Intelligent metasurface near-far field multi-beam generation method

Abstract

The invention provides an intelligent metasurface near-far field multi-beam generation method, which realizes near-field multi-point focusing, far-field multi-beam forming and near-far field integrated multi-user metasurface coefficient design through field source rapid iteration on the basis of an intelligent metasurface equivalent surface source model. The method is characterized in that 1) an intelligent metasurface model based on an equivalent surface source simulates response of a metasurface to electromagnetic waves; 2) an intelligent metasurface scattering propagation model based on a Green's formula, wherein the intelligent metasurface scattering propagation model is used for accurately describing behaviors of the metasurface in electromagnetic wave transmission; (3) a near-field multi-point focusing technology is realized through appointed energy distribution, so that accurate control of energy in a near field is ensured; and 4) a far-field multi-beam generation method is adopted to realize energy directional distribution and beam forming in a far-field multi-user scene. The method has wide potential in the application of the intelligent metasurface, is suitable for wireless communication and wireless energy transmission scenes, and provides an efficient near-far field integrated solution.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a near-field and far-field multi-beam generation method based on an intelligent metasurface. Background Art

[0002] In recent years, as an emerging wireless communication technology, Reconfigurable Intelligent Surface (RIS) has attracted widespread attention. The intelligent metasurface is composed of a large number of adjustable reflection units. By adjusting the phase and amplitude of each unit, the incident electromagnetic wave can be flexibly manipulated to achieve beamforming, reflection direction control, channel enhancement and other functions.

[0003] In wireless communication systems, multi-beam forming technology is an important means to improve system transmission efficiency and anti-interference capabilities. Traditional multi-beam forming relies on complex RF link design and algorithm optimization, which makes it difficult to apply in low-cost, low-power scenarios. Smart metasurfaces have the ability to generate multiple beams in different spatial regions, and can achieve flexible beamforming in both near and far fields, which has broad application prospects.

[0004] However, existing multi-beam generation methods based on smart metasurfaces are usually limited to a single scenario, for example, they are only applicable to far-field or near-field beam generation, and cannot take into account multiple communication needs. As communication scenarios become more complex, the needs of near-field communication and far-field communication often coexist. How to use smart metasurfaces to achieve multi-beam generation that supports both near-field and far-field has become a major challenge in the current technological development.

[0005] Therefore, a smart metasurface near-field and far-field multi-beam generation method is proposed, which can flexibly control the near-field and far-field beam distribution while reducing the hardware complexity, which is of great significance for improving the performance of future wireless communication systems. Summary of the invention

[0006] In view of the problems and shortcomings of the prior art, the present invention proposes a metasurface near- and far-field multi-beam generation method based on the improved Gerchberg-Saxton (GS) iteration on the basis of considering the actual physical model of the intelligent metasurface. By alternating projection of field sources, near-field multi-point focusing, far-field multi-beam forming and near- and far-field integrated multi-user metasurface coefficient design are realized.

[0007] The present invention proposes a near-field and far-field multi-beam generation method for an intelligent metasurface, which is characterized by comprising the following steps:

[0008] First, the intelligent metasurface model based on equivalent surface source:

[0009] Smart metasurfaces are surface distributions composed of periodic small resonant scatterers. Due to their subwavelength scattering unit spacing and electrically negligible thickness, smart metasurfaces can be homogenized. According to the surface equivalence theorem, the incident electromagnetic field will induce current and magnetic flux in each unit. Based on the homogenized model, the position-dependent induced current and magnetic flux in each unit can be replaced by the surface average effective parameters.

[0010] Furthermore, through homogenization, the metasurface can be modeled as a planar sheet S with an average current density on the electromagnetic surface. The surface S is a rectangle located in the xy plane, expressed as:

[0011]

[0012] in, and are the unit vectors in the x and y directions respectively, L x and L y are the length and width of the surface respectively;

[0013] Second, the intelligent metasurface scattering propagation model based on Green’s formula:

[0014] In the metasurface model, when the incident wave excites the metasurface, the surface S forms an equivalent two-dimensional source, and the field radiated by each source It is composed of the superposition of spherical waves radiating outward from the center:

[0015]

[0016] Among them, the partial derivative From area z - Point to z + , source component Q s (r 0 ) is the singlet component, radiating a simple monopolar spherical wave G(rr 0 ), source component Q d (r 0 ) is the doublet component, the radiating dipole When the two source components make E(r) satisfy the second Helmholtz identity in the entire area, we can obtain:

[0017]

[0018] Furthermore, the radiation field of the metasurface is given by the equivalent surface source E(r 0 ) are generated by the incident wave E in (r 0 ) caused by the secondary source, according to the generalized sheet transition conditions (GSTC), we can get:

[0019] E(r 0 )=Γ(r 0 )E in (r 0 ) (4)

[0020] Among them, Γ(r 0 ) is the macroscopic modulation coefficient of the metasurface S, and the scattering field of the metasurface under any excitation can be calculated:

[0021]

[0022] Furthermore, using the Rayleigh-Sommerfeld diffraction approximation, formula (5) is further simplified to:

[0023]

[0024] Where R is the distance from the field to the source, calculate;

[0025] Optionally, for the near-field case, by introducing the Fresnel diffraction approximation, formula (6) is further simplified to:

[0026]

[0027] Among them, formula (7) satisfies the condition that the radiation field is in the Fresnel diffraction region, that is,

[0028] Optionally, for the far-field case, by introducing the Fraunhofer diffraction approximation, formula (6) is further simplified to:

[0029]

[0030] Among them, formula (9) satisfies the condition that the radiation field is in the Fraunhofer diffraction region, that is,

[0031] Third, the near-field multi-point focusing method for specifying energy distribution:

[0032] For the vertical distance z from the hypersurface S f The field E(x,y,z) on the focusing plane f ), according to formula (7), it can be further simplified as:

[0033]

[0034] in,

[0035] From formula (9), we can see that E(x,y,z f ) can be regarded as E'(x 0,y 0 ) is the two-dimensional Fourier transform E(x,y,z f )=FrT(E'(x 0 ,y 0 )), FrT is defined as Fourier transform, and its spatial sampling frequencies are and

[0036] The equivalent field of the metasurface S can also be obtained by the inverse transformation of the focusing surface:

[0037] Γ(x 0 ,y 0 )E in (x 0 ,y 0 )=FrT -1 (E(x,y,z f )) (10)

[0038] Among them, FrT -1 Defined as the inverse Fourier transform;

[0039] Furthermore, the energy distribution is specified by introducing a weight factor describing the electromagnetic intensity of the focus. There are M focus points on the focusing plane. The relative amplitude is set to 1 at the focus position and 0 at the non-focus position. i is the weight factor of the ith focus, which represents the ratio of the ith focus to the first focus, where w 1 =1, so the field distribution of the virtual focusing surface is:

[0040]

[0041] Furthermore, the equivalent field of the metasurface S is obtained by inverse diffraction:

[0042] E equal (x,y)=FrT -1 (E Virtual (x,y,z f )) (12)

[0043] Furthermore, the diffraction field of the focusing plane is:

[0044] E focal (x,y,z f )=FrT(E equal (x 0 ,y 0 )) (13)

[0045] Furthermore, in order to describe the desired intensity ratio of each focus, k i is defined as the ratio of the intensity of the ith focus to the intensity of the first focus;

[0046] Optional, it should be emphasized that w i is the weight factor of the i-th focus, which is not equal to k i ,Since the control amplitude of the metasurface is corrected to 1, formula (12)(13) is not a completely reversible process;

[0047] Furthermore, to achieve maximum diffraction efficiency, the focal intensity and The maximum value needs to be taken. At the same time, in order to achieve a specific focus intensity ratio, a weight factor is introduced to regulate the intensity of the i-th focus. The maximization problem is transformed into solving Φ(x 0 ,y 0 ) and

[0048] Furthermore, since the focus intensity and phase are related, the problem to be solved is a transcendental equation and cannot be solved accurately. The GS iterative process is used to solve the approximate solution;

[0049] Furthermore, in the Pth cycle, the focal intensity of the focusing surface is The desired focus strength is:

[0050]

[0051] Further, the weight factor is updated as:

[0052]

[0053] Furthermore, the weight factor The set focus intensity ratio is achieved through step-by-step iteration;

[0054] Furthermore, the diffraction efficiency η is used to characterize how much reflected electromagnetic wave energy is concentrated at a specified focal position, which is defined as the ratio of the electric field intensity of each focal point on the focusing surface to the intensity of the incident electromagnetic wave:

[0055]

[0056] Furthermore, the root mean square error σ is used to describe the ability of the metasurface to control electromagnetic waves:

[0057]

[0058] Optionally, when multiple focal points are not on the same focusing plane, a multi-layer iterative method can be used for rapid regulation;

[0059] Fourth, far-field multi-beam generation method with specified energy allocation:

[0060] Furthermore, for the far-field case, when When , we can get:

[0061]

[0062] Furthermore, assuming z≈R, formula (8) can be simplified to:

[0063]

[0064] Among them, θ is the pitch angle of the far-field radiation field, φ is the direction angle of the far-field radiation field, satisfying x = Rsinθcosφ, y = Rsinθsinφ, z = Rcosθ;

[0065] Furthermore, based on the spectral domain expression of the solution of the simple harmonic Maxwell equations in the passive region in a three-dimensional rectangular coordinate system, the field at any point (x, y, z) in space can be obtained as follows:

[0066]

[0067] Among them, F(k x ,k y ) is the spectrum of the plane wave, k x , k x , k x are the components of the spatial wave number k on the coordinate axis, and satisfy

[0068] Furthermore, by transforming the spectral integral into the angle domain, formula (20) is further simplified to:

[0069]

[0070] Among them, F(θ,φ) is the spectrum of the wave coming from the (θ,φ) direction and satisfies

[0071] Furthermore, formula (21) is simplified to:

[0072]

[0073] Furthermore, according to formula (19) and formula (22), a transformation pair between the surface source and the far-field radiation field is formed, and the GS iterative logic is used to quickly solve the approximate solution. The process is analogous to the multi-point focusing method of specifying energy distribution.

[0074] Optionally, the near-field multi-point focusing method and the far-field multi-beam forming method of energy designated allocation can be used together to achieve near-field and far-field unified multi-user beamforming assisted by a metasurface;

[0075] Optionally, the intelligent metasurface near-field and far-field multi-beam generation method is not limited to the above-mentioned single polarization assumption and can be applied to multi-polarization situations.

[0076] Beneficial Effects

[0077] It can be seen from the above that compared with the prior art, the above technical solution has the following beneficial effects:

[0078] (1) Improve the efficiency of near-field and far-field multi-beam generation. By improving the GS iterative algorithm, the invention can quickly achieve precise control of the field source. The improved algorithm can iterate more efficiently, thereby accelerating the calculation process of near-field multi-point focusing and far-field multi-beam forming. This effectively overcomes the computational complexity and efficiency bottlenecks in traditional methods, especially in large-scale intelligent metasurface applications, and can better cope with the needs of multiple users in complex environments.

[0079] (2) Taking into account both near-field and far-field performance. The above method takes into account the actual physical model of the smart metasurface and realizes the unified design of near-field multi-point focusing and far-field multi-beamforming through iterative optimization. This near-field and far-field integrated design can significantly improve the performance of the metasurface, enabling it to achieve both local precise control (near-field focusing) and stable signal transmission over a large range (far-field beamforming) in different application scenarios, thereby enhancing the versatility and wide application of smart metasurfaces.

[0080] (3) Multi-user scenario optimization design. The present invention also proposes a unified metasurface coefficient design scheme for multi-user application requirements. By precisely controlling the metasurface unit, customized services can be provided to multiple users at the same time, and multi-beam simultaneous generation and transmission can be achieved while specifying energy allocation, greatly improving the flexibility of multi-user communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a schematic diagram of a near-field and far-field multi-beam generation method for an intelligent metasurface;

[0082] Figure 2 It is a schematic diagram of modeling the equivalent surface source of the hypersurface homogenization;

[0083] Figure 3 is a schematic diagram of the metasurface multi-point focusing method for specifying energy distribution;

[0084] Figure 4 is a flow chart of the metasurface multi-point focusing algorithm for specifying energy distribution;

[0085] Figure 5 is a schematic diagram of a metasurface multi-beam forming method for specifying energy distribution;

[0086] Figure 6 is a flow chart of the metasurface multi-beamforming algorithm with specified energy allocation; DETAILED DESCRIPTION

[0087] In order to clarify the purpose, implementation scheme and technical advantages of the present invention, the present invention is further described in detail below in combination with specific embodiments and with reference to the accompanying drawings.

[0088] A near-field and far-field multi-beam generation method for an intelligent metasurface, characterized in that: Figure 1 As shown in the figure, through rapid iteration of the field source, near-field multi-point focusing, far-field multi-beamforming and near-field and far-field integrated multi-user metasurface coefficient design are realized, including the following steps:

[0089] First, the intelligent metasurface model based on equivalent surface source:

[0090] Smart metasurfaces are surface distributions composed of periodic small resonant scatterers. Due to their subwavelength scattering unit spacing and electrically negligible thickness, smart metasurfaces can be homogenized. According to the surface equivalence theorem, the incident electromagnetic field will induce current and magnetic flux in each unit. Based on the homogenized model, the position-dependent induced current and magnetic flux in each unit can be replaced by the surface average effective parameters.

[0091] like Figure 2 As shown in Figure 2, by homogenization, the metasurface can be modeled as a planar sheet S with an average current density on the electromagnetic surface. The surface S is a rectangle located in the xy plane and is expressed as:

[0092]

[0093] in, and are the unit vectors in the x and y directions respectively, L x and L y are the length and width of the surface respectively;

[0094] Furthermore, the modeling and analysis of the super-surface scattering composed of finite-size units is transformed into the modeling and analysis of the equivalent surface current source. Based on Maxwell's equations, the electric and magnetic fields of the incident electromagnetic wave are related to the surface current and magnetic flow:

[0095]

[0096] Where n is the normal vector of the smart hypersurface, E t and H t are the electric field and magnetic field components on the smart metasurface unit, respectively. Therefore, macroscopic control of the metasurface can be achieved by changing the equivalent current.

[0097] Second, the intelligent metasurface scattering propagation model based on Green’s formula:

[0098] In the metasurface model, when the incident wave excites the metasurface, the surface S forms an equivalent two-dimensional source, and the field radiated by each source It is composed of the superposition of spherical waves radiating outward from the center:

[0099]

[0100] Among them, the partial derivative From area z - Point to z + , source component Q s (r 0 ) is the singlet component, radiating the monopolar spherical wave G(rr 0 ), source component Q d (r 0 ) is the doublet component, the radiating dipole When the two source components make E(r) satisfy the second Helmholtz identity in the entire area, we can obtain:

[0101]

[0102] Furthermore, the radiation field of the metasurface is given by the equivalent surface source E(r 0 ) are generated by the incident wave E in (r 0 ) caused by the secondary source, according to the generalized sheet transition conditions (GSTC), we can get:

[0103] E(r 0 )=Γ(r 0 )E in (r 0 ) (5)

[0104] Among them, Γ(r 0 ) is the macroscopic modulation coefficient of the metasurface S, and the scattering field of the metasurface under any excitation can be calculated:

[0105]

[0106] Furthermore, using the Rayleigh-Sommerfeld diffraction approximation, formula (6) is further simplified to:

[0107]

[0108] Where R is the distance from the field to the source, calculate;

[0109] Optionally, for the near-field case, by introducing the Fresnel diffraction approximation, formula (7) is further simplified to:

[0110]

[0111] Among them, formula (8) satisfies the condition that the radiation field is in the Fresnel diffraction region, that is,

[0112] Optionally, for the far-field case, by introducing the Fraunhofer diffraction approximation, formula (7) is further simplified to:

[0113]

[0114] Among them, formula (9) satisfies the condition that the radiation field is in the Fraunhofer diffraction region, that is,

[0115] Third, the near-field multi-point focusing method with designated energy distribution:

[0116] The near-field multi-point focusing method for energy designated distribution is as follows Figure 3 As shown in Figure 2, the coefficient configuration is quickly optimized by iterating between the focusing plane and the metasurface. f The field E(x,y,z) on the focusing plane f ), according to formula (8), it can be further simplified as:

[0117]

[0118] in,

[0119] From formula (10), we can see that E(x,y,z f ) can be regarded as E'(x 0 ,y 0 ) is the two-dimensional Fourier transform E(x,y,z f )=FrT(E'(x 0 ,y 0 )), FrT is defined as Fourier transform, and its spatial sampling frequencies are and

[0120] The equivalent field of the metasurface S can also be obtained by the inverse transformation of the focusing surface:

[0121] Γ(x 0 ,y 0 )E in (x 0 ,y 0 )=FrT -1 (E(x,y,z f )) (11)

[0122] Among them, FrT -1 Defined as the inverse Fourier transform;

[0123] Furthermore, the energy allocation is realized by introducing a weight factor describing the electromagnetic intensity of the focus. Assuming that there are M focus points on the focusing plane, the relative amplitude is set to 1 at the focus position and 0 at the non-focus position, w i is the weight factor of the ith focus, which represents the ratio of the ith focus to the first focus, where w 1 =1, so the field distribution of the virtual focusing surface is:

[0124]

[0125] Furthermore, the equivalent field of the metasurface S is obtained by inverse diffraction:

[0126] E equal (x 0 ,y 0 )=FrT -1 (E Virtual (x,y,z f )) (13)

[0127] Furthermore, the macro-control coefficient of the metasurface is:

[0128]

[0129] Optionally, for a phase-only metasurface, A(x 0 ,y 0 ) is corrected to 1, and the surface equivalent field of the metasurface is:

[0130]

[0131] Furthermore, the diffraction field of the focusing plane is:

[0132] E focal (x,y,z f )=FrT(E equal (x 0 ,y 0 )) (16)

[0133] Furthermore, in order to describe the desired intensity ratio of each focus, k i is defined as the ratio of the intensity of the ith focus to the intensity of the first focus;

[0134] Optional, it should be emphasized that w i is the weight factor of the i-th focus, which is not equal to k i , since the control amplitude of the metasurface is corrected to 1, formula (13)(14)(15)(16) is not a completely reversible process;

[0135] Furthermore, to achieve maximum diffraction efficiency, the focal intensity and The maximum value needs to be taken. At the same time, in order to achieve a specific focus intensity ratio, a weight factor is introduced to regulate the intensity of the first focus. The maximization problem is transformed into solving Φ(x 0 ,y 0 ) and

[0136] Furthermore, since the focal intensity and phase are related, the problem to be solved is a transcendental equation and cannot be solved accurately. The GS iterative process is used to solve the approximate solution. The process is as follows: Figure 4 As shown;

[0137] Further, assuming that in the Pth cycle, the focal intensity of the focusing surface is The desired focus strength is:

[0138]

[0139] Further, the weight factor is updated as:

[0140]

[0141] Furthermore, the weight factor The set focus intensity ratio is achieved through step-by-step iteration;

[0142] Furthermore, the diffraction efficiency η is used to characterize how much reflected electromagnetic wave energy is concentrated at a specified focal position, which is defined as the ratio of the electric field intensity of each focal point on the focusing surface to the intensity of the incident electromagnetic wave:

[0143]

[0144] Furthermore, the root mean square error σ is used to describe the ability of the metasurface to control electromagnetic waves:

[0145]

[0146] Optionally, when multiple focal points are not on the same focusing plane, a multi-layer iterative method can be used for rapid regulation;

[0147] Fourth, far-field multi-beam generation method with specified energy allocation:

[0148] The far-field multi-beam forming method for specifying energy allocation is as follows Figure 5 As shown in Figure 1, the coefficient configuration is quickly optimized by iterating between the far-field radiation pattern and the metasurface. When , we can get:

[0149]

[0150] Furthermore, assuming z≈R, formula (9) can be simplified to:

[0151]

[0152] Among them, θ is the pitch angle of the far-field radiation field, φ is the direction angle of the far-field radiation field, satisfying x = Rsinθcosφ, y = Rsinθsinφ, z = Rcosθ;

[0153] Furthermore, based on the spectral domain expression of the solution of the simple harmonic Maxwell equations in the passive region in a three-dimensional rectangular coordinate system, the field at any point (x, y, z) in space can be obtained as follows:

[0154]

[0155] Among them, F(k x ,k y ) is the spectrum of the plane wave, k x , k x , k x are the components of the spatial wave number k on the coordinate axis, and satisfy

[0156] Furthermore, by transforming the spectral integral into the angle domain, formula (22) is further simplified to:

[0157]

[0158] Among them, F(θ,φ) is the spectrum of the wave coming from the (θ,φ) direction and satisfies

[0159] Furthermore, formula (23) is simplified to:

[0160]

[0161] Furthermore, according to formula (22) and formula (25), a transformation pair between the surface source and the far-field radiation field is formed, and the GS iterative logic is used to quickly solve the approximate solution. The process is as follows: Figure 6 As shown;

[0162] Furthermore, the energy allocation is specified by introducing a weight factor describing the beam strength. Assuming that M beams are generated in the far field, the relative amplitude is set to 1 at the beam angle and 0 at the non-beam angle. i is the weight factor of the ith beam, which represents the ratio of the ith beam to the first beam, where w 1 =1, so the virtual far-field distribution is:

[0163]

[0164] Furthermore, combining formula (24) and formula (25), we can obtain the equivalent field E of the metasurface S: equal (x,y);

[0165] Furthermore, the macro-control coefficient of the metasurface is:

[0166]

[0167] Optionally, for a phase-only metasurface, A(x 0 ,y 0 ) is corrected to 1;

[0168] Furthermore, combined with the equivalent field E of the metasurface S equal (x, y) and formula (22), we can get the far-field diffraction field E of the metasurface far (θ,φ);

[0169] Furthermore, in order to describe the desired intensity ratio of each beam, k i is defined as the ratio of the intensity of the ith beam to the intensity of the first beam;

[0170] Optional, it should be emphasized that w i is the weight factor of the ith beam, which is not equal to k i ,Since the control amplitude of the metasurface is corrected to 1, formula (22)(25) is not a completely reversible process;

[0171] Furthermore, to achieve maximum diffraction efficiency, beam intensity and The maximum value needs to be taken. At the same time, in order to achieve a specific beam intensity ratio, a weight factor is introduced to regulate the intensity of the i-th beam. The maximization problem is transformed into solving Φ(x 0 ,y 0 ) and

[0172] Furthermore, suppose that in the Pth cycle, the i-th beam intensity of the far-field radiation field is The desired beam strength is:

[0173]

[0174] Further, the weight factor is updated as:

[0175]

[0176] Furthermore, the weight factor The set beam intensity ratio is achieved through step-by-step iteration;

[0177] Furthermore, the diffraction efficiency η is used to characterize how much reflected electromagnetic wave energy is concentrated at a specified focal position, which is defined as the ratio of the electric field intensity of each focal point on the focusing surface to the intensity of the incident electromagnetic wave:

[0178]

[0179] Furthermore, the root mean square error σ is used to describe the ability of the metasurface to control electromagnetic waves:

[0180]

[0181] Optionally, the near-field multi-point focusing method and the far-field multi-beam forming method of energy designated allocation can be used together to achieve near-field and far-field unified multi-user beamforming assisted by a metasurface;

[0182] Optionally, the intelligent metasurface near-field and far-field multi-beam generation method is not limited to the above-mentioned single polarization assumption and can be applied to multi-polarization situations.

Claims

1. A method for near-field and far-field multi-beam generation of an intelligent metasurface, characterized in that: include: Based on the actual physical model of the smart metasurface, a metasurface near-field and far-field multi-beam generation method based on improved Gerchberg-Saxton (GS) iteration is proposed. By alternating the field source iteration, near-field multi-point focusing, far-field multi-beam forming and near-field and far-field integrated metasurface coefficient design are realized. The method is characterized by comprising the following steps: First, the intelligent metasurface model based on equivalent surface source; Second, the intelligent metasurface scattering propagation model based on Green’s function; Third, near-field multi-point focusing with specified energy distribution; Fourth, far-field multi-beam generation with specified energy allocation.

2. According to the method of claim 1, the intelligent super surface model based on equivalent surface source is characterized in that: Based on the surface equivalence theorem, the incident electromagnetic field will induce current and magnetic flux in the metasurface unit. The induced current and magnetic flux in each unit can be replaced by the surface average effective parameters. Furthermore, the metasurface is modeled as a planar sheet S with an average electromagnetic surface current density. The surface S is a rectangle located in the xy plane and is expressed as: in, and are the unit vectors in the x and y directions respectively, L x and L y are the length and width of the surface respectively.

3. According to the method of claim 1, the intelligent metasurface scattering propagation model based on Green's function is characterized in that: When the incident wave excites the metasurface, the surface S forms an equivalent two-dimensional source, whose radiation field is composed of The superposition of spherical waves radiating outward from the equivalent source center composition: Among them, the partial derivative The radiation field is directed from the surface, n is the surface normal unit vector, and the source component Q s (r0) is the singlet component, the source component Q d (r0) is the doublet component, G(r-r0) is the Green function; The source components make the radiation field E(r) satisfy the second Helmholtz identity in the entire area The equivalent surface source of the metasurface satisfies E(r0)=Γ(r0)E in (r0), where Γ(r0) is the metasurface spatial control coefficient, E in (r0) is the incident wave excitation; Furthermore, based on the Rayleigh-Sommerfeld diffraction approximation, the radiation field of the metasurface at any position (x, y, z) in free space is expressed as: Where R is the distance from the field to the source, Calculate, λ is the wavelength.

4. According to the method of claim 3, the radiation field of the metasurface under near-field conditions is expressed as: in, The near field is in the Fresnel diffraction region, satisfying The radiation field of the metasurface under far-field conditions is expressed as: The far field is in the Fraunhofer diffraction region and satisfies 5. The method according to claim 1, wherein the near-field multi-point focusing of the specified energy distribution comprises: Construct a transformation pair of metasurface equivalent source and focusing surface according to radiation conditions; By assigning weights to different focusing points, the weights are continuously modified in multiple alternating iterations of equivalent source and focusing plane.

6. The method according to claim 5, wherein the transformation pair of the metasurface equivalent source and the focusing surface is constructed according to the radiation condition, characterized in that: The vertical distance from the hypersurface S is z f The field E(x,y,z f ) can be expressed as: in, E(x,y,z f ) can be regarded as the two-dimensional Fourier transform E(x,y,z f )=FrT(E'(x0,y0)), FrT is defined as Fourier transform, and its spatial sampling frequencies are and The equivalent source of the metasurface is obtained by the inverse transformation of the focusing surface: Γ(x0,y0)E in (x0,y0)=FrT -1 (E(x,y,z f )) Among them, FrT -1 is the inverse Fourier transform.

7. The method according to claim 5, wherein the weights are assigned to different focus points and the weights are continuously corrected in multiple alternating iterations of equivalent sources and focus planes, characterized in that: The weight factor describing the electromagnetic intensity of the focus is introduced to achieve the specified distribution of energy. There are M focusing points on the focusing surface, w i is the weight factor of the ith focus, which represents the ratio of the ith focus to the first focus, where w1 = 1; In the Pth cycle, the i-th focus intensity of the focusing surface is The desired focus strength is: Further, the weight factor is updated as: The diffraction efficiency η is used to characterize how much reflected electromagnetic wave energy is concentrated at a specified focal position, and is defined as the ratio of the electric field intensity at each focal point on the focusing surface to the intensity of the incident electromagnetic wave: Furthermore, the root mean square error σ is used to describe the ability of the metasurface to control electromagnetic waves: Furthermore, during the iteration process, the higher the diffraction efficiency, the less the focusing loss; the smaller the root mean square error, the better the energy distribution.

8. The method according to claim 1, wherein the far-field multi-beam generation of the specified energy allocation comprises: Construct a transformation pair of metasurface equivalent source and far-field beam according to radiation conditions; By assigning weights to different far-field beams, the weights are continuously modified in multiple alternating iterations of equivalent sources and far-field beams.

9. The method according to claim 8, wherein a transformation pair of a metasurface equivalent source and a far-field beam is constructed according to radiation conditions, characterized in that: The far-field beam is calculated by equivalent source: Among them, θ is the pitch angle of the far-field radiation field, φ is the direction angle of the far-field radiation field, and R is the distance from the far-field observation point to the metasurface; The equivalent source of the metasurface is obtained by inverse transformation of the far-field beam: Furthermore, the spatial control coefficient of the metasurface is analyzed through surface equivalent source analysis.

10. The method according to claim 8, wherein the weights are assigned to different far-field beams and the weights are continuously modified in multiple alternating iterations of the equivalent source and the far-field beam, characterized in that: The weight factor describing the beam strength is introduced to achieve the specified energy distribution. The far-field radiation includes M beams, w i is the weight factor of the ith beam, which represents the ratio of the ith beam to the first beam, where w1 = 1; In the Pth cycle, the i-th beam intensity of the far-field radiation field is The desired beam strength is: Further, the weight factor is updated as: The diffraction efficiency η is used to characterize how much reflected electromagnetic wave energy is concentrated at a specified beam position, and is defined as the ratio of the electric field intensity of each beam of the radiation field to the intensity of the incident electromagnetic wave: Furthermore, the root mean square error σ is used to describe the ability of the metasurface to control electromagnetic waves: Furthermore, during the iteration process, the higher the diffraction efficiency, the less the focusing loss; the smaller the root mean square error, the better the energy distribution effect.

Images