A method for generating terahertz spatiotemporal sagniton based on linearly polarized light excited metasurface

Abstract

The application discloses a method for generating terahertz spatiotemporal skyrmions based on linearly polarized light excitation super surface, and relates to the technical field of terahertz photonics and topological photonics. The method comprises the following steps: designing a super surface unit with a symmetry breaking structure; making a single beam of terahertz linearly polarized light pass through the super surface unit; the super surface unit simultaneously excites two beams of orthogonal linearly polarized components with a preset amplitude ratio and a phase difference, i.e., co-polarized transmission light and cross-polarized transmission light, which are naturally coaxially superimposed to form a spatiotemporal double half sub topological texture in a momentum-frequency space; and making the superimposed light field pass through a quarter-wave plate, so that the spatiotemporal Bimeron is converted into a complete spatiotemporal skyrmion. The generated spatiotemporal skyrmion can be flexibly regulated by the rotation angle of the super surface unit, and the order of the skyrmion number can be regulated by cascading multiple designed structures.

Description

Technical Field

[0001] This invention relates to the field of terahertz photonics technology, specifically to a method for generating terahertz spacetime skyrmions based on linearly polarized light excitation of a metasurface. Background Technology

[0002] The concept of a skyrmion originated from the unified field theory proposed by British particle physicist Tony Skyrme in 1962. It initially appeared as a topological soliton solution, its essential characteristic being the combination of vector configuration and topological stability. In recent years, with the interdisciplinary integration of topological physics and optics, the skyrmion concept has been successfully extended to optical systems, giving rise to the emerging research direction of "optical skyrmions," which has rapidly grown into a key branch in topological photonics and structured light field manipulation. Optical skyrmions have shown significant potential in many cutting-edge applications, including optical communication, high-precision micro-displacement measurement, disturbance-resistant optical information transmission, and reconfigurable photonic signal processing, attracting increasing academic attention and research investment.

[0003] However, current research on optical skyrmions primarily focuses on the pure spatial dimension, with their topological configurations typically defined in a static transverse plane. Systematic exploration of temporal degrees of freedom remains relatively weak, significantly limiting the information capacity of topological light fields and the flexibility of their dynamic manipulation. To address this bottleneck, Professor Zhan Qiwen's research group at the University of Shanghai for Science and Technology pioneered the proposal and experimental verification of the existence of spacetime skyrmions in 2025. This research successfully constructed a polarization texture structure with stable topological invariants in the spatiotemporal domain (e.g., the x–t plane) by synergistically fusing transverse orbital angular momentum with the vector degrees of freedom of the ultrashort pulse light field. This breakthrough not only effectively extends the research paradigm of optical skyrmions from a single spatial topology to a spatiotemporally combined topology but also marks a significant paradigm shift in this field. Specific experimental results are as follows: Figure 1 As shown.

[0004] Compared to spatial skyrmions, spacetime skyrmions exhibit more significant research value in terms of their physical implications, and their application prospects are also more promising. On the one hand, the introduction of the time dimension effectively expands the configuration space of the optical field topology, allowing the topological state to exhibit dynamic behavior that evolves over time during propagation, thus providing new degrees of freedom for high-dimensional information encoding and flexible control. On the other hand, spacetime skyrmions naturally combine ultrafast time response characteristics with the robustness of topology protection, demonstrating unique functional advantages and application effectiveness in cutting-edge fields such as ultra-high-speed optical information processing, high-capacity optical communication systems, and topological optical storage.

[0005] The terahertz band occupies a unique position in the electromagnetic spectrum, combining high bandwidth and strong penetration capabilities, and shows significant application potential in fields such as sixth-generation mobile communication, ultrafast spectroscopy, and quantum information science. Terahertz spacetime skyrmions can directly use their topological configurations as information carriers. Their topological invariants are inherently robust to continuous deformation and weak perturbations, naturally possessing noise-resistant and distortion-resistant information encoding characteristics. Simultaneously, their vector field distribution contains multiple physical degrees of freedom that can be independently or collaboratively controlled, providing a structural foundation for achieving high-dimensional encoding and robust transmission. Therefore, in-depth research into the excitation mechanism and detection methods of terahertz spacetime skyrmions will not only help deepen the understanding of the physical implications of terahertz light fields from a topological perspective, but will also provide key theoretical support and experimental evidence for the development of future high-capacity, highly interference-resistant communication systems and quantum information encoding technologies, possessing significant scientific exploration value and engineering application prospects.

[0006] Based on the type of vector involved, optical skyrmions can be classified into various categories such as electromagnetic field vectors, spin vectors, and Stokes vectors. According to the differences in the topological configuration of the vector spin direction, they can be further distinguished into different forms such as Néel-type, Anti-type, Bloch-type, and Janus-type. Currently, the main focus of skyrmion-related research is still concentrated in the optical frequency band, and experimental verification of spacetime skyrmions is also limited to the optical band. Research on spacetime skyrmions in the terahertz band has not yet been publicly reported. Based on existing literature, research on spacetime skyrmions mainly revolves around the various topological configurations exhibited by Stokes vectors, and their realization can be roughly summarized into two typical schemes.

[0007] The first type of generation scheme is achieved using spectral manipulation techniques. In 2026, the AFAbouraddy research team at the University of Florida successfully generated a spacetime optical meron (i.e., a skyrmion half-particle with a topological charge of 1 / 2) with three-dimensional localization characteristics using this technique. Their experimental setup consists of a multi-stage spectral transformation link composed of a chirped grating, a spatial light modulator, and a phase plate. First, the spectral components of the ultrashort pulse are spatially expanded in the frequency domain plane. Then, through spectral transformation and coordinate transformation operations, the spectral distribution is reconstructed into a radial arrangement. Finally, through a birefringent metasurface polarization mask placed on the spectral surface, point-by-point polarization manipulation is performed on each spectral position, ultimately mapping the spin texture to the frequency-momentum joint space.

[0008] The second implementation scheme is based on a two-beam superposition mechanism. In 2025, Professor Zhan Qiwen's team at the University of Shanghai for Science and Technology experimentally realized a spacetime skyrmion for the first time using this method. The technical route is as follows: First, a linearly polarized ultrafast light pulse is divided into two equal paths. One path is mapped to frequency-momentum space via a 4F optical system and subjected to precise complex amplitude modulation using a spatial light modulator placed on this plane. It is then restored to the spacetime domain via the 4F system again, ultimately being reconstructed into a spacetime vortex light field carrying orbital angular momentum. The other path remains a simple Gaussian beam. The two beams are finally combined and coaxially coherently superimposed, forming a topological texture in the spacetime plane. It should be noted that the configuration directly generated by this linearly polarized two-beam superposition is a spacetime bimeron; by introducing a quarter-wave plate in the subsequent optical path, it can be converted into a spacetime skyrmion with unit topological charge.

[0009] In summary, current methods for generating spacetime skyrmions can be categorized into two types, each with its own principles and significant differences in implementation paths and technological bottlenecks. The first type is based on spectral manipulation strategies, achieving programmable control of the spacetime topology by point-by-point manipulation of the geometric configuration and polarization distribution within the spectral plane. However, this approach relies on a multi-stage spectral transformation link consisting of chirped gratings, spatial light modulators, and phase plates. The system structure is cumbersome, and the precision requirements for polarization modulation are extremely stringent. Furthermore, the high cost and significant insertion loss associated with precision optical components pose significant challenges to its integrated application. The second type is based on the principle of two-beam interference superposition. Its core lies in precisely controlling the amplitude ratio and phase difference of two orthogonal linearly polarized components (x-polarization and y-polarization) to synthesize a vector light field distribution with skyrmion topology in the spacetime domain. Compared to the first type of scheme, this method avoids the energy loss problem caused by point-by-point polarization encoding. However, its implementation requires three cascaded physical steps: "beam splitting - modulation - beam combining". This involves the complex amplitude modulation operation of the spatial light modulator and places high demands on the collimation accuracy of the optical path and the time synchronization of the two pulses. The overall system's structural compactness is still constrained.

[0010] Among the two methods mentioned above, the two-beam superposition method is more suitable as a foundational platform for exploring the physical mechanisms of spatiotemporal topological light fields due to its relatively simple system architecture and intuitive control. However, this approach still relies on separate optical paths and bulk components, and its environmental stability and integration need to be improved. Summary of the Invention

[0011] The technical problem to be solved by this invention is how to provide a simple and robust method for generating terahertz spacetime skyrmions based on linearly polarized light excitation of metasurfaces.

[0012] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for generating terahertz spacetime skyrmions based on linearly polarized light excitation of a metasurface, the method comprising the following steps:

[0013] A metasurface unit is designed so that when a single beam of linearly polarized terahertz light is incident, the light passes through the metasurface unit, which simultaneously excites two orthogonally circularly polarized components with a preset amplitude ratio and phase difference: a co-polarized spacetime vortex and a cross-polarized background light. The two components are naturally coaxially superimposed, thereby realizing the on-chip integrated generation of terahertz spacetime skyrmions.

[0014] A further technical solution is that: the metasurface unit includes a silicon dioxide substrate and a plurality of grating structures embedded in the silicon dioxide substrate in an array, the grating structure including an upper silicon grating layer and a lower grating unit;

[0015] The upper silicon grating layer extends along the y-direction to the edge of the silicon dioxide substrate, has a width w along the x-direction, and a thickness t2 along the z-direction. The lower grating unit has a zigzag configuration, including a lower silicon grating strip extending along the y-direction and a silicon microstructure array located at both ends of the lower silicon grating strip and extending in the opposite direction along the x-direction. The lower silicon grating strip has a width w along the x-direction and a thickness t2 along the z-direction. The silicon microstructure array includes cubic units made of silicon material arranged in a period a along the y-direction. The cubic units have a side length p and a thickness t2. The silicon microstructure array on the positive x-direction side is located in the positive y-direction region, and the silicon microstructure array on the negative x-direction side is located in the negative y-direction region. The difference in spacing between the centers of the two silicon microstructures along the y-direction is ap. The zigzag configuration of the lower grating unit disrupts the mirror symmetry of the grating structure about the xz plane.

[0016] The upper silicon grating layer and the lower silicon grating strip are relatively misaligned along the x-direction. The offset distance of the boundary of the upper silicon grating layer in the positive x-direction relative to the boundary of the lower silicon grating strip in the positive x-direction is denoted as k. This misalignment relationship destroys the vertical mirror symmetry, double rotational symmetry, and mirror symmetry about the yz plane of the grating structure along the z-direction.

[0017] The lower grating unit is embedded inside the silicon dioxide substrate, and the upper silicon grating layer is disposed on the upper surface of the lower grating unit; the terahertz wave modulation function of the grating junction is jointly undertaken by the upper silicon grating layer and the lower grating unit.

[0018] The beneficial effects of the above technical solution are as follows: The method realizes the direct construction of a novel topological structure in the momentum-frequency space of the terahertz band—the spacetime skyrmion—based on a symmetry-broken grating structure. The structure initially designed in this application only has a relative dislocation relationship between the upper and lower grating layers along the x-direction, without a silicon cube structure. At this point, the transmitted co-polarized linearly polarized light contains a linearly polarized spacetime vortex light, but no cross-polarized linearly polarized component. Further, a silicon cube structure is introduced into the structure to break additional symmetry and excite a linearly polarized conversion channel, generating a linearly polarized component orthogonal to the chirality of the original incident light. The two beams with orthogonal linear polarization and different orbital angular momentum cross-superimpose in the spacetime domain, providing an effective carrier for the generation of spacetime skyrmions. By rotating the structure to change the dislocation direction of the upper and lower layers, the skyrmion number can be adjusted, and the skyrmion configuration can be adjusted by changing the fast axis direction of the quarter-wave plate to 45° or -45°. Attached Figure Description

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0020] Figure 1 This is a schematic diagram comparing the concepts of spatial skyrmions and spacetime skyrmions in the background technology;

[0021] Figure 2 This is a flowchart illustrating the principle of generating terahertz spacetime skyrmions based on metasurfaces as described in an embodiment of the present invention.

[0022] Figure 3 This is a schematic diagram of the physical process by which the metasurface unit described in the embodiment of the present invention is excited by co-polarized spatiotemporal vortex and cross-polarized background light under the incident terahertz linearly polarized light, and then coaxially superimposed, passing through a 1 / 4 wave plate.

[0023] Figure 4 This is a schematic diagram of the overall three-dimensional structure of the double-layer misaligned grating structure described in the embodiment of the present invention;

[0024] Figure 5 yes Figure 4 Top view of the structure shown;

[0025] Figure 6 yes Figure 4 The cross-sectional view of the structure shown along the yz plane is used to illustrate the misalignment relationship between the upper and lower grating layers.

[0026] Figure 7 yes Figure 4 The cross-sectional view of the structure shown along the xz plane is used to illustrate the misalignment relationship between the upper and lower grating layers.

[0027] Figure 8This is a schematic diagram of the theoretical model of the dual-resonance four-port time-coupled mode established in an embodiment of the present invention;

[0028] Figure 9 It is a graph showing the ratio of the amplitudes of the co-polarized and cross-polarized components required to generate spacetime skyrmions as a function of spatial coordinates.

[0029] Figure 10 This is a schematic diagram of a cascade structure used to generate second-order spacetime skyrmions;

[0030] Figure 11 This is a schematic diagram of the spatiotemporal Bimeron vector distribution formed by the superposition of linear polarizations in front of a quarter-wave plate.

[0031] Figure 12 The left-middle figure shows the simulated phase distribution of the co-polarized y-linear polarization component in the momentum-frequency space, which is a vortex phase structure. The right-middle figure shows the simulated amplitude distribution of the cross-polarized x-linear polarization component in the momentum-frequency space.

[0032] Figure 13 The left image shows the amplitude distribution of the cross-polarized x-linearly polarized component in the momentum-frequency space obtained from the simulation, while the right image shows the phase distribution of the cross-polarized x-linearly polarized component in the momentum-frequency space obtained from the simulation, which is an approximately uniform phase characteristic.

[0033] Figure 14 It is a multipole decomposition scattering power contribution diagram of cross-polarization components, used to explain the polarization conversion mechanism induced by symmetry breaking;

[0034] Figure 15 This is a schematic diagram of the Bimeron vector distribution (left) with a skymin number of +1 generated by linear polarization superposition and its Poincaré sphere coverage (right);

[0035] Figure 16 This is a schematic diagram of the vector distribution (left) and Poincaré sphere coverage (right) of inverse skyrmions with a skyrmion number of +1 and polarity of -1 after passing through a +45° waveplate;

[0036] Figure 17 This is a schematic diagram of the vector distribution (left) and Poincaré sphere coverage (right) of positive skyrmions with a skyrmion number of +1 and polarity of +1 after passing through a -45° waveplate;

[0037] Figure 18 The diagram shows the distribution of the Bimeron vector with a skymin number of -1 after the structure is rotated 180° and the diagram of the Poincaré sphere covering (right).

[0038] Figure 19The diagram shows the vector distribution of positive skyrmions with a number of -1 and a polarity of -1, generated by the structure after being rotated 180° and passing through a +45° waveplate (left) and the diagram of the Poincaré sphere cover (right).

[0039] Figure 20 The diagram shows the vector distribution of inverse skyrmions with a skyrmion number of -1 and polarity of +1 generated by the structure after rotating 180° and passing through a -45° waveplate (left) and the diagram of the Poincaré sphere covering (right).

[0040] Figure 21 The diagram shows the second-order spatiotemporal Bimeron vector distribution generated by the cascaded structure (left) and the ellipticity diagram (right).

[0041] Figure 22 The diagram shows the second-order inverse spacetime skyrmion vector distribution (left) and ellipticity diagram (right) generated after the cascaded structure passes through a +45° waveplate.

[0042] Among them: 1. Metasurface unit; 2. Grating structure; 21. Upper silicon grating layer; 22. Lower grating unit; 221. Lower silicon grating strip; 222. Silicon microstructure array; 23. Silicon dioxide substrate. Detailed Implementation

[0043] 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 a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0044] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0045] A key phenomenon discovered in this invention application is that when two layers of structural dislocations are introduced into a metasurface, incident linearly polarized light can excite a target co-polarized spatiotemporal vortex component in the frequency-momentum space. Simultaneously, the additionally introduced mirror symmetry breaking induces a polarization conversion of linear polarization, resulting in a cross-polarized component orthogonal to it in the transmission field. Theoretical analysis shows that this phenomenon originates from the quasi-continuous bound state supported by the metasurface unit, which simultaneously realizes the construction of a spatiotemporal phase vortex and the reversal of the linear polarization state. The vortex phase of the co-polarized component can be intuitively characterized by calculation using the scattering matrix, while the generation mechanism of the cross-polarized component can be revealed using multipole analysis. Further research reveals that near the resonance frequency, the co-polarized linearly polarized component exhibits a spatiotemporal vortex structure, while the cross-polarized component has a high amplitude, and its phase is approximately uniformly distributed within the target region. These characteristics provide the necessary physical conditions for the superposition of two beams of light to form a spatiotemporal skyrmion.

[0046] This discovery provides important physical evidence and innovative clues for this project: if the amplitude and phase distribution of two orthogonally linearly polarized beams generated by the quasi-continuous domain bound states in the metasurface—a co-polarized spacetime vortex and a cross-polarized background beam—satisfy specific superposition conditions, it is expected to directly generate a spacetime bimeron, and generate a spacetime skyrmion through a quarter-wave plate without any additional modulation optical path.

[0047] like Figures 2-3 As shown, this invention discloses a method for generating terahertz spacetime skyrmions based on linearly polarized light excitation of a metasurface. The core of the method is to simultaneously excite two orthogonally polarized components with a preset amplitude ratio and phase difference—a co-polarized spacetime vortex and a cross-polarized background light—under the incidence of a single beam of linearly polarized terahertz light by precisely designing the complex amplitude response of the metasurface unit. These two components are naturally coaxially superimposed, thereby directly realizing the on-chip integrated generation of terahertz spacetime skyrmions.

[0048] The above steps will be explained in detail below with reference to specific content:

[0049] Design of metasurface unit 1:

[0050] Under the incident light of a single beam of linearly polarized terahertz light, the single beam of linearly polarized terahertz light passes through the metasurface unit 1; the metasurface unit 1 simultaneously excites two orthogonally polarized components with a preset amplitude ratio and phase difference: a co-polarized spatiotemporal vortex and a cross-polarized background light, and the two are naturally coaxially superimposed to realize the on-chip integrated generation of terahertz spatiotemporal skyrmions.

[0051] This application combines temporal coupled-mode theory (TCMT), multipole analysis theory, and polarized beam superposition theory to systematically study the formation mechanism and configuration characteristics of spacetime skyrmions based on metasurfaces. Metasurface devices are fabricated, and the full vector field characterization of terahertz spacetime skyrmions is performed. This application integrates the three discrete physical processes of traditional "beam splitting-controlling-beam combining" into a "single physical process" within the metasurface, achieving for the first time a novel on-chip integrated generation pathway for terahertz spacetime skyrmions, opening a new direction for the efficient generation and integrated application of spacetime topological optical fields. It should be noted that the topological structure generated by the metasurface is in frequency-momentum space. In experimental observation, a 4F system is needed to convert it to the physical spacetime domain for characterization. However, this does not affect the integrated characteristics of the metasurface as the core generation device—the 4F system serves only as a necessary measurement conversion means, similar to using a spectrum analyzer to observe the signal output of a signal generator.

[0052] Furthermore, the metasurface unit 1 includes a silicon dioxide substrate 23 and a plurality of arrayed grating structures 2 embedded in the silicon dioxide substrate 23. The grating structure 2 includes an upper silicon grating layer 21 and a lower grating unit 22. The grating structure 2 proposed in this invention fully considers the feasibility of actual micro-nano fabrication processes, constructing a double-layer staggered grating structure on the silicon dioxide substrate 23. Figures 4-7 As shown, the metasurface unit 1 includes a silicon dioxide substrate 23 and a plurality of grating structures 2 arranged in an array embedded in the silicon dioxide substrate 23. The grating structure 2 includes an upper silicon grating layer 21 and a lower grating unit 22.

[0053] The upper silicon grating layer 21 extends along the y-direction to the edge of the silicon dioxide substrate 23, has a width w along the x-direction, and a thickness t2 in the z-direction. The lower grating unit 22 has a zigzag configuration, including a lower silicon grating strip 221 extending along the y-direction and a silicon microstructure array 222 located at both ends of the lower silicon grating strip 221 and extending in the opposite direction along the x-direction. The lower silicon grating strip 221 has a width w along the x-direction and a thickness t2 in the z-direction. The silicon microstructure array 222 includes cubic units made of silicon material arranged in a period a along the y-direction. The cubic units have a side length p and a thickness t2. The silicon microstructure array on the positive x-direction side is located in the positive y-direction region, and the silicon microstructure array on the negative x-direction side is located in the negative y-direction region. The difference in spacing between the centers of the two silicon microstructures along the y-direction is ap. The zigzag configuration of the lower grating unit 22 disrupts the mirror symmetry of the grating structure 2 about the xz plane.

[0054] The upper silicon grating layer 21 and the lower silicon grating strip 221 are relatively misaligned along the x-direction. The offset distance of the boundary of the upper silicon grating layer 21 in the positive x-direction relative to the boundary of the lower silicon grating strip 221 in the negative x-direction is denoted as k. This misalignment relationship destroys the vertical mirror symmetry, double rotational symmetry, and mirror symmetry about the yz plane of the grating structure 2 along the z-direction.

[0055] The lower grating unit 22 is embedded inside the silicon dioxide substrate 23, and the upper silicon grating layer 21 is disposed on the upper surface of the lower grating unit 22; the terahertz wave modulation function of the grating structure 2 is jointly undertaken by the upper silicon grating layer 21 and the lower grating unit 22.

[0056] Preferably, the thickness of the silicon dioxide substrate 23 is t1=500 μm; the thickness of the upper silicon grating layer 21 and the lower silicon grating strip 221 is t2=10 μm, and the width along the x direction is w=35.52 μm; the boundary of the upper silicon grating layer 21 in the positive x direction is offset by a distance k=5.328 μm in the negative x direction relative to the boundary of the lower silicon grating strip 22 in the positive x direction; the cube unit has a side length p=14.47 μm, a thickness of t2=10 μm, and is arranged in an array along the y direction with a period a=96 μm; wherein, the silicon microstructure array located on the positive x direction side is set in the positive y direction region, the silicon microstructure array located on the negative x direction side is set in the negative y direction region, and the spacing difference between the centers of the two silicon microstructures along the y direction is ap=81.53 μm.

[0057] Through the above structural design, the zigzag configuration of the lower grating unit disrupts the mirror symmetry of the grating structure 2 about the xz plane; at the same time, the relative misalignment between the upper and lower layers disrupts the vertical mirror symmetry along the z direction, the double rotational symmetry (C2), and the mirror symmetry about the yz plane. The above symmetry breaking strategies work together to achieve precise control of the radiation characteristics and topological features of the light field mode.

[0058] The generation of spacetime vortices during transmission was analyzed using time-coupled-mode theory, and a dual-resonance, four-port time-coupled-mode model was established. The structure designed in this application, with y-linear polarization incident light, is illustrated in the schematic diagram of the established time-coupled-mode. Figure 8 As shown, the established dynamic equations for the time-coupled mode are:

[0059] (1)

[0060] in:

[0061] (2)

[0062] Let A be the complex amplitude of the two resonant modes (corresponding to +k and -k, respectively); ω0 be the resonant frequency; and γ be the radiation attenuation rate. S+ and S- are the amplitudes of the incident and emitted waves, respectively (the superscript T indicates transpose). K is the coupling matrix from the incident wave to the resonant mode, and D is the coupling matrix from the resonant mode to the emitted wave. C is the direct scattering matrix without resonance (i.e., the Fabry-Perot background), where the reflection coefficient r and the transmission coefficient t satisfy r² + t² = 1; the initial phase ϕ depends on the choice of the reference plane. Energy conservation and reciprocity require C to be a unitary and symmetric matrix. S is the total scattering matrix including the resonance effect. When an external incident wave with frequency ω excites resonance, the expression for S is as follows:

[0063] (3)

[0064] Here, matrices K, D, and C are interconnected through energy conservation and time reversal symmetry, as shown below:

[0065] (4)

[0066] Using the above relationship, the simplified S-matrix yields the following expression for the scattering coefficient transmitted through four ports after passing through the structure described in this application, taking the incident light at port 1 as an example:

[0067] (5)

[0068] Where γ1-γ4 correspond to the losses of the four ports respectively, the real and imaginary parts are extracted to obtain:

[0069] (6)

[0070] The expression for the vortex phase is: When a spacetime vortex is generated, the phase accumulates to 2πl around the center point of the phase vortex, where l represents the topological charge of the spacetime vortex. At the center of the spacetime vortex, there should be a dark point with zero amplitude, at which point Im(S14) and Re(S14) should both be zero. The condition for this to be satisfied is:

[0071] (7)

[0072] When the structure is the most basic grating, i.e., the top and bottom layers of the grating are aligned, and there are no microcube structures on both sides, the structure has high symmetry: it satisfies top-bottom mirror symmetry, xz mirror symmetry, yz mirror symmetry, and C2 symmetry. In this case, t≠0 always holds, and γ1 = γ2 = γ3 = γ4. The only condition required to generate a dark point with zero amplitude is:

[0073] (8)

[0074] At this point, the system only presents a single dark node line and cannot form isolated topological dark points or phase vortices.

[0075] When dislocations in the upper and lower layers break the structural symmetry, the breaking of yz mirror symmetry and C2 symmetry causes γ1 and γ2, and γ3 and γ4 to no longer be constant. The breaking of upper and lower symmetry causes γ1 and γ3, γ2 and γ4 to no longer be constant. At this point, the conditions for generating a dark point with zero amplitude become more stringent:

[0076] (9)

[0077] The dark nodal line transforms into a single dark point, thereby generating a momentum-frequency domain vortex phase around it. A spacetime vortex component containing transverse orbital angular momentum is generated in the co-polarized linearly polarized light. At this point, there is no orthogonal polarization transformation in the linearly polarized light because the structure retains xz mirror symmetry. This symmetry provides a conserved "symmetry quantum number" for the electromagnetic field under normal incidence conditions. Under this mirror operation, one linearly polarized component exhibits odd symmetry, and the other even symmetry; therefore, they are orthogonal to each other in terms of symmetry. Since the scattering process must satisfy mirror invariance, an incident field from odd-symmetric polarization cannot couple to an even-symmetric outgoing polarization channel, and vice versa. This results in a strict prohibition of linear-to-linear cross-polarization transformation under this symmetry.

[0078] To excite orthogonally linearly polarized light, this application employs an additional symmetry-breaking method. Specifically, it introduces microstructure units made of silicon material periodically at both ends of the grating to further break the xz mirror symmetry of the structure. The cross-polarization conversion can be verified using multipole analysis. Taking the cross-polarization transmittance of y-polarized incident light and x-polarized emitted light as an example, the expression for the transmittance is:

[0079] (10)

[0080] This expression consists of the scattered power components of the electric dipole moment (ED), magnetic dipole moment (MD), toroidal dipole moment (TD), electric quadrupole moment (EQ), and magnetic quadrupole moment (MQ), and is calculated using the following integral form:

[0081] (11)

[0082] Where c and ω These are the speed and angular frequency of the electromagnetic field (light), respectively. (Subscript) , In a Cartesian coordinate system, x, y, z are represented. It is the current density distribution in the unit cell, and its expression is:

[0083] (12)

[0084] Their far-field scattering power can be expressed by the following formula:

[0085] (13)

[0086] By calculating the multipole moment components in different directions using the above formula, we can further calculate the power contribution of the multipole moment in different directions to the scattering, and reconstruct the scattering rate of cross-polarization. This can help verify and explain why additional symmetry breaking contributes to the excitation of cross-polarization.

[0087] At this point, a linearly polarized beam is incident on the light source, and the outgoing light consists of a pair of orthogonally polarized beams. The co-polarized beam is light with a spacetime vortex phase, while the cross-polarized beam is excited by additional symmetry breaking, producing a relatively high amplitude and uniform phase. These two beams, generated by the beam being split into two after passing through the grating structure designed in this application, are naturally coaxial and can generate a spacetime bimeron when superimposed. After passing through a quarter-wave plate, they become a spacetime skyrmion. This series of changes can be explained by the theory of beam superposition and the effect of the quarter-wave plate. The specific explanation is as follows: First, the relationship between linearly polarized light and circularly polarized light after passing through the quarter-wave plate is analyzed using the Mueller matrix of the quarter-wave plate. This transforms the analysis from the linear polarization basis to the circular polarization basis, which can be facilitated by the theory of circular polarization superposition. Finally, the Mueller matrix of the quarter-wave plate is used to return to the linear polarization basis. In the analysis, this set of theories can perfectly explain the generation of topological textures, the control of configuration, and the generation of higher-order topological textures. The specific principles are as follows.

[0088] When the light is incident with y-linear polarization according to the structure shown in this application, and the analysis is performed under the linear polarization basis, the co-polarized linear polarization components in the transmission exhibit a spacetime vortex, and the cross-polarized light components are excited with relatively uniform phase. This application can express the transmission at this time as:

[0089] (14)

[0090] in, This represents the cross-polarized x-line polarization component after passing through the broken grating. This represents the co-polarized y-linear polarization component after passing through the broken grating. and This refers to the amplitude distribution of the two circularly polarized components in momentum-frequency space. and It refers to the phase distribution of the two linearly polarized components in the momentum-frequency space.

[0091] The outgoing pair of orthogonally linearly polarized components can be converted from linear polarization to circular polarization using a quarter-wave plate. Two types of quarter-wave plates can be used: one is an ideal quarter-wave plate with a fast axis azimuth of +45°, and the other is an ideal quarter-wave plate with a fast axis azimuth of -45°. The changes in the Stokes parameters after passing through the quarter-wave plate can be expressed using the Mueller matrix as follows:

[0092] (15)

[0093] The Mueller matrix is ​​a 4×4 real matrix specifically used to describe the transformation of the incident Stokes parameters (S0, S1, S2, S3) by a quarter-wave plate. The above and below equations describe the Stokes parameters (S0, S1, S2, S3) of the output light from the grating, respectively. These Stokes parameters (S0', S1', S2', S3') after transformation by an ideal quarter-wave plate with a major axis azimuth angle of 45° and an ideal quarter-wave plate with a major axis azimuth angle of -45° are expressed using the Mueller matrix. It is worth noting that when calculating the Mueller matrix, for an ideal quarter-wave plate with a major axis azimuth angle of 45°, θ=45°, δ=90°; for an ideal quarter-wave plate with a major axis azimuth angle of -45°, θ=-45°, δ=90°.

[0094] This application first takes an ideal quarter-wave plate with a fast axis azimuth angle of +45° as an example to perform beam superposition analysis. A linearly polarized beam of y-polarized light is incident on a grating. The transmitted y-polarized light ([S1,S2,S3]T=[-1,0,0]T) is a spacetime vortex. After passing through the quarter-wave plate, [S1', S2', S3']T=[0,0,1]T, which becomes a right-handed circularly polarized spacetime vortex. The y-polarized light excited during transmission ([S1,S2,S3]T=[1,0,0]T) becomes a left-handed circularly polarized beam with uniform amplitude and phase after passing through the quarter-wave plate ([S1', S2', S3']T=[0,0,-1]T). The overall transmission at this point is represented as:

[0095] (16)

[0096] This indicates right-handed circular polarization after passing through the grating. This indicates left-handed circular polarization after passing through the grating. and This refers to the phases corresponding to the two circularly polarized components. When the orthogonal linearly polarized components pass through an ideal quarter-wave plate with a fast axis azimuth angle of +45°, , The two components are naturally coaxial and superimposed. Generating a spacetime skyrmion behind a quarter-wave plate requires certain conditions to be met regarding amplitude and phase.

[0097] First, there's the amplitude condition. The amplitude ratio condition determines the reversal of the three-dimensional vector, i.e., the S3' parameter. The relationship between the S3' parameter and the amplitude is:

[0098] (17)

[0099] in The amplitude ratio of two orthogonally polarized beams, i.e., the ratio of co-polarized light to cross-polarized light excited by the additional symmetry breaking after the design structure, is the amplitude relationship required to generate spacetime skyrmions, as shown in the figure. Figure 9 As shown, this application allows observation that at the central dark spot, V=0, and S3'=±1 (+ when the spacetime vortex is left-handed, - when it is right-handed); as it evolves towards the edge of the vortex, A1 increases and A2 decreases, achieving A1>>A2 at a certain location, V=∞, at which point S3'= 1 (when the spacetime vortex is left-handed, it is negative; when it is right-handed, it is positive), which satisfies the complete reversal of the Stokes vector, meaning the Stokes vector can be completely covered on the Poincaré sphere. This application defines a parameter polarity p to describe the center direction of the normalized Stokes S-vector. The polarity p = ±1, where the direction is determined: vertically upward is defined as positive, and vertically downward is defined as negative. Depending on the incident y-linear polarization, whether the outgoing spacetime vortex is left-handed or right-handed circularly polarized depends on the angle between the major axes of the quarter-wave plate and the incident y-linear polarization. The polarity can be adjusted by adjusting the quarter-wave plate.

[0100] The phase difference condition affects the rotation direction of the three-dimensional vector. This application defines a parameter called vorticity v to describe the phase difference, which can be expressed in the following form:

[0101] (18)

[0102] By adjusting the major axis angle of the quarter-wave plate and the 180° rotation of the structure, the phase rotation direction of the spacetime vortex can be adjusted, ultimately achieving four skyrmions with two polarities (p=±1) and two vorticities (v=±1). The specific explanation is as follows:

[0103] This application defines the skymin number of skyminions as:

[0104] (19)

[0105] The expression for the skymon number consists of two parts: the first part indicates that the skymon number is equal to the normalized Poincaré sphere coverage area; the second part indicates that it is simultaneously affected by polarity p and vorticity v. According to the physical definition, when the skymon number and polarity have the same sign, a positive skymon is produced; when the signs are opposite, an inverse skymon is produced.

[0106] In the initial structure ( Figure 4 In the y-polarized light incident on and passing through the designed structure, a clockwise rotating spacetime vortex is excited in the co-polarized component. By adjusting the angle of the major axis (fast axis) of the quarter-wave plate (from +45° to -45°), the phase of the spacetime vortex can be selectively generated in either the right-hand circularly polarized component (+45°) or the left-hand circularly polarized component (-45°), while the other circularly polarized state, orthogonal to it, maintains a uniform phase distribution. Due to the different chirality of the circularly polarized light carrying the spacetime vortex, according to Expression 17, the generated polarity p is reversed, specifically manifested as a reversal of the center vector direction. Simultaneously, due to the difference in the chirality of the circularly polarized light where the spacetime vortex resides, according to Expression 18, the vorticity v generated by the phase difference also reverses, thus evolving different topological configurations. It is noteworthy that the synchronous reversal of polarity p and vorticity v keeps the skyrmion number Nsk constant, indicating that the number of skyrmions generated before and after passing through the quarter-wave plate in the fixed structure is conserved and independent of the angle of the wave plate. Thus, under these conditions, two skyrmion configurations (positive and negative) with a skyrmion number of +1 were successfully prepared. The negative configuration is formed when the major axis angle of the quarter-wave plate is +45°, and the positive configuration is formed when it is -45°.

[0107] Furthermore, when the aforementioned metasurface structure is rotated 180° in-plane, its modulation characteristics of the optical field change significantly. Under the same y-polarized light incidence, the rotation direction of the transmitted co-polarized spacetime vortex reverses, becoming counterclockwise, which directly leads to a change in the skyrmion number. The polarity distribution is also controlled by the quarter-wave plate: as shown in Expression 17, when the angle between the major axes of the waveplate is set to +45°, the right-hand circularly polarized component still exhibits a spacetime vortex with polarity p=+1; when the angle between the major axes of the waveplate is adjusted to -45°, the left-hand circularly polarized component exhibits a spacetime vortex with polarity p=-1. Thus, the angle of the quarter-wave plate directly determines the polarization state of the emitted circularly polarized light, which further affects the circular polarization distribution of the spacetime vortex and ultimately dominates its polarity selection. On the other hand, the 180° rotation of the structure causes the rotation direction of the spacetime vortex to change from clockwise to counterclockwise, directly altering the rotational evolution law of the phase difference. The phase reversal after the structure rotation is exactly opposite to the initial state. According to Expression 18, the vorticity v of the system reverses sign at this time. Combined with Expression 19, it can be seen that after the structure rotates 180°, the overall skyrmion number reverses to -1. Based on this structure, by finely adjusting the major axis angle of the quarter-wave plate, two topological configurations (positive and negative) with a skyrmion number of -1 can also be achieved as needed. When the major axis angle of the quarter-wave plate is +45°, it is the positive configuration, and when it is -45°, it is the negative configuration.

[0108] In summary, the polarity can be adjusted by changing the major axis angle of the quarter-wave plate, while the vorticity v of the spacetime skyrmion can be adjusted by rotating the structure by 180°. Ultimately, two configurations and two skyrmion numbers are achieved, resulting in a total of four cases.

[0109] The following is the realization of a higher-order spacetime skyrmion. Taking the structure designed in this application, with a major axis angle of +45° through a quarter-wave plate as an example, the analysis is as follows: An incident y-polarized terahertz wave, after passing through the designed metasurface structure, becomes co-polarized y-linearly polarized. When the two layers of the structure designed in this application are aligned and cascaded (structure as follows) Figure 10 As shown in the diagram, the silicon grating structure plays a crucial role in generating first-order spacetime skyrmions, while the underlying silicon dioxide primarily serves as a substrate for the fabrication process. During cascading, the silicon grating structure remains unchanged, the substrate silicon dioxide thickness becomes t1' = 20 μm, and the distance between the upper and lower gratings in the cascaded arrangement is t3 = 224 μm. This distance is filled with SU8 with a dielectric constant of 1.58, and the upper grating is further protected by SU8 with a thickness of t4 = 64 μm. The transmitted light is then incident on y-polarized light, and the expression for this transmitted light is... At this point, the spacetime vortex phase accumulated through the designed structure is twice that of before, which is... At this point, the structure still satisfies the symmetry breaking condition, which can excite cross-polarized light. The cross-polarized light has a relatively high amplitude and a relatively uniform phase. The amplitude satisfies the condition of complete reversal of the three-dimensional vector in Expression 17. As for the phase condition, since the phase of the spacetime vortex is twice that before, the vorticity v of the skyrmion calculated according to Expression 18 is also twice, and the rotation of the three-dimensional vector becomes a two-turn rotation. At this point, the spacetime skyrmion is a second-order spacetime skyrmion.

[0110] We have already discussed the case of spacetime skyrmions generated by circular polarization superposition after passing through a quarter wave plate. We will now continue to discuss spacetime bimerons generated by linear polarization superposition before passing through a quarter wave plate. Using the structure designed in this application, we will reverse-engineer the result with a major axis angle of +45° after passing through the quarter wave plate. It is worth noting that once the structure is fixed, the result of linear polarization superposition is also fixed, and is actually independent of the major axis angle of the quarter wave plate. The results analyzed with a major axis angle of +45° and a major axis angle of -45° are the same.

[0111] This application denotes the Stokes parameters after passing through a 1 / 4 waveplate with a major axis angle of +45° as S1', S2', and S3'. According to Expression 15, the relationship between these parameters and the Stokes parameters before passing through the 1 / 4 waveplate is: S1 = -S3', S2 = S2', S3 = S1'. The topological texture at this point is a spacetime Bimeron. A related schematic diagram can be found in [the diagram]. Figure 11 .

[0112] Figures 12-14 This reflects the generation of the amplitude and phase of a pair of orthogonally linearly polarized beams in transmitted light as expected in this application, as simulated using Comsol. Figure 12 The left figure shows the phase distribution of the co-polarized y-linear polarization component in the momentum-frequency space obtained from the simulation, revealing the vortex phase structure; Figure 12 The right figure shows the amplitude distribution of the co-polarized y-linear polarization component in the momentum-frequency space obtained from the simulation. Figure 13 The left figure shows the amplitude distribution of the cross-polarized x-linear polarization component in the momentum-frequency space obtained from the simulation. Figure 14 It is a multipole decomposition scattering power contribution diagram of cross-polarization components, used to explain the polarization conversion mechanism induced by symmetry breaking; Figure 13 The right figure shows the phase distribution of the cross-polarized x-linear polarization component in the momentum-frequency space obtained from the simulation, demonstrating its approximately uniform phase characteristics.

[0113] The design of this application was verified using COMSOL simulation. The structure of the design is as follows: Figure 4 As shown, the spacetime vortex of the co-polarized y-linearly polarized light is still preserved. The amplitude and phase are as follows: Figure 12As shown. Because the introduced additional microstructural units disrupt the xz mirror symmetry, higher linearly polarized cross-x polarization amplitudes can be excited ( Figure 13 (Left figure) This X-ray polarization excitation can be explained using multi-level decomposition. The result of multi-level decomposition using Expression 13 is as follows: Figure 14 As shown. Through multi-level decomposition, according to expression 10, it can be seen that a large orthogonal x-polarization amplitude can be excited. At the same time, the phase of the orthogonal x-polarization is a relatively uniform phase, as shown... Figure 13 As shown in the figure on the right.

[0114] Figures 15-17 The topological texture is the linear polarization superposition of the structure before rotation and after passing through a 1 / 4 wave plate. Figure 15 This is a schematic diagram of the Bimeron vector distribution (left) with a skymin number of +1 generated by linear polarization superposition and its Poincaré sphere coverage (right); Figure 16 This is a schematic diagram of the vector distribution (left) and Poincaré sphere coverage (right) of inverse skyrmions with a skyrmion number of +1 and polarity of -1 after passing through a +45° waveplate; Figure 17 This is a schematic diagram of the vector distribution (left) and Poincaré sphere coverage (right) of positive skyrmions with a skyrmion number of +1 and polarity of +1 after passing through a -45° waveplate.

[0115] The combination of the two produces as follows Figure 15 The left figure shows a Bimeron with a skymin number of +1. This application will vector-map it onto a Poincaré sphere as follows: Figure 15 The right figure shows how to achieve full coverage of a Poincaré sphere. When the generated skyrmion texture passes through a quarter-wave plate, and the major axis angle of the quarter-wave plate is +45°, an inverse skyrmion with a polarity p=-1 and a skyrmion number of +1 is generated, as shown in the figure. Figure 16 As shown in the left figure, Figure 16 The right figure shows that full coverage of the Poincaré sphere can still be achieved. When the major axis angle of the quarter-wave plate is -45°, a positive skyrmion with a skyrmion number of +1 and polarity p=+1 is produced, as shown in the figure. Figure 17 As shown.

[0116] Figures 18-20 This is the topological texture after linear polarization superposition and passing through a 1 / 4 waveplate when the structure is rotated 180°. Figure 18 This is a schematic diagram of the Bimeron vector distribution with a skymin number of -1 generated by the superposition of linear polarizations after the structure is rotated 180°. Figure 19 This is a schematic diagram of the vector distribution of positive skyrmions with a number of -1 and a polarity of -1, generated by the structure after being rotated 180° and passing through a +45° waveplate. Figure 20 This is a schematic diagram of the vector distribution of inverse skyrmions with a number of -1 and a polarity of +1, generated by rotating the structure 180° and passing it through a -45° waveplate.

[0117] When the structure is rotated 180°, the skyrmion number changes to -1. When two linearly polarized particles are superimposed, the Bimeron with a skyrmion number of -1... Figure 18 As shown. When passing through a quarter-wave plate with a major axis angle of +45°, the polarity of the skyrmion remains p=-1, but it is now a positive skyrmion, as... Figure 19 As shown. Similarly, when passing through a quarter-wave plate with a major axis angle of -45°, the polarity of the skyrmion produced is still p=+1, but it is now an inverse skyrmion, as shown. Figure 20 As shown.

[0118] Figures 21-22 This is for the generation of higher-order topological textures. Figure 21 The diagram shows the second-order spatiotemporal Bimeron vector distribution generated by the cascaded structure (left) and the ellipticity diagram (right). Figure 22 The diagram shows the second-order inverse spacetime skyrmion vector distribution (left) and ellipticity diagram (right) generated after the cascaded structure passes through a +45° waveplate.

[0119] When this application is in accordance with... Figure 10 When the structure is cascaded as shown, the transmitted light contains second-order spacetime vortexes in both linearly polarized and co-polarized y-polarized beams, while cross-polarized x-polarized beams are excited. The second-order spacetime bimeron produced by the superposition of two orthogonally linearly polarized beams is as follows: Figure 21 As shown. A second-order inverse skyrmion is produced when passing through a quarter-wave plate with a major axis angle of +45°, such as... Figure 22 As shown, by adjusting the quarter-wave plate and the rotating structure, even richer configurations and skyrmion numbers can still be generated. It is worth noting that the second-order spacetime vortex light in co-polarized y-polarization does not have a completely linear phase surrounding a point due to simulation errors, resulting in... Figure 22 The central vector of the inverse second-order spacetime skyrmion shown has a slight split.

[0120] In summary, this application proposes an on-chip integration scheme based on symmetry-broken metasurfaces. In the momentum-frequency space of the terahertz band, a spacetime bimeron is directly constructed by utilizing the natural coaxial superposition of co-polarized spatiotemporal vortices excited by a single beam of linearly polarized light and cross-polarized background light. This bimeron is then converted into a complete spacetime skyrmion via a quarter-wave plate. By adjusting the metasurface rotation angle and the fast axis direction of the waveplate, the polarity (p) and vorticity (v) of the skyrmion can be independently controlled, achieving various topological configurations (positive / inverse) with a skyrmion number Nsk = ±1. Furthermore, this can be extended to higher-order topological states through structural cascading. This work deeply integrates symmetry-broken design with topological photonics, providing a novel pathway for the efficient and tunable on-chip generation of terahertz spacetime skyrmions and their application in high-dimensional topological light fields.

[0121] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Unless otherwise specified, an element defined by the phrase "comprising..." or "including..." does not exclude the presence of additional elements in the process, method, article, or terminal device that includes said element. Additionally, in this document, "greater than," "less than," "exceeding," etc., are understood to exclude the stated number; "above," "below," "within," etc., are understood to include the stated number.

[0122] Although the above embodiments have been described, those skilled in the art, once they understand the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the above descriptions are merely embodiments of the present invention and do not limit the scope of patent protection of the present invention. Any equivalent structural or procedural transformations made using the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for generating terahertz spacetime skyrmions based on linearly polarized light excitation of a metasurface, characterized in that, The method includes the following steps: Design a metasurface unit (1) to allow the single beam of linearly polarized terahertz light to pass through the metasurface unit (1) under the incident light of a single beam of linearly polarized terahertz light. The metasurface unit (1) simultaneously excites two orthogonal circularly polarized components with a preset amplitude ratio and phase difference: a co-polarized spacetime vortex and a cross-polarized background light. The two are naturally coaxially superimposed to realize the on-chip integrated generation of terahertz spacetime skyrmions.

2. The method for generating terahertz spacetime skyrmions based on linearly polarized light-excited metasurfaces as described in claim 1, characterized in that: The metasurface unit (1) includes a silicon dioxide substrate (23) and a plurality of grating structures (2) embedded in the silicon dioxide substrate (23) in an array. The grating structure (2) includes an upper silicon grating layer (21) and a lower grating unit (22). The upper silicon grating layer (21) extends along the y-direction to the edge of the silicon dioxide substrate (23), has a width w along the x-direction, and a thickness t2 in the z-direction; the lower grating unit (22) has a z-shaped configuration, including a lower silicon grating strip (221) extending along the y-direction and a silicon microstructure array (222) located at both ends of the lower silicon grating strip (221) and extending in the opposite direction along the x-direction; the lower silicon grating strip (221) has a width w along the x-direction and a thickness t2 in the z-direction; The silicon microstructure array (222) includes cubic units made of silicon material arranged in a periodic a along the y direction. The cubic units have a side length of p and a thickness of t2. The silicon microstructure array on the positive x-direction side is located in the positive y-direction region, and the silicon microstructure array on the negative x-direction side is located in the negative y-direction region. The difference in spacing between the centers of the two silicon microstructures along the y-direction is ap. The zigzag configuration of the lower grating unit (22) disrupts the mirror symmetry of the grating structure (2) about the xz plane. The upper silicon grating layer (21) and the lower silicon grating strip (221) are relatively misaligned along the x direction. The offset distance of the boundary of the upper silicon grating layer (21) in the positive x direction relative to the boundary of the lower silicon grating strip (221) in the negative x direction is denoted as k. This misalignment relationship destroys the vertical mirror symmetry, double rotational symmetry and mirror symmetry about the yz plane of the grating structure (2) along the z direction. The lower grating unit (22) is embedded inside the silicon dioxide substrate (23), and the upper silicon grating layer (21) is disposed on the upper surface of the lower grating unit (22); the terahertz wave modulation function of the grating structure (2) is jointly undertaken by the upper silicon grating layer (21) and the lower grating unit (22).

3. The method for generating terahertz spacetime skyrmions based on linearly polarized light-excited metasurfaces as described in claim 2, characterized in that: The thickness of the silicon dioxide substrate (23) is t1=500 μm; the thickness of the upper silicon grating layer (21) and the lower silicon grating strip (221) is t2=10 μm, and the width along the x direction is w=35.52 μm; the boundary of the upper silicon grating layer (21) in the positive x direction is offset by a distance k=5.328 μm in the negative x direction relative to the boundary of the lower silicon grating strip (22) in the positive x direction; the side length of the cube unit is p=14.47 μm, the thickness is t2=10 μm, and it is arranged in an array along the y direction with a period a=96 μm; wherein, the silicon microstructure array on the positive x direction side is set in the positive y direction region, the silicon microstructure array on the negative x direction side is set in the negative y direction region, and the spacing difference between the centers of the two silicon microstructures along the y direction is ap=81.53 μm.

4. The method for generating terahertz spacetime skyrmions based on linearly polarized light-excited metasurfaces as described in claim 2, characterized in that: The dielectric constant of the upper silicon grating layer (21) and the lower grating unit (22) is 11.

9.

5. The method for generating terahertz spacetime skyrmions based on linearly polarized light-excited metasurfaces as described in claim 2, characterized in that: The dielectric constant of the silicon dioxide substrate (23) is 3.4.

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