be formed by a metal layer with, for each area element, an opening in the metal layer. A size of the openings in the metal layer may be position-dependent. Different types of area elements may be mixed with each other on the impedance surface. Further examples of area elements that are applicable in the context of the present disclosure are described for example in EP 3084882 A1.

The metasurface antenna 100 further comprises at least one feeding element 20 for irradiating the impedance surface 10 with second electromagnetic field radiation. The second electromagnetic field radiation corresponds to an excitation field for causing the metasurface antenna 100 to radiate the first electromagnetic field radiation. The first electromagnetic field radiation may be radiated to the same side of the impedance surface 10 from which the second electromagnetic field radiation impinges on the impedance surface 10, or to the opposite side, depending on the implementation. Although shown in the center of the impedance surface 10, the at least one feeding element 20 may be arranged at any other position along the impedance surface 10 and may also be spaced apart from the impedance surface 10. Also, in some implementations, the irradiated second electromagnetic field radiation may be anisotropic with respect to the center of the impedance surface 10.

The metasurface antenna 100 further comprises a conductive ground plane 30. The conductive ground plane 30 may be a metallic ground plane, such as a metal sheet/layer, for example. The conductive ground plane 30 is spaced apart from the impedance surface 10. Accordingly, a respective equivalent transverse transmission line is formed between the impedance surface 10 and the ground plane 30 for each position on the impedance surface 10. The metasurface antenna 100 yet further comprises an engageable structure 40. The engageable structure 40 has a plurality of states and is engageable to transition between these states. The engageable structure 40 may be engageable by a control signal. The states of the engageable structure 40 may be mechanical or electrical states. Importantly, a transition from one state of the engageable structure 40 to another is associated with an alteration of an electric length of the equivalent transverse transmission line for at least one position (possibly, for a plurality of positions) on the impedance surface 10. The plurality of states of the engageable structure 40 correspond to respective beam patterns of the first electromagnetic field radiation that is radiated by the impedance surface 10 in reaction to being irradiated with the second electromagnetic field radiation by the at least one feeding element 20. That is, for each one of the states, the first electromagnetic field radiation may have a respective corresponding beam pattern. Thus, the beam pattern of the first electromagnetic field radiation can be changed by controlling the engageable structure 40 to transition between states.

Although the engageable structure 40 is shown in Fig. 1 as arranged between the impedance surface 10 and the ground plane 30, this is not necessarily the case and the particular choice of arrangement shown should not be construed to be limiting. In fact, it suffices for the engageable structure to be arranged such that a transition from one state of the engageable structure 40 to another is associated with an alteration of the electric length of the equivalent transverse transmission line for at least one position (possibly, for a plurality of positions) on the impedance surface 10.

Although not shown in Fig. 1, the metasurface antenna 100 is understood to also encompass multi-layer structures with multiple active/dielectric layers arranged between the impedance surface 10 and the ground plane 30.

As noted above, the engageable structure 40 has a plurality of different states between which it can transition. Each state corresponds to a respective beam pattern of the radiated field (the first electromagnetic field radiation) of the metasurface antenna 100. Advantageously, the beam patterns to which the plurality of states correspond relate to snapshots of a continuous change of the beam shape and/or beam pointing direction of the first electromagnetic field radiation from an initial state of the beam shape and/or beam pointing direction to a final state of the beam shape and/or beam pointing direction. The impedance surface 10 may be designed (e.g., by the method set out in EP 3084882 Al) to produce the desired initial beam pattern for a ground state of the engageable structure 40. Transitioning of the engageable structure 40 from the ground state will then lead to a change in the beam pattern away from the initial beam pattern. Appropriate choice of the states of the engageable structure 40 allows to change the beam pattern of the first electromagnetic field radiation in a controlled manner. A method for choosing/determining the states of the engageable structure 40 (i.e., a method for designing a metasurface antenna according to embodiments of the disclosure) will be described in more detail below. Although the ground state of the engageable structure 40 is indicated above to correspond to the initial beam pattern, this is not necessarily the case and the ground state may correspond to any given one among a sequence of beam patterns from the initial state to the final state.

The plurality of states of the engageable structure 40 are defined by a finite number of control parameters. Each state of the engageable structure 40 is associated with a respective set of values of these control parameters. The control parameters may be referred to as control points. Thus, by changing the values of the control parameters, the engageable structure 40 can be made to transition between states, which in turn leads to a change in the beam pattern of the first electromagnetic field radiation.

One advantage of the metasurface antenna 100 according to embodiments of the disclosure is that the number of the control parameters can be smaller than a number of available degrees of freedom of the impedance surface 10. Therein, available degrees of freedom are understood to be those degrees of freedom for which parameter values differ from one element of the impedance surface to the next. The elements may correspond to elements of area (cells) into which the impedance surface is partitioned. For example, the available degrees of freedom of the impedance surface 10 can be constructed as follows: select among the degrees of freedom of each element those degrees of freedom that could potentially differ from one element to the next into a first set of degrees of freedom for the element. Then, build the union (e.g., Boolean union) of the first sets for the plural elements to obtain a second set of degrees of freedom. The cardinality (i.e., element count) of the second set of degrees of freedom corresponds to the total number of available degrees of freedom of the impedance surface 10. The available degrees of freedom may also be referred to as degrees of freedom in a subset of degrees of freedom of elements of the surface pattern of the impedance surface, wherein the subset of degrees of freedom includes all those degrees of freedom for which parameters differ from one element to the next. Then, the number of the control parameters may be smaller than the number of degrees of freedom in the subset of degrees of freedom. As an example, for the elements relating to a (position-dependent) metallic pattern provided on a dielectric substrate of constant thickness, the thickness of the dielectric substrate is not an available degree of freedom for a given element. In one example, the number of the control parameters may be smaller than the number of available degrees of freedom by at least a factor of 2.

In alternative implementations, the number of the control parameters may be smaller than a number of degrees of freedom of a far field of the first electromagnetic field radiation. The number of the control parameters may be smaller than the number of degrees of freedom of the far field of the first electromagnetic field radiation by at least a factor of 2.

In general, the number of degrees of freedom of a typical metasurface antenna is approximated by N 2 + 2 N, where N = p D/l, with D the diameter of the smallest enclosing sphere for the metasurface antenna. The first term corresponds to the maximum theoretical gain of an aperture antenna of the given diameter and is clearly dominant for antennas above 15 wavelengths.

Implementation examples of the metasurface antenna 100 will be described next. Notably, the list given below is understood to be non-limiting and non-exhaustive.

Without intended limitation, it is assumed that the basic architecture of the metasurface antenna corresponds to a modulated metasurface antenna, featuring one or more layers of embedded features, constituting the modulated sheet (i.e., impedance surface, or metasurface). The impedance surface has collectively and dominantly inductive or capacitive transversal impedance for the elements of the impedance surface. The metasurface antenna features a fixed metasurface modulation (i.e., a fixed impedance surface, in the sense that it has a fixed surface pattern, for example). Configured as such, the metasurface antenna exploits a leaky-wave radiation mechanism that operates on a variable surface-wave impedance, which is linked to the (mesoscale, i.e., wavelength scale) average of the impedance tensor distribution across the antenna surface. The surface-wave impedance variation is required to occur, possibly as average, at the mesoscale level or above this scale. The average may be due, for instance, to the presence of a number of identical microscale (subwavelength) cells with a binary state.

A basic solution according to embodiments of the disclosure implies a variable value of average constitutive parameters (e.g., dielectric permittivity) of a structure supporting the surface wave, which does not alter, at least to first degree, the metasurface modulation (surface pattern) and corresponding average sheet impedance of the impedance surface.

A first category (type-I) of implementations involves varying a thickness and/or density of the material or layered structure supporting the impedance surface (i.e., supporting the leaky wave). This includes dielectrics made from elastic and/or flexible materials or including variable (micro-)structures actuated with mechanical, electromechanical and/or electrical means.

A second category (type-II) of implementations involves embedded features constituting a variable reactive loading on the transverse transmission line, associated to a single metasurface cell at the microscale (i.e., subwavelength scale), obtained with electromechanical/electronic means.

In one such possible implementation, the metasurface antenna comprises, in addition to the parts mentioned above, a dielectric support structure. The impedance surface 10 is provided on one side of the dielectric support structure and the ground plane 30 is arranged on the other side of the dielectric support structure, opposite the impedance surface 10. The dielectric support structure may be a dielectric layer, for example. The ground plane 30 is not necessarily in contact with the dielectric support structure and may be separated therefrom, for example, by a gas-filled layer or vacuum. The engageable structure 40 is coupled to the dielectric support structure. For example, the engageable structure 40 may contact at least a portion of the dielectric support structure or may be embedded in the dielectric support structure. The dielectric support structure is configured so that a dielectric permittivity between the impedance surface 10 and the ground plane 30 changes for at least one position (possibly, for a plurality of positions) on the impedance surface 10 when the engageable structure 40 transitions between states. To achieve this aim, at least one property or characteristic of the dielectric support structure may be altered by the coupling to the engageable structure 40 when the engageable structure 40 transitions between states. For example, the dielectric support structure may be deformable or movable by the engageable structure 40. Notably, a change in the dielectric permittivity between the impedance surface 10 and the ground plane 30 corresponds to a change of electric length of the equivalent transverse transmission line for at least one position (possibly, for a plurality of positions) on the impedance surface 10.

The above implementation is understood to also include, for example, the case of powders, which can flow from one position to another, even outside the“RF-active” portion of the metasurface antenna, as well as the case of a so-called e-ink panel in which small spheres filled with dielectrics of different permittivity, one hemisphere each, are rotated in such a way to move the one half toward or away from the ground plane.

In one example of the above implementation, a sectional side view of which is shown in Fig. 2, the dielectric support structure 50 is deformable or movable. Although the ground plane 30 contacts the dielectric support structure 50, this is not necessarily the case and the ground plane 30 may be separated from the dielectric support structure 50 by a spacer layer (e.g., gas-filled or vacuum). The dimensions (e.g., thickness) of the elements of the metasurface antenna shown in Fig. 2 may not be to scale.

For deforming or moving the dielectric support structure 50, the engageable structure 40 comprises one or more movable portions 41 contacting the dielectric support structure 50. The engageable structure 40 further comprises an actuating part (or actuating parts) 42 for inducing movement of the one or more movable portions 41. Here, movement of the movable parts 41 can be linear motion or rotary motion, for example. Fig. 2 shows the non-limiting example of extendable/retractable pins that push against the dielectric support structure 50. In some cases, the pins may be extendable/retractable through respective openings in the ground plane 30. For example, the metasurface antenna 100 may comprise, as the engageable structure 40, a regular lattice bed of metallic pins that can be selectively retracted through the ground plane, with either two or many positions, and that can contact the dielectric support structure 50 for moving and/or deforming the dielectric support structure 50. The bed of metallic pins may be attached to a flexible structure to allow for controlling movement of the metallic pins by a reduced number of actuators. In this case, the number of actuators (e.g., actuating parts 24) may be much smaller than the number of metallic pins. The actuating part(s) 42 may operate under control of a control signal/unit (not shown). As noted above, deforming or moving the dielectric support structure 50 will result in a change of the dielectric permittivity between the impedance surface 10 and the ground plane 30, which in turn affects the electric length of the equivalent transverse transmission line for at least one position (possibly, for a plurality of positions) on the impedance surface 10.

Specifically, the dielectric support structure 50 may be deformable (flexible and/or elastic). Then, the one or more movable portions 41 may be arranged in such manner that movement thereof causes alteration of a density and/or thickness of the dielectric support structure 50 between the conductive ground plane 30 and the impedance surface 10 for at least one position (possibly, for a plurality of positions) on the impedance surface 10. For example, the movable portions 41 may relate to microcells with flat/elongated conductive elements that can be alternatively oriented in parallel or in perpendicular to the conductive ground plane 10. In this case, the one or more movable portions 41 may be arranged between the conductive ground plane 30 and the dielectric support structure 50. As another example, the one or more movable elements 41 may relate to pins slidably arranged in respective opening in the conductive ground plane 30 (as noted above), to be selectively extended from and retracted through their respective opening. The pins may be conductive/metallic or made from a dielectric. The pins may be arranged in a regular lattice.

In another example of the above implementation, a sectional side view of which is shown in Fig. 3, the engageable structure 40 comprises one or more actuatable elements 43 coupled to or embedded into the dielectric support structure 50. Fig. 3 shows the example of actuatable elements 43 embedded into the dielectric support structure 50. The actuatable elements 43 can be (micro-)structures, for example. They may be actuated by mechanical, electromechanical, and/or electrical means. The actuatable elements 43 may also form an active layer that is in laminar contact with the dielectric support structure 50. The actuatable elements 43 may be piezoelectric crystals or nematic crystals, for example. Regardless of their implementation and arrangement, it is understood that the actuatable elements 43 are configured to deform or move the dielectric support structure 50. Further, the actuatable elements 43 may cause an alteration of the density and/or thickness of the dielectric support structure 50 for at least one position (possibly, for a plurality of positions) on the impedance surface 10. The dimensions (e.g., thickness) of the elements of the metasurface antenna shown in Fig. 3 may not be to scale.

Another example of the above implementation relates to a case where the engageable structure 40 and the dielectric support structure 50 form a layered structure incorporating (for example, next to the ground plane 30) an array of identical microcells with conducting elements which can be alternatively oriented perpendicular or parallel to the ground plane 30. A change of orientation may be effected magnetically, for example. Alternatively, the microcells may include high permittivity dielectric (thick) pins.

Another example includes a case where the engageable structure 40 and the dielectric support structure 50 form a layered structure incorporating an array of identical microcells split in two halves by the geometric plane of the ground plane 30, partially filled with dielectric powder which can be selectively displaced from one half to the other. Displacement of the powder may be effected by a switchable static electric field, for example.

Another example of the above implementation relates to a case where the engageable structure 40 and the dielectric support structure 50 form a layered structure (e.g., a two-layer structure) incorporating (for example, next to the ground plane 30), an array of BST (Barium Strontium Titanate) crystals, piezoelectric crystals, nematic crystals, or similar variable permittivity elements.

In the above examples, the one or more actuatable elements 43 coupled to or embedded into the dielectric support structure 50 or the microcells may be actuated or controlled in a combined manner, so that the number of control parameters is smaller (e.g., much smaller) than the number of actuatable elements 43 or microcells.

In another possible implementation, the engageable structure 40 is coupled to the ground plane 30, which is deformable (flexible and/or elastic) or movable so that a distance between the impedance surface 10 and the ground plane 30 changes for at least one position (possibly, for a plurality of positions) on the impedance surface 10 when the engageable structure 40 transitions between states. In particular, the distance can be altered/modified in a position-dependent manner.

In one example of this implementation, the engageable structure 40 comprises or is formed by a plurality of electrically interconnected shape-memory alloy cells. In this case, the engageable structure 40 may be seen as part of the ground plane 30, so that the ground plane 30 can be said to be constituted by an array of electrically interconnected shape-memory alloy cells.

In another example of this implementation, the engageable structure 40 comprises one or more movable portions 41 contacting the conductive ground plane 30 for deforming or moving the conductive ground plane 30. The engageable structure 40 further comprises an actuating part (or actuating parts) 42 for inducing movement of the one or more movable portions 41. Here, movement of the movable parts 41 can be linear motion or rotary motion, for example. The actuating part(s) 42 may operate under control of a control signal/unit. The movable portions 41 may be arranged to deform the conductive ground plane 30 in a direction perpendicular to the impedance surface 10 (i.e., towards or away from the impedance surface 10). Two examples of this configuration will be described below. In both examples, the metasurface antenna also comprises a dielectric support structure 50, wherein the impedance surface 10 is provided on one side of the dielectric support structure 50 and the ground plane 30 is arranged on the other side of the dielectric support structure, opposite the impedance surface 10. In the first example, the ground plane 30 is separated from a dielectric layer 52 of the dielectric support structure 50 by a spacer layer 54. In this case, it suffices if the ground plane 30 is deformable. In the second example, the ground plane 30 and the dielectric support structure (e.g., dielectric layer) 50 are in laminar contact with each other. In this case, both the ground plane 30 and the dielectric support structure 50 need to be deformable (preferably, to identical or similar degree). In the first example, which is schematically illustrated in Fig. 4A, the dielectric support structure 50 is a two- layer substrate and comprises a dielectric layer 52 and a spacer layer 54, the latter arranged between the dielectric layer 52 and the conductive ground plane 30. The spacer layer 54 may be air-filled, gas-filled, or empty (vacuum). The conductive ground plane 30 is deformable (e.g., flexible and/or elastic), as noted above. The one or more movable portions 41 of the engageable structure 40 are arranged to contact the conductive ground plane 30. Therein, the movable portions 41 are arranged/configured to, when moved, deform the conductive ground plane 30 in a direction perpendicular to the impedance surface 10. Such deformation of the conductive ground plane 30 locally alters the distance between the conductive ground plane 30 and the impedance surface 10. For example, the deformable ground plane 30 may be actuated at a limited number of points by mechanical means (e.g. piston-spring pairs displaced perpendicularly to the antenna surface by a (single) rotating profiled surface), or electromechanical means, (e.g., inch-worm piezo actuators). These means may be seen as implementation examples of the movable portion(s) 41 of the engageable structure 40 (possibly, together with the actuating part(s) 42). Deformation of the conductive ground plane 30 implies that the thickness of the spacer layer 54 is locally altered, whereas the dielectric layer 52 may be fixed with regard to position and shape.

In the second example, which is schematically illustrated in Fig. 4B, the conductive ground plane 30 and the dielectric support structure (e.g., dielectric layer) 50 are in laminar contact with each other. As noted above, both the conductive ground plane 30 and the dielectric support structure 50 are deformable (e.g., flexible and/or elastic). For example, the dielectric support structure 50 may be formed of silicone rubber. Also in this case, the movable portions 41 are arranged/configured to, when moved, deform the conductive ground plane in a direction perpendicular to the impedance surface 10. Such deformation of the conductive ground plane 30 locally alters the distance between the conductive ground plane 30 and the impedance surface 10. Moreover, such deformation may locally alter the thickness and density of the dielectric support structure 50 (e.g., dielectric layer). Also here, the deformable ground plane 30 may be actuated at a limited number of points by mechanical means (e.g. piston-spring pairs displaced perpendicularly to the antenna surface by a (single) rotating profiled surface), or electromechanical means, (e.g., inch-worm piezo actuators). These means may be seen as implementation examples of the movable portion(s) 41 of the engageable structure 40 (possibly, together with the actuating part(s) 42).

The dimensions (e.g., thickness) of the elements of the metasurface antennas shown in Fig. 4A and Fig. 4B may not be to scale.

The above implementations and examples fall into the first category of implementations (type-I). Implementations and examples that fall into the second category of implementations (type-ll) will be described next. In one such implementation, the engageable structure 40 is part of or forms an active conductive layer arranged between the impedance surface 10 and the ground plane 30.

In another such implementation, the engageable structure 40 comprises a plurality of conductive elements that are selectively interconnectable. Selectively interconnecting the conductive elements allows to alter the dielectric permittivity between the impedance surface 10 and the ground plane 30 for at least one position (possibly, for a plurality of positions) on the impedance surface 10. Therein, each of the conductive elements may present a reactive load. Individual conductive elements or groups of conductive elements may be associated with respective area elements (cells) of the impedance surface (metasurface cells). The individual reactive loads may themselves be variable. Further, a variable load may be obtained by changing a connectivity within groups of conductive elements.

For example, the metasurface antenna may include a two-layer dielectric substrate embedding an active layer constituted by an array of identical metallizations (possibly many per metasurface cell), which can be selectively connected, conductively or capacitively, under electrical control (e.g., with MEMS, Pi N diodes, varactors, BST cells, etc.). As another example, the metasurface antenna may include a three-layer dielectric structure, with two thin metallization layers separating the dielectric layers, each metallization layer hosting an array of features, with active interconnections along each layer and possibly from one layer to the other. As yet another example, one of the metallization layers may be featureless and may constitute the ground plane.

A specific example of a metasurface antenna 500 that relates to a type-1 implementation will be described next with reference to Fig. 5 to Fig. 13. This metasurface antenna 500 may be used for beam scanning, for example. Also here, the dimensions (e.g., thickness) of the elements of the metasurface antenna shown in the figures may not be to scale.

The basic structure of the metasurface antenna 500 is schematically illustrated in Fig. 5A (exploded perspective view) and Fig. 5B (schematic sectional side view). The diameter of the metasurface antenna 500 may be 0(1) to 0(10) times the wavelength l for which the metasurface antenna is designed (e.g., 10l for 15GFIz). For feeding mechanisms other than single-point in-plane feeding, such as multi-point and/or out-of- plane feeding, the antenna dimensions may be different. As in the case of the metasurface antenna 400 in Fig. 4A, the metasurface antenna 500 comprises an impedance surface 10 that is provided on one side of a dielectric layer 52. The dielectric 52 layer may have a thickness of below 1mm to few mm (e.g., 0.8mm). The dielectric layer 52 is separated from the conductive ground plane 30 by a spacer layer 54, which may be vacuum or gas-filled (e.g., air-filled), for example. The spacer layer 54 may have a thickness of below 1mm to few mm (e.g., 1mm). As is indicated by vertical arrows in Fig. 5B, the ground plane 30 may be tilted (and possibly flexed or otherwise deformed), relative to the impedance surface 10 by the engageable structure. Then, the states of the engageable structure may correspond to different tilt angles of the ground plane 30. In particular, the present example assumes three different tilt angles (and possibly, intermediate angles), of which one corresponds to a ground state of the engageable structure. Notably, the engageable structure is not shown in this figures, neither is the excitation element.

Fig. 6 illustrates a possible choice of the configuration of the area elements (cells) of the impedance surface 10. The exemplary cell 60 is of square shape and includes a square opening 62 in a metallized layer 61. The impedance surface 10 may be periodically tiled into a plurality of such cells. The edge length (size) Lo of the cell 60 may be the same for all cells of the impedance surface 10. The edge length (size) L 1 of the opening 62 may differ from one cell to the next. In particular, the size L 1 may vary smoothly across the impedance surface 10, from one cell to the next, to achieve a desired impedance pattern (with position-dependent impedance) across the impedance surface 10.

Fig. 7A, Fig. 7B, and Fig. 7C illustrate the design process leading from the surface impedance to the inductive load (bottom part of the antenna structure) provided by each metasurface cell (metasurface cell and evanescent surface wave field above it). Respective quantities may be shown as seen from below along the transverse transmission line modelling the complete structure, as far as the surface wave propagation on the impedance surface is concerned. The process proceeds from the impedance map (Fig. 7A) to the inductance of the cell loading (Fig. 7C), through the map of the sizes of the (openings in the) individual cells across the impedance surface (Fig. 7B). At each cell, the lower part of the structure has to provide a capacitance that exactly compensates the inductive load at the desired frequency, so as to obtain resonance of the transverse transmission line. The impedance map and thus the load map correspond to the antenna in its rest position, which in this example case implies that the antenna radiates a tilted beam when in the rest condition.

Fig. 8A, Fig. 8B, and Fig. 8C illustrate the required surface impedance for different scan angles of the beam, i.e., the impedance seen looking from above the metasurface onto the transverse transmission line of each cell. Fig. 8A relates to a scan angle of 20° (degrees), Fig. 8B relates to a scan angle of 45° (which is the beam in the rest position), and Fig. 8C relates to a scan angle of 65° . For other scan angles in the range from 20° to 65° , the impedance maps will be an interpolation between respective two adjacent impedance maps. To obtain resonance, the bottom part of the antenna structure (i.e., the structure below the metasurface) shall be altered to match the desired change in load impedance (i.e., from the actual impedance map for the rest position to the required impedance maps for different scan angles). According to embodiments of the disclosure, this alteration is achieved by providing the engageable structure that can transition between plural states and thereby alters the length of the transverse transmission line (possibly in a position- dependent manner).

Fig. 9 schematically illustrates the change in capacitance required to achieve desired impedance maps for a scan angle of 30° (left panel), a scan angle of 45 ° (rest position; center panel), and a scan angle of 60° (right panel). In the rest position the capacitance is constant across the antenna. It reaches two extreme distributions at the two opposite ends of the scan range. The desired change in capacitance can be achieved for example by tilting or flexing the ground plane 30, or by an electronic implementation using voltage controlled capacitors, for example. Fig. 10A, Fig. 10B, and Fig. IOC schematically illustrate the corresponding beams 11 at respective scan angles of 30° , 45° , and 60° .

Fig. 11A, Fig. 11B, and Fig. 11C illustrate details of the variation in capacitance that is required to scan the beam from 30 ° to 60 ° . Fig. 11A shows the required capacitance variation along each radial direction under different scan conditions. Therein, the horizontal axis indicates the azimuth angle (i.e., a specific radial direction) and the vertical axis indicates the desired scan angle. In the example at hand, the required capacitance is substantially constant along each radial ray. In other cases, there may be variations in capacitance also in this direction, depending on the specific requirements, such as beam shape stability, side lobe requirements, implementation choices, etc. As can be seen from Fig. 11A, the required capacitance is uniform for all radial directions for a scan angle of 45° , which corresponds to the rest position in the present example. This is in line with the center panel in Fig. 9. Further, Fig. 11B shows the required capacitance profiles for different scan angles as a function of azimuth (horizontal axis). Curve 1110 relates to a scan angle of 60° , curve 1120 relates to a scan angle of 45° , and curve 1130 relates to a scan angle of 30° . Fig. 11C shows the required capacitance profiles for different azimuths as a function of scan angle (horizontal axis). Curve 1140 relates to an azimuth of 180° , curve 1150 relates to an azimuth of 90° , and curve 1160 relates to an azimuth of 0° . Therein, an azimuth of 90° may correspond to a tilt axis of the ground plane.

As noted above, the required capacitance profiles could be achieved by an electronic implementation (e.g., using voltage controlled capacitors). The same could also be achieved by a simple mechanical implementation that, for example, involves tilting or deforming (flexing) the ground plane. This is schematically illustrated in Fig. 12A, Fig. 12B, and Fig. 12C. To make the ground plane deformation more symmetrical, it may be necessary to choose a different scan angle for the rest position, with reference to the extreme scan angles. For example, for a mechanical implementation and a desired range of beam scan angles from 20° to 65° , the rest position could be implemented for a scan angle of 45 ° , which is (unlike the above example with scan angles ranging from 30° to 60°) not the center of the beam scan angle range. Accordingly, Fig. 12A, Fig. 12B, and Fig. 12C illustrate scan angles of 20° , 45 ° , and 65° , respectively, wherein the ground plane deformations for 20° and 65° are substantially symmetric.

This can also be seen from Fig. 13A, Fig. 13B, and Fig. 13C, which illustrate, for the aforementioned mechanical implementation, details of the variation in the air gap thickness between the ground plane and the dielectric layer supporting the metasurface that is required to scan the beam from 30° to 60° . Fig. 13A shows the variation required along each radial direction for the capacitance under different scan conditions. Therein, the horizontal axis indicates the azimuth (i.e., radial direction) and the vertical axis indicates the desired scan angle. In the example at hand, the required air gap thickness is substantially constant along each radial ray. In other cases there may be variations in capacitance also in this direction, depending on the specific requirements, such as beam shape stability, side lobe requirements, implementation choices, etc. As can be seen from Fig. 13A, the required air gap thickness is uniform for all radial directions for a scan angle of 45° , which corresponds to the rest position. Fig. 13B shows the required air gap thickness profiles for different scan angles as a function of azimuth (horizontal axis). Curve 1310 relates to a scan angle of 30° , curve 1320 relates to a scan angle of 45° , and curve 1330 relates to a scan angle of 60° . Fig. 13C shows the required air gap thickness profiles for different azimuths as a function of scan angle (horizontal axis). Curve 1340 relates to an azimuth of 0 ° , curve 1350 relates to an azimuth of 90° , and curve 1360 relates to an azimuth of 180° . As can be seen from these figures, the required air gap thickness is not symmetrical for the desired beam scan angle range and chosen rest position, which could be addressed by choosing a different rest position.

As can also be seen for example from Fig. 13A, Fig. 13B, and Fig. 13C, the actual number of control points necessary to achieve the required ground plane deformations may be quite small, especially if some degradations are acceptable in the beam shape across the scan range, as the variations are non-linear both across the surface and across the scan range. In general, the higher the beam quality, the larger the number of control points that is necessary.

Needless to say, many other beam patterns can be obtained by implementing different impedance maps at the resonance condition for the transverse transmission line, in line with metasurface antennas and methods according to embodiments of the disclosure. Clearly, the actual possibility to obtain such shapes and the related degree of accuracy are linked to the degrees of freedom available in the control of the transverse resonance condition across the metasurface (e.g., for each cell).

Design of Variable Metasurface Antennas

Next, methods of designing (variable) metasurface antennas accordingto embodiments of the disclosure will be described. These metasurface antennas are, in line with the above, metasurface antennas that radiate first electromagnetic field radiation (e.g., having a certain beam pattern (beam shape and/or beam pointing direction)). The metasurface antenna typically comprises a patterned impedance surface with a position- dependent impedance across the surface, at least one feeding element for irradiating the impedance surface with second electromagnetic field radiation, a conductive ground plane that is spaced apart from the impedance surface, so that a respective equivalent transverse transmission line is formed between the impedance surface and the ground plane for each position on the impedance surface, and an engageable structure with a plurality of states that is engageable to transition between states. A transition from one state to another is associated with an alteration of an electric length of the equivalent transverse transmission line for at least one position (possibly, for a plurality of positions) on the impedance surface. As such, the methods described below may be applied to any of the metasurface antennas described above, i.e., they may be used as a design procedure for arriving at a desired metasurface antenna in line with the above embodiments, implementations, and examples.

An example of such method 1400 is illustrated, in flowchart form, in Fig. 14. The method aims at designing a metasurface antenna that allows to vary the beam pattern of the radiated first electromagnetic field radiation in accordance with a desired sequence of beam patterns. The desired sequence of beam patterns may for example relate to a scanning motion of the beam, i.e., may relate to a (possibly smooth) sequence of elevation angles of the pointing direction of the beam. It may also relate to a widening or narrowing of the beam. In general, the desired sequence of beam patterns of the first electromagnetic field radiation relates to a continuous change of the beam pattern (beam shape and/or beam pointing direction) of the first electromagnetic field radiation from an initial state of the beam pattern (beam shape and/or beam pointing direction) to a final state of the beam pattern (beam shape and/or beam pointing direction).

At step_S1410, for a desired sequence of beam patterns of the first electromagnetic field radiation, a plurality of snapshots is determined. Each snapshot corresponds to a respective beam pattern in the sequence. If the desired sequence of beam patterns is a smooth sequence, the snapshots provide a discretized representation of the desired sequence. It is noted that intermediate beam patterns that correspond to a beam pattern in between two snapshots may be approximately achieved during operation of the eventual metasurface antenna by interpolation between states of the engageable structure.

At step S1420. for one of the snapshots, a first position-dependent target impedance for the impedance surface is determined based on the beam pattern indicated by the snapshot and characteristics of the second electromagnetic field radiation. In particular, the first position-dependent target impedance is determined so that irradiation of the impedance surface having the first position-dependent target impedance with the second electromagnetic field radiation would result in the metasurface antenna radiating the first electromagnetic field radiation with the beam pattern indicated by the snapshot.

At step S1430. for the one of the snapshots, a surface pattern for the impedance surface is determined based on the first position-dependent target impedance. This is done so that the impedance surface provided with the surface pattern would have the first position-dependent target impedance when the engageable structure is in a first state.

Step S1430 may involve determining, as the surface pattern, a position-dependent quantity indicative of geometric characteristics of the impedance surface on the basis of the first position-dependent target impedance and a relationship between geometric characteristics of the impedance surface and corresponding impedance values. Said step S1430 may further involve (virtually) partitioningthe impedance surface into a plurality of elements of area (cells). Then, the relationship between geometric characteristics of the impedance surface and corresponding impedance values becomes a relationship between geometric characteristics of the elements of area and corresponding impedance values. For this partitioned impedance surface, obtaining the surface pattern may comprise, for each of the plurality of elements of area, obtaining geometric characteristics of the element of area on the basis of the first position-dependent target impedance and the relationship between geometric characteristics of the elements of area and the corresponding impedance values. The geometric characteristics of each element of area may determine its actual physical shape or configuration. For example, the geometric characteristics of an element of area may relate to a configuration of a conducting structure of predetermined shape provided on the dielectric material for the element of area, to a thickness of the dielectric material, to a configuration of one or more openings in a metal layer for the element of area. Additional detail on the geometric characteristics of elements of area (cells) can be found, for example, in EP 3084882 Al, relevant part of which are hereby incorporated in their entirety. It is noted in this regard that the impedance surface may include elements of area of different type, i.e., may be composed of a mixture of different types of elements of area.

At step S1440. for each of the remaining snapshots, a respective second position-dependent target impedance for the impedance surface is determined based on the beam pattern indicated by the respective one of the remaining snapshots and characteristics of the second electromagnetic field radiation. This is done so that irradiation of the impedance surface having the second position-dependent target impedance with the second electromagnetic field radiation would result in the metasurface antenna radiating the first electromagnetic field radiation with the beam pattern indicated by the respective one of the remaining snapshots. A difference between the first position-dependent target impedance and the second position- dependent target impedance may correspond to a position-dependent impedance variation.

At step S1450. for each of the remaining snapshots, a position-dependent alteration amount in the electric length of the equivalent transverse transmission line is determined based on the respective second position- dependent target impedance and the first position-dependent target impedance (e.g., based on the position- dependent impedance variation). This is done so that the impedance surface provided with the surface pattern (as determined at step S1430) would have the second position-dependent target impedance when the position-dependent change amount in the electric length of the equivalent transverse transmission line is applied. This step may involve determining the position-dependent alteration amount on the basis of the second position-dependent target impedance (e.g., based on the position-dependent impedance variation) and a relationship between geometric characteristics of the impedance surface, values of electric length of the equivalent transverse transmission line, and corresponding impedance values. Finally, at step S1460. for each of the remaining snapshots, a respective state of the engageable structure that would implement the respective position-dependent alteration amount in the electric length of the equivalent transverse transmission line is determined based on characteristics of the engageable structure.

For example, two sets of model functions (e.g., basis functions) could be defined, the first linked to the desired position-dependent impedance variation and the second linked to the structure (e.g., an adjustment mechanism) of the engageable structure that controls the electrical length of the transverse transmission line. Then, a mapping between the two sets can be defined. Fixing the first set to give the best approximation of the desired impedance variation (and likewise, desired variation of the radiation pattern), the number of terms in the second model (and thus, the number of control points) can be chosen to achieve a desired precision/accuracy of the adjustment mechanism (and thus, of the impedance variation). The first set is essentially dictated by the shape of the metasurface antenna (e.g., disc or rectangle), the second set is representative of the modes of the adjustment mechanism (e.g., the states that the engageable structure can attain, such as the deformation modes of a flexible ground plane, etc.). Depending on the dominant elements in the first set, it is possible to choose a suitable second set (e.g., having the same symmetries), select a subset of it sufficient to achieve an error below a desired maximum error in fitting the first set. Based thereon, the number, position and characteristics, (e.g. motion range) of the control points can be selected.

Steps S1410 to S1430 of method 1400 may be performed iteratively to refine the determination of the surface pattern. For example, after each iteration, the beam pattern indicated by the snapshot may be compared to a fourth electromagnetic field radiation that would be radiated by the impedance surface provided with the determined surface pattern in reaction to being irradiated by the second electromagnetic field radiation. Then, depending on a result of the comparison, at least one of the model function of the first position-dependent target impedance and the second electromagnetic field radiation may be adjusted and steps S1410 to S1430 may be repeated to obtain an adjusted surface pattern. This repetition may be performed for a predetermined number of times or until a desired accuracy of the resulting electromagnetic field radiation is achieved.

As noted above, it is desirable that the states of the engageable structure are defined by a finite number of control parameters, with each state associated with a respective set of values of the control parameters. Preferably, the number of control parameters is smaller than the number of available degrees of freedom of the metasurface. The number of control parameters can be reduced, for example, by expanding the position- dependent alteration amount in step S1460 based on some set of basis functions defined on a domain corresponding to the antenna surface, for example a unit disc or square, with one basis function for each of control parameters intended for defining the states of the engageable structure. Accordingly, method 1400 may comprise (e.g., as part of step S1460), for each of the remaining snapshots, performing a modal decomposition of the position-dependent alteration amount in terms of a set of base modes that are chosen in accordance with a geometric characteristic of the engageable structure and the control parameters for the engageable structure.

This may involve assuming a desired range of point-wise variation of the impedance and associating it with a way to enact it. The underlying system will have itself a set of control parameters, with a corresponding range of variation over the antenna surface. Then an expansion is applied to these parameters. Thereafter the number of actual control parameters can be reduced by using only a finite number of elements for each set of basis functions, each describing one of the control parameters. Therein, the number can be chosen to be sufficient for determining the surface impedance tensor with the desired flexibility and accuracy within a selected range. Clearly one could first expand the surface impedance tensor and then link this first expansion to the previous one to have full control of the design process involved in the definition of the complete structure and control electronics.

In some embodiments, step S1420 of determining the first position-dependent target impedance for the impedance surface based on the beam pattern indicated by the snapshot and the characteristics of the second electromagnetic field radiation may comprise the steps of method 1500, which is illustrated, in flowchart form, in Fig. 15. Method 1500 comprises steps S1510 to S1530.

At step S1510. a first modal representation is determined on the basis of the beam pattern indicated by the snapshot in terms of a set of base modes that are chosen in accordance with a model function of the first position-dependent target impedance. Therein, it may be advantageous if the set of base modes is determined in such manner that each of the base modes may propagate on the impedance surface if the impedance surface were provided with a position-dependent impedance in accordance with the model function.

Obtaining the first modal representation may include decomposing the beam pattern indicated by the snapshot into a plurality of first modes. Each of the plurality of first modes may correspond to a respective one of the set of base modes.

At step S1520. a second modal representation is determined on the basis of the second electromagnetic field radiation and the model function in terms of the set of base modes.

Obtaining the second modal representation may include decomposing the second electromagnetic field radiation into a plurality of second modes. Each of the plurality of second modes may correspond to a respective one of the set of base modes.

At step S1530. the first position-dependent target impedance is obtained on the basis of the first modal representation and the second modal representation by determining values for a plurality of parameters of the model function for maximizing an overlap between the first modal representation and the second modal representation. For example, one of the plurality of parameters of the model function may relate to a period of spatial modulation of the first position-dependent target impedance on the impedance surface. As another example, the model function may relate to a decomposition of the first position-dependent target impedance into a plurality of terms, each relating to a spline wavelet. Likewise, the model function may relate to a decomposition of the first position-dependent target impedance into a plurality of products of spline wavelets and phase factors.

In some implementations, step S1530 may involve calculating a reaction integral of the beam pattern indicated by the snapshot and a third electromagnetic field radiation that would be radiated by an impedance surface having a position-dependent impedance in accordance with the model function and being irradiated by the second electromagnetic field radiation. Then, the first position-dependent target impedance can be obtained by maximizing the reaction integral.

If the beam pattern indicated by the snapshot has been decomposed into a first plurality of first modes and the third electromagnetic field radiation has been decomposed into a second plurality of first modes, obtaining the first position-dependent target impedance may involve, for each of the set of base modes for which a corresponding first mode in the first plurality of first modes and a corresponding first mode in the second plurality of first modes exists, calculating an outer product between the corresponding first modes.

Steps S1510, S1520, and S1530 may correspond to steps S501, S502, and S503, respectively, in EP 3084882 Al, the description of which is herewith incorporated by reference.

Likewise, in some embodiments step S1440 of determining the respective second position-dependent target impedance for the impedance surface based on the beam pattern indicated by the respective one of the remaining snapshots and the characteristics of the second electromagnetic field radiation may comprise the steps of method 1600, which is illustrated, in flowchart form, in Fig. 16. Method 1600 comprises steps S1610 to S1630.

At step S1610. a third modal representation is determined on the basis of the beam pattern indicated by the respective one of the remaining snapshots in terms of a set of base modes that are chosen in accordance with a model function of the first position-dependent target impedance (e.g., the set of base modes of step S1510). This step may proceed in analogy to step S1510 described above.

At step S1620. a fourth modal representation is determined on the basis of the second electromagnetic field radiation and the model function in terms of the set of base modes. This step may proceed in analogy to step S1520 described above.

At step S1630. the second position-dependent target impedance is determined on the basis of the third modal representation and the fourth modal representation by determining values for a plurality of parameters of the model function for maximizing an overlap between the third modal representation and the fourth modal representation. This step may proceed in analogy to step S1530 described above. Steps S1610, S1620, and S1630 may again correspond to steps S501, S502, and S503, respectively, in EP 3084882 Al, with the first modal representation replaced by the third modal representation, the second modal representation replaced by the fourth modal representation, and the first position-dependent target impedance replaced by the second position-dependent target impedance.

Broadly speaking, method 1400 with methods 1500 and 1600 implementing steps thereof may be said to relate to determining a variable surface pattern for an impedance surface so that the beam pattern of the electromagnetic field radiation can be changed using a minimum number of control points, determined on the basis of requirements on the smoothness and precision of the resulting antenna pattern modifications.

Another example of a specific description of the design of a variable metasurface antenna according to embodiments of the disclosure will be given next. To this end, the following quantities are defined:

E s actual electromagnetic field radiated by the structure, intended as a discrete or a continuous set of instances

E i electromagnetic field incident on the structure (second electromagnetic field radiation), assumed to be fixed;

E r required/desired radiated field (first electromagnetic field radiation), intended as a discrete or a continuous set of instances

Z s surface impedance tensor of the impedance surface S(x, h), intended as a discrete or a continuous set of instances.

Furthermore, Z 0 is the free-space wave impedance and k 0 is the free-space wave propagation constant. The field radiated by the impedance surface is then given by

The required radiated field is often known only in square modulus of the far-field pattern, i.e., as directivity pattern D r =│E r │, and successive projections are applied using a suitable Fourier basis (e.g., plane, spherical or cylindrical waves) to reconstruct the complete far-field information in amplitude and phase. After an initial reconstruction based on the main geometrical characteristics of the desired metasurface antenna, such as diameter or side lengths, for example, the successive projection cycle operates using the field E s radiated by the structure. The possible radiation from the exciter, i.e. the portion of E i reaching the far-field, may also be accounted for in the process by adding it to E s or subtracting it from E r according to the type of exciter. Assuming that the structure implementing the impedance surface is divided into a plurality of layers A l, l = 1,2, ... L, at least one of which is fixed and at least one can be modified under external control, for example via a number of actuators, the fixed layers are denoted , i = 1,2, .. . I and the variable layers are denoted

,j = 1,2, . .. J, with {i} È { j } = {l}, {i} Ç { j } = Ø. The variable layer(s) may correspond to or be coupled to the engageable structure. Further, a discrete or continuous set of states S v is defined, each corresponding to a value of the surface impedance tensor Z s,v determined by variations in any of the variable layers resulting into a radiated field

Then, the design may involve the following steps:

The impedance surface is (virtually) sub-divided into a plurality of elements of area (cells) constituting the surface pattern. Then, a partition G = {G k , k = 1,2, .. . K} of å is chosen such that G k Ì S and U k G k = S.

If the set of states is discrete the total number of possible states of the impedance surface will be N = ] K . The design goal is to select a configuration of the layers that achieves the set of radiated fields with the minimum number of control points.

Next, a desired characteristic of the position-dependent target impedance is selected.

The surface impedance tensor is specified as Z s,v = Z s,v (C ), where C = { c 1 , c 2 , c 3 ... } is a set of parameters characterizing the impedance surface, linked to geometry and physical characteristics, such as, for example, the (equivalent) material permittivity or permeability. In most cases the surface impedance is linked to C via a second intermediate set of parameters Q = {q 1 , q 2 , q 3 ... } to better separate the surface impedance tensor representation, for example based on a set of continuous basis functions, from that of the geometry and physical characteristics of the layer (e.g., the size and orientation of the metasurface elements and the vertical position of the ground plane). The parameters Q are defined on the whole surface å while the parameters C are defined on the partition G. The physical characteristics of the portions G k of the surface determine the link between C and Q, i.e., the mapping Q = Y(C, k ).

Then, the set of surface impedances { Z s>v } is obtained that achieves the desired variations of the radiation pattern and the corresponding values of the parameters C and Q are derived, i.e., two sets of parameters C = { C v } and Q = { Q v }.

Next, the following steps are iterated until the desired smoothness and precision of over the entire

variation range is achieved.

1. Choose a ground state for the impedance surface { Z S,Y } and fix the corresponding elements of C g of C and Q g of Q. 2. Partition the sets C and Q into two subsets each; C f and C v corresponding to the fixed and variable layers, respectively; repeat for the set Q.

3. For each of the plurality of elements of area G k , define a geometry characteristics of the element area in the fixed layers on the basis of the values C f = {c f 1 , c f 2 , c f 3 ... }.

4. For each of the plurality of elements of area G k , define a variable geometry and/or physical characteristics of the element area in the variable layers on the basis of the values C v = {c v 1 , c v 2 , c v 3 ... }.

5. Derive the corresponding tentative surface impedance {Z' s,y } via the values of Q Y = { q1 y , q2 y , q3 y ... } derived from the C Y = { c1 Y , c2 Y ... }.

6. Evaluate the smoothness and precision of the tentative solution according to a suitable minimization criterion, for instance one based on a distance functional

where a is the Lagrange multiplier. Other optimization criteria could

be applied as well, e.g., to include a penalty for complexity.

Thereby, the best-fit surface impedance together with the definition of the structure that implements

it can be obtained.

As the optimization criteria in step 6 can be adapted to any desired level of smoothness and precision, the design of the fixed and variable layers is optimized, and is suitable for obtaining, in particular, the simplest implementation based on the partition operation in step 2. In fact, this defines a design criterion that minimizes the number and complexity of the variable layers, for example by reducing the range of shapes of the ground plane to the minimum or one that minimizes the range of the control signal for the actuators.

Clearly, a proper selection of the representations underlying the two sets of parameters C and Q, i.e. that maps them into the corresponding physical quantities (e.g., geometry and surface impedance), is of importance in the final result. As an example, choosing a set of basis functions for the surface impedance defined on the unit square may not be as good as choosing one defined on the unit disc, depending on a shape of the metasurface antenna. In the same way, for a two-axis beam scanning antenna, choosing a square grid for the position controls of the ground plane will result in higher complexity than selecting an azimuthal partitioning of the unit disc.

Notably, for some cases the approach described above can be applied in a simplified, possibly heuristic manner. For instance, it may be desired to obtain an azimuth-elevation scanning of a beam with, for example, 25dBi gain, i.e.- a -3dB beam width of about 7.5° (degrees). It is further assumed that the scan range in this example is (0-360° )x(0-70°) and that it is acceptable to have a gain variation of 3dB as a result of beam scanning. Some simple geometrical considerations on the complete coverage of the desired scan region with discs of 7.5° diameter lead to a total of about 350 beam positions, with a minimum of about 50 positions in azimuth.

For this example, it will be assumed that the variable metasurface antenna is implemented with a mechanical scan solution based on a movable ground plane that allows to change the distance from the dielectric slab above it so that different radial lines will be at a different distance. The profile of the ground plane variation over azimuth is roughly sinusoidal and a few harmonics will suffice to obtain a good approximation of the exact shape required to have a clean beam. To obtain the fundamental harmonic, i.e. one cycle over 360 degrees, 2 control points will roughly be sufficient. Four control points will yield the second harmonic, eight control points will yield the third harmonic, and so forth. Accordingly, 32 control points would be sufficient for five harmonics, with a period of 72 ° . It is not difficult to see that achieving the desired 50 positions with five harmonics means to be able to adjust their phase in steps of 36° , as the beam width is 7.5° , i.e. about 72/10 corresponding to a phase change 360/10. Finally considering a full excursion of 1mm peak-to-peak for the ground plane, corresponding to a half cycle for the fundamental harmonic, and a decay of the fifth harmonic of 1/10 leads to steps of 0.02mm for each step of 36° , which appears to be feasible with reasonable accuracy. In conclusion, 32 control points would be sufficient for an azimuth-elevation scanning with a 7.5 ° beam. This number is to be compared to the more than 2500 control points that typically would be required to adjust the individual cells (elements of area) of the same antenna (i.e., of the same metasurface).

It should be noted that the method features described above may correspond to respective apparatus (i.e., metasurface antenna) features that may not be explicitly described, for reasons of conciseness, and vice versa. The disclosure of the present document is considered to extend also to such apparatus (i.e., metasurface antenna) and vice versa.

For example, the present disclosure also relates to an apparatus comprising a processor and a memory coupled to the processor, wherein the processor is configured (e.g., when executing instructions stored in the memory) to perform any one of the methods described throughout the disclosure.

Further, the present disclosure also relates to a computer-readable storage medium containing instructions for execution by a processor that cause the processor to perform any one of the methods of encoding or decoding described throughout the disclosure.

Technical Results

Prototypes have been realized of the basic (flat) modulated surface (metasurface) excited by a surface wave travelling across the modulated surface. These prototypes have demonstrated the possibility to control the shape and polarization of the radiated beam. Prototypes for both modulated dielectric thickness and single layer metallized patches solutions have been realized. Feasibility of the beam scanning for spot beams and shaped beams has been demonstrated by these prototypes. Computer modelling has been used to assess the feasibility of further configurations.

Providing a variable metasurface according to embodiments of the disclosure can be used to achieve different metasurface designs with the same basic structure. Therefore, the theoretical performance limits are the same as those of fixed metasurfaces. While the practical implementation of the modification mechanism (i.e., the engageable structure) may introduce additional limitations, these limitations are linked to the modification mechanism used. Accordingly, simple low-cost mechanical implementations may be bound to offer less accurate control, while for instance a liquid crystal matrix control could achieve fine tuning, possibly at the expenses of reaction time in the pattern change.

It should be noted that the description and drawings merely illustrate the principles of the proposed metasurface antenna and design method. Those skilled in the art will be able to implement various arrangements that, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples and embodiment outlined in the present document are principally intended expressly to be only for explanatory purposes to help the reader in understanding the principles of the proposed method and system. Furthermore, all statements herein providing principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass equivalents thereof.




 
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