A method for electromagnetic wave spatiotemporal frequency domain modulation based on digitally programmable transmissive metasurface

Abstract

The present invention discloses a method for spatiotemporal frequency domain modulation of electromagnetic waves based on a digitally programmable transmissive metasurface. Based on the Huygens-Fresnel principle, the present invention establishes a systematic theory for spatiotemporal frequency domain modulation of monochromatic waves and non-monochromatic waves based on a digitally coded metasurface, combines the dynamic surface coding of the digitally coded metasurface to illustrate the spatiotemporal frequency domain response, and verifies the effectiveness of the designed transmissive metasurface to verify the rationality of the theory, laying a foundation for the application prospects of digitally coded metasurfaces in wireless communications, intelligent perception and radar systems.

Description

Technical Field

[0001] The present invention relates to the technical field of signal modulation based on digitally programmable transmissive metasurfaces, and in particular to a method for electromagnetic wave spatiotemporal frequency domain modulation based on digitally programmable transmissive metasurfaces. Background Art

[0002] Digitally programmable metasurfaces can achieve modulation of electromagnetic waves in the time, space, and frequency domains by dynamically reconstructing the unit structure of the aperture, thereby building a bridge connecting metasurfaces and electronic information.

[0003] At present, the research on digital programmable metasurfaces is conducted in the space-frequency domain or space-time domain. In the space-frequency domain analysis, each dynamic unit of the metasurface is regarded as a valid unit in the frequency domain through Fourier transform, but the instantaneous information will be lost in this process. In the space-time analysis, the metasurface surface is instantaneously analyzed, so the instantaneous information is retained. These works have explained the space-time-frequency modulation of electromagnetic waves based on the space-frequency modulation and space-time modulation of metasurfaces, but there is still a lack of systematic and effective analysis of the space-time-frequency modulation of electromagnetic waves based on metasurfaces, especially for the case of non-monochromatic electromagnetic waves that are prevalent in most applications of radar or communication systems. Summary of the invention

[0004] In view of this, the object of the present invention is to provide a method for space-time and frequency domain modulation of electromagnetic waves based on a digitally programmable transmissive metasurface, which is used to realize space-time and frequency domain modulation of monochromatic waves and non-monochromatic waves.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A method for electromagnetic wave spatiotemporal frequency domain modulation based on a digitally programmable transmissive metasurface comprises the following steps:

[0007] Step S1, designing the initial aperture coding of the digital programmable transmissive metasurface to generate a far-field in a desired direction, then adding a far-field phase modulation term on the basis of the initial aperture coding to obtain a first aperture coding, and then dynamically switching the first aperture coding at a certain rate to dynamically change the far-field phase to achieve phase modulation within the far-field range;

[0008] Step S2, designing a second aperture code of the digital programmable transmissive metasurface, and dynamically changing the far-field direction by switching the second aperture code at a certain rate, so that the far-field of the metasurface can change its spatial direction with time, thereby realizing spatiotemporal modulation;

[0009] Step S3: Combining the first aperture-face coding and the second aperture-face coding, so that the far-field of the digitally programmable transmissive metasurface changes spatial orientation and phase over time.

[0010] Furthermore, the expression of the far field in the desired direction is:

[0011]

[0012]

[0013]

[0014]

[0015]

[0016] In the formula, M and N are the number of units in the x and y directions of the metasurface, and U t,mn is the instantaneous aperture field, θ and are the azimuth and elevation angles of the far field, A t represents the gain, P represents the unit cycle length, φ(t) represents the signal phase, R o represents the vertical distance between the point source and the hypersurface, Where x, y and z represent the coordinates of the far field.

[0017] Furthermore, the initial surface coding of the digitally programmable transmissive metasurface is specifically designed by:

[0018] The far-field in the desired direction is obtained by performing inverse Fourier transform on the far-field.

[0019] Furthermore, the first interface coding is specifically performed by U(u,v;t)exp jφ After inverse Fourier transform, we get: U(u, v; t) represents the far field in the desired direction, and φ represents the far-field phase modulation term.

[0020] Furthermore, in step S2, the corresponding instantaneous aperture field U is designed for the far-field U(u, v; t) in different desired directions. t,mn , thereby obtaining the corresponding second surface code.

[0021] Furthermore, the step S3 specifically includes:

[0022] A far-field phase modulation term is added on the basis of the second aperture face coding, that is, the second aperture face coding is combined with the first aperture face coding, and the second aperture face coding is switched at a certain rate so that the far-field of the digitally programmable transmissive metasurface changes spatial direction and phase over time, thereby realizing space-time frequency modulation.

[0023] Furthermore, the certain rate is specifically 50 MHz.

[0024] The beneficial effects of the present invention are:

[0025] Based on the Huygens-Fresnel principle, the present invention establishes a systematic theory of the space-time frequency domain modulation of monochromatic waves and non-monochromatic waves based on digitally coded metasurfaces, combines the dynamic surface coding of the digitally coded metasurfaces to illustrate the space-time frequency domain response, and verifies the effectiveness of the designed transmission metasurface to verify the rationality of the theory, laying a foundation for the application prospects of digitally coded metasurfaces in wireless communications, intelligent perception and radar systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A schematic diagram of a digitally programmable transmissive metasurface provided by the present invention;

[0027] Figure 2 a is a schematic diagram of the interaction between the unit structure and the electromagnetic wave in the digitally programmable transmissive metasurface provided by the present invention;

[0028] Figure 2 b is a schematic diagram of the structure of a unit in a digitally programmable transmissive metasurface provided by the present invention;

[0029] Figure 2 c is a transmission coefficient simulation result diagram of a unit structure in a digitally programmable transmission metasurface provided by the present invention;

[0030] Figure 2 d is a transmission coefficient simulation result diagram of a unit structure in a digitally programmable transmission metasurface provided by the present invention;

[0031] Figure 3 a is a waveform diagram of the digitally programmable transmissive metasurface provided by the present invention under a 28 GHz monochromatic wave;

[0032] Figure 3 b is a waveform diagram of the digital programmable transmissive metasurface provided by the present invention under a linear frequency modulation wave;

[0033] Figure 3 c is a spectrum diagram of the digitally programmable transmissive metasurface provided by the present invention under a 28 GHz monochromatic wave;

[0034] Figure 3 d is a spectrum diagram of the digitally programmable transmissive metasurface provided by the present invention under a linear frequency modulation wave;

[0035] Figure 4 a is a schematic diagram of directional radiation generated by the digital programmable transmissive metasurface provided by the present invention after the aperture coding is designed;

[0036] Figure 4 b is the digital programmable transmissive metasurface provided by the present invention based on Figure 4Schematic diagram of the far-field pattern under the designed oral-facial coding in a;

[0037] Figure 5 a is Figure 4 The pattern of the designed surface coding in a when the initial phase φ = 0°;

[0038] Figure 5 b is Figure 4 The pattern of the designed aperture coding in a when the initial phase φ = 180°;

[0039] Figure 5 c is a schematic diagram of the switching sequence of the phase parameter φ within one cycle;

[0040] Figure 5 d is a schematic diagram of the spectrum obtained when φ1 = 0°, φ2 = 90°, φ3 = 180° and φ4 = 270°;

[0041] Figure 6 a is a schematic diagram of the modulation spectrum of a monochromatic wave;

[0042] Figure 6 b is a schematic diagram of the modulation spectrum of the linear frequency modulation wave;

[0043] Figure 6 c is a schematic diagram of the time-frequency spectrum of a monochromatic wave;

[0044] Figure 6 d is a schematic diagram of the time-frequency spectrum of the linear frequency modulation wave;

[0045] Figure 7 a is a schematic diagram of the spatial frequency spectrum of a monochromatic wave;

[0046] Figure 7 b is a schematic diagram of the spatial frequency spectrum of a non-monochromatic wave;

[0047] Figure 8 A schematic diagram of the beam scanning results between -20° and 20° with an interval of 10° obtained for switching the aperture coding;

[0048] Fig. 9 a is Figure 5 a and Figure 5 Schematic diagram of the far-field amplitude performance of the aperture coding in b;

[0049] Fig. 9 b is Figure 5 a and Figure 5 Schematic diagram of the far-field phase performance of the aperture coding in b;

[0050] Fig. 9 c is a schematic diagram of the main lobe spectrum of the metasurface when the interface coding is switched at a switching speed of 10 MHz;

[0051] Fig. 9 d is a schematic diagram of the main lobe spectrum of the metasurface when the interface coding is switched at a switching speed of 20 MHz. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] The present invention provides a method for spatiotemporal frequency domain modulation of electromagnetic waves based on a digitally programmable transmissive metasurface. Before describing the method of the present invention in detail, the principles on which the present invention is based are explained first. The principles on which the present invention is based specifically include: 1. Basic principles; 2. Description of the principles of interaction between the unit structure in the digitally programmable transmissive metasurface and electromagnetic waves; 3. Description of the principles of interaction between the digitally programmable transmissive metasurface and electromagnetic waves.

[0054] More specifically, the above principle is:

[0055] 1. Basic principles of the present invention

[0056] Specifically, the digitally programmable transmissive metasurface of the present invention is as follows: Figure 1 As shown in Figure 1, the scattering field of the metasurface is derived according to the Huygens-Fresnel principle. Specifically, assuming that the aperture field of the digital programmable metasurface is U(x', y', t), the far-field S(x, y, z; t) is expressed as:

[0057]

[0058] In formula (1), x, y and z are the coordinates of the far field, x' and y' are the coordinates of the aperture field, and c is the speed of light;

[0059] Correspondingly, the spectrum of the far-field is obtained by Fourier transforming formula (1):

[0060]

[0061] In formula (2), f represents Fourier transform, c is the speed of light, and k is the wave number in free space;

[0062] Based on equations (1) and (2), the instantaneous or frequency-dependent scattering field of the metasurface can be designed by specifying sufficient coding sequence changes for each unit of the digitally programmable metasurface.

[0063] When the far-field pattern is specified, the coding sequence corresponding to the metasurface can be uniquely determined based on formulas (1) and (2). It is worth noting that the frequency-dependent scattering pattern is not an instantaneous pattern, but a pattern converted from the accumulated time-domain signal by Fourier transform. However, if the specified time-domain pattern is equivalent to the specified frequency-domain pattern in Fourier transform, the synthetic coding sequence of the metasurface is the same in both cases.

[0064] 2. Principle of interaction between unit structure and electromagnetic waves in digitally programmable transmissive metasurface

[0065] like Figure 2 As shown in Figure b, each unit contains a four-layer metal structure. The surface current is input from the fourth layer and transmitted to the first layer through the metal column. Two PIN diodes are attached to the first layer with the same direction. The second and third layers are used to feed the diodes, and the third layer is also an isolation layer, which is used to block the direct coupling between the first and fourth layers. The DC voltage of the third layer is maintained at 1.8V, and the DC voltage of the second layer is switched between 0V and 3.3V. Since the threshold voltage of the PIN diode is 1.2V, the surface current of the first layer will flow in opposite directions when the DC voltage of the second layer is 0V and 3.3V. The corresponding binary states are represented as "1" and "0", respectively, which is the digital coding of the unit. Specifically, the code "1" indicates that diode 1 is in the on state and diode 2 is in the off state, and the code "0" indicates that diode 1 is in the off state and diode 2 is in the on state.

[0066] Figure 2 c and Figure 2 d shows the transmission coefficient simulation results of the unit structure, and it is found that the transmission coefficients of the unit in the 0 state and the 1 state are 0.95e at 28GHz. j36.8° and 0.96e -j137.3° .

[0067] Figure 2 a shows the interaction diagram of the unit structure and electromagnetic waves. Considering the general case, the digital programmable metasurface is composed of a time-varying point source signal O(0,0,-R o ; t) = Ae jφ(t) Irradiation, where R o represents the vertical distance between the point source and the metasurface, A represents the signal amplitude, and φ(t) represents the signal phase.

[0068] According to formula (1), the unit at a point P(x p ,y p ) can be expressed as follows:

[0069]

[0070] In formula (3), x p ,y p represents the coordinates of the incident point, A represents the signal amplitude, φ(t) represents the signal phase,

[0071] The instantaneous frequency of the incident wave can be expressed as:

[0072]

[0073] Since φ(t) can be defined arbitrarily, the instantaneous frequency f t may not be a constant, since the transmission coefficient of the unit structure is dispersive and non-monochromatic incident waves maintain a dispersive transmission coefficient.

[0074] For an accurate calculation, the instantaneous frequency of the incident wave can be evaluated and the corresponding transmission coefficient at each time instant can be used. However, for narrowband incident waves, the instantaneous frequency can be considered to be the center frequency f c , then the transmission coefficient can be regarded as a constant corresponding to the center frequency. Since the unit structure is determined by binary coding, the time-varying transmission coefficient can be written as:

[0075] Γ(x p ,y p ; t) = (C(t)⊙1)Γ (1) (x p ,y p ;f c )+(C(t)⊙0)Γ (0) (x p ,y p ;f c ) (5)

[0076] In formula (5), ⊙ is the XOR operator, and the center frequency f c is set to 28 GHz, C(t) represents the binary coding of the metasurface, Γ (1) represents the unit transmission coefficient of the code “1”, Γ (0) Represents the unit transmission coefficient of code "0".

[0077] Then the output waveform of the unit structure can be written as:

[0078] U(x p ,y p ; t) = I(x p ,y p ; t)Γ(x p ,y p ; t) (6)

[0079] 3. Principle of interaction between digitally programmable transmissive metasurface and electromagnetic waves

[0080] Based on formula (1) and formula (6), the far-field pattern of the entire digital coding metasurface can be expressed as:

[0081]

[0082] In formula (7), θ is the far field pitch angle,

[0083] Substituting formula (3) and formula (5) into formula (7), and discretizing the metasurface area according to the unit period p, the far-field pattern can be calculated using the following equation:

[0084]

[0085]

[0086]

[0087] In formula (8)-formula (10), θ and are the azimuth and elevation angles of the far field, U t,mn is the instantaneous aperture field, M, N are the number of units in the x-direction and y-direction of the metasurface, and P represents the unit period length;

[0088] From formula (8), it can be seen that the instantaneous far-field field U(u, v; t) is the instantaneous aperture field U t,mn Conversely, the instantaneous aperture field is the inverse discrete Fourier transform of the instantaneous far-field.

[0089] In summary, based on the above three principles, assuming that the digitally programmable transmissive metasurface described in the present invention includes 400 (20×20) unit structures, the spatiotemporal frequency domain characteristics of the metasurface can be calculated by formula (8).

[0090] Figure 3 a. Figure 3 b. Figure 3 c. Figure 3 d, Figure 4 a and Figure 4 b represents the instantaneous far-field characteristics of the digitally programmable transmissive metasurface when it is illuminated by monochromatic and non-monochromatic waves, where Figure 3 a and Figure 3 c shows the waveform and spectrum of the 28 GHz monochromatic wave, respectively. Therefore, based on formula (8), the digital programmable transmissive metasurface can be designed to generate directional radiation through the surface coding, as follows: Figure 4 As shown in a, the pattern of the mouth surface coding is as follows Figure 5 As shown in a.

[0091] Figure 3 b and Figure 3d are the waveform and spectrum of the linear frequency modulation wave, with a bandwidth of 10MHz and a pulse width of 7.5us. Figure 4 b shows the far-field pattern of the metasurface under the same aperture coding state. The high consistency between the two indicates that the dispersion of narrow-band non-monochromatic waves has almost no effect on the radiation field characteristics.

[0092] From the above analysis, if the aperture coding remains unchanged, the digitally coded metasurface can only perform spatial modulation on the electromagnetic waves. If the aperture coding can be dynamically controlled, the time-frequency modulation of the electromagnetic waves can be achieved.

[0093] Figure 5 a. Figure 5 b shows the initial phase φ = 0° and φ = 180°, respectively, assuming that U(u, v; t) is Figure 4 a far-field pattern, then U(u,v;t)exp jφ represents the same pattern with an additional phase, and the corresponding mouth-to-face coding can be obtained by performing an inverse discrete Fourier transform on it.

[0094] Generally, the phase parameter φ can be arbitrarily set to φ1, φ2, φ3, φ4 in each cycle period, such as Figure 5 As shown in (c), the switching sequence of φ can be regarded as the time domain coding of the digital coding metasurface, and the corresponding spectrum can be calculated according to the specific time domain coding.

[0095] Figure 5 d is the spectrum obtained when φ1=0°, φ2=90°, φ3=180° and φ4=270°, and the interface coding switching rate is set to 50 MHz.

[0096] To compare the response of monochromatic and non-monochromatic waves, the metasurface is set up by Figure 5 a and Figure 5 The interface coding of b is switched periodically at a rate of 50 MHz. Based on formula (8), Figure 6 a. Figure 6 b. Figure 6 c. Figure 6 d and Figure 7 a. Figure 7 b gives the calculated time-frequency spectrum and space-time spectrum of the far-field radiation of the metasurface. Figure 6 a and Figure 6 In b, the main lobe of the spectrum is different from that of the incident wave, and the harmonic components are generated by the metasurface-based phase modulation. In addition, due to the group delay distortion of the transmission path, the in-band flatness of the linear frequency modulation wave is affected. Figure 6 c and Figure 6 The time-frequency spectrum of d shows that there are frequency transitions at any time. Figure 7 a and Figure 7b are the empty spectra of monochromatic and non-monochromatic waves, respectively. Since the specified far-field pattern is a directional beam, the metasurface-based phase modulation is only effective within the main beam range, so the frequency conversion of the far-field only exists within the main beam range.

[0097] Example 1

[0098] Based on the above principle, this embodiment provides a method for spatiotemporal frequency domain modulation of electromagnetic waves based on a digitally programmable transmissive metasurface, comprising the following steps:

[0099] Step S1, designing the initial aperture coding of the digital programmable transmissive metasurface to generate a far-field in a desired direction, then adding a far-field phase modulation term on the basis of the initial aperture coding to obtain a first aperture coding, and then dynamically switching the first aperture coding at a certain rate to dynamically change the far-field phase to achieve phase modulation within the far-field range;

[0100] Specifically, the expression of the far field in the desired direction is:

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] In the formula, M and N are the number of units in the x and y directions of the metasurface, and U t,mn is the instantaneous aperture field, θ and are the azimuth and elevation angles of the far field, A t represents the gain, P represents the unit cycle length, φ(t) represents the signal phase, R o represents the vertical distance between the point source and the hypersurface, Where x, y and z represent the coordinates of the far field.

[0107] Specifically, the initial surface coding of the digital programmable transmissive metasurface is designed by:

[0108] It is obtained by performing inverse Fourier transform on the far field in the desired direction.

[0109] Specifically, the first interface encoding is performed by:

[0110] For U(u,v;t)exp jφAfter inverse Fourier transform, we get: U(u, v; t) represents the far field in the desired direction, and φ represents the far-field phase modulation term.

[0111] Step S2: design the second aperture coding of the digital programmable transmissive metasurface, that is, design the corresponding instantaneous aperture field U for the far-field U(u, v; t) in different desired directions. t,mn , obtain the corresponding second aperture face code, and dynamically change the far-field direction by switching the second aperture face code at a certain rate, so that the far-field of the metasurface can change the spatial direction with time, thereby realizing spatiotemporal modulation;

[0112] Step S3, adding a far-field phase modulation term on the basis of the second aperture face coding, that is, combining the second aperture face coding with the first aperture face coding, and switching the second aperture face coding at a certain rate so that the far-field of the digitally programmable transmissive metasurface changes spatial direction and phase over time, thereby realizing spatiotemporal frequency modulation.

[0113] Specifically, the above-mentioned certain rate is 50 MHz.

[0114] In order to verify the correctness of the method provided in this embodiment, this embodiment also conducted tests, specifically:

[0115] In order to verify the rationality of the spatiotemporal frequency domain modulation of electromagnetic waves based on digitally coded metasurfaces, the performance of the digitally coded transmission metasurface containing 100 (10×10) units was tested. Only a monochromatic wave source was used for verification in the test.

[0116] Figure 8 , Fig. 9 a. Fig. 9 b. Fig. 9 c. Fig. 9 d shows the test results of the metasurface, where Figure 8 The beam scanning results of -20° to 20° with an interval of 10° obtained by switching the metasurface surface coding are given; Fig. 9 a and Fig. 9 b Yes Figure 5 a and Figure 5 The performance of the far-field amplitude and phase of the two aperture codings in b was verified. It can be seen from the figure that the far-field patterns of the two aperture coding radiations are similar, with only slight differences caused by quantization errors, and the phase is successfully flipped within the main lobe range. Finally, the time-frequency modulation based on the metasurface is tested by observing the spectrum of the main lobe when the metasurface coding is periodically switched. The switching speeds of 10MHz and 20MHz were used during the test. Fig. 9 c and Fig. 9d shows the test spectrum, and it is observed that the harmonic components appear in the expected manner, indicating that the metasurface successfully achieves time-frequency modulation of the incident wave.

[0117] The matters not described in detail in the present invention are all known technologies to those skilled in the art.

[0118] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for electromagnetic wave spatiotemporal frequency domain modulation based on a digitally programmable transmissive metasurface, characterized in that: The steps include: Step S1, designing the initial aperture coding of the digital programmable transmissive metasurface to generate a far-field in a desired direction, then adding a far-field phase modulation term on the basis of the initial aperture coding to obtain a first aperture coding, and then dynamically switching the first aperture coding at a certain rate to dynamically change the far-field phase to achieve phase modulation within the far-field range; Step S2, designing a second aperture code of the digital programmable transmissive metasurface, and dynamically changing the far-field direction by switching the second aperture code at a certain rate, so that the far-field of the metasurface can change its spatial direction with time, thereby realizing spatiotemporal modulation; Step S3, combining the first aperture-face coding and the second aperture-face coding, so that the far-field of the digitally programmable transmissive metasurface changes spatial orientation and phase over time; The expression of the far field in the desired direction is: In the formula, M and N are the number of units in the x and y directions of the metasurface, and U t,mn is the instantaneous aperture field, θ and are the azimuth and elevation angles of the far field, A t represents the gain, P represents the unit cycle length, φ(t) represents the signal phase, R o represents the vertical distance between the point source and the hypersurface, Where x, y and z represent the coordinates of the far field; c is the speed of light.

2. According to claim 1, a method for electromagnetic wave spatiotemporal frequency domain modulation based on a digitally programmable transmissive metasurface is characterized in that: The initial surface coding of the digital programmable transmissive metasurface is specifically designed by: The far-field in the desired direction is obtained by performing inverse Fourier transform on the far-field.

3. The electromagnetic wave spatiotemporal frequency domain modulation method based on a digitally programmable transmissive metasurface according to claim 2, characterized in that: The first interface coding is specifically performed by U(u,v;t)exp jφ After inverse Fourier transform, we get: U(u, v; t) represents the far field in the desired direction, and φ represents the far-field phase modulation term.

4. The electromagnetic wave spatiotemporal frequency domain modulation method based on a digitally programmable transmissive metasurface according to claim 3, characterized in that: In step S2, the corresponding instantaneous aperture field U is designed for the far-field U(u, v; t) in different desired directions. t,mn , thereby obtaining the corresponding second surface code.

5. The electromagnetic wave spatiotemporal frequency domain modulation method based on a digitally programmable transmissive metasurface according to claim 4, characterized in that: The step S3 specifically includes: A far-field phase modulation term is added on the basis of the second aperture face coding, that is, the second aperture face coding is combined with the first aperture face coding, and the second aperture face coding is switched at a certain rate so that the far-field of the digitally programmable transmissive metasurface changes spatial direction and phase over time, thereby realizing space-time frequency modulation.

6. The electromagnetic wave spatiotemporal frequency domain modulation method based on a digitally programmable transmissive metasurface according to claim 5, characterized in that: The certain rate is specifically 50 MHz.

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