Design method and system of non-uniformly modulated spatiotemporal encoding metasurface

Abstract

The application discloses a design method and system of a non-uniform modulation space-time coding metasurface, comprising the following steps: (1) obtaining a time coding sequence and a corresponding modulation frequency allocated to each metasurface unit of the space-time coding metasurface; (2) a digital control module generates a time control signal according to the time coding sequence and inputs the time control signal to the corresponding metasurface unit, wherein the time control signal is updated at the modulation frequency; (3) a single-tone electromagnetic wave is generated by a feed antenna and irradiated to the space-time coding metasurface to produce wave-matter interaction with each metasurface unit, so that each metasurface unit radiates electromagnetic waves outward; (4) the equivalent reflection coefficient and the spatial scattering energy of the space-time coding metasurface at different frequencies are calculated, and it is judged whether the preset requirement is reached; if not, adjustment is made until the preset requirement is reached. The application has high spectrum utilization and good scattering reduction effect.

Description

Technical Field

[0001] This invention relates to the field of artificial electromagnetic materials technology, and in particular to a design method and system for a non-uniformly modulated spatiotemporally encoded metasurface. Background Technology

[0002] Novel artificial electromagnetic materials are composed of artificially designed metamaterial units arranged in space in a periodic or aperiodic manner. Because the size of these units is typically kept within the subwavelength range or even smaller, they possess the ability to precisely control electromagnetic waves, thus attracting widespread attention in the engineering and scientific communities. As a two-dimensional version of metamaterials, metasurfaces have a longitudinal dimension much smaller than their operating wavelength, offering advantages such as small size, low insertion loss, and high integration, enabling more flexible manipulation of electromagnetic waves. In 2014, the concepts of digitally encoded and programmable metasurfaces were first proposed, innovatively using digital signals "0" and "1" to characterize the electromagnetic parameters of the metasurface. Furthermore, by loading tunable elements onto the metasurface units, the metasurface gains the ability to control electromagnetic waves in real time. Further, combining digital signal processing and other technologies, by introducing the concept of time modulation into digitally encoded programmable metasurfaces, the metasurface achieves joint control of electromagnetic waves in the spatial and frequency domains, thus forming a new research system for spatiotemporally encoded metasurfaces.

[0003] In traditional spatiotemporally coded metasurfaces, all metasurface units are modulated using a uniform modulation frequency or a fixed difference frequency, resulting in nonlinear harmonics that appear as integer multiples of the modulation frequency. However, the spectral utilization between harmonics is almost zero, leading to very low spectral efficiency. Furthermore, traditional spatiotemporally coded metasurfaces have the following drawbacks: First, the scattering patterns on different harmonics are identical, which can accumulate over time to form high-energy pulses. High scattering peaks always exist at lower harmonics, making it impossible to achieve uniform diffusion of scattered energy across the spectrum. The scattered energy is limited to integer multiples of a single modulation frequency, and there is a physical limit to scattering reduction. Summary of the Invention

[0004] Purpose of the invention: This invention addresses the problems existing in the prior art by providing a design method and system for a non-uniform modulation spatiotemporal coded metasurface. The designed spatiotemporal coded metasurface has higher spectral efficiency and better scattering reduction effect.

[0005] Technical solution: This invention provides a design method for a non-uniform modulation spatiotemporally coded metasurface, comprising the following steps:

[0006] (1) Obtain the time coding sequence and corresponding modulation frequency assigned to each metasurface unit of the spatiotemporally coded metasurface;

[0007] (2) The digital control module generates a time control signal according to the time coding sequence and inputs it to the corresponding metasurface unit, wherein the time control signal is updated according to the modulation frequency;

[0008] (3) A single-tone electromagnetic wave is generated by a feed antenna and irradiates the spatiotemporally encoded metasurface, generating wave-matter interaction with each metasurface unit, causing each metasurface unit to radiate electromagnetic waves outward.

[0009] (4) Calculate the equivalent reflection coefficient and spatial scattering energy of the spatiotemporally coded metasurface at different frequencies to determine whether the preset requirements are met. If not, adjust the time coding sequence and corresponding modulation frequency of each metasurface unit until the preset requirements are met.

[0010] Furthermore, the time control signal satisfies:

[0011]

[0012]

[0013] In the formula, Q m,n (t) represents the value of the time control signal of the (m,n)th metasurface unit of the spatiotemporally encoded metasurface at time t. The modulation frequency f is represented by m,n The corresponding period, f m,n Let L represent the modulation frequency assigned to the (m,n)th metasurface unit, and L represent the length of the time-coded sequence. Indicates T m,n After dividing the time into L time slots, the width of each time slot is s, and each time slot is assigned a corresponding time code. m,n (l) represents the time encoding of the (m,n)th metasurface unit assigned to time slot l, C[s m,n (l)] indicates s m,n (l) The corresponding time control signal value, G m,n (t) represents the width τ m,n The period is T m,n A rectangular pulse signal.

[0014] Furthermore, the temporal reflectance coefficient of the spatiotemporally encoded metasurface satisfies:

[0015] Γ m,n (t)=R(Q m,n (t)),0 <t≤T m,n

[0016] In the formula, Γ m,n (t) is the time-domain reflection coefficient of the (m,n)th metasurface unit for the incident electromagnetic wave, Q m,n(t) represents the value of the time control signal of the (m,n)th metasurface element at time t, and R(·) represents the electromagnetic wave generation function of the metasurface element in response to the input signal.

[0017] Furthermore, the equivalent reflection coefficient is calculated according to the following formula:

[0018]

[0019]

[0020] In the formula, β m,n (f) represents the equivalent reflection coefficient of the (m,n)th metasurface unit at frequency f, where α m,n [·] represents the time-domain reflection coefficient Γ. m,n The formula for calculating the Fourier coefficients of (t), f c f is the frequency of the electromagnetic wave emitted by the feed antenna. m,n T represents the modulation frequency assigned to the (m,n)th metasurface unit. m,n The modulation frequency f is represented by m,n The corresponding period, Γ m,n (t) represents the time-domain reflection coefficient of the (m,n)th metasurface unit for the incident electromagnetic wave. Represents the set of integers.

[0021] Furthermore, the spatial scattering energy is calculated according to the following formula:

[0022]

[0023] In the formula, s(θ,φ,t) represents the spatial scattered energy at time t with elevation angle θ and azimuth angle φ, M and N are the number of rows and columns of the hypersurface unit on the spatiotemporally encoded hypersurface, respectively, and E m,n (θ,φ) represents the center frequency f of the (m,n)th metasurface unit. c Far-field pattern at β m,n (f) represents the equivalent reflection coefficient of the (m,n)th metasurface unit at frequency f, d x and d y These are the period lengths of the spatiotemporally encoded metasurface unit along the x and y axes, respectively, λ. c It is the operating wavelength.

[0024] Furthermore, the modulation frequency is a prime multiple of the modulation fundamental frequency Δf.

[0025] Furthermore, the spatiotemporally encoded metasurface is any one of the following: transmissive, reflective, or active radiative, and each metasurface unit integrates one or more active devices.

[0026] Furthermore, the modulation frequencies of each metasurface unit are independent and uncorrelated.

[0027] Furthermore, the time-coded sequences of each metasurface unit are independent and uncorrelated.

[0028] This invention also provides a design system for a non-uniform modulation spatiotemporally coded metasurface, comprising:

[0029] The parameter acquisition module is used to acquire the time coding sequence and the corresponding modulation frequency assigned to each metasurface unit of the spatiotemporally coded metasurface.

[0030] A digital control module is used to generate a time control signal based on a time-coded sequence and input it to the corresponding metasurface unit, wherein the time control signal is updated according to the modulation frequency;

[0031] The feed antenna is used to generate single-tone electromagnetic waves that illuminate the spatiotemporally encoded metasurface, generating wave-matter interactions with each metasurface unit, causing each metasurface unit to radiate electromagnetic waves outward.

[0032] The calculation module is used to calculate the equivalent reflection coefficient and spatial scattering energy of the spatiotemporally encoded metasurface at different frequencies;

[0033] The adjustment module is used to determine whether the equivalent reflection coefficient and spatial scattering energy meet the preset requirements. If not, it adjusts the time coding sequence and corresponding modulation frequency of each metasurface unit until the preset requirements are met.

[0034] Compared with the prior art, the beneficial effects of this invention are:

[0035] 1. By introducing the dimension of modulation frequency, this invention fills the gap in the theory of non-uniform modulation of spatiotemporal coded metasurfaces, and obtains a non-uniform modulation spatiotemporal coded metasurface with different modulation frequencies, thus broadening the application prospects of spatiotemporal coded metasurfaces.

[0036] 2. The harmonic intervals generated by the spatiotemporal coding metasurface of the present invention are no longer fixed, thus improving the spectral utilization rate;

[0037] 3. This invention applies a prime number non-uniform modulation strategy to a spatiotemporally encoded metasurface. Due to the properties of prime numbers (prime numbers cannot be divided by 1 and their own natural numbers), the scattered wave energy is more evenly distributed on the harmonics of each prime number modulation frequency, thereby breaking through the scattering limit of traditional metasurfaces and realizing a metasurface with ultra-low scattering characteristics.

[0038] 4. The spatiotemporal coded metasurface designed in this invention can jointly control electromagnetic waves in the spatial and frequency domains, thus broadening the degrees of freedom of the spatiotemporal coded metasurface and enabling even better scattering reduction effects in the spatial and spectral domains. Attached Figure Description

[0039] Figure 1 A schematic flowchart illustrating the steps of an embodiment of the design method for a non-uniform modulation spatiotemporally coded metasurface provided by the present invention;

[0040] Figure 2 Examples of various parts of the spatiotemporal coded metasurface are shown below, where (a) is a conceptual diagram of the spatiotemporal coded metasurface under uniform modulation, (b) is a conceptual diagram of the spatiotemporal coded metasurface under non-uniform modulation, (c) is the spatial coding matrix of the spatiotemporal coded metasurface, and (d) is the temporal coding sequence of the spatiotemporal coded metasurface.

[0041] Figure 3 This is a schematic diagram of the physical process of an embodiment of the design method for non-uniform modulation spatiotemporal coded metasurfaces provided by the present invention;

[0042] Figure 4 It is the harmonic order matrix and its far-field scattering diagram for a general non-uniform modulation case;

[0043] Figure 5 It is the harmonic order matrix and its far-field scattering diagram for the case of prime number non-uniform modulation;

[0044] Figure 6 The maximum scattering power spectrum and angular frequency spread diagrams under different modulation schemes are shown. (a) is the maximum scattering power spectrum of the spatiotemporally coded metasurface under different modulation schemes, (b) is the angular frequency spread diagram under uniform modulation, (c) is the angular frequency spread diagram under general non-uniform modulation, and (d) is the angular frequency spread diagram under prime number non-uniform modulation. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] This embodiment provides a design method for a non-uniform modulation spatiotemporal coded metasurface, such as Figure 1 As shown, it includes the following steps:

[0047] (1) Obtain the time coding sequence and corresponding modulation frequency assigned to each metasurface unit of the spatiotemporally coded metasurface.

[0048] In this spatiotemporally coded metasurface, the modulation frequencies of each metasurface unit are independent and uncorrelated. The total number of modulation frequencies for the spatiotemporally coded metasurface can be one or more. When there is only one modulation frequency, it corresponds to the traditional far-field scattering of spatiotemporally coded metasurfaces. When there are multiple modulation frequencies, some metasurface units are allowed to use the same modulation frequency. The modulation frequency can be any value, preferably a prime multiple of the fundamental modulation frequency Δf, thereby achieving a spatiotemporally coded metasurface with ultra-low scattering characteristics. For example, a spatiotemporally coded metasurface using prime-number non-uniform modulation could have modulation frequencies of 5Δf, 7Δf, 13Δf, 17Δf, 19Δf, 23Δf, 29Δf, and 31Δf. The time-coded sequences assigned to each metasurface unit are also independent and uncorrelated.

[0049] The spatiotemporally encoded metasurface can be any of the following types: transmissive, reflective, or active radiative, and each metasurface unit integrates one or more active devices.

[0050] (2) The digital control module generates a time control signal based on the time encoding sequence and inputs it to the corresponding metasurface unit.

[0051] The time control signal is updated according to the modulation frequency, specifically satisfying the following:

[0052]

[0053]

[0054] In the formula, Q m,n (t) represents the value of the time control signal of the (m,n)th metasurface unit of the spatiotemporally encoded metasurface at time t. The modulation frequency f is represented by m,n The corresponding period, f m,n Let L represent the modulation frequency assigned to the (m,n)th metasurface unit, and L represent the length of the time-coded sequence. Indicates T m,n After dividing the time into L time slots, the width of each time slot is s, and each time slot is assigned a corresponding time code. m,n (l) represents the time encoding of the (m,n)th metasurface unit assigned to time slot l, C[s m,n (l)] indicates s m,n (l) The corresponding time control signal value, G m,n (t) represents the width τ m,n The period is T m,nThe rectangular pulse signal. C[·] is a mapping function for time encoding, used to generate time control signals. For example, the time-encoded sequence can be considered as a discrete sequence composed of time-encoded symbols 0 and 1, while the time control signal can be considered as an analog signal. The time control signal corresponding to time-encoded symbol 0 in the time-encoded sequence is a voltage of 0V, while the time control signal corresponding to time-encoded symbol 1 is a voltage of 1.4V. The magnitude of the voltage depends on the specific design of the metasurface unit.

[0055] (3) A single-tone electromagnetic wave is generated by a feed antenna and irradiates the spatiotemporally encoded metasurface, generating wave-matter interaction with each metasurface unit, causing each metasurface unit to radiate electromagnetic waves outward.

[0056] The temporal reflectance coefficient of the spatiotemporally encoded metasurface satisfies:

[0057] Γ m,n (t)=R(Q m,n (t)),0 <t≤T m,n

[0058] In the formula, Γ m,n (t) is the time-domain reflection coefficient of the (m,n)th metasurface unit for the incident electromagnetic wave, Q m,n (t) represents the value of the time control signal of the (m,n)th metasurface element at time t, and R(·) represents the electromagnetic wave generation function of the metasurface element in response to the input signal.

[0059] The reflection coefficient is set to be expressed as follows: and Let represent the amplitude and phase of the reflection coefficient, respectively. The amplitude and phase of the reflection coefficient are determined by the time control signal. For example, for a 1-bit phase reflective metasurface, when the time code symbol in the time code sequence is 0, the phase of the output electromagnetic wave is 0 and the amplitude is 1, so the reflection coefficient is expressed as exp(j0). When the time code symbol in the time code sequence is 1, the phase of the output electromagnetic wave is π and the amplitude is still 1, so the reflection coefficient is expressed as exp(jπ).

[0060] (4) Calculate the equivalent reflection coefficient and spatial scattering energy of the spatiotemporally coded metasurface at different frequencies to determine whether the preset requirements are met. If not, adjust the time coding sequence and corresponding modulation frequency of each metasurface unit until the preset requirements are met.

[0061] According to Fourier series theory, the reflection coefficient Γ of the metasurface unit is... m,n (t) can be expanded in the frequency domain as follows:

[0062]

[0063] Where α m,n [k] is the equivalent reflection coefficient of the (m,n)th metasurface unit at the k-th harmonic frequency, which can be determined by the following formula:

[0064]

[0065]

[0066] Γ m,n [l] represents the time-domain reflection coefficient of the (m,n)th metasurface unit in time slot l.

[0067] Under non-uniform modulation, when the feed antenna generates an exp(j2πf) c An electromagnetic wave of frequency t) is incident on a metasurface. There are three cases of harmonic coupling between metasurface units: Consider two modulation frequencies f... m,,n and f p,q spatiotemporal encoded metasurface unit, k m,n and k p,q The harmonic orders of the two are respectively:

[0068] 1) f≠f c +k m,n f m,n ≠f c +k p,q f p,q Neither of the two metasurface units can generate electromagnetic harmonics at frequency f;

[0069] 2) f = f c +k m,n f m,n ≠f c +k p,q f p,q Only the modulation frequency is f m,n The metasurface units generate electromagnetic harmonics at frequency f;

[0070] 3) f = f c +k m,n f m,n =f c +k p,q f p,q Both metasurface units can generate electromagnetic harmonics at frequency f and are coupled to each other;

[0071] Based on the harmonic coupling conditions described above, the equivalent reflection coefficient β of the non-uniform modulation spatiotemporal coded metasurface at frequency f is... m,n (f) can be expressed as:

[0072]

[0073] in, Represents the set of integers; Substitute α m,n [k], we can obtain The expression is as follows:

[0074]

[0075] According to array antenna theory, the far-field scattering pattern S(θ,φ,f) of a non-uniformly modulated spatiotemporally coded metasurface at frequency f can be expressed as:

[0076]

[0077] In the formula, s(θ,φ,t) represents the spatial scattered energy at time t with elevation angle θ and azimuth angle φ, M and N are the number of rows and columns of the hypersurface unit on the spatiotemporally encoded hypersurface, respectively, and E m,n (θ,φ) represents the center frequency f of the (m,n)th metasurface unit. c Far-field pattern at d x and d y These are the period lengths of the spatiotemporally encoded metasurface unit along the x and y axes, respectively, λ. c It is the operating wavelength.

[0078] This embodiment also provides a design system for a non-uniform modulation spatiotemporal coded metasurface, including:

[0079] The parameter acquisition module is used to acquire the time coding sequence and the corresponding modulation frequency assigned to each metasurface unit of the spatiotemporally coded metasurface.

[0080] A digital control module is used to generate a time control signal based on a time-coded sequence and input it to the corresponding metasurface unit, wherein the time control signal is updated according to the modulation frequency;

[0081] The feed antenna is used to generate single-tone electromagnetic waves that illuminate the spatiotemporally encoded metasurface, generating wave-matter interactions with each metasurface unit, causing each metasurface unit to radiate electromagnetic waves outward.

[0082] The calculation module is used to calculate the equivalent reflection coefficient and spatial scattering energy of the spatiotemporally encoded metasurface at different frequencies;

[0083] The adjustment module is used to determine whether the equivalent reflection coefficient and spatial scattering energy meet the preset requirements. If not, it adjusts the time coding sequence and corresponding modulation frequency of each metasurface unit until the preset requirements are met.

[0084] The system provided in this embodiment of the invention can be used to execute the method provided in Embodiment 1 of the invention, and has the corresponding functions and beneficial effects of executing the method.

[0085] It is worth noting that the system can be implemented in software and / or hardware. The various units and modules included are divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved. In addition, the specific names of each functional unit are only for easy differentiation and are not used to limit the scope of protection of this invention.

[0086] The embodiments described above are merely illustrative. The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art will clearly understand that each implementation can be achieved using software plus necessary general-purpose hardware platforms, or it can be implemented solely through hardware, as long as the function or purpose can be achieved.

[0087] The following experiment demonstrates an embodiment of the invention. In the experiment, the spatiotemporal coded metasurface is an 8×8 reflective metasurface. Each spatiotemporal coded metasurface integrates a PIN diode. The spatiotemporal coded metasurface units exhibit different electromagnetic responses according to different time modulation signals from the control module. The electromagnetic responses are 0° and 180° phase, corresponding to "0" and "1" in the spatiotemporal coding matrix, respectively. In this embodiment, there are three possible numbers of modulation frequencies: a single modulation frequency, four non-prime modulation frequencies, and eight prime modulation frequencies, corresponding to uniform modulation, general non-uniform modulation, and prime-number non-uniform modulation, respectively.

[0088] Figure 2 (a) and (b) are conceptual diagrams of spatiotemporally coded metasurfaces under uniform and non-uniform modulation, respectively. A uniformly modulated spatiotemporally coded metasurface has one and only one modulation frequency, f0, across the entire array. A non-uniformly modulated spatiotemporally coded metasurface has multiple modulation frequencies, which are related to the coordinates of the elements and can be represented by a modulation frequency matrix. Figure 2 (c) is the spatial coding matrix of the spatiotemporal coding metasurface, corresponding to the initial coding situation of each unit. Figure 2 (d) is the time-coded sequence of the spatiotemporally encoded metasurface, where "0" and "1" determine the sequence. Figure 2 Whether the sequence of the spatial encoding matrix in (c) is flipped. For example, when the temporal encoding is 0, Figure 2 In (c), 0s in the spatial encoding matrix are flipped to 1s, and 0s are flipped to 1s; when the temporal encoding is 1, Figure 2The spatial coding matrix in (c) remains unchanged. In this embodiment, there are two sets of temporally coded sequences with coding lengths L of 8 and 16, respectively. Figure 2 The spatial encoding matrix in (c) is according to Figure 2 The time-coded sequences in (d) are flipped sequentially to form spatiotemporal coding matrices with coding lengths of 8 and 16, respectively.

[0089] Figure 3 The lower right corner shows a spatiotemporal coding matrix with a coding length of L=8, representing a typical non-uniform modulation case. Each column (along the x-axis) of the spatiotemporal coding metasurface uses the same modulation frequency. The time-coded sequence and modulation frequency on the 8×8 units constitute... Figure 3 The spatiotemporal coding matrix is ​​shown in the lower right corner. Figure 3 At the bottom, the digital control module is simplified to an FPGA chip, but in practice, control operations can be performed by a dedicated digital signal control module. Figure 3 The FPGA control module in the middle operates under general non-uniform modulation conditions, according to Figure 3 The spatiotemporal coding matrix shown in the lower right corner provides the corresponding time control signal for the spatiotemporal coding metasurface unit.

[0090] Figure 4 This is the harmonic order matrix and its far-field scattering plot for a typical non-uniform modulation case. In this example, the maximum energy scattered by a copper sheet of the same size as the spatiotemporally encoded metasurface is used as a reference, and the far-field scattering plot is normalized. In this embodiment, E m,n (θ,φ) is unified as cosθ. In this example, the number of modulation frequencies in a typical non-uniform modulation case is 4, the fundamental frequency is Δf, and the modulation frequencies are 10, 15, 20, and 25 times the fundamental frequency, respectively. Therefore, modulation frequencies 10Δf, 15Δf, 20Δf, and 25Δf are applied to the cells in columns 1 / 5, 2 / 6, 3 / 7, and 4 / 8, respectively. The spatiotemporal coding matrix adopts a coding length L = 8, as shown below. Figure 2 (c) and (d) or Figure 3 As shown in the lower right corner, the harmonic order matrix can be used to better understand the coupling between harmonics in non-uniform modulation. Figure 4 (a), (b), and (d) respectively demonstrate the frequency f c +10Δf、f c +15Δf and f c The harmonic order matrix and far-field scattering plot at +25Δf. It can be seen that these frequencies are the first harmonics of columns 1 / 5, 2 / 6, and 4 / 7, respectively. (Refer to...) Figure 4 (a), at frequency f cAt +10Δf, only the first harmonics of the elements in column 1 / 5 participate in far-field scattering synthesis; other elements do not satisfy the coupling condition at this frequency, and their equivalent reflection coefficient is forced to 0. It is also noted that the equivalent reflection coefficient α... m,n [k] is affected by the attenuation factor sinc(k / L). When k approaches ∞, the equivalent reflection coefficient approaches 0. Figure 4 The harmonic order matrix in (a) consists only of 1 and ∞, corresponding to the coupling situation between harmonics (2). Figure 4 The same applies to (b) and (d). Figure 4 (c), (e), and (f) demonstrate the frequency f. c +20Δf、f c +30Δf、f c The harmonic order matrix and its far-field scattering plot at +40Δf are shown. It can be seen that at these frequencies, multiple columns of spatiotemporally coded metasurface units with different modulation frequencies participate in the far-field scattering synthesis, corresponding to the coupling between harmonics (see section 3). Figure 4 (c), at frequency f c At +20Δf, the elements in columns 1 / 5 and 3 / 7 participate with equivalent reflection coefficients of the second and first orders, respectively. Figure 4 (c) In the far-field scattering calculation on the right, it can be seen that when harmonic coupling occurs in case 3), the effect of far-field scattering reduction is worse than in case 2).

[0091] Figure 5 This is the harmonic order matrix and far-field scattering diagram for the prime-number non-uniform modulation case. In this example, the prime-number non-uniform modulation case has 8 modulation frequencies, with a fundamental frequency of Δf. The modulation frequencies are 5, 7, 13, 17, 19, 23, 29, and 31 times the fundamental frequency. Therefore, the modulation frequencies 5Δf, 7Δf, 13Δf, 17Δf, 19Δf, 23Δf, 29Δf, and 31Δf are applied to the units in columns 1-8 in sequence. Since the modulation frequencies are all prime multiples of the fundamental frequency, this modulation method is also called the prime-number non-uniform modulation strategy. The spatiotemporal coding matrix adopts a coding length L = 8, as shown below. Figure 2 As shown in (c) and (d). Figure 5 (a) and (b) show the harmonic order matrix consisting only of 1(2) and ∞ and its far-field scattering plot, corresponding to the coupling situation between harmonics (2). Figure 5Figures (c)-(d) show the harmonic order matrix and its far-field scattering diagram when the first coupling occurs between different columns, corresponding to the coupling situation between harmonics (3). Benefiting from the property of prime numbers (prime numbers cannot be divided by any natural number other than 1 and themselves), the prime number non-uniform modulation strategy has two advantages: First, at the first harmonic frequency, only one modulation frequency participates in far-field scattering synthesis, while units with other modulation frequencies do not participate in far-field scattering synthesis; Second, when the first coupling occurs between different columns, the harmonic order k is sufficiently large, and the equivalent reflection coefficient, under the influence of the attenuation factor sinc(k / L), still achieves a good far-field scattering reduction despite the occurrence of harmonic coupling. Figure 5 For example, in frequency f (c), c At +35Δf, columns 1 and 2 participate in the far-field scattering calculation with equivalent reflection coefficients of the 7th and 5th orders, respectively. It can be seen that, compared to... Figure 4 Unlike general non-uniform modulation, when harmonic coupling occurs (3), the effect of far-field scattering reduction is very close to that of case (2).

[0092] Figure 6 (a) shows the maximum scattering power spectrum of the spatiotemporally coded metasurface under different modulation schemes. In this example, the fundamental modulation frequency Δf = 10 kHz, and there are three modulation schemes: 1. Uniform modulation (spatial-time coded matrix with coding length L = 8); 2. Prime-number non-uniform modulation (spatial-time coded matrix with coding length L = 8); 3. Prime-number non-uniform modulation (spatial-time coded matrix with coding length L = 16). Comparing modulation scheme 1 and scheme 2, it can be seen that under uniform modulation, the spatiotemporally coded metasurface exhibits greater electromagnetic scattering at low-order harmonics, while the electromagnetic wave energy after prime-number non-uniform modulation is not only spatially dispersed but also further uniformly distributed in the frequency domain. Comparing modulation scheme 2 and scheme 3, it can be seen that the coding length of the spatiotemporally coded matrix is ​​not the main reason for the uniform distribution of electromagnetic scattering in the frequency domain. Figure 6 Figures (b)-(d) show the angular frequency spread diagrams for uniform modulation, general non-uniform modulation, and prime-number non-uniform modulation, respectively. The angular frequency spread diagrams provide a better illustration of the joint manipulation of electromagnetic waves by the spatiotemporally coded metasurface in both the spatial and frequency domains. In this example, the angular frequency spread diagram is defined as the maximum energy of the far-field scattered electromagnetic wave within the azimuth angle range of 0 to 360°, written as:

[0093]

[0094] The expression S(θ,φ,f) is the far-field scattering expression of the spatiotemporally encoded metasurface at frequency f, written as:

[0095]

[0096] exist Figure 6 In examples (b)-(d), the coding length of the spatiotemporal coding matrix is ​​8, and the modulation base frequency is 10kHz. (Refer to...) Figure 6 In (b), under uniform modulation, the far-field scattering energy is mainly concentrated in low-order harmonics, and there are blank spectrum resources, resulting in low spectrum utilization; refer to Figure 6 (c) In general, uniform modulation increases the utilization of spectrum resources, but due to... Figure 4 It can be seen that the scattered energy still exhibits strong harmonic coupling in the spatial domain, and the angular frequency diffusion diagram shows that the scattered energy is also concentrated near the lower harmonics; from Figure 6 As can be seen from (d), under the condition of non-uniform prime number modulation, electromagnetic scattering energy can be distributed more evenly in the spatial and frequency domains, realizing a spatiotemporally encoded metasurface with ultra-low scattering characteristics. Figure 6 The effectiveness of non-uniform modulation methods for controlling electromagnetic waves in the spatial and frequency domains of spatiotemporally coded metasurfaces is demonstrated, and a non-uniform modulation strategy that enables spatiotemporally coded metasurfaces to have ultra-low scattering characteristics is presented.

[0097] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

Claims

1. A design method for a non-uniform modulation spatiotemporally coded metasurface, characterized in that, Includes the following steps: (1) Obtain the time coding sequence and corresponding modulation frequency assigned to each metasurface unit of the spatiotemporally coded metasurface; the modulation frequency is the modulation fundamental frequency. It is a prime multiple of the others; the modulation frequencies of each metasurface unit are independent and uncorrelated. (2) The digital control module generates a time control signal according to the time coding sequence and inputs it to the corresponding metasurface unit, wherein the time control signal is updated according to the modulation frequency; (3) A single-tone electromagnetic wave is generated by a feed antenna and irradiates the spatiotemporally encoded metasurface, generating wave-matter interaction with each metasurface unit, causing each metasurface unit to radiate electromagnetic waves outward. (4) Calculate the equivalent reflection coefficient and spatial scattering energy of the spatiotemporally coded metasurface at different frequencies, and determine whether the preset requirements are met. If not, adjust the time coding sequence and corresponding modulation frequency of each metasurface unit until the preset requirements are met. The equivalent reflection coefficient is calculated according to the following formula: , , In the formula, Indicates the first The equivalent reflection coefficient of a metasurface unit at frequency f Time-domain reflection coefficient The formula for calculating the Fourier coefficients, The frequency of the electromagnetic waves emitted by the feed antenna. Indicates the first The modulation frequency assigned to each metasurface unit Indicates modulation frequency The corresponding period, For the first The time-domain reflection coefficient of an incident electromagnetic wave for a metasurface unit cell. Represents the set of integers.

2. The design method for a non-uniform modulation spatiotemporal coded metasurface according to claim 1, characterized in that, The time control signal satisfies: , , In the formula, The first term representing the spatiotemporally encoded metasurface The value of the time control signal of each metasurface unit at time t. Indicates modulation frequency The corresponding period, Indicates the first The modulation frequency assigned to each metasurface unit, where L represents the length of the time-coded sequence. Indicates will After dividing the time into L time slots, the width of each time slot is determined, and each time slot is assigned a corresponding time code. Indicates the first The time encoding of each metasurface unit assigned to time slot l express The corresponding time control signal value, For width is The period is A rectangular pulse signal.

3. The design method for a non-uniform modulation spatiotemporal coded metasurface according to claim 1, characterized in that, The temporal reflectance coefficient of the spatiotemporally encoded metasurface satisfies: , In the formula, For the first The time-domain reflection coefficient of an incident electromagnetic wave for a metasurface unit cell. Indicates the first The value of the time control signal of each metasurface unit at time t. This represents the generation function of the electromagnetic wave in response to an input signal by a metasurface element.

4. The design method for a non-uniform modulation spatiotemporal coded metasurface according to claim 1, characterized in that, The spatial scattering energy is calculated according to the following formula: , In the formula, The pitch angle at time t is and azimuth angle The spatial scattering energy at coordinates, where M and N are the number of rows and columns of the hypersurface unit on the spatiotemporally encoded hypersurface, respectively. For the first The center frequency of each metasurface unit Far-field radiation pattern at that location, Indicates the first The equivalent reflection coefficient of a metasurface unit at frequency f and These are the period lengths of the spatiotemporally encoded metasurface units along the x and y axes, respectively. It is the operating wavelength.

5. The design method for a non-uniform modulation spatiotemporal coded metasurface according to claim 1, characterized in that, The spatiotemporally encoded metasurface can be any of the following types: transmissive, reflective, or active radiative, and each metasurface unit integrates one or more active devices.

6. The design method for a non-uniform modulation spatiotemporal coded metasurface according to claim 1, characterized in that, The time-coded sequences of each metasurface unit are independent and uncorrelated.

7. A design system for a non-uniform modulation spatiotemporally coded metasurface, characterized in that, include: The parameter acquisition module is used to acquire the time coding sequence and the corresponding modulation frequency assigned to each metasurface unit of the spatiotemporally coded metasurface. The modulation frequency is the modulation base frequency. It is a prime multiple of the others; the modulation frequencies of each metasurface unit are independent and uncorrelated. A digital control module is used to generate a time control signal based on a time-coded sequence and input it to the corresponding metasurface unit, wherein the time control signal is updated according to the modulation frequency; The feed antenna is used to generate single-tone electromagnetic waves that illuminate the spatiotemporally encoded metasurface, generating wave-matter interactions with each metasurface unit, causing each metasurface unit to radiate electromagnetic waves outward. The calculation module is used to calculate the equivalent reflection coefficient and spatial scattering energy of the spatiotemporally encoded metasurface at different frequencies; The adjustment module is used to determine whether the equivalent reflection coefficient and spatial scattering energy meet the preset requirements. If they do not meet the requirements, the time coding sequence and the corresponding modulation frequency of each metasurface unit are adjusted until the preset requirements are met. The equivalent reflection coefficient is calculated according to the following formula: , , In the formula, Indicates the first The equivalent reflection coefficient of a metasurface unit at frequency f Time-domain reflection coefficient The formula for calculating the Fourier coefficients, The frequency of the electromagnetic waves emitted by the feed antenna. Indicates the first The modulation frequency assigned to each metasurface unit Indicates modulation frequency The corresponding period, For the first The time-domain reflection coefficient of an incident electromagnetic wave for a metasurface unit cell. Represents the set of integers.

Images