Metasurface for electromagnetic waves, antenna system and method for designing metasurface

Abstract

The invention relates to a metasurface for electromagnetic waves. The metasurface comprises unit cells; each of the unit cells has a unique phase response and includes a plurality of independent scatterers. Furthermore, the present disclosure relates to a method for designing a metasurface for electromagnetic waves, where the method comprises providing unit cells in the metasurface, where each of the unit cells has a unique phase response and comprises a plurality of independent scatterers.

Description

Technical Field

[0001] The present disclosure relates to a metasurface for electromagnetic waves, an antenna system and a method for designing a metasurface. The present disclosure relates to a computer program and a computer-readable storage medium. Background Art

[0002] The metasurface for electromagnetic waves is an artificially generated surface that modulates the behavior of electromagnetic waves. Here, "artificially generated" should be understood as a metasurface that is not a surface that already exists in nature. For example, the metasurface can modulate at least one of the amplitude, phase, and polarization of the electromagnetic wave reflected by the metasurface when incident on the metasurface or the electromagnetic wave transmitted (i.e., propagated) through the metasurface when incident on the metasurface, depending on the type of the metasurface (i.e., whether the metasurface is a reflective metasurface or a transmissive metasurface). In other words, in the case where the metasurface is a reflective metasurface, the electromagnetic wave incident on the metasurface can be reflected by the metasurface. In the case where the metasurface is a transmissive metasurface, the electromagnetic wave incident on the metasurface can be transmitted (i.e., propagated) through the metasurface. Alternatively, a portion of the metasurface can modulate the electromagnetic wave incident on the metasurface by reflecting the electromagnetic wave, while another portion of the metasurface can modulate the electromagnetic wave incident on the metasurface by transmitting or allowing the electromagnetic wave to pass through the metasurface. The metasurface for electromagnetic waves may also be referred to as an "electromagnetic metasurface." Since electromagnetic waves can be transmitted through and / or reflected by a metasurface, the term "reflective and / or transmissive metasurface" can be used as a synonym for the term "electromagnetic metasurface". A metasurface for electromagnetic waves may include a subwavelength structure (e.g., a nanostructure) for modulating the behavior of electromagnetic waves. In the following, the terms "metasurface for electromagnetic waves", "electromagnetic metasurface", and "reflective and / or transmissive metasurface" are abbreviated as the term "metasurface". Summary of the invention

[0003] The metasurface includes unit cells, wherein each unit cell in the unit cell has a unique phase response. For example, in a unit cell group in a unit cell of a metasurface, the unit cell may cover a 2π phase shift, wherein each unit cell in the unit cell group may have a unique phase response. The terms "phase shift" and "phase change" may be used as synonyms. That is, in a 2π phase shift between unit cells of a metasurface, the phase response of each unit cell in a unit cell covering a 2π phase shift may be unique. The above-mentioned unit cell group (covering a 2π phase shift) may form a super cell of a metasurface, i.e., may be referred to as a "super cell". In a metasurface, the above-mentioned unit cell group (i.e., a super cell) may be repeated. Therefore, in two or more super cells of a metasurface, there may be corresponding unit cells having the same unique phase response. The repetition of the super cell, i.e., the repetition of the unit cell group covering a 2π phase shift, may be periodic. In order to determine the effect of the metasurface on electromagnetic waves incident on the metasurface, the unit cells of the metasurface may be designed accordingly. In conventional design methods for designing metasurfaces and their unit cells, the level of approximation involved in assigning local reflection coefficients and / or transmission coefficients (depending on whether the metasurface is a reflective and / or transmissive metasurface) to individual unit cells in the metasurface is not clear. This conventional design method may only be effective for slowly changing structures, and may lead to inaccurate efficiency estimates when the meta-atomic geometry of the metasurface changes rapidly from one unit cell to the next (for example, in aperiodic or quasi-periodic structure of the metasurface). In addition, conventional methods for designing metasurfaces only focus on the phase masking or phase gradient between two adjacent unit cells (i.e., the effect of two adjacent unit cells on the phase of the electromagnetic wave or the difference in the effect on the phase between two adjacent unit cells), without considering their amplitude changes (i.e., the effect of two adjacent unit cells on the amplitude of the electromagnetic wave). The expression "close to each other" and the term "adjacent" can be used as synonyms.

[0004] In other words, the conventional design method for designing a metasurface calculates the efficiency and accuracy of the reflection and / or transmission of electromagnetic waves by the metasurface to be designed based on the phase response of the unit cells in the metasurface to be designed. However, the amplitude response of each unit cell of the metasurface may easily lead to errors in the final reflected beam and / or transmitted beam (when the electromagnetic wave is incident on the metasurface) and its efficiency. In the conventional design method, the amplitude response of each unit cell of the metasurface is expected to be or assumed to be the maximum possible value, which can be regarded as a value close to 1 without considering its influence in the beamforming process of the electromagnetic wave incident on the metasurface. In fact, this conventional design method produces a metasurface with a set of unit cells, which have different reflection amplitudes and transmission amplitudes independent of each other. This is like an array of radiators whose elements radiate with different input powers. Therefore, in the conventional design method, there may be errors in the reflected main beam and the transmitted main beam (when the electromagnetic wave is incident on the metasurface) and errors in the efficiency estimation.

[0005] In addition, in traditional design methods, due to the inconsistencies and limitations of the design process, the phase response of each unit cell of the metasurface to be designed may not be as accurate as the designer expects. In other words, the above errors can be found in the phase response of each unit cell due to three reasons. First, this may come from the inconsistency between the design expectation and the numerically achievable. For example, in order to achieve a unit cell with a phase response of 90 degrees (i.e., π / 2), the design of the unit cell should give or accurately produce this phase response. However, due to the physical property limitations of the meta-atoms and unit cells of the metasurface, this is impossible in most cases. For the above-mentioned expected phase response, as an example, in traditional design methods, a phase response between 85 degrees and 95 degrees can generally be regarded as an appropriate response. However, these deviations in the phase response of the unit cell may cause considerable errors in the beamforming process.

[0006] Another reason for the above-mentioned error in the expected phase response of the unit cell in the traditional design method may be the realized phase response of each unit cell associated with the numerical calculation. The realized phase response may be affected by the manufacturing process, which will change the overall result. Another reason for the above-mentioned error is that in the traditional design method, the analysis of the metasurface is based on the Floquet-Bloch (FB) theory. In order to calculate the phase response of each unit cell in the periodic structure of the metasurface, the FB theory assumes that the unit cell is repeated periodically to form a periodic structure with countless identical unit cells. In this way, for example, for quasi-periodic structures, the mutual coupling between unit cells may not be a perfect estimate.

[0007] Based on all the above inconsistencies, conventional design techniques are not efficient enough for practical purposes. Based on the issues mentioned in the conventional design methods of metasurfaces, there are three main deficiencies in the performance of metasurfaces. Typically, when an electromagnetic wave is incident on the corresponding metasurface, a high specular reflection occurs in the metasurface. This means that a considerable portion of the incident power of the electromagnetic wave incident on the metasurface is reflected back in the direction of the specular. In addition, due to the above different inconsistencies in the design process of the conventional design method, different grating lobes may exist in the reflection pattern, as well as sidelobe levels that are higher than the expected amount. Finally, mirror reflections may exist in conventionally designed metasurfaces.

[0008] In view of the above, the present disclosure is intended to provide an improved metasurface and an improved method for designing a metasurface. The purpose of the present disclosure is to provide a metasurface that can overcome at least one of the above-mentioned defects of metasurfaces designed using traditional design methods. Therefore, the purpose may be to provide a method for designing a metasurface that overcomes at least one of the above-mentioned defects of traditional design methods.

[0009] These and other objects are achieved by the solutions of the present disclosure as described in the independent claims. Advantageous implementations are further specified in the dependent claims.

[0010] A first aspect of the present disclosure provides a metasurface for electromagnetic waves. The metasurface includes unit cells, each of which has a unique phase response and includes a plurality of independent scatterers.

[0011] In other words, the unit cell (i.e., the phase gradient of the unit cell) obeys Snell's law. That is, the individual scatterers of each unit cell have the same phase response or contribute together to a unique phase of the unit cell.

[0012] For example, each unit cell in a unit cell of a supercell (i.e., a group of unit cells covering a 2π phase shift) of a metasurface may have a unique phase response and include multiple independent scatterers. The unit cells of the supercell comply with Snell's law. That is, the phase gradient of the unit cells of the supercell complies with Snell's law.

[0013] Optionally, the region of the metasurface where the independent scatterers are arranged or placed can be referred to as a "meta-atom". The above region, i.e., the meta-atom, can be a periodic region. For example, a meta-atom of the metasurface can be the smallest periodic region in the metasurface including one or more independent scatterers.

[0014] The metasurface can be considered as a homogeneous medium for the incident electromagnetic wave incident on the metasurface. In this case, the following conditions are satisfied:

[0015]

[0016] In the above formula, U c represents the size of the unit cell, n1 and n2 are the lossless refractive indices of the two half-spaces on either side of the metasurface. The metasurface can be a sub-wavelength thin periodic structure. i ” is the incident angle of the normal vector of the metasurface plane. The term “n 1,2 " represents the reflected diffraction order n1 of the incident electromagnetic wave and the transmitted diffraction order n2 of the incident electromagnetic wave.

[0017] The group of unit cells in the unit cell of the metasurface can cover a 2π phase shift, and the unit cells of the group are arranged closely to each other. In other words, the group of unit cells in the unit cell can cover a 2π phase shift in its response, and the unit cells of the group are arranged closely to each other. The group of unit cells can be referred to as a "super cell". In other words, the unit cells in the super cell of the metasurface can cover a 2π phase shift. Within the above-mentioned group, that is, within the super cell, the unit cells of the group (i.e., the super cell) have different phase responses relative to each other. That is, each unit cell of the group has a different phase response relative to one or more other unit cells of the group. The expressions "unit cell of a super cell" and "unit cell in a super cell" can be used as synonyms.

[0018] At least two of the unit cells of the metasurface may have different phase responses. This may be achieved by having different numbers of independent scatterers and / or different forms of scatterers in the at least two unit cells. Additionally or alternatively, the different phase responses may be caused by any differences in the structure of the unit cells that may cause a phase shift. For example, at least two unit cells of a supercell (i.e., a group of unit cells covering a 2π phase shift) may have different phase responses. This may be achieved by having different numbers of independent scatterers and / or different forms of scatterers in the at least two unit cells of the supercell. Additionally or alternatively, the different phase responses may be caused by any differences in the structure of at least two unit cells of the supercell that may cause a phase shift.

[0019] In an implementation of the first aspect, a plurality of independent scatterers are arranged in a two-dimensional lattice.

[0020] Arrangement of multiple independent scatterers in a two-dimensional lattice allows for a more uniform metasurface to be formed for an incident electromagnetic wave. Arrangement of multiple independent scatterers in a two-dimensional lattice allows for spatial oversampling for designing a metasurface. This improves the design of the metasurface, thereby improving the metasurface. Spatial oversampling allows for compensation of errors caused during the design process of the metasurface, thereby improving the metasurface resulting from the design process.

[0021] In an implementation of the first aspect, each unit cell in the unit cell is divided into sub-unit cells, each sub-unit cell includes one or more independent scatterers among a plurality of independent scatterers, wherein the phase response of the sub-unit cells of the unit cell converges to the phase response of the unit cell.

[0022] For example, each unit cell of a supercell of a metasurface may be divided into sub-unit cells, each sub-unit cell comprising one or more independent scatterers among a plurality of independent scatterers, wherein the phase response of the sub-unit cells of the unit cell converges to the phase response of the unit cell.

[0023] In spatial oversampling for designing a metasurface (which is allowed due to multiple independent scatterers of a unit cell), each sub-unit cell can be interpreted as a quantizer by which a received signal (corresponding to one or more incident electromagnetic waves) is quantized into a desired reflected or transmitted signal (one or more electromagnetic waves) according to its transfer function. Therefore, dividing the unit cell into sub-unit cells allows for improved metasurfaces because it supports spatial oversampling for designing a metasurface, thereby allowing for compensation of errors caused by the design process of the metasurface. Therefore, an improved metasurface can be achieved.

[0024] The unit cell of the supercell may include the same number of subunit cells. The number of scatterers in the subunit cells may be different from each other. Alternatively, the subunit cells may be meta-atoms of the metasurface. For example, the subunit cells of the unit cell may be meta-atoms of the metasurface. The subunit cells of the supercell may be meta-atoms.

[0025] In an implementation of the first aspect, the plurality of independent scatterers of each unit cell in the unit cell are arranged in a two-dimensional lattice. The unit cell can be divided into sub-unit cells, so that each sub-unit cell includes a row and / or column of one or more independent scatterers in the plurality of independent scatterers.

[0026] For example, multiple independent scatterers of each unit cell of the super cell can be arranged in a two-dimensional lattice, wherein the unit cell can be divided into sub-unit cells such that each sub-unit cell includes rows and / or columns of one or more independent scatterers among the multiple independent scatterers.

[0027] Multiple independent scatterers per unit cell of a metasurface can enable more control over the power of electromagnetic waves reflected or transmitted from the metasurface. Arranging multiple independent scatterers in a two-dimensional lattice can provide more control in two dimensions, if applicable.

[0028] In an implementation of the first aspect, each of the unit cells is divided into sub-unit cells, so that the number of sub-unit cells is equal to the number of multiple independent scatterers, and each of the sub-unit cells includes a corresponding independent scatterer among the multiple independent scatterers.

[0029] In an implementation manner of the first aspect, a group of unit cells in the unit cell covers a 2π phase shift, and the unit cells of the group are arranged closely to each other.

[0030] The expression “a group of unit cells in a unit cell covers a 2π phase shift” may be understood to mean “a group of unit cells in a unit cell covers a 2π phase change in its response.” The terms “phase shift” and “phase change” may be used as synonyms.

[0031] A group of unit cells covering a 2π phase shift may be referred to as a super cell. In other words, the unit cells of the super cell may cover a 2π phase shift, wherein the unit cells of the super cell are arranged next to each other.

[0032] In an implementation of the first aspect, the unit cell group includes 2 of the unit cells. B unit cells, the group of 2 B The unit cells are arranged next to each other, and B is an integer greater than or equal to 1.

[0033] In an implementation of the first aspect, the unit cell group includes a one-dimensional arrangement of sub-unit cells. The sub-unit cells of the unit cell group may be designed such that a difference between an achieved transfer response of a sub-unit cell and an expected transfer response of the sub-unit cell caused by a design error when designing the sub-unit cell to achieve an expected transfer response is at least partially compensated by a difference between an expected transfer response of a second sub-unit cell immediately preceding the sub-unit cell and an achieved transfer response of the second sub-unit cell.

[0034] The above optional features are examples of designing a metasurface using spatial oversampling. Due to the above error compensation, the metasurface is improved compared to a metasurface designed using a conventional design method, i.e., a design method without the concept of spatial oversampling. In the above case, a one-dimensional arrangement of subunit cells of a unit cell group is considered for designing the metasurface.

[0035] In one implementation of the first aspect, the difference between the expected transfer response of the second sub-unit unit and the achieved transfer response of the second sub-unit unit is added to the expected transfer response of the sub-unit unit to at least partially compensate for the difference between the achieved transfer response of the sub-unit unit and the expected transfer response of the sub-unit unit caused by design errors when designing the sub-unit unit to achieve the expected transfer response.

[0036] In other words, by adding the difference between the expected transfer response of the immediately preceding sub-unit unit and the achieved transfer response of the immediately preceding sub-unit unit to the expected transfer response of the sub-unit unit, the difference between the achieved transfer response of the sub-unit unit and the expected transfer response of the sub-unit unit caused by design errors when designing the sub-unit unit to achieve the expected transfer response is at least partially compensated.

[0037] In an implementation of the first aspect, the unit cell group includes a two-dimensional arrangement of subunit cells. The subunit cells of the unit cell group may be designed such that: a difference between an achieved transfer response of the subunit cell and an expected transfer response of the subunit cell caused by a design error when designing the subunit cell to achieve an expected transfer response is at least partially compensated by:

[0038] - a difference between a desired transfer response of a second subunit cell immediately preceding the subunit cell in the first dimension and the achieved transfer response of the second subunit cell,

[0039] - a difference between a desired transfer response of a third subunit cell immediately preceding the subunit cell in the second dimension and the achieved transfer response of the third subunit cell.

[0040] The above optional features are examples of designing a metasurface using spatial oversampling. Due to the above error compensation, the metasurface is improved compared to a metasurface designed using a conventional design method, i.e., a design method without the concept of spatial oversampling. In the above case, a two-dimensional arrangement of subunit cells of a unit cell group is considered for designing the metasurface.

[0041] In one implementation of the first aspect, the difference between the achieved transfer response of a sub-unit unit and the expected transfer response of the sub-unit unit caused by a design error when designing the sub-unit to achieve the expected transfer response is at least partially compensated by adding an average value of the difference between the expected transfer response of the second sub-unit unit and the achieved transfer response of the second sub-unit unit and the difference between the expected transfer response of the third sub-unit unit and the achieved transfer response of the third sub-unit unit to the expected transfer response of the sub-unit unit.

[0042] In this document, the terms "first", "second", "third", etc. may be used only to distinguish the elements from each other, and do not necessarily provide an order for the elements. For example, the terms "second" and "third" of the above-mentioned "second subunit unit" and "third subunit unit" are only used to distinguish them from each other and other subunit units. These terms are not used to specify (e.g., the second or third subunit unit in a sequence of subunit units.

[0043] In an implementation of the first aspect, the achieved transfer response of the subunit cell is designed to achieve a desired transfer response of the subunit cell using information about design errors and information about mutual coupling of subunit cells of the unit cell group.

[0044] Using information about design errors and about the mutual coupling of subunit cells of a group of unit cells (i.e., a supercell) allows compensation for errors caused by the design process and therefore allows the realization of improved metasurfaces compared to metasurfaces designed using traditional design methods.

[0045] In an implementation of the first aspect, the respective transfer responses of the respective subunit cells include an amplitude response and a phase response of the respective subunit cells.

[0046] Considering the amplitude response in addition to the phase response allows for the realization of improved metasurfaces compared to metasurfaces designed using conventional design methods.

[0047] In an implementation of the first aspect, the desired transfer response of the corresponding subunit cell includes an amplitude response of 1 and a phase response equal to 2π divided by the number of unit cells covering a 2π phase shift.

[0048] In an implementation of the first aspect, the design error includes an error caused by design inconsistency and an error caused by a two-dimensional periodic structure of unit cells of a unit cell group having the same phase response for design assumptions.

[0049] For example, design errors may include errors due to design inconsistencies and errors due to the design assumption of a two-dimensional periodic structure of unit cells with the same phase response. The assumption may be that all unit cells are identical to the designed unit cells, which may lead to errors.

[0050] In an implementation of the first aspect, the metasurface includes a plurality of unit cell groups.

[0051] In other words, the metasurface includes multiple super units, i.e., multiple super units. That is, when designing a metasurface, multiple such unit cell groups (i.e., multiple super units) can be considered, and therefore, the unit cell groups (i.e., super units) can be repeated in the metasurface. The number of unit cell groups (i.e., the number of super units) in the metasurface considered when designing the metasurface can be referred to as the super-super unit size. That is, when the super-super unit size of the metasurface is 1, only this group (i.e., one group) of unit cells is considered; when the super-super unit size of the metasurface is 2, two unit cell groups are considered, and so on.

[0052] Increasing the number of unit cell groups (i.e., the number of supercells) considered when designing a metasurface to more than one (i.e., to two or more) allows increasing the power of the desired reflection angle of an electromagnetic wave incident on the metasurface and allows reducing the mirror direction as well as reducing the mirror reflection angle.

[0053] In order to realize the metasurface according to the first aspect of the present disclosure, part or all of the implementation methods and optional features of the above-mentioned first aspect may be combined with each other.

[0054] A second aspect of the present disclosure provides an antenna system, which includes the metasurface according to the first aspect of the present disclosure.

[0055] The antenna system may include one or more antennas. The one or more antennas may be configured to transmit electromagnetic waves to the metasurface and / or receive electromagnetic waves from the metasurface. In other words, the metasurface may be configured to modulate electromagnetic waves transmitted by the one or more antennas and / or received by the one or more antennas.

[0056] The metasurface may be configured to perform beam pointing of electromagnetic waves incident on the metasurface. One or more antennas and the metasurface may be arranged so that electromagnetic waves emitted by one or more antennas are incident on the metasurface. Additionally or alternatively, one or more antennas and the metasurface may be arranged so that: electromagnetic waves destined for (e.g., emitted to) one or more antennas are incident on the metasurface. In other words, one or more antennas may be configured to emit and / or receive electromagnetic waves via the metasurface. That is, the metasurface may be configured to modulate electromagnetic waves emitted by one or more antennas and / or electromagnetic waves received by one or more antennas.

[0057] The description of the antenna system of the second aspect, for example, the description of the metasurface, may be correspondingly valid for the metasurface according to the first aspect of the present disclosure.

[0058] The antenna system of the second aspect and its implementation and optional features achieve the same advantages as the metasurface of the first aspect and its corresponding implementation and corresponding optional features.

[0059] In order to implement the antenna system according to the second aspect of the present disclosure, part or all of the implementations and optional features of the above-mentioned second aspect may be combined with each other.

[0060] A third aspect of the present disclosure provides a method for designing a metasurface for electromagnetic waves, wherein the method includes providing unit cells in the metasurface, wherein each of the unit cells has a unique phase response and includes multiple independent scatterers.

[0061] The description of the metasurface of the first aspect is correspondingly valid for the method of the third aspect.

[0062] In an implementation of the third aspect, the method includes: arranging a plurality of independent scatterers in a two-dimensional lattice.

[0063] In an implementation of the third aspect, the method includes: dividing each unit cell in the unit cell into sub-unit cells, each sub-unit cell includes one or more independent scatterers among a plurality of independent scatterers, wherein the phase response of the sub-unit cells of the unit cell converges to the phase response of the unit cell.

[0064] In an implementation of the third aspect, the method includes: arranging multiple independent scatterers of each unit cell in a unit cell in a two-dimensional lattice, and dividing the unit cell into sub-unit cells, so that each sub-unit cell includes rows and / or columns of one or more independent scatterers among the multiple independent scatterers.

[0065] In an implementation of the third aspect, the method includes: dividing each unit cell in the unit cells into sub-unit cells, so that the number of sub-unit cells is equal to the number of multiple independent scatterers, and each sub-unit cell in the sub-unit cells includes a corresponding independent scatterer in the multiple independent scatterers.

[0066] In an implementation of the third aspect, the method includes providing a unit cell group in the unit cell, wherein the unit cells in the unit cell group cover a 2π phase shift and are arranged next to each other.

[0067] In an implementation of the third aspect, the method includes: providing a unit cell group, the unit cell group including 2 of the unit cells B unit cells, the group of 2 B The unit cells are arranged next to each other, and B is an integer greater than or equal to 1.

[0068] In an implementation of the third aspect, the unit cell group includes a one-dimensional arrangement of sub-unit cells. The method may include: designing the sub-unit cells of the unit cell group to achieve a desired transfer response, so that: a difference between the achieved transfer response of the sub-unit cell and the desired transfer response of the sub-unit cell caused by a design error is at least partially compensated by a difference between the desired transfer response of a second sub-unit cell immediately preceding the sub-unit cell and the achieved transfer response of the second sub-unit cell.

[0069] In an implementation of the third aspect, the method includes: at least partially compensating for the difference between the realized transfer response of the sub-unit unit and the expected transfer response of the sub-unit unit caused by a design error by adding the difference between the expected transfer response of the second sub-unit unit and the realized transfer response of the second sub-unit unit to the expected transfer response of the sub-unit unit.

[0070] In an implementation of the third aspect, the unit cell group includes a two-dimensional arrangement of sub-unit cells. The method may include: designing the sub-unit cells of the unit cell group to achieve a desired transfer response, such that: a difference between the achieved transfer response of the sub-unit cell caused by the design error and the desired transfer response of the sub-unit cell is at least partially compensated by:

[0071] - a difference between a desired transfer response of a second subunit cell immediately preceding the subunit cell in the first dimension and the achieved transfer response of the second subunit cell,

[0072] - a difference between a desired transfer response of a third subunit cell immediately preceding the subunit cell in the second dimension and the achieved transfer response of the third subunit cell.

[0073] It can be assumed that the first dimension represents the same row and the second dimension represents the same column. These differences can apply to the previous subunit cells in the same row and the same column.

[0074] In an implementation of the third aspect, the method includes: at least partially compensating for the difference between the achieved transfer response of the sub-unit unit and the expected transfer response of the sub-unit unit caused by a design error by adding an average value of the difference between the expected transfer response of the second sub-unit unit and the achieved transfer response of the second sub-unit unit and the difference between the expected transfer response of the third sub-unit unit and the achieved transfer response of the third sub-unit unit to the expected transfer response of the sub-unit unit.

[0075] In an implementation of the third aspect, the method includes designing an achieved transfer response of the subunit cell to achieve a desired transfer response of the subunit cell using information about design errors and information about mutual coupling of subunit cells of the unit cell group.

[0076] In an implementation of the third aspect, the respective transfer responses of the respective sub-unit cells include an amplitude response and a phase response of the respective sub-unit cells.

[0077] In an implementation of the third aspect, the desired transfer response of the corresponding subunit cell includes an amplitude response of 1 and a phase response equal to 2π divided by the number of unit cells covering the 2π phase shift.

[0078] In an implementation of the third aspect, the design error includes an error caused by design inconsistency and an error caused by a two-dimensional periodic structure of unit cells of a unit cell group having the same phase response for design assumptions.

[0079] In an implementation of the third aspect, the method includes designing a metasurface by considering a plurality of unit cell groups.

[0080] That is, the method may include designing a metasurface by considering a plurality of supercells.

[0081] The method of the third aspect and its implementation and optional features achieve the same advantages as the metasurface of the first aspect and its corresponding implementation and corresponding optional features.

[0082] In order to implement the method according to the third aspect of the present disclosure, part or all of the implementations and optional features of the third aspect described above may be combined with each other.

[0083] A fourth aspect of the present disclosure provides a computer program, which includes instructions. When the program is executed by a computer, the instructions enable the computer to execute the method according to the third aspect of the present disclosure or any implementation thereof.

[0084] In other words, a computer program is provided, the computer program comprising program code, which, when implemented on a processor, executes the method according to the third aspect of the present disclosure or any implementation thereof.

[0085] A fifth aspect of the present disclosure provides a computer-readable storage medium, which includes instructions. When the instructions are executed by a computer, the computer executes the method described in the third aspect of the present disclosure or any implementation thereof.

[0086] In other words, a computer-readable storage medium storing an executable program code is provided, and when the executable program code is executed by a processor, the method according to the third aspect or any implementation thereof is executed.

[0087] A sixth aspect of the present disclosure provides a computer, comprising a memory and a processor, wherein the memory and the processor are configured to store and execute program code to perform the method according to the third aspect or any implementation thereof.

[0088] A seventh aspect of the present disclosure provides a non-transitory storage medium, which stores executable program code. When the executable program code is executed by a processor, the method described in the third aspect or any implementation thereof is executed.

[0089] The computer program according to the fourth aspect, the computer-readable storage medium according to the fifth aspect, the computer according to the sixth aspect, and the non-transitory storage medium according to the seventh aspect respectively achieve the same advantages as the metasurface described in the first aspect and its corresponding implementation methods and corresponding optional features.

[0090] It should be noted that all devices, elements, units and devices described in this application can be implemented in software or hardware elements or any type of combination thereof. All steps performed by various entities described in this application and functions described as being performed by various entities are intended to represent that the corresponding entity is suitable for or configured to perform the corresponding steps and functions. Although in the description of the following specific embodiments, the specific functions or steps to be performed by the external entity are not reflected in the description of the specific detailed elements of the entity performing the specific steps or functions, it should be clear to the technician that these methods and functions can be implemented by corresponding software or hardware elements or any combination thereof. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] The above-mentioned various aspects and their implementation methods will be explained in the following description of specific embodiments in conjunction with the accompanying drawings, in which:

[0092] Figure 1 An example of a metasurface according to an embodiment of the present disclosure is shown;

[0093] Figure 2 An example of a method for designing a metasurface according to an embodiment of the present disclosure is shown;

[0094] Figure 3 An example of a metasurface according to an embodiment of the present disclosure is shown;

[0095] Figure 4 An example of a subunit cell of a group of unit cells covering a 2π phase shift of a metasurface according to an embodiment of the present disclosure is shown, wherein beam steering in one dimension is assumed;

[0096] Figure 5 An example of a method for designing a metasurface according to an embodiment of the present disclosure is shown, wherein beam pointing in one dimension is assumed;

[0097] Figure 6 An example of a subunit cell of a unit cell group covering a 2π phase shift (i.e., covering a 2π phase change in its phase response) in a metasurface according to an embodiment of the present disclosure is shown, wherein beam steering in two dimensions is assumed;

[0098] Figure 7 An example of a method for designing a metasurface according to an embodiment of the present disclosure is shown, wherein beam pointing in two dimensions is assumed;

[0099] Figure 8 and Fig. 9 The normalized power patterns of four different examples of the metasurface according to the embodiments of the present disclosure in the spatial angle domain are shown respectively;

[0100] Fig.10 and Fig.11Examples of metasurfaces according to embodiments of the present disclosure are shown respectively.

[0101] In the figures, corresponding elements are marked with the same reference numerals. DETAILED DESCRIPTION

[0102] Figure 1 An example of a metasurface according to an embodiment of the present disclosure is shown. Figure 1 The metasurface of is an example of a metasurface according to the first aspect of the present disclosure. The description of the metasurface according to the first aspect is for Figure 1 The metasurface is correspondingly effective.

[0103] Figure 1 The metasurface 1 is a metasurface for electromagnetic waves. The metasurface 1 includes a unit cell 2 (in Figure 1 In the figure, only one of the unit cells 2 is shown. Each of the unit cells 2 has a unique phase response and includes a plurality of independent scatterers 3. Figure 1 As shown, each unit cell 2 includes k independent scatterers 31 to 3 k , where k is an integer greater than or equal to 2 (k≥2).

[0104] The multiple independent scatterers 3 of each unit cell 2 allow for spatial oversampling for designing the metasurface 1. This improves the design of the metasurface 1, thereby improving the metasurface 1. The spatial oversampling allows for compensation of errors introduced during the design process of the metasurface 1, thereby improving the metasurface 1 resulting from the design process. More details about the metasurface 1 are described with reference to other figures, for example, Figure 3 , Fig.10 and Fig.11 .

[0105] Figure 1 The metasurface 1 may be part of an antenna system. For more details about such an antenna system, reference is made to the description of the antenna system according to the second aspect of the present disclosure.

[0106] Figure 2 An example of a method for designing a metasurface according to an embodiment of the present disclosure is shown. Figure 2 The method is an example of the method according to the third aspect of the present disclosure. The description of the method according to the third aspect is for Figure 2 The method is accordingly effective.

[0107] like Figure 2As shown, a method for designing a metasurface includes providing a unit cell in the metasurface, wherein each of the unit cells has a unique phase response and includes a plurality of independent scatterers. For example, in a unit cell group in a unit cell of the metasurface, the unit cell may cover a 2π phase shift, wherein each of the unit cells in the unit cell group may have a unique phase response. The above-mentioned unit cell group (covering a 2π phase shift) may form a super cell of the metasurface, i.e., may be referred to as a "super cell". In the metasurface, the above-mentioned unit cell group (i.e., a super cell) may be repeated. Therefore, in two or more super cells of the metasurface, there may be corresponding unit cells having the same unique phase response. The repetition of the super cell, i.e., the repetition of the unit cell group covering a 2π phase shift, may be periodic. This is Figure 2 is shown as step S1 of the method. Therefore, Figure 2 The method can be used to design Figure 1 Metasurface 1. More details about the method for designing a metasurface are described with reference to other figures, for example, Figure 4 , Figure 5 , Figure 6 and Figure 7 .

[0108] Figure 3 An example of a metasurface according to an embodiment of the present disclosure is shown. Figure 3 The metasurface 1 is Figure 1 Example of metasurface 1. Therefore, Figure 1 Description of Figure 3 The metasurface 1 is effective, and additional optional features are mainly described below.

[0109] Figure 3 A plurality of unit cells 2 of the metasurface 1 are shown. Figure 3 , showing in detail the three unit cells 21, 22 and 2 n The number of unit cells is only an example and does not limit the present disclosure. Each of the unit cells 2 of the metasurface 1 includes a plurality of independent scatterers 3 . Figure 3 The number of multiple independent scatterers 3 of each unit cell 2 shown in the figure is only an example and does not limit the present disclosure. The phase response of the unit cell 2 of the metasurface 1 conforms to Snell's law. That is, the independent scatterers 3 of each unit cell 2 have the same phase response or contribute to the unique phase response of the unit cell 2 together.

[0110] like Figure 3As shown, the plurality of independent scatterers 3 of the corresponding unit cell 2 can be arranged in a two-dimensional lattice. a independent scatterers 3 can have m columns, or m independent scatterers 3 can have a rows, where m and a are both integers greater than or equal to 2 (m≥2, a≥2). In other words, m is the number of columns of the independent scatterers 3 in the unit cell 2, and a is the number of rows of the independent scatterers 3 in the unit cell 2.

[0111] The multiple scatterers 3 of the unit cell 2 of the metasurface 1 are independent. Figure 3 The corresponding surface currents i are independent of each other. nam Optionally, at least two of the unit cells 2 of the metasurface 1 may have different numbers of independent scatterers 3 .

[0112] Figure 1 The metasurface 1 and Figure 3 The following applies to all metasurfaces 1. Each unit cell in the unit cell 2 can be divided into sub-unit cells, each sub-unit cell includes one or more independent scatterers in the plurality of independent scatterers 3, and the phase response of the sub-unit cells of the unit cell converges to the phase response of the unit cell ( Figure 1 and Figure 3 In other words, the multiple independent scatterers 3 of each unit cell 2 of the metasurface allow each unit cell in the unit cell 2 of the metasurface 1 to be divided into sub-unit cells, each sub-unit cell including at least one independent scatterer from the multiple independent scatterers 3, wherein the phase response of the sub-unit cell of the unit cell converges to the phase response of the unit cell. Optionally, each unit cell in the unit cell 2 can be divided into sub-unit cells, which have the same phase response as the unit cell and include at least one scatterer from the multiple independent scatterers 3 of the unit cell.

[0113] In order to design the unit cell 2 of the metasurface 1, the following three main assumptions based on different metasurface models and criteria can be satisfied. For example, the phase gradient (phase change) between the unit cells 2 of the metasurface 1 conforms to Snell's law, which stipulates that each unit cell in the unit cell 2 has a unique phase response. This criterion produces the following situation, that is, the independent scatterers 3 of the unit cell 2 have the same phase response or contribute to a unique phase response together.

[0114] When designing the metasurface 1, the metasurface 1 can be regarded as a uniform medium for incident electromagnetic waves incident on the metasurface 1. In this case, the following conditions are satisfied:

[0115]

[0116] In the above formula, U crepresents the size of the unit cell, n1 and n2 are the lossless refractive indices of the two half-spaces on both sides of the metasurface. Metasurface 1 can be a sub-wavelength thin periodic structure. Angle "θ i ” is the incident angle of the normal vector of the metasurface plane. The term “n 1,2 " represents the reflected diffraction order n1 of the incident electromagnetic wave and the transmitted diffraction order n2 of the incident electromagnetic wave.

[0117] Therefore, in a unit cell 2 of a metasurface 1 including a plurality of independent scatterers 3, there is more than one received signal sample (when the signal is received in the form of an electromagnetic wave incident on the metasurface) in the same aperture size of the unit cell 2. This means that the received signal can be oversampled using at least twice the spatial sampling rate compared to a conventional metasurface (i.e., a metasurface in which each unit cell includes only one independent scatterer). This oversampling depends on the density ratio Dr of the unit cells 2 of the metasurface 1, wherein the density ratio Dr of the unit cells in the unit cell 2 defines the number of sub-unit cells in the unit cell 2. That is, the greater the density ratio Dr of the unit cells, the greater the number of sub-unit cells, and vice versa. Therefore, each sub-unit cell of the unit cell 2 of the metasurface 1 can be interpreted as a quantizer, by which the received signal should be quantized into a desired reflection signal and / or transmission signal according to its transfer function.

[0118] Providing multiple independent scatterers 3 for each unit cell 2 of the metasurface 1 can be called a dense unit cell concept. That is, due to the dense unit cell concept, each unit cell in the unit cell 2 of the metasurface 1 includes multiple independent scatterers 3. The dense unit cell concept (i.e., each unit cell includes multiple independent scatterers 3) brings two improvements: the uniformity of the metasurface 1 can be estimated more accurately. Another improvement of the dense unit cell concept is the possible spatial oversampling of the received signal, which can reduce the quantization error by faster spatial sampling than Nyquist. The unit cell including multiple independent scatterers can be called a "dense unit cell".

[0119] Optionally, in order to design a metasurface 1 in which each unit cell 2 includes multiple independent scatterers, the Delta-Sigma concept can be used in time signal processing to spatially oversample the metasurface. In time domain signal processing that can be used for analog-to-digital converters, oversampling may cause quantization errors to appear at a higher frequency related to the sample center frequency. Therefore, the relevant bandwidth can be retrieved by filtering with a low-pass filter. In this way, unwanted noise can be omitted. A similar concept is used in the spatial domain to design the metasurface 1, allowing beams to be formed in the metasurface by Delta-Sigma oversampling, thereby limiting the unwanted noise to the invisible radiation region in the k-space or spatial angle domain. The above-mentioned use of the Delta-Sigma concept in spatial oversampling to design the metasurface 1 allows the mutual coupling between unit cells that each include multiple independent scatterers, such as the mutual coupling between sub-unit cells. Mutual coupling increases with the increase of the density ratio Dr of the unit cells of the metasurface. Mutual coupling may limit the improvement of the accuracy and efficiency of the beam pattern.

[0120] Furthermore, based on the conventional design (modeling) of metasurfaces using the Floquet-Bloch theorem (FB theorem), the design process may not have intrinsic errors because the FB theorem finds the unit cell response of unit cell 2 of metasurface 1 by assuming a periodic structure with identical unit cells. However, this assumption may not hold true due to the different interactions of each unit cell with the incident electromagnetic wave (when the electromagnetic wave is incident on metasurface 1). This mismatch between the designed unit cells and their actual responses may result in errors in the response of metasurface 1, which generally affects the performance and efficiency of metasurface 1. Furthermore, in conventional design methods for designing metasurfaces, for example, in metasurfaces with non-periodic unit cells, the mutual response of the unit cells cannot be correctly estimated when the unit cells vary very drastically. Since this mutual response of different unit cells is ignored in conventional methods or is assumed to be a constant value based on the FB theorem, this mutual response may add another error to the final design. The above-mentioned use of the Delta-Sigma concept in spatial oversampling to design metasurfaces can offset the above-mentioned errors. Reference Figures 4 to 7 This is described in detail, where Figure 4 and Figure 5 In the example of , assuming that only one dimension of the subunit cell of the metasurface is used to design the metasurface, Figure 6 and Figure 7 In the example of FIG. 5 , it is assumed that two dimensions of the subunit cells of the metasurface are used to design the metasurface.

[0121] In the following, the steps of designing a reflective metasurface are described with reference to an example of a method for designing a metasurface. This description is correspondingly valid for designing a transmissive metasurface. For the following description, reference is made to Figure 1 or Figure 3 metasurface. In addition, in the present disclosure, a unit cell including multiple independent scatterers may be referred to as a "dense unit cell". A unit cell group in a dense unit cell 2 of a metasurface 1 (each dense unit cell 2 includes multiple independent scatterers 3) may cover a 2π phase shift, wherein the unit cells of the group are arranged closely to each other. The expression "unit cell set" may be used as a synonym for the expression "unit cell group". A unit cell group covering a 2π phase shift may be referred to as a "super cell". In the metasurface design, the number of dense unit cells in a super cell may be calculated by the desired number of bits (B). B may be an integer greater than or equal to 1. In a super cell, there may be 2 B dense unit cells. Each dense unit cell can be divided into sub-unit cells, where each sub-unit cell includes one or more independent scatterers of the multiple independent scatterers of the dense unit cell. That is, the sub-unit cell can divide the dense unit cell into a group of m smaller parts, where m is an integer greater than or equal to 2 (m≥2). Ideally, the sub-unit cells of the dense unit cell can have the same phase response. Therefore, each super unit of the metasurface 1 can include 2 B m sub-unit cells. The arrangement of the sub-unit cells may depend on the design requirements. In other words, the arrangement and topology of the sub-unit cells may be related to the beam pointing dimension (which may be one dimension or two dimensions) and the topology of multiple independent scatterers in the dense unit cells.

[0122] Assume a rectangular 2D lattice of multiple independent scatterers within the unit cell, such as Figure 3 As shown by way of example, the number of independent scatterers in a sub-unit cell may be "a", where the unit cell 2 may include m sub-unit cells. In other words, the unit cell 2 may include m sub-unit cells, where each sub-unit cell may include a independent scatterers, where a and m are integers greater than or equal to 2 (a≥2, m≥2). Therefore, according to Figure 1 or Figure 3 The supercell of the metasurface can have a·m·2 B In a traditional metasurface, each unit cell contains only one independent scatterer, and there may be only 2 scatterers in the supercell. Bscatterers. Based on this, the density ratio Dr of a unit cell (i.e., a dense unit cell) including multiple independent scatterers can be defined as the number of sub-unit cells in the unit cell (i.e., a dense unit cell). In order to achieve appropriate reflection or refraction in the metasurface, the unit cells forming the super cell cover a 2π phase shift (2π phase change), and the phase gradient in the super cell conforms to the generalized Snell's law (GSL), as shown below:

[0123]

[0124] In the above formula, the term "n i ” and “n r ” are the refractive indices of the input and output media, respectively, and the term “θ i ” and “θ r ” are the propagation angles of the incident and refracted electromagnetic waves when the electromagnetic wave is incident on the metasurface. For example, in the reflection working mode in free space (i.e., there is free space on both sides of the metasurface), the term “n i ” and “n r ” is the refractive index of air (n i =n r =1).

[0125] Assume one-dimensional beam pointing, such as Figure 4 By way of example, only the phase change in the plane parallel to the beam pointing plane may be of interest, and therefore the subunit cells in the unit cell may be selected as a columnar array of independent scatterers perpendicular to the plane. In this way, the number of columnar arrays in the unit cell may determine the density ratio of the design. According to the generalized Snell's law, it may be assumed that each of the above subunit cells has the same response. Optionally, this means that, ideally, each of the above subunit cells has an amplitude response close to or equal to 1 and a phase response that complies with the generalized Snell's law. The ideal response is given by the term "g" in the following formula: n "express:

[0126]

[0127] In the above formula, the term "g n ” is the ideal transfer response of the unit cell. Due to some errors in the design process of the metasurface, this is not its realized response. |g n | and g n are the ideal (expected) amplitude and phase of each subunit cell, respectively. represents the initial phase in the first sub-unit cell of the sub-unit cell of the unit cell. B” This expression refers to the number of unit cells in the supercell, that is, the number of unit cells in the metasurface that cover a 2π phase shift.

[0128] As mentioned above, there may be some errors in the design process. For example, the designed unit cell may not be completely in line with the requirements, and the amplitude response and phase response of the unit cell may be slightly inconsistent with the ideal transfer response of the designed (expected) unit cell. The numerical analysis used in the design process can treat the incident electromagnetic wave (when the electromagnetic wave is incident on the metasurface) as a completely plane wave. This means that waves with arbitrary wavefronts are not estimated. Using the dense unit cell concept, the mutual response of the sub-unit cells in the super cell of the metasurface may increase.

[0129] To address these issues, the present disclosure proposes a design approach that can control errors and allow the design of unit cells based on these main criteria, including their amplitude response, phase response, mutual response, and ultimately the overall performance of the metasurface, rather than just based on their phase response. The techniques proposed below can design metasurfaces based on the mentioned criteria and combine the criteria to optimize the results. For example, since the unit cell includes multiple independent scatterers, the above-mentioned Delta-Sigma concept helps to optimize the design method that can be based on spatial oversampling of the unit cell.

[0130] Figure 4 An example of a sub-unit cell of a group of unit cells covering a 2π phase shift of a metasurface when beam steering is assumed in one dimension according to an embodiment of the present disclosure is shown.

[0131] exist Figure 4 In FIG. 4 , a subunit cell 4 of a unit cell of a metasurface (i.e., a subunit cell 4 of a supercell) is shown, wherein the unit cells form a unit cell group covering a 2π phase shift, wherein it is assumed that the design is performed with reference to one dimension. In the following, a unit cell group covering a 2π phase shift is referred to as a supercell. Figure 4 , for the subunit cells of the unit cell 2 in the unit cell group covering the 2π phase shift, subunit cells 41, 42 and 4 N , wherein the unit cells of the group are arranged next to each other, and thus the above sub-unit cells are arranged next to each other. The number of sub-unit cells is only an example and does not limit the present disclosure. In the unit cell group covering a 2π phase shift, there may be N=2 B Dr subunits, of which 2 B is the number of unit cells in the unit cell group covering the 2π phase shift (B is an integer greater than or equal to 1, B≥1), and Dr is the density ratio of the unit cells in the unit cell of the metasurface, which defines the number of sub-unit cells in the unit cell.

[0132] Figure 4 The example shows that when an electromagnetic wave is incident on the metasurface and thus incident on Figure 4 The incident electromagnetic wave 5a of the subunit cell 4 of the supercell is shown as an example. In addition, the corresponding reflected electromagnetic wave 5b reflected from the metasurface is shown. i ” and “θ r ” represent the propagation angles of the incident beam 5a and the refracted beam 5b respectively.

[0133] Figure 4 The bottom shows each subunit cell 41, 42, ... 4 of the super unit. N The realized reflection coefficients V1, V2...V N The reflection coefficient can be between 0 and 1 (0 ≤ V n ≤1). The x-axis is the index n of the subunit cell 4 of the super unit, where n is greater than or equal to 1 and less than or equal to N=2 B ·Dr. The y-axis is the transfer response (TR).

[0134] To achieve Figure 4 The example of the reflection coefficient of the subunit cell 4 of the supercell shown can be implemented Figure 5 Methods for designing metasurfaces.

[0135] Figure 5 An example of a method for designing a metasurface when beam pointing in one dimension is assumed according to an embodiment of the present disclosure is shown. Figure 5 Description, reference Figure 4 The supercell is a unit cell group in the unit cell of the metasurface covered with a 2π phase shift. Figure 5 In the drawings, the abbreviation “TR” stands for “Transfer Response”, the abbreviation “MR” stands for “Mutually Response”, and the abbreviation “SUC” stands for “Sub-Unit Cell”.

[0136] Figure 5 The method is based on a recursive design algorithm based on the Delta-Sigma concept. In this algorithm, the goal is to transform the desired transfer response g of the subunit cell 4 of the super unit cell into n Converted into an optimized series of complex transfer responses V n (i.e., realize the transfer response), complex transfer response V n The calculation is to minimize the error. Figure 5 In the algorithm diagram, g n represents the input series of the ideal desired transfer response of the subunit cell as a supercell. In addition, W n The series is the transfer response of the subunit cell 4 during the design process (i.e., the design transfer response), Vn The series is the realized transfer response of the subunit cell 4, which can take into account the inconsistency of the subunit cell 4 due to the supercell. i and the mutual response of the subunit cell 4 of the supercell s The error caused by Figure 5 In, S n The series is the result of numerically modeling the design using the Floquet-Bloch theorem. As can be seen from the figure, there is a Delta process and a Sigma process at each stage of the algorithm.

[0137] The delta process transfers the response g from the expectation n Subtract the subunit cell 4 from the subunit cell of the supercell n The implementation passes the response V n , to calculate the nth subunit cell 4 n The error in e n The Sigma process converts the error e n Add to the next expected delivery response g n+1 Up, g n+1 Represents the adjacent subunit cell 4 n+1 , that is, the transfer response of the n+1th subunit cell.

[0138] in other words, Figure 5 The approach for designing metasurfaces assumes a supercell, i.e. a group of unit cells covering a 2π phase shift, comprising a one-dimensional arrangement of subunit cells. Figure 5 The method comprises: designing a sub-unit cell of a unit cell group (ie, a super unit cell) 4 n To achieve the desired delivery response g n , so that: due to design error caused by the sub-unit unit 4 n The implementation passes the response V n With subunit unit 4 n The expected delivery response g n The difference between n The second subunit unit 4 in front n–1 The expected delivery response g n–1 With the second subunit unit 4 n–1 The implementation passes the response V n–1 The difference between n–1 Compensation. With reference to this point, Figure 5 The method comprises: placing the second subunit unit 4 n–1 The expected delivery response g n–1 With the second subunit unit 4 n–1 The implementation passes the response V n–1 The difference between the two is added to subunit cell 4n The expected delivery response g n to at least partially compensate for the sub-unit cell 4 caused by design errors. n The implementation passes the response V n With subunit unit 4 n The expected delivery response g n The difference between.

[0139] like Figure 5 As shown, subunit unit 4 n The implementation passes the response V n Designed to use information about design errors and information about the mutual coupling of sub-unit cells of a unit cell group (ie, super cell) to realize sub-unit cell 4 n The expected delivery response g n The corresponding subunit cell 4 n The desired transfer response may include an amplitude response of 1 and an amplitude response equal to 2π divided by the number of unit cells covering a 2π phase shift (i.e., 2 B ) (i.e., the number of unit cells in the supercell). Design errors can include errors due to design inconsistencies. i(n) and the error e caused by the two-dimensional periodic structure of the unit cells of the unit cell group assuming the same phase response for the design S(n) That is, the error e S(n) is caused by the use of the Floquet-Bloch theorem to numerically model the design.

[0140] therefore, Figure 5 The algorithm used in the method for designing metasurfaces allows the design process to take into account the inconsistencies arising from imperfect subunit cell design and modeling inefficiencies (due to the use of the Floquet-Bloch theorem) and compensate for them through negative feedback. As can be seen from the algorithm, the mutual responses originating from other neighboring subunit cells are mitigated by the process. As mentioned above, the generalized Snell's law (GSL) stipulates that all subunit cells in a unit cell with multiple independent scatterers (i.e., a dense unit cell) can have the same transfer response, and they can all have the same desired transfer response g n The sub-unit cells in a unit cell may collectively contribute to a unique phase response of the unit cell.

[0141] Figure 5 The Delta and Sigma processes of the algorithm can be vector operations so that they can control both amplitude and phase. Figure 5 As shown, when considering design errors (e.g., errors caused by design inconsistencies) i(n)and the error e caused by the two-dimensional periodic structure of the unit cells of the unit cell group assuming the same phase response for the design S(n) ) before the nth subunit cell 4 n The output W of the Sigma process n can be considered as the nth subunit cell 4 n After the update, the expected delivery response is expected. At this stage, based on W n The designer of the metasurface will come up with a physical structure that can produce the same n The closest possible transfer response. This can be done according to traditional methods for designing metasurfaces.

[0142] Next, the nth subunit cell 4 can be calculated using conventional design methods based on Floquet-Bloch theory n The delivery response to obtain S n In order to consider the correct mutual response, the influence of this error can be eliminated, which is done in the mutual response correction stage (for the nth subunit cell 4 n ,exist Figure 5 ) is completed. Next, Figure 5 The algorithm can be obtained by adding the correct mutual response to S n Let's calculate the nth subunit unit 4 n The implementation response V n This process is Figure 5 The algorithm is shown in the figure as "Response Correction". For the nth subunit cell 4 n , the final value of the transfer response (i.e. the achieved transfer response) is V n , which is the nth subunit cell 4 n The actual behavior of the interaction with the incident electromagnetic wave. For the next stage (i.e. the n+1th subunit cell 4 n+1 ), from the nth subunit cell 4 n The expected delivery response g n Subtract the nth subunit cell 4 from n Implementation of V n , and the result e n (is the error) is added to the next sub-unit unit (i.e., the n+1th sub-unit unit 4 n+1 )'s expected delivery response g n+1 The above-mentioned n-th subunit unit 4 nThe steps of step 1 can be continued for at least one supercell. Optionally, for better performance, the algorithm can be continued for a larger number of supercells. To compare the effect of this, the beam pattern of the reflected wave can be modeled. After the beam pattern is calculated, the error between the design beam pattern and the desired beam pattern determines the appropriate number of supercells for achieving better performance. More details on this will be provided in conjunction with Fig.11 Give a description.

[0143] exist Figure 5 The algorithmic stage of the method for designing metasurfaces can be written to achieve the transfer response V n–1 As follows: V n–1 =g n–1 +e n–1 In the next stage, the transfer response V n As follows: V n =g n +g n–1 –V n–1 +e n . Replace V in the above formula n–1 , the next stage of implementation transfers the response V n It can be written as: n =g n +g n–1 –g n–1 –e n +e n+1 From the above formula, it can be seen that the errors generated in adjacent stages of the algorithm are subtracted from each other so that they compensate each other. In other words, the error e caused by the design process i(n) and e S(n) Subunit cell 4 n The realization transfer response V of (nth subunit cell) n With subunit unit 4 n The expected delivery response g n The difference between n , may be at least partially formed by the subunit cell 4 immediately adjacent to the n The expected transfer response g of the second subunit cell (n–1th subunit cell) n–1 The second subunit cell realizes the transfer response V n–1 The difference between n–1 Make compensation.

[0144] As described above, this can be achieved through the Delta-Sigma concept, which allows the error to be shaped without using more accurate sub-unit cells or increasing the number of unit cells (reducing the phase gradient of the unit cell). Since the unit cell 2 of the metasurface 1 includes multiple independent scatterers, that is, they are dense unit cells, the Delta-Sigma concept can be used. In contrast, conventional metasurfaces have unit cells, each of which includes only one independent scatterer, and conventional methods for designing metasurfaces do not use the Delta-Sigma concept. The above-mentioned algorithm for one-dimensional beam pointing can also be applied to two-dimensional beam pointing. That is, the Delta-Sigma concept for designing metasurfaces can be applied to two-dimensional beam pointing. This point will be combined below. Figure 6 and Figure 7 Give a description.

[0145] Figure 6 An example of a sub-unit cell of a unit cell group covering a 2π phase shift (ie, covering a 2π phase change in the phase response) in a metasurface when beam pointing in two dimensions is assumed according to an embodiment of the present disclosure is shown. Figure 6 Corresponds to Figure 4 , among which, according to Figure 6 , a metasurface is designed considering a two-dimensional arrangement of subunit cells covering a group of unit cells (i.e., a supercell) with a 2π phase shift. Figure 4 Description of Figure 6 The additional optional features or differences are correspondingly valid and are mainly described below.

[0146] like Figure 6 As shown, for two-dimensional beam pointing, the super unit can have a two-dimensional phase gradient (PG) according to the desired reflection angle. These phase gradients PG are Figure 6 , and can be calculated using the generalized Snell's law (GSL) respectively. According to the GSL formula, the number of subunit cells of the supercell in the x-direction and the y-direction can be obtained respectively. This allows the formation of a two-dimensional supercell. The transfer response sampling can be performed as a two-dimensional weight matrix, such as Figure 6 The process of generating response samples can be composed of three stages: obtaining the horizontal response sample (RS) of the first row of the two-dimensional super unit; obtaining the vertical response sample (RS) of the first column of the two-dimensional super unit; according to the Delta-Sigma concept, calculating the individual response samples of the sub-unit cells of the super unit based on the two-dimensional algorithm (assuming a two-dimensional arrangement of the sub-unit cells), as shown in Figure 7 As shown. Figure 6In the embodiment, different subunit cells 4 of the super unit are numbered with indexes "q" and "p", where "q" is the index of the y-axis and "p" is the index of the x-axis. Each of the indexes "q" and "p" may be greater than or equal to 1 and less than or equal to 2. B Dr, where, in each direction of the two-dimensional arrangement, 2 B is the number of unit cells in the unit cell group covering the 2π phase shift (B is an integer greater than or equal to 1, B≥1), and Dr is the density ratio of the unit cells in the unit cell of the metasurface, which defines the number of sub-unit cells in the unit cell.

[0147] Figure 6 Each subunit cell of the supercell is shown on the right 11 , 4 12 ……4 QP The realized reflection coefficient V 11 、V 12 ……V qp To achieve Figure 6 The example of the reflection coefficient of the subunit cell 4 of the supercell shown can be implemented Figure 7 Methods for designing metasurfaces.

[0148] Figure 7 An example of a method for designing a metasurface when beam steering in two dimensions is assumed according to an embodiment of the present disclosure is shown. Figure 7 Corresponds to Figure 5 , among which, according to Figure 7 ,The 2D arrangement of sub-unit cells of a unit cell group is considered when designing the metasurface. Figure 5 Description of Figure 7 The additional optional features or differences are correspondingly valid and are mainly described below.

[0149] Because in Figure 5 The one-dimensional nature of the Delta-Sigma concept used in the algorithm, Figure 5 The one-dimensional algorithm can calculate the error caused by designing the metasurface in one dimension. Therefore, for a two-dimensional matrix (or lattice) of subunit cells, such as Figure 6 As shown, Figure 5 The algorithm can minimize the error in one direction. To apply the Delta-Sigma concept to the two-dimensional case, Figure 7 A two-dimensional algorithm is proposed in which similarly exploits Figure 5 One-dimensional Delta-Sigma concept. Figure 7 The two-dimensional algorithm considers the subunit cell 4 qp Start generating a sample response, where for the first row (same x-axis value) and first column (same y-axis value), you can use Figure 5 One-dimensional algorithm. Figure 6 and Figure 7 As shown, for the subunit cell 4 of the super unit qp , the two-dimensional algorithm can consider the previous adjacent neighboring units in two directions, that is, the previous adjacent adjacent sub-unit unit in the y direction 4 q–1,p (vertical neighbor) and the previous adjacent neighbor subunit cell 4 in the x direction q,p–1 (Horizontally adjacent). Figure 7 As shown, for the adjacent sub-unit cell 4 in the y direction q–1,p , the Delta process is from the previous adjacent sub-unit cell 4 in the y direction q–1,p The expected delivery response g (q–1)p Subtract the previous adjacent subunit cell 4 in the y direction q–1,p The implementation passes the response V (q–1)p , to calculate the previous adjacent subunit cell 4 in the y direction q–1,p The error in e (q–1)p Indicates. Figure 7 As shown, for the adjacent sub-unit cell 4 in the x direction q,p–1 , the Delta process is from the previous adjacent sub-unit cell in the x direction 4 q,p–1 The expected delivery response g q(p–1) Subtract the previous adjacent subunit cell 4 in the x direction q,p–1 The implementation passes the response V q(p–1) , to calculate the preceding adjacent subunit cell 4 in the x direction q,p–1 The error in e q(p–1) In other words, the two-dimensional algorithm can be used in the Delta process for the front neighbor unit cell 4 in the y direction q–1,p and the front neighbor unit cell 4 in the x direction q,p–1 Calculate the error e (q–1)p and e q(p–1) These errors e (q–1)p and e q(p–1) The average can be taken to provide the average error of the previous neighbor sub-unit cell in both directions as a common Delta output. Therefore, the common Delta output (i.e., the average error) includes the error e about the previous neighbor sub-unit cell in both directions. (q–1)p and e q(p–1) The Sigma process adds this average error, the common Delta output error, to the expected transfer response g. qp On the other hand, the expected delivery response g qp Represents subunit cell 4 q,pFrom this stage, the rest of the process is as follows Figure 5 The algorithm is outlined in 4 to generate subunit cells q,p The implementation passes the response V qp . All subunit cells in a two-dimensional arrangement (i.e., 4 q,p , where 1 <q,p≤2 B Dr) Repeat the above algorithm steps to define all response samples (RS) in one supercell for the desired reflection, i.e. the transmission response. All samples can be vectors and therefore contain amplitude and phase. This means that all operations can be vector operations.

[0150] In other words, Figure 7 As an example, for designing a metasurface, it can be assumed that a unit cell group (ie, a super cell) covering a 2π phase shift includes a two-dimensional arrangement of sub-unit cells. The method for designing a metasurface may include: designing a sub-unit cell of a unit cell group 4 q,p To achieve the desired delivery response g qp , so that: Subunit cell 4 caused by design error q,p The implementation passes the response V qp With subunit unit 4 q,p The expected delivery response g qp The difference between is at least partially compensated by:

[0151] - in the first dimension (eg, in the x-direction) next to the subunit cell 4 q,p The second subunit unit 4 in front q,p–1 The expected delivery response g q(p–1) With the second subunit unit 4 q,p–1 The implementation passes the response V q(p–1) The difference between q(p–1) ,

[0152] - in the second dimension (e.g., in the y direction) next to the subunit cell 4 q,p The third subunit unit 4 in front q–1,p The expected delivery response g (q–1)p With the third subunit unit 4 q–1,p The implementation passes the response V (q–1)p The difference between (q–1)p .

[0153] It can be assumed that the first dimension represents the same row and the second dimension represents the same column. These differences can apply to the previous subunit cells in the same row and the same column.

[0154] like Figure 7 As shown, the method includes: by placing the second sub-unit 4 q,p–1 The expected delivery response gq(p–1) With the second subunit unit 4 q,p–1 The implementation passes the response V q(p–1) The difference between q(p–1) and the third subunit cell 4 q–1,p The expected delivery response g (q–1)p With the third subunit unit 4 q–1,p The implementation passes the response V (q–1)p The difference between (q–1)p The average value is added to subunit cell 4 q,p The expected delivery response g qp to at least partially compensate for the sub-unit cell 4 caused by design errors. q,p The implementation passes the response V qp With subunit unit 4 q,p The expected delivery response g qp The difference between.

[0155] Reference Figure 7 , in order to analyze the performance of the two-dimensional algorithm, for W qp and V qp , the following relationship holds, where "W qp " indicates the sub-unit cell 4 in the design process q,p The transfer response, “V qp " indicates subunit cell 4 q,p The implementation delivers the response.

[0156]

[0157] By substituting the following relationship into the above equation for subunit cell 4 q,p The implementation passes the response V qp In the formula

[0158] V q(p-1) =g q(p-1) +e q(p-1)

[0159] V (q-1)p =g (q-1)p +e (q-1)q

[0160] About Subunit Unit 4 q,p The implementation passes the response V qp The formula can be simplified to:

[0161]

[0162] Use the formula for the normalized array factor with discrete weights V qp The power pattern of the two-dimensional periodic structure of the sub-unit cell of the supercell of the metasurface can be written as:

[0163]

[0164] In the above formula, the term “ψ x ” and “ψ y ” as summarized in the following formula:

[0165]

[0166] In the above formula, the terms "k0", "d x ” and “d y ” are the free space wave number, the size of the subunit cell in the x direction and the size of the subunit cell in the y direction, respectively. The reflection parameter “θ r "and Respectively relative to the z-axis (θ r ) and the x-axis The two-dimensional reflection angles are in the order Figure 6 shown.

[0167] The above sub-unit unit 4 q,p The implementation passes the response V qp Plugging the simplified formula of into the above formula for the normalized array factor, the actual radiation pattern can be retrieved as follows:

[0168]

[0169] In the above equation, the ideal pattern and the error pattern, which directly affect the performance of the metasurface, can be separated. Due to the inherent characteristics of the above Delta-Sigma concept, from the corresponding subunit cell 4 q,p The error in e qp Subtract the corresponding subunit unit 4 from q,p The front neighbor unit cell 4 q,p–1 and 4 q–1,p The average error in ), which is applicable to the Delta-Sigma concept. Delta-Sigma technology can shape the noise to the invisible radiation pattern area. As described above in conjunction with the one-dimensional Delta-Sigma algorithm, the results of the Delta-Sigma algorithm can be improved by considering more than one super unit, that is, considering sub-unit cells of two or more super units for the algorithm. This provides more samples for the algorithm, so it can converge to the optimal response asymptotically. Two-dimensional super-super cells can be used in the design of metasurfaces, where the two-dimensional super-super cell can be a basic periodic block including two or more super units (rather than one super unit).

[0170] As mentioned above Figure 4 , Figure 5 , Figure 6 and Figure 7 As shown and described, the Delta-Sigma algorithm for beamforming can determine the coefficients of each sub-unit cell based on the Delta-Sigma concept to mitigate the effects of mutual coupling in the metasurface. The Delta-Sigma algorithm can control the phase response and amplitude response to compensate for the errors and inconsistencies in the phase and amplitude of each sub-unit cell. Therefore, as described above with reference to Figure 4 , Figure 5 , Figure 6 and Figure 7 An exemplary description of the method for designing metasurfaces can push noise and unwanted power into the invisible radiation region, which significantly improves the efficiency of the metasurface.

[0171] Figure 8 and Fig. 9 The normalized power patterns in the spatial angle domain of four different examples of the metasurface according to the embodiments of the present disclosure are shown respectively.

[0172] In order to analyze the performance of the metasurface that can be produced by the method for designing a metasurface according to the present disclosure, as shown in FIG. Figure 4 , Figure 5 , Figure 6 and Figure 7 An exemplary description of Figure 8 Three different scenarios are compared in . That is, Figure 8 Three normalized power patterns of electromagnetic waves (e.g., beams) reflected from a metasurface under three different scenarios are shown. Figure 8 (a) shows the normalized power pattern for an ideal scenario, in which the unit cells of the metasurface radiate perfectly, the mutual coupling between the unit cells is neglected, and the unit cells reflect the incident normal electromagnetic wave at a desired reflection angle of 60 degrees. This is a scenario where each unit cell radiates exactly the required phase using only one independent scatterer (e.g., a metaatom) and the reflection coefficient is 1. This scenario is artificial (i.e., does not exist in real life). It describes a reflective metasurface with 100% efficiency and is merely a benchmark example for comparison purposes. Figure 8 (b) shows a scenario in which the power pattern of an electromagnetic wave incident on the metasurface is analyzed with one scatterer in each unit cell, which indicates a density ratio of 1 (Dr = 1), as shown in Figure 8 (a) is the case. However, in Figure 8 In the scenario of (b), the mutual coupling between unit cells and between scatterers is calculated and considered. Since the distance between scatterers may be less than half a wavelength based on the generalized Snell's law, the efficiency reduction is acceptable, such as Figure 8(b) This is the case with passive reflective metasurfaces in real life. This is one of the reasons why reflective metasurfaces are actually inefficient. Figure 8 In the third scenario shown in (c), the study Figure 8 (a) is a metasurface of the scenario, except that each unit cell of the metasurface includes two independent scatterers (i.e., the metasurface includes dense unit cells). In the third scenario, it is assumed that the density ratio is 2 (Dr=2), that is, each unit cell has two sub-unit cells, wherein each sub-unit cell includes a corresponding scatterer of the two independent scatterers of the unit cell, and the mutual coupling between the sub-unit cells and between the independent scatterers is considered. In addition, in the third scenario, discrete coefficients are assigned based on the Delta-Sigma technique to mitigate mutual coupling, as shown in FIG. Figures 4 to 7 In other words, Figure 8 (c) shows an example of a metasurface whose unit cell includes multiple independent scatterers, produced by an example of a method for designing a metasurface according to the present disclosure.

[0173] Figure 8 All power patterns of (a), (b), and (c) are normalized to Figure 8 (c) The maximum power of the scenario. Figure 8 The y-axis of the graphs is the normalized power pattern in dB, and the x-axis of these graphs is the spatial angle domain. The term "K" is the wave number, which is measured in radians per meter. It represents the spatial frequency of the electromagnetic wave. The term "K0" is the wave number or spatial frequency of the electromagnetic wave in free space and is usually considered a reference value for the wave number. The term "K x ” is the wave number of the surface electromagnetic wave in the metasurface structure in the x direction. For comparison purposes, the wave number in different materials is optionally expressed relative to the wave number in free space. Figure 8 Retrieved from, Figure 8 The power pattern in scenario (c) has the highest value in the desired direction, and the mirror reflection is –20 dB smaller than the main beam reflection. On the other hand, the mirror reflection is –14 dB smaller than the main reflection. Figure 8 In the scenario of (c), it is assumed that only one supercell is considered for the design of the metasurface, that is, the design is based on an ultra-supercell size of 1 (USC size = 1), which means that the Delta-Sigma algorithm is only applied to one supercell. The ultra-supercell size indicates the number of supercells considered when designing the metasurface using the Delta-Sigma algorithm.

[0174] As mentioned above, higher performance can be achieved when the Delta-Sigma algorithm is applied to more than one supercell (i.e., super-supercell size is greater than 1, USC size>1). In this way, the Delta-Sigma algorithm can determine the transfer response of all sub-unit cells in the super-supercell. To illustrate the impact of considering more than one supercell, i.e., considering super-supercells of size greater than 1 (USC size>1), Fig. 9 The normalized power patterns of four different USC sizes (USC size = 1, 2, 3, and 4) are compared. Fig. 9 As shown, a larger USC size brings a larger power at the desired reflection angle, on the other hand, the mirror direction is significantly reduced and the mirror reflection angle is also significantly reduced. Fig. 9 The y-axis of the graphs is the normalized power pattern in dB, and the x-axis of these graphs is the spatial angle domain. The term "K" is the wave number, which is measured in radians per meter. It represents the spatial frequency of the electromagnetic wave. The term "K0" is the wave number or spatial frequency of the electromagnetic wave in free space and is usually considered a reference value for the wave number. The term "K x ” is the wave number of the surface electromagnetic wave in the metasurface structure in the x-direction. For comparison purposes, the wave numbers in different materials are optionally expressed relative to the wave number in free space.

[0175] Fig.10 and Fig.11 Examples of metasurfaces according to embodiments of the present disclosure are shown respectively.

[0176] Fig.10 The metasurface is Figure 1 An example of a metasurface, therefore, Figure 1 Description of Fig.10 The metasurface is correspondingly effective. Fig.10 An example of a unit cell 2 of a metasurface is shown on the left. As shown, the unit cell 2 includes two sub-unit cells 4, wherein each sub-unit cell 4 includes two independent scatterers 3. That is, the four independent scatterers 3 of the unit cell 2 can be divided into two sub-unit cells 4, so that each sub-unit cell 4 includes two independent scatterers 3. In other words, for example, at 100 GHz, the metasurface is designed to have a density ratio Dr of 2 (Dr=2). Since sub-terahertz frequencies suffer from high attenuation, this frequency can be selected, but the proposed technology can be applied to any frequency. As Fig.10As shown, a unit cell 2 including two sub-unit cells 4 is designed. The designed sub-unit cells 4 (e.g., independent scatterers 3) may have different phase responses and amplitude responses so as to provide appropriate reflection coefficients according to the algorithm requirements of the Delta-Sigma algorithm. The number of sub-unit cells 4 per unit cell 2 and the number of independent scatterers 3 per sub-unit cell 4 are only examples and do not limit the present disclosure.

[0177] The two independent scatterers 3 of each sub-unit cell 4 of the unit cell 2 can be two metal radiators 101. The two metal radiators can operate together, and the response of both of them can form the response of the corresponding sub-unit cell 4. In this way, there is a large degree of freedom to control the response of each sub-unit cell 4 of the unit cell 2. Each of the radiators (i.e., independent scatterers) can have different arc angles (e.g., α1, α2), connection lengths (e.g., L1, L2), rotation angles (e.g., β1, β2), inner radius (R i ) and outer radius (R o ).exist Fig.10 On the right side of the figure, layers 101, 102 and 103 of the designed metasurface are shown exemplarily. Layers 101 and 103 can be made of metal, such as copper. Layer 101 can be a metal strip for forming a metal radiator, thereby forming an independent scatterer 3. Layer 103 can be a ground layer. Layer 102 can be a substrate layer. For example, substrate layer 102 can be made of a material called "RT / Duroid 6002". Substrate layer 102 can be made of a dielectric substrate, the dielectric constant of which can be selected to be 2.9, the dielectric substrate is a low-loss material, and provides good (excellent) high-frequency performance. That is, substrate layer 102 can be made of one or more low-loss materials (for example, one or more low-loss dielectric materials) that provide good (excellent) high-frequency performance. Due to the good (excellent) mechanical and electrical properties, the above materials can be reliably used in multilayer board construction.

[0178] Fig.11 An example of a super cell 6 including four unit cells 21, 22, 23 and 24 is shown. That is, these four unit cells 21, 22, 23 and 24 form a unit cell group covering a 2π phase shift. Fig.11 As shown, each unit cell 2 may include two sub-unit cells 4, wherein each sub-unit cell 4 includes two independent scatterers 3. Therefore, Fig.11 The super unit 6 includes eight sub-unit cells 41, 42, 43, 44, 45, 46, 47 and 48. The number of unit cells 2 in each super unit 6, the number of sub-unit cells 4 in each unit cell 2, the number of independent scatterers 3 in each unit cell 2 and the number of independent scatterers 3 in each sub-unit cell 4 are only examples and do not limit the present disclosure. Fig.11 For more details, refer to Fig.10 Description.

[0179] The present disclosure has been described in conjunction with various embodiments as examples and in conjunction with implementations. However, from a study of the drawings, the present disclosure and the independent claims, other variations will be understood and implemented by those skilled in the art when implementing the claimed subject matter. In the claims and in the specification, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" does not exclude a plurality. A single element or other unit may fulfil the functions of several entities or items described in the claims. The fact that certain measures are recited in mutually different dependent claims does not in itself mean that a combination of these measures cannot be used in an advantageous implementation.

Claims

1. A metasurface (1) for electromagnetic waves, wherein: - the metasurface (1) comprises a unit cell (2); Each of the unit cells (2) has a unique phase response and comprises a plurality of independent scatterers (3).

2. The metasurface (1) according to claim 1, wherein: - The plurality of independent scatterers (3) are arranged in a two-dimensional lattice.

3. The metasurface (1) according to claim 1 or 2, wherein: - Each unit cell (2) in the unit cell (2) is divided into sub-unit cells (4), each sub-unit cell (4) includes one or more independent scatterers (3) among the multiple independent scatterers (3), wherein the phase response of the sub-unit cell (4) of the unit cell (1) converges to the phase response of the unit cell.

4. The metasurface (1) according to claim 3, wherein: - the plurality of independent scatterers (3) of each of the unit cells (2) are arranged in a two-dimensional lattice; and The unit cell (2) is divided into the sub-unit cells (4) such that each sub-unit cell (4) comprises a row and / or a column of one or more independent scatterers (3) among the plurality of independent scatterers (3).

5. The metasurface (1) according to claim 3, wherein: - Each unit cell (2) in the unit cells (2) is divided into the sub-unit cells (4), so that the number of the sub-unit cells (4) is equal to the number of the multiple independent scatterers (3), and each sub-unit cell (4) in the sub-unit cells (4) includes a corresponding independent scatterer (3) in the multiple independent scatterers (3).

6. The metasurface (1) according to any one of the preceding claims, wherein: A group of unit cells (2, 6) in the unit cell (2) covers a 2π phase shift, the unit cells (2, 6) of the group being arranged next to each other.

7. The metasurface (1) according to claim 6, wherein: - the unit cell group (2, 6) includes 2 of the unit cells (2) B unit cells (2, 6), the 2 B The unit cells (2, 6) are arranged next to each other, and B is an integer greater than or equal to 1.

8. The metasurface (1) according to claim 6 or 7, wherein: - the unit cell group (2) comprises a one-dimensional arrangement of the sub-unit cells (4); - the subunit cell (4) of the unit cell group (2, 6) is designed such that: when designing the subunit cell to achieve the desired transfer response (g n ) due to design error (e i(n) 、e S(n) ) causes the subunit cell to achieve a transfer response (V n ) and the desired transfer response (g) of the subunit cell n ) n ), at least in part by the desired transfer response (g) of a second subunit cell immediately preceding the subunit cell n–1 ) and the second subunit cell achieves a transfer response (V n–1 ) n–1 ) for compensation.

9. The metasurface (1) according to claim 8, wherein: - by transferring the desired transfer response (g) of the second subunit cell n–1 ) and the achieved transfer response of the second subunit cell (V n–1 ) between n–1 ) added to the desired transfer response of the subunit cell (g n ) to at least partially compensate for the design of the subunit cell to achieve the desired transfer response (g n ) due to the design error (e i(n) 、e S(n) ) caused by the realized transfer response of the subunit cell (V n ) and the desired transfer response (g) of the subunit cell n ) between n ).

10. The metasurface (1) according to claim 6 or 7, wherein: - the unit cell group (2) comprises a two-dimensional arrangement of the sub-unit cells (4); - the subunit cell (4) of the unit cell group (2, 6) is designed such that: when designing the subunit cell to achieve the desired transfer response (g qp ) due to design error (e i(qp) 、e S(qp) ) causes the subunit cell to achieve a transfer response (V qp ) and the desired transfer response (g) of the subunit cell qp ) is at least partially compensated by: - the expected transfer response (g) of a second subunit cell immediately preceding the subunit cell in the first dimension q(p–q) ) and the second subunit cell achieves a transfer response (V q(p–q) ) q(p–1) ), - the desired transfer response (g) of a third subunit cell immediately preceding the subunit cell in the second dimension (q–1)p ) and the third subunit cell realizes the transfer response (V (q–1)p ) (q–1)p ).

11. The metasurface (1) according to claim 10, wherein: - by transferring the desired transfer response (g) of the second subunit cell q(p–1) ) and the achieved transfer response of the second subunit cell (V q(p–1) ) between q(p–1) ) and the desired transfer response (g (q–1)p ) and the achieved transfer response (V (q–1)p ) between (q–1)p ) is added to the expected transfer response (g qp ) to at least partially compensate for the design of the subunit to achieve the desired transfer response (g qp ) due to the design error (e i(qp) 、e S(qp) ) caused by the realized transfer response of the subunit cell (V qp ) and the desired transfer response (g) of the subunit cell qp ) between the above mentioned differences.

12. The metasurface (1) according to any one of claims 8 to 11, wherein: - the achieved transfer response of the subunit cell (V n ; V qp ) is designed as follows: using the design error (e i(n) 、e S(n) ;e i(qp) 、e S(qp) ) and information about the mutual coupling of the sub-unit cells (4) of the unit cell group (2, 6) to achieve the desired transfer response (g n ; g qp ).

13. The metasurface (1) according to any one of claims 8 to 12, wherein: - The corresponding transfer response (g) of the corresponding subunit cell (4) n 、V n ; g qp 、V qp ) includes the amplitude response and phase response of the corresponding sub-unit cell (4).

14. The metasurface (1) according to any one of claims 8 to 13, wherein: - the expected transfer response (g) of the corresponding subunit cell (4) n ; g qp ) comprises an amplitude response of 1 and a phase response equal to 2π divided by the number of said unit cells (2, 6) covering said 2π phase shift.

15. The metasurface (1) according to any one of claims 8 to 14, wherein: - the design error (e i(n) 、e S(n) ;e i(qp) 、e S(qp) ) includes errors due to design inconsistencies (e i(n) ;e i(qp) ) and the error (e) caused by the two-dimensional periodic structure of the unit cell (2) of the unit cell group assuming the same phase response for the design S(n) ;e S(qp) ).

16. The metasurface (1) according to any one of claims 6 to 15, wherein: The metasurface (1) comprises a plurality of the unit cell groups (2, 6).

17. An antenna system comprising a metasurface (1) according to any one of the preceding claims.

18. A method for designing a metasurface for electromagnetic waves, wherein: The method comprises: - providing (S1) unit cells in the metasurface, wherein each of the unit cells has a unique phase response and comprises a plurality of independent scatterers.

19. The method according to claim 18, wherein: The method comprises: - providing a unit cell group (2, 6) of the unit cell (2), wherein the unit cells in the unit cell group (2, 6) cover a 2π phase shift and are arranged next to each other.

20. The method according to claim 19, wherein: - the unit cell group (2) comprises a one-dimensional arrangement of the sub-unit cells (4); - The method comprises: designing the subunit cells of the unit cell group (2, 6) to achieve a desired transfer response (g n ), so that: due to design error (e i(n) 、e S(n) ) causes the subunit cell to achieve a transfer response (V n ) and the desired transfer response (g) of the subunit cell n ) n ), at least in part by the desired transfer response (g) of a second subunit cell immediately preceding the subunit cell n–1 ) and the second subunit cell achieves a transfer response (V n–1 ) n–1 ) for compensation.

21. The method according to claim 20, wherein: The method comprises: - by transferring the desired transfer response (g) of the second subunit cell n–1 ) and the achieved transfer response of the second subunit cell (V n–1 ) between n–1 ) added to the desired transfer response of the subunit cell (g n ) to at least partially compensate for the design error (e i(n) 、e S(n) ) caused by the realized transfer response of the subunit cell (V n ) and the desired transfer response (g) of the subunit cell n ) between n ).

22. The method according to claim 19, wherein: - the unit cell group (2) comprises a two-dimensional arrangement of the sub-unit cells (4); - The method comprises: designing the subunit cells of the unit cell group (2, 6) to achieve a desired transfer response (g qp ), so that: by the design error (e i(qp) 、e S(qp) ) causes the subunit cell to achieve a transfer response (V qp ) and the desired transfer response (g) of the subunit cell qp ) is at least partially compensated by: - the expected transfer response (g) of a second subunit cell immediately preceding the subunit cell in the first dimension q(p–q) ) and the second subunit cell achieves a transfer response (V q(p–q) ) q(p–1) ), - the desired transfer response (g) of a third subunit cell immediately preceding the subunit cell in the second dimension (q–1)p ) and the third subunit cell realizes the transfer response (V (q–1)p ) (q–1)p ).

23. The method according to claim 22, wherein: The method comprises: - by transferring the desired transfer response (g) of the second subunit cell q(p–1) ) and the achieved transfer response of the second subunit cell (V q(p–1) ) between q(p–1) ) and the desired transfer response (g (q–1)p ) and the achieved transfer response (V (q–1)p ) between (q–1)p ) is added to the expected transfer response (g qp ) to at least partially compensate for the design error (e i(qp) 、e S(qp) ) caused by the realized transfer response of the subunit cell (V qp ) and the desired transfer response (g) of the subunit cell qp ) between the above mentioned differences.

24. A computer program comprising instructions which, when executed by a computer, cause the computer to perform the method according to any one of claims 18 to 23.

25. A computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to perform the method according to any one of claims 18 to 23.

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