Metasurface design and manufacturing method capable of realizing third-order singular point

Abstract

The invention relates to a metasurface design and manufacturing method capable of realizing a third-order singular point. According to one embodiment, the metasurface design is based on a non-Hermite system of a plurality of coupling resonance units, and the construction of a third-order resonance singular point (EP3) is realized by precisely regulating and controlling the coupling strength and loss difference between the resonance units. Compared with a traditional second-order singular point, the EP3 disclosed by the invention has higher response sensitivity to system disturbance, and is suitable for application scenes such as ultra-sensitive sensing and the like.

Description

Technical Field

[0001] The present application generally relates to the technical field of optical metamaterials and terahertz devices, and specifically to a terahertz metasurface structure capable of realizing a third-order singular point based on a non-Hermitian coupling mechanism, and its application in devices such as third-order singular point response control. Background Art

[0002] In recent years, the study of non-Hermitian physics in photonic systems has attracted widespread attention. By introducing non-Hermitian properties such as dissipation, gain, or asymmetric coupling, the system can exhibit a rich variety of spectral exotic behaviors. In particular, at exceptional points (EPs), the system's eigenvalues ​​and eigenstates simultaneously degenerate, leading to a series of unique physical effects such as nonreciprocal transmission, enhanced response, nontrivial geometric phase, and ultrasensitivity to perturbations.

[0003] Among them, second-order exceptional points (EP2), as the most common form of EP, have been extensively studied theoretically and experimentally on multiple platforms and have been applied to fields such as optical sensing, laser design, and wavefront manipulation. However, with the in-depth exploration of the complexity of non-Hermitian systems, higher-order exceptional points, especially third-order exceptional points (EP3), have gradually attracted the attention of researchers. EP3 not only involves the simultaneous degeneracy of three eigenstates, but also has a more complex spectral topology than EP2. Its response function exhibits higher-order non-analytical behavior with parameter changes, which is expected to bring better performance in high-sensitivity detection and topological control.

[0004] The terahertz (THz) frequency band (0.1–10 THz), located between microwaves and infrared, combines unique physical properties such as low photon energy and high spatial resolution. Notably, THz waves can directly couple to the vibrational modes of biomacromolecules such as proteins, DNA, and viruses, giving them a natural advantage in biomolecule recognition and detection. Therefore, the construction of higher-order EPs not only provides a new platform for studying exotic optical phenomena but also offers unprecedented opportunities for achieving ultrasensitive sensing.

[0005] Although some theoretical work has explored the possibility of EP3 in quantum systems or mechanical systems, there are still many challenges in realizing controllable, designable and measurable EP3 based on optical metasurfaces, such as constructing a non-Hermitian system structure with clear EP3 behavior that can be applied to the THz band. Summary of the Invention

[0006] In order to solve at least one of the above technical problems in the prior art, the present application is proposed. The embodiments of the present application provide a method for implementing EP3 in a non-Hermitian hybrid system based on the terahertz band, a metasurface structure design thereof, and a device using the metasurface design.

[0007] According to an exemplary embodiment, a terahertz metasurface structure for realizing a third-order singular point is provided, characterized in that the structure comprises: a substrate layer; a first layer of open ring resonator array formed on the substrate layer; an isolation layer formed on the substrate layer for realizing isolation between different layer structures; and a second layer of open ring resonator array formed on the isolation layer, wherein the first layer of open ring resonator array and the second layer of open ring resonator array constitute a three-mode coupling system, and the geometric parameters of the layer structure enable the system to satisfy the third-order eigenvalue degeneracy.

[0008] In some embodiments, the units of the first layer of split ring resonator array are composed of two different first split ring resonators and a second split ring resonator, the units of the second layer of split ring resonator array include a third split ring resonator, and the three split ring resonators correspond to the three modes.

[0009] In some embodiments, the first open ring resonator and the second open ring resonator are respectively a square open ring resonator and a double open ring resonator, and the third open ring resonator is a double open ring resonator, wherein the opening directions of the square open ring resonator and the double open ring resonator are different.

[0010] In some embodiments, the second split-ring resonator and the third split-ring resonator constitute a second-order resonant singular point system, and the first split-ring resonator and the second split-ring resonator are coupled in a weak coupling manner, and there is zero coupling between the first split-ring resonator and the third split-ring resonator.

[0011] In some embodiments, the split ring resonators of the first layer and the second layer are offset in the lateral direction, and / or there is a rotation angle between the split ring resonators.

[0012] In some embodiments, the geometric parameters of the layer structure are obtained through a machine learning model such as a neural network.

[0013] In some embodiments, the substrate layer comprises a double-sided polished silicon wafer.

[0014] In some embodiments, the isolation layer is made of a dielectric polymer, and a thickness of the isolation layer is greater than a height of the first layer of split ring resonator array.

[0015] In some embodiments, the thickness of the isolation layer is in the range of 2-5 μm to achieve coupling regulation between the upper and lower structures.

[0016] According to an exemplary embodiment, a method for preparing the aforementioned terahertz metasurface structure is also provided, the method comprising the following steps: preparing a substrate layer, and spin-coating a photoresist on the substrate layer and subjecting it to heat treatment to form a uniform film layer; exposing and developing the structure of the first layer of the open ring resonator array; depositing a metal film by electron beam evaporation, and obtaining the first layer of the open ring resonator array by solvent stripping; spin-coating an isolation layer, and exposing and baking; spin-coating a photoresist on the isolation layer and subjecting it to heat treatment to form a uniform film layer; exposing and developing the structure of the second layer of the open ring resonator array; and depositing a metal film by electron beam evaporation, and obtaining the second layer of the open ring resonator array by solvent stripping.

[0017] According to an exemplary embodiment, a terahertz device is also provided, characterized by including the aforementioned terahertz metasurface structure. The device can be an optical device, a sensor device, or a control device. The device exhibits characteristics such as polarization state evolution, scattering matrix degradation, and phase singularities related to non-Hermitian singularities within the operating frequency band, and can be used to implement sensitive sensing, topological filters, or controllable singularity sources in the terahertz band.

[0018] Based on some embodiments, the non-Hermitian terahertz (THz) metasurface proposed and designed in this application can support high-order topological responses of EP3 singular points, wherein the EP3 structure exhibits unique spectral evolution trajectories and response characteristics, and has significant potential in polarization selectivity, directional non-reciprocity, and sensitivity enhancement. This provides new ideas and feasible solutions for the design of high-dimensional topological optical devices, non-Hermitian sensing devices, and THz control devices with working frequency bands in the THz band. Therefore, the THz metasurface designed in this application has good device adjustability and integration capabilities, and can be widely used in high-sensitivity detection, topological lasers, wavefront control devices, and information processing platforms in the THz band. In some specific embodiments, through the combination of theoretical modeling, neural network-assisted design, and experimental verification, the present invention provides a systematic solution for the structured realization of high-order singular points in the THz band.

[0019] The foregoing and other features and advantages of the present invention will become apparent from the following description of exemplary embodiments in conjunction with the accompanying drawings. It should be understood that the illustrated embodiments do not necessarily achieve all of these advantages. Thus, the present invention may be embodied or implemented in a manner that achieves or optimizes one advantage or group of advantages as taught herein without necessarily achieving other advantages as taught or illustrated herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The above and other purposes, features, and advantages of the present application will become more apparent through a more detailed description of the embodiments of the present application in conjunction with the accompanying drawings. The accompanying drawings are intended to provide a further understanding of the embodiments of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the present application and do not constitute a limitation of the present application. In the drawings, the same reference numerals generally represent the same components or steps.

[0021] Figure 1 A schematic diagram showing the structure and size of SRR in a metasurface structure according to a specific embodiment of the present application is shown;

[0022] Figure 2 A schematic structural diagram of an EP2 metasurface for constructing an EP3 system according to a specific embodiment of the present application is shown;

[0023] Figure 3 A schematic structural diagram of an EP3 metasurface according to a specific embodiment of the present application is shown;

[0024] Figure 4 Schematic diagram showing the coupling relationship between two SRRs in the metasurface structure according to the present application;

[0025] Figure 5 A schematic diagram showing the merging of EP3 metasurface eigenvalue evolution according to a specific embodiment of the present application;

[0026] Figure 6 An optical microscope photograph of the EP3 metasurface according to a specific embodiment of the present application is shown. DETAILED DESCRIPTION

[0027] The following describes exemplary embodiments of the terahertz metasurface structure and its construction method for realizing the third-order singular point (EP3) provided by the present invention with reference to the accompanying drawings. Obviously, the embodiments described with reference to the accompanying drawings are only part of the embodiments of the present application, rather than all the embodiments of the present application. In the accompanying drawings, the same reference numerals generally represent the same components. It should be understood that the dimensions, sizes and orientations of the components shown in the drawings are not necessarily drawn to scale, and they may be different from the embodiments shown here for implementation. In addition, some embodiments may combine any suitable combination of features from two or more drawings. Unless otherwise specified, the scientific and technological terms used herein have the meanings commonly understood by those skilled in the art.

[0028] Before describing the technical solution of the present invention, the terms used herein are defined as follows:

[0029] The term "exotic point" (EP) refers to the phenomenon in which multiple eigenvalues ​​and eigenstates of a system merge simultaneously when the eigenvalues ​​(such as frequency and energy) of the system vary with a certain parameter. In this state, the system exhibits significant changes in physical properties, such as enhanced sensitivity and topological properties. This type of EP typically occurs in resonant systems and is also referred to herein as a "resonance singular point."

[0030] The term "third-order singular point" (EP3) or "third-order non-Hermitian singular point" refers to a non-Hermitian system in which three eigenvalues ​​and their corresponding eigenstates simultaneously degenerate at the same frequency or parameter value. Compared to lower-order singular points (EP2), EP3s exhibit higher-order spectral nonlinearity, more complex topological structures, and higher-dimensional physical responses.

[0031] The term "metasurface" refers to micro-nanostructures with artificially designed structures on the micrometer or subwavelength scale, with thicknesses significantly smaller than the operating wavelength. Metasurfaces typically manipulate the propagation characteristics of electromagnetic waves, including reflection, refraction, and absorption, by designing structural units (such as metal rings and wires) of varying shapes, sizes, and arrangements.

[0032] The term "non-Hermitian system" refers to a physical system with asymmetric coupling or dissipative mechanisms, where the Hamiltonian or energy operator does not satisfy Hermitian conditions. Non-Hermitian systems often introduce complex eigenvalues, leading to asymmetric degeneracy of the system's eigenvalues ​​and eigenstates, such as the formation of singularities.

[0033] Coupled Mode Theory (CMT) is a theoretical approach used to describe the energy transfer and coupling between multiple physical systems, such as resonators and optical fibers. This theory allows the derivation of coupling strength, frequency detuning, and loss characteristics between modes, thereby analyzing the system's frequency-domain response and singularity characteristics.

[0034] The term "temporal coupled mode theory" (TCMT) is an extension of coupled mode theory to the time domain and is often used to describe time-dependent coupling phenomena. This theory is particularly well-suited for analyzing and predicting asymmetric coupling between modes in non-Hermitian systems and the resulting eigenvalue degeneracy, such as the formation of EP points.

[0035] The term "split-ring resonator" or "split-ring resonator" (SRR) is a typical artificial structural unit used to achieve resonant control of electromagnetic waves in metamaterials and metasurfaces. It was first proposed by Pendry et al. to achieve negative magnetic permeability (μ < 0) and has been applied to electromagnetic response enhancement, resonant absorption, and polarization control in the terahertz, microwave, and even visible light bands.

[0036] The term "terahertz band" refers to the region of the electromagnetic spectrum with frequencies between 0.1THz and 10THz, between microwaves and infrared light. The terahertz band has unique penetrating and controllable properties, making it widely used in imaging, communications, materials testing, and other fields.

[0037] The term "predicted neural network" (PNN) refers to an artificial neural network used for model optimization and prediction. It can predict the nonlinear relationship between structure and response by learning patterns and relationships from large amounts of data. In some embodiments of the present invention, a PNN can be used to learn the relationship between SRR structural geometric parameters and EP3 eigenfrequencies and modal degeneracy behavior, thereby achieving rapid prediction and optimization.

[0038] The term "intermediate isolation layer" or "dielectric isolation layer" refers to a dielectric layer used to isolate different hierarchical structures in a metasurface structure. In the embodiments of this article, for example, materials with good optical and electrical properties (such as SU8) can be used to ensure the electromagnetic coupling and physical properties of the upper and lower layers. Stability.

[0039] As mentioned in the background technology section, achieving controllable and designable EP3 based on metasurfaces faces several challenges. For example, the multimode coupling conditions required for EP3 and the fine parameter matching in the complex frequency space are difficult to achieve in actual periodic structures. Secondly, most current design methods rely primarily on parameter scanning and empirical adjustment, lacking systematic design strategies and structure-parameter mapping relationships, making it difficult to accurately predict and control the EP3 position. In addition, experimental feasibility issues such as structural size, material loss, and spectral measurement limitations also restrict the practical implementation of EP3 in metasurfaces.

[0040] To this end, in an exemplary embodiment of the present invention, a method combining theoretical modeling and structural design is provided to efficiently construct a non-Hermitian system structure with clear EP3 behavior in the THz band. This systematic and experimentally verifiable solution is conducive to promoting its application in the fields of non-Hermitian optics and topological photonics.

[0041] In some embodiments, a non-Hermitian system structure with EP3 behavior generally includes three modes and corresponding three resonators (resonators), which together constitute a three-mode coupling system. In theory, a metasurface structure with EP3 response in the terahertz band can be designed based on the non-Hermitian coupling theory. This structure obtains EP3 points with spectral degeneracy characteristics by realizing resonant interference and non-Hermitian coupling of three modes in the frequency domain and parameter space, showing high-dimensional characteristic response, ultra-strong perturbation sensitivity and topological diversity. A non-Hermitian system composed of three effectively coupled terahertz resonators utilizes characteristic frequency regulation and precise adjustment of coupling strength to make the eigenvalues ​​of the system triple-degenerate in the complex frequency space, thereby constructing an EP3 singular point.

[0042] In one embodiment, a three-coupled resonator system model can be established through coupled-mode theory, theoretically deriving the necessary conditions for achieving EP3, including the matching relationship between resonant frequency, loss coefficient, and coupling constant. Furthermore, through a structure mapping method, the theoretical model can be applied to the design of terahertz metasurfaces with specific geometric parameters and material compositions. The designed structure, through geometric configuration control and synergistic interaction with material parameters, achieves positional control and topological connection of EP3 feature points within a two-dimensional or three-dimensional parameter space, thus meeting processing and measurement requirements.

[0043] Regarding the structure of the metasurface, the inventors of the present application recognize that the resonant EP3 system can be realized by expanding the EP2 system. To this end, in some embodiments, the EP3 metasurface structure can be designed as a double-layer metasurface structure. For example, three metal split ring resonators (SRRs) are arranged in different layers, and controlled coupling therebetween is used to achieve a complete merging of eigenvalues ​​and eigenstates. Specifically in terms of structural design, two metal SRRs with similar geometric structures but slightly different parameters are first designed to construct the EP2 system. The resonant frequency and loss coefficient can be tuned by adjusting the geometric parameters of the EP2 structure (described in detail below). Afterwards, the EP3 structure is realized by introducing a third perturbation SRR on the basis of the EP2 structure, which will be described in detail below.

[0044] Figure 1 The structure and size diagram of a metal split ring resonator (SRR) that can be used to construct an EP3 metasurface structure according to an embodiment of the present application is shown. The reason why SRR is chosen as the basis for constructing the metasurface structure in this paper is that SRR has a high degree of controllability. SRR can be made of metal materials such as Au. Figure 1As shown in the figure, the metal SRR unit is a resonant ring structure with an open shape. The geometric parameters that define its structure include, for example, the ring length a, the ring width b, the metal line width w, and the opening gap g. By adjusting these geometric parameters, the eigenfrequency and radiation loss of the SRR can be flexibly controlled, thereby achieving fine control of the coupling strength and non-Hermitian characteristic parameters (resonant frequency, loss coefficient).

[0045] Figure 1 Specifically, two SRR unit structures are shown. As shown in the left figure, the SRR unit is a square resonator with two openings. The two openings are set on the two opposite sides of the ring length and separated by a metal wire or metal strip in the middle. The right figure shows another SRR unit structure, which is a square split ring resonator. The split ring is set in the middle of the ring length on one side. In one embodiment, the sizes of these two SRR units can be adjusted to obtain resonant rings of different structures / sizes. On this basis, by different structural / geometric parameters (such as a i ,b i ,w i ,g i , Figure 1 In the example, SRR units (where i can be 1 or 2) can be combined to obtain EP2 and then implement EP3 system, which is exemplified below.

[0046] As described above, the resonant EP3 system can be realized by expanding the EP2 system. Figure 2 FIG. 1 shows a schematic structural diagram of an EP2 metasurface that can be used to construct an EP3 metasurface structure according to an embodiment of the present application. Figure 2 As shown in FIG, the EP2 structure is composed of two SRR units (for the convenience of description, they are respectively referred to as SRR2 and SRR3 in this article), wherein the upper figure shows a top view and the lower figure shows a front view. The two SRR units are arranged on the substrate and can be located in the same plane or between two adjacent layers (the figure shows that the two SRRs are located in two adjacent layers, SRR2 is located in the lower layer and SRR3 is located in the upper layer). They have certain structural differences to introduce frequency detuning. For example, Figure 2 The figure shows that both SRR units are dual split-ring resonators, but differ in at least one of their structural parameters a, b, w, and g. Furthermore, the two SRR units are spatially arranged to form resonant coupling, using a lateral or longitudinal offset in a two-dimensional plane, a vertical distance in three-dimensional space, or a rotational or torsional angle relative to each other. This coupling structure supports interference between the two eigenmodes and common-mode extinction, thereby forming a second-order singular point (EP2) under specific parameter conditions, providing a foundation for constructing EP3.

[0047] According to the TCMT theory, it can be deduced that the condition for such a system to form a resonant EP2 is that ω1-ω2=0 or γ1-γ2=0, where ω1 / ω2 and γ1 / γ2 represent the eigenfrequency and gain / loss coefficient of the two coupled resonators, respectively. Since the difference in the resonant frequency and / or loss coefficient of the two resonators is related to the geometric parameters of the two resonators (for example, the loop length and width of the SRRs) and the spatial position (for example, the offset between the SRRs), the structures of SRR2 and SRR3 can be designed to construct an EP2 system.

[0048] Continue to refer to Figure 2 In one embodiment, SRR2 is located on a substrate (e.g., a silicon substrate) and is spin-coated with a 2-5 μm (e.g., 3 μm) thick isolation layer with stable thermal properties, such as an SU8 glue layer. SRR3 is located on top of the isolation layer and is displaced from SRR2 in the y direction. Preferably, SRR3 is exposed to the air, which is conducive to its micro-perturbative interaction with the external environment or the analyte to be measured, thereby achieving highly sensitive detection of external analytes. Although the figure shows that the two are spaced apart in the y direction, in some examples, the two can also partially overlap in the y direction. In addition, although only one SRR2 and SRR3 are shown in the figure, it can be understood that the two resonators can be periodically arranged in the x and y directions to realize a superlens structure.

[0049] For example, by adjusting the parameters d2 (interlayer displacement) and b3 (ring width / side length of SRR3), the complex coupling coefficient between the resonators can be precisely controlled. In this embodiment, b3 is one of the key parameters. It mainly affects the resonant frequency and has almost no effect on the loss coefficient. Therefore, it can be considered as a degree of freedom for optimizing the EP condition. Through reasonable design, the complex characteristic frequencies of the two modes can be merged in the parameter space, that is, ω1-ω2=0, thereby meeting the conditions for the formation of EP2. For example, see Figure 4 The right figure shows how the system's characteristic frequency varies with d2 when b3 is fixed (e.g., 48 μm). It demonstrates that when d2 is ±12 μm, the complex frequencies of the two modes merge. The above describes the construction of the SRR-based EP2 system using exemplary parameters. However, it should be understood that the aforementioned structural parameters are merely illustrative and not limiting, and SRR2 and SRR3 can also be designed with other structural parameters.

[0050] Based on the EP2, the inventors of this application have realized a reasonable path to construct an EP3 system based on coupling theory. For example, the Lorentz coupling model can be used to describe the asymmetric coupling and loss distribution between the three resonators, and the conditions for EP3 formation can be analytically derived and the design parameter space can be constructed. Specifically, the inventors found that, assuming that the resonant EP3 system includes three modes: mode 1, mode 2, and mode 3, one SRR corresponds to each mode, and mode 2 and mode 3 are EP2 systems constructed according to the aforementioned method. On this basis, if mode 1 and mode 3 are designed to have no coupling (the coupling coefficient of the two is zero), and the coupling between mode 1 and mode 2 is weak, the system meets the conditions for forming EP3. In other words, the resonant EP3 system can be regarded as a resonant EP2 system composed of mode 2 and mode 3, and mode 1 with weak coupling to mode 2 is introduced as a perturbation. The overall behavior of the system is mainly determined by the resonant EP2 system, but the introduction of mode 1 induces the resonant EP2 system to the EP3 state. In this way, the difficulty of constructing EP3 can be significantly reduced. In this example, two key factors for achieving resonance EP3 are: weak coupling k1 between mode 1 and mode 2 and zero coupling k3 = 0 between mode 1 and mode 3.

[0051] Specifically in terms of structural design, in order to construct a resonant EP3 system, in one embodiment, the resonant EP3 system can be constructed in the designed Figure 2 Based on the dual-resonance structure EP2 shown, a third resonator (denoted as SRR1 in this article) is introduced. This resonator can be located in the same layer as SRR2 and has no displacement difference in the longitudinal direction (y direction). It can achieve the different required coupling strengths between the three modes, including almost zero coupling between SRR1 and SRR3, and weak coupling between SRR1 and SRR2.

[0052] Figure 3 The schematic diagram of the three-dimensional structure of the EP3 metasurface based on the above design ideas is shown in FIG. Figure 3 As shown, the terahertz metasurface structure of this embodiment is arranged on a substrate (silicon wafer) and formed into a double-layer structure. For example, it can be formed on the substrate layer by photolithography and metal deposition processes. Among them, the upper layer SRR3 and the lower layer SRR2 constitute the main coupling channel, and the lower layer also includes a perturbation resonator SRR1, and SRR1 forms a weak coupling with SRR2, while forming basically no coupling (zero coupling) with SRR3. The upper and lower structures can be isolated by a dielectric layer (for example, epoxy resin, etc.), for example, its thickness is greater than the height of the SRR1 and SRR2 resonators in the lower layer. Preferably, the thickness can be controlled at, for example, 2-5μm, to achieve coupling regulation between the upper and lower structures, thereby forming a stable three-mode (resonator) non-Hermitian coupling system, and the EP3 condition can be met by designing or adjusting the geometric parameters of the layer structure, so that the system satisfies the third-order eigenvalue degeneracy.

[0053] In one embodiment, the pattern of resonator SRR1 is different from that of SRR2 and SRR3. For example, it is selected as a square split-ring resonator, and the opening directions of the double split-ring resonators of SRR1, SRR2 and SRR3 are different. This asymmetric structure is conducive to breaking the symmetrical arrangement behavior and exciting richer coupling behavior, thereby realizing resonance EP3.

[0054] In one embodiment, the structure can achieve the EP3 state in the frequency space by optimizing the geometric parameters and spatial positions of each SRR. Figure 3 In a dual-layer structure, the third-order singular point EP3 can be achieved by regulating the lateral offset of the split-ring resonators in the first (lower) and second (upper) layers, and / or by setting a rotation angle between them (for example, the horizontal axis of SRR1 is rotated relative to the horizontal axes of SRR2 / SRR3). Additionally, frequency detuning can be generated by controlling the geometric size difference between the two layers of SRRs, and the coupling strength between adjacent resonant modes can be further controlled by controlling the vertical distance between the upper and lower structures.

[0055] Figure 4 The figure shows the coupling relationship curve of the two resonant rings in the metasurface structure according to an embodiment of the present application. A third perturbation SRR1 is introduced into the aforementioned EP2 structure to realize the EP3 structure, for example, SRR1 is uncoupled with SRR3 in the EP2 structure, but weakly coupled with the other SRR2. Figure 4 Figure a) on the left shows a curve of the change of the intrinsic complex frequency of SRR1 and SRR2 with the lateral distance d1 (in μm) between them. Re(ω) and Im(ω) represent the real and imaginary parts of the complex frequency ω, respectively. The dotted line represents the respective resonant frequencies in the uncoupled state, and the solid line represents the resonant frequency after coupling. It can be seen that with the increase of d1, the real and imaginary parts of the system's eigenvalues ​​are slightly offset compared to a single resonator, indicating that under the condition of no displacement difference in the y direction, SRR1 and SRR2 are weakly coupled.

[0056] Figure 4 Figure b) shows the curve of the change of the intrinsic complex frequency of SRR1 and SRR3 with the structural parameter b3 (in μm) of SRR3. When b3 increases from 40 μm to 60 μm, the resonant frequency of the single resonator SRR3 drops from 0.64 THz to 0.53 THz, while the eigenvalue after coupling hardly changes, especially when b3 is around 56 μm, the imaginary part hardly changes, that is, there is no direct coupling between SRR1 and SRR3 at this time, and the coupling coefficient κ3 between the two is 0.

[0057] Figure 4Figure c) on the right also shows a curve of the change of the intrinsic complex frequency of SRR2 and SRR3 with the lateral distance d2 (in μm) between them. It can be seen that when d2 = 12 μm, there is an EP2 coupling relationship between SRR2 and SRR3. This structure and coupling relationship help to form a three-mode degenerate EP3 state.

[0058] In some embodiments, in order to improve the efficiency and accuracy of the design of EP3 structure and position control, relevant system parameters can be obtained by training a machine learning model. The machine learning model can be implemented using a predictive neural network (PNN), which may include machine learning models such as CNN, RNN, and Transformer. Through model training, it is possible to learn the patterns and relationships in a large amount of data, thereby predicting the nonlinear relationship between high-dimensional structural parameters and EP3 target characteristics (for example, spectral response, etc.). Furthermore, through the global optimization algorithm of the predictive neural network, it is possible to efficiently screen the optimal structural parameters close to the EP3 conditions in the high-dimensional parameter space, thereby improving the design efficiency of metasurface structures with high-order singular points such as EP3, and achieving accurate position prediction and coupling control.

[0059] In one embodiment, a predictive neural network model designed for the aforementioned dual-layer metasurface structure can be used to learn the relationship between the structural geometric parameters and the EP3 characteristic frequency, polarization state, and eigenspectrum, enabling rapid prediction and fine-tuning of the EP3 position. The neural network inputs can include, for example, the geometric parameters of the dual-layer SRR structure, interlayer distance, and / or relative twist angle. The output is the real and imaginary parts of the eigenvalues ​​of the scattering matrix, which are used to identify the precise location of the EP3 point and its response characteristics.

[0060] In one embodiment, to accurately locate EP3 in a high-dimensional parameter space, a large-scale parameter sweep is first performed using CMSOL to collect multiple sets of sample data (e.g., 5,000 sets). Based on this data, a PNN is trained to predict the real and imaginary parts of the three complex eigenfrequencies in the system. The model input consists of a seven-dimensional normalized geometric parameter vector b1, g1, b2, a3, b3, d1, and d2, and the output is six parameters: the real and imaginary parts of the complex frequencies of the three SRRs. The PNN network includes multiple hidden layers, each with multiple (e.g., 64 or 128) neurons, and adjacent layers are fully connected.

[0061] In one embodiment, to precisely locate the resonant EP3 point in a high-dimensional parameter space, a global optimization strategy can be employed to find the geometric parameter set that best approximates the resonant EP3 condition. Given the complex high-dimensional and multimodal nature of the model, a differential evolution algorithm can be used for global search. This algorithm is then combined with the two previously trained predictive neural networks (PNNs) to minimize the EP3 condition function by continuously iterating the geometric parameters.

[0062] Figure 5 A schematic diagram illustrates the evolution of the eigenfrequency of an EP3 metasurface structure during structural parameter control according to an embodiment of the present application, specifically showing the evolution trend of the system's eigenfrequency with parameter d2. As shown in the figure, under certain specific parameters, the three eigenvalue trajectories merge in the complex frequency domain, with the real parts of the complex frequencies crossing and the imaginary parts anticrossing, converging to a single point. This constitutes a third-order degenerate EP3 feature point, thus verifying that the design principles of this application can construct an EP3 metasurface structure.

[0063] The following describes the preparation method of the EP3 supersurface structure of the embodiment of the present application.

[0064] Based on the structural design, the dual-layer terahertz metasurface structure of the present embodiment can be fabricated through micro-nanofabrication processes such as photolithography and metal deposition to precisely achieve the target coupling conditions. As previously described, according to one embodiment of the present application, the designed structure is based on a dual-layer metal SRR, located on the upper and lower layers, separated by a dielectric layer such as SU8.

[0065] In one embodiment, the preparation steps may be as follows:

[0066] (1) Preparing a substrate layer. Preferably, a high-resistivity double-sided polished silicon wafer is selected as the substrate, with a thickness of 1-5 mm and a resistivity greater than 10 kΩ·cm to ensure good transmission performance in the terahertz band;

[0067] (2) Pre-treating the substrate (silicon) surface using reactive ion etching (RIE) to improve photoresist adhesion;

[0068] (3) Spin-coating photoresist and heat-treating to form a uniform film layer. For example, spin-coating a 1-2 μm thick UV photoresist on the wafer, and then pre-baking it at a high temperature (e.g., 60-120°C) for a certain period of time;

[0069] (4) Pattern exposure and development. For example, a photolithography device (e.g., a DWL66+ direct write lithography system) is used to expose the first layer pattern of the SRR array structure, and then baked on a hot plate to harden the film. Developing is then performed using a developer and fixed with deionized water.

[0070] (5) Depositing a metal film (e.g., a 100-300 nm thick gold film) by electron beam evaporation and stripping it with a solvent such as acetone to obtain a first layer structure; in steps 4 and 5, precise alignment of the layer structure pattern (e.g., achieving precise parameters such as d1) and metal preparation can be achieved by high-precision direct writing lithography (DWL) and electron beam evaporation;

[0071] (6) Spin-coat the intermediate isolation layer, and perform UV exposure and high-temperature baking to form a stable support platform. For example, spin-coat a 2-5 μm thick SU8 layer and pre-bake it at a high temperature (e.g., 60-120°C) for a certain period of time. Expose it with UV light, followed by further hard baking at a high temperature (e.g., 200-500°C) for a certain period of time to form a stable intermediate layer.

[0072] (7) Repeat the above steps to form a second layer of SRR structure, spin-coat photoresist on the isolation layer and heat-treat it to form a uniform film layer. For example, the structure of the second layer of SRR array is exposed and developed using a photolithography device, and a metal film is deposited by electron beam evaporation, and then the second layer of SRR array is obtained by solvent stripping. In this case, the upper and lower layers of patterns can be laminated by precise overlay alignment.

[0073] Figure 6 An optical photograph of the EP3 metasurface according to an embodiment of the present application is shown, which is an optical microscope photograph of the EP3 metasurface structure after preparation by actual photolithography and metal deposition process. As shown in the figure, since the solidified SU8 is transparent or translucent in the visible light range, the overall morphology of the three SRR arrangements and their pattern consistency can be clearly observed through an optical microscope. Each SRR is periodically arranged in a two-dimensional plane to form an SRR array. In this embodiment, b3 = 40 μm, d2 = -12 μm. It can be seen that the double-layer metasurface structure of this embodiment has good processing feasibility and dimensional control accuracy, which provides a basic guarantee for the experimental realization of EP3. It can also be understood that the process flow described above can ensure the high precision and good repeatability of the double-layer THz metasurface structure, so the corresponding EP3 metasurface structure can be prepared based on other structural parameters (which are obtained, for example, by a neural network model).

[0074] An exemplary embodiment of the present invention further provides a device comprising the aforementioned EP3 metasurface structure, which may be a terahertz device, such as an optical device, a sensor device, or a control device, such as a high-dimensional topological optical device, a non-Hermitian sensor device, and a terahertz control device. As described above, the EP3 metasurface structure of the device exhibits characteristics such as polarization state evolution, scattering matrix degradation, and phase singularities associated with non-Hermitian singularities within the operating frequency band. Therefore, it can be used to realize sensitive sensing, topological filters, or controllable singularity sources in the terahertz band, and can be specifically applied to 6G communication devices.

[0075] The above description of the terahertz metasurface structure with EP3 response of the present application, with reference to the accompanying drawings, realizes a controllable EP3 singularity in the THz metasurface, demonstrating excellent controllability and device potential. It can be widely used in high-sensitivity biosensors, topological lasers, wavefront control devices, and information processing platforms in the THz band. In some embodiments, a systematic and verifiable solution is provided by combining theoretical design, neural network optimization, and experimental verification. This structure and its design method can also be extended to other bands and platforms, and has important significance in photon control, topological optics, and sensing applications.

[0076] It should be understood that although terms such as "first" or "second" may be used herein to describe different components or features, these components or features are not limited to these terms. The above terms are used only to distinguish one component from another, and are not used to emphasize order, positional relationships, etc. For example, a first component may be referred to as a second component, and a second component may be referred to as a first component without departing from the scope of this disclosure. In other words, modifiers such as "first" and "second" without quantifiers are interchangeable.

[0077] As used herein, words such as "include," "comprising," "having," and the like are open ended words meaning "including but not limited to," and are used interchangeably therewith. The words "or" and "and" as used herein mean the words "and / or," and are used interchangeably therewith, unless the context clearly indicates otherwise. The word "such as" as used herein means the phrase "such as, but not limited to," and is used interchangeably therewith.

[0078] While various embodiments of the present application have been described above, the foregoing description is illustrative and non-exhaustive, and is not intended to limit the disclosed embodiments. Many combinations, modifications, and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. Therefore, the scope of protection of this application shall be determined by the scope of the claims.

Claims

1. A terahertz metasurface structure for realizing a third-order singular point, characterized in that: The structure includes: substrate layer; a first layer of split ring resonator array formed on the substrate layer; an isolation layer formed on the substrate layer and used to isolate different layer structures; and A second layer of split ring resonator array is formed on the isolation layer, The first layer of split ring resonator array and the second layer of split ring resonator array constitute a three-mode coupling system, and the geometric parameters of the layer structure enable the system to satisfy third-order eigenvalue degeneracy.

2. The metasurface structure according to claim 1, wherein The units of the first layer of split ring resonator array are composed of two different first split ring resonators and a second split ring resonator, the units of the second layer of split ring resonator array include a third split ring resonator, and the three split ring resonators correspond to the three modes.

3. The metasurface structure according to claim 2, wherein: The first split ring resonator and the second split ring resonator are respectively a square split ring resonator and a double split ring resonator, and the third split ring resonator is a double split ring resonator, wherein the square split ring resonator and the double split ring resonator have different opening directions.

4. The metasurface structure according to claim 2, wherein: The second split ring resonator and the third split ring resonator form a second-order resonant singular point system, and the first split ring resonator and the second split ring resonator are coupled in a weak coupling manner, and there is zero coupling between the first split ring resonator and the third split ring resonator.

5. The metasurface structure according to claim 1 or 2, wherein: The split ring resonators of the first layer and the second layer are offset in the lateral direction, and / or there is a rotation angle between the split ring resonators.

6. The metasurface structure according to claim 1, wherein: The substrate layer includes a double-sided polished silicon wafer.

7. The metasurface structure according to claim 1, wherein: The isolation layer is made of a dielectric polymer, and a thickness of the isolation layer is greater than a height of the first layer of split ring resonator array.

8. The metasurface structure according to claim 7, wherein: The thickness of the isolation layer is in the range of 2-5 μm to achieve coupling regulation between the upper and lower structures.

9. A method for preparing the terahertz metasurface structure according to any one of claims 1 to 8, characterized in that: The method comprises: preparing a substrate layer, and spin-coating a photoresist on the substrate layer and performing a heat treatment to form a uniform film layer; exposing and developing the structure of the first layer of the split ring resonator array; Depositing metal films by electron beam evaporation and obtaining the first layer of split ring resonator arrays by solvent stripping; Spin-coat the isolation layer, and perform exposure and baking; Spin-coating photoresist on the isolation layer and subjecting it to heat treatment to form a uniform film layer; exposing and developing the structure of the second layer split ring resonator array; and The metal film was deposited by electron beam evaporation, and the second layer of split-ring resonator arrays was obtained by solvent lift-off.

10. A terahertz device, comprising the terahertz metasurface structure according to any one of claims 1 to 8, wherein the device is an optical device, a sensor device or a control device.

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