A Design Method for Reconfigurable Non-Hermitian Metasurfaces Based on Singular Point Phase Properties

Abstract

This invention discloses a reconfigurable non-Hermitian metasurface design method based on the phase characteristics of singular points. Utilizing the 2π-encircling phase characteristics of singular points, combined with PB phase and the properties of phase change materials, the phase of the entire metasurface array is reconstructed. The method of this invention is ingeniously designed, not only manipulating the phase information of the unit structure but also utilizing phase change materials to achieve phase reconstruction, and can be used for the integration of multiple functions.

Description

Technical Field

[0001] This invention belongs to the field of micro-nano optics and coded metasurface technology. It focuses on utilizing the singular point phase characteristics in non-Hermitian metasurfaces and combining them with phase change materials. It mainly relates to a method for realizing reconfigurable non-Hermitian metasurfaces. Background Technology

[0002] Singularities (EPs) are singularities associated with open systems. The gain and loss of energy endow the system with non-Hermitian properties. When parity-time (PT) symmetry is established, non-Hermitian Hamiltonians can exhibit a completely true spectrum. Simultaneously, the orthogonality of eigenstates is broken, making the eigenstates (along with eigenvalues) potentially degenerate at certain points, thus realizing EPs. Many interesting phenomena emerge at non-Hermitian singularities, such as one-way non-reflection, coherent perfect absorption, enhanced sensing, and 2π topological phase.

[0003] Metasurfaces are periodic arrangements of artificial subwavelength antennas with different shapes and sizes, exhibiting superior optical performance compared to traditional optical antennas. Ingenious structural parameter design can enable metasurfaces to display unique properties not found in their intrinsic materials, such as negative refractive index and negative permittivity. Materials possessing these properties do not exist in nature, thus metasurface research has significantly broadened the research content and scope in fields such as electromagnetics, optics, and materials science, with far greater application prospects. To date, metasurface-based nano-optical devices have been widely applied in holograms, waveplates, and superlenses.

[0004] To reveal the underlying physical mechanism, a complex symmetric 2×2 matrix Hamiltonian can efficiently describe this non-Hermitian system.

[0005]

[0006] Where ω x and ω y These represent the resonant frequencies in the x and y directions, respectively, and the detuning is δ = ω. x –ω y =0. γ x and γ y Let γ represent the loss in the x and y orientations, and g represent the coupling strength between the two directions. Loss parameter γ x and γ y It can be controlled by geometric dimensions or strong plasma coupling.

[0007]

[0008] and Eigenvalues ​​and corresponding eigenstates can be obtained directly:

[0009]

[0010] By changing the coupling strength *g*, the eigenstates of the system rotate by 45° during the PT-symmetric phase transition. The evolution of the corresponding eigenvalues ​​is described by two intersecting Riemannian plates centered at EP in the non-Hermitian system. When *g* > Γ, the system is in a PT-symmetric phase with two eigenvalues ​​having the same imaginary part but different real parts. When *g* < Γ, the system is in a PT-symmetric broken phase, with the two eigenvalues ​​sharing the same real part but different imaginary parts. When *g* = Γ, i.e., at EPs, the eigenvalues ​​(ω) of the system... ± =E0) and eigenstates They have all degenerated.

[0011] To visualize EPS, consider a 2×2 transfer matrix. The transfer matrix can be described as...

[0012]

[0013] Where r ij It is a complex transmission with incident state j and exiting polarization state i, where {i, j} ∈ {x, y}. The corresponding eigenvalues ​​can be derived as follows:

[0014]

[0015] Where λ 1,2 These are the complex eigenvalues ​​of the 2×2 transfer matrix. To find the EPs in the metasurface, four complex reflection spectra are first obtained using software simulation, and then the eigenvalues ​​of the reflection matrix as a function of frequency can be obtained. Furthermore, the transfer matrix is ​​described using a circular polarization basis, and the four circularly polarized reflection spectra can be obtained from linearly polarized reflection.

[0016]

[0017] Where, r lr Defined as the complex transmission of left-handed circularly polarized (LCP) outgoing and right-handed circularly polarized (3RCP) incident, with other components deduced similarly. When r lr r rl When the amplitude equals 0, i.e., one of the cross-polarizations is zero, EPs appear. Furthermore, a complete 2π phase accumulates around the EP. This singular behavior of amplitude and phase is unique to EPs in non-Hermitian metasurface systems, providing a more intuitive way to observe them.

[0018] In recent years, there has been a large amount of research on singularities in non-Hermitian metasurfaces, but most studies are limited to single exponents (EPs) at fixed frequencies. The ability to simultaneously realize two or more EPs not only expands the design flexibility of metasurfaces but also facilitates the functionalization and device integration of non-Hermitian metasurfaces, making it a current research focus in this field. Summary of the Invention

[0019] The present invention aims to overcome the above-mentioned shortcomings of the prior art and provide a reconfigurable non-Hermitian metasurface design method based on singular point phase characteristics.

[0020] This invention utilizes the phase characteristics of singular points on non-Hermitian metasurfaces. By changing the size of the structure surrounding the singular points, a surrounding 2π phase is obtained, and by utilizing the properties of phase change materials, a reconfigurable non-Hermitian metasurface is realized.

[0021] The technical solution of the present invention is as follows:

[0022] A design method for reconfigurable non-Hermitian metasurfaces based on singularity phase characteristics utilizes the phase characteristics of singularities in non-Hermitian metasurfaces and the phase transition material VO2. When VO2 changes from an insulating state to a metallic state, the phase of the metasurface is reconfigured, enabling functional switching. The method includes the following steps:

[0023] 1) Construction of Nanostructure Units: The nanostructure unit comprises three layers: a bottom metal reflective layer, a middle dielectric substrate, and a structure consisting of periodically arranged metal and VO2 phase change material combinations with different lengths, widths, and rotation angles placed on the substrate. An xoy coordinate system is established with the right-angled sides of the structural unit as the x-axis and y-axis. In the structure, the metal nanobricks have a side length L1 along the y-axis and a width W1 along the x-axis; the VO2 nanobricks are placed adjacent to the metal nanobricks, with a side length L2 along the x-axis and a width W2 along the y-axis. At a selected operating frequency, sixteen nanostructures of different sizes are optimized using electromagnetic simulation software. The optimized structural parameters include: the periodic side length P of the structural unit, the thickness h1 of the metal reflective layer, the thickness h2 of the substrate layer, and the side lengths L1 and L2, widths W1 and W2, and height h3 of the metal and VO2 combination structure, as well as the positional change Δy of the VO2 nanobricks along the y-axis.

[0024] 2) Determine the parameters of the metal nanobrick when VO2 is in the insulating state: By optimizing the length and width L1 and W1 of the metal nanobrick, CST simulation was used to determine that it can achieve good polarization conversion function in a wide band.

[0025] 3) Optimize the singularity of the nanostructure when VO2 is in the metallic state: Based on the optimized metallic nanobrick in step 2), change the length L2 of the VO2 nanobrick and the position Δy of its vertical movement along the y-axis, and use CST simulation to determine the singularity.

[0026] 4) By changing the parameters around the singularity optimized in step 3), sixteen nanostructures are optimized to satisfy the 2π phase change.

[0027] 5) Determine the two holographic images I A and I BPhase distribution: Based on the principle of computational holography, the GS algorithm is used to analyze pattern I. A and Image I B The two target images are processed to obtain two phase distribution matrices, where I A The phase distribution is continuous phase, I B The phase distribution is a sixteen-step gradient phase.

[0028] 6) Arrangement of nanostructure array: First, change the rotation angle of the metal nanobricks, and use the PB phase to satisfy I A The continuous phase distribution; by utilizing sixteen optimized nanostructures, the phase distribution of the entire metasurface array is altered to satisfy I B The phase distribution of the sixteen steps.

[0029] 7) Observing the nanoarray arranged in step 6), when VO2 is in an insulating state, using circularly polarized light of frequency f incident perpendicularly on the metasurface, the first holographic image I can be reproduced in the nanoarray. A By changing the temperature to transform VO2 from an insulating state to a metallic state, phase reconstruction of the entire array is achieved. When right-handed circularly polarized light with frequency f is incident perpendicularly on the metasurface, a second holographic image I can be reproduced in the nanobrick array. B .

[0030] Furthermore, in step 1), the three different materials are a bottom metal reflective layer, a SiO2 substrate layer, and an upper metal and VO2 combined structure layer, wherein the metal material is Au.

[0031] Furthermore, the sixteen nanostructures contained in the nanostructure array in step 4) have different phase responses: when right-handed circularly polarized light of frequency f is incident perpendicularly on the metasurface along the z-axis, the phases of the sixteen nanostructures are “179.516°”, “157.975°”, “135.051°”, “111.558°”, “89.857°”, “66.649°”, “46.193°”, “23.247°”, “0.697°”, “-23.176°”, “-46.102°”, “-66.571°”, “-91.430°”, “-112.881°”, “-134.458°”, and “-158.693°”.

[0032] Furthermore, the GS algorithm optimization process in step 5) is completed using MATLAB software, where the target holographic image I... A and I B The optimization objective is input into the algorithm, and the optimization function is set as the error between the reconstructed holographic information and the target hologram. The error function is defined as follows:

[0033]

[0034] Where I is the target image, I′ is the image reconstructed by the algorithm, and i and j represent the row and column numbers of the pixels, respectively; the output consists of two holographic images I. A and I B .

[0035] Preferably, in step 5), pattern I A and Pattern I B They are all 100×100 pixels.

[0036] Furthermore, by rationally arranging the types of nanostructures corresponding to each pixel region, phase reconstruction of the nanostructure array can be achieved after VO2 undergoes a phase transition.

[0037] This invention employs a simple combined L-structure, its innovation lying in utilizing the phase characteristics of non-Hermitian singularities. By surrounding the singularities with a structure, an ET phase with 2π phase coverage can be obtained. By combining the ET and PB phases and utilizing the phase transition properties of phase change materials, phase reconstruction of the entire metasurface array can be achieved. This structure enables the integration and switching of multiple functional applications. Therefore, this invention has significant reference value and practical implications in the research of actively controlled metasurfaces and applications of non-Hermitian singularities.

[0038] The advantages of this invention are: by utilizing the phase characteristics of the singularity point 2π surrounding, combined with the PB phase and the characteristics of the phase change material, the phase reconstruction of the entire metasurface array can be achieved. The method of this invention is ingeniously designed, not only manipulating the phase information of the unit structure, but also using the phase change material to achieve phase reconstruction, and can operate multiple functions in an integrated manner. Attached Figure Description

[0039] Figure 1(a) is a schematic diagram and top view of the unit structure of an embodiment of the present invention, wherein 1 is an Au metal reflective layer, 2 is a SiO2 dielectric substrate, 3 is a VO2 nanobrick, and 4 is an Au nanobrick; Figure 1(b) is a top view of Figure 1(a).

[0040] Figure 2 This is a reflection amplitude diagram of the unit structure when VO2 is in an insulating state, as shown in this embodiment of the invention.

[0041] Figure 3 This is a schematic diagram showing the relationship between the two cross-polarization phases and the rotation angle of the unit structure at the operating frequency when VO2 is in the insulating state, according to an embodiment of the present invention.

[0042] Figure 4 This is a reflection amplitude diagram of the unit structure when VO2 is in the metallic state in an embodiment of the present invention;

[0043] Figure 5This is a schematic diagram showing the relationship between the two cross-polarization phases and the rotation angle of the unit structure at the operating frequency when VO2 is in the metallic state, according to an embodiment of the present invention.

[0044] Figure 6(a) shows the relationship between the real part of the intrinsic values ​​and the frequency of the unit structure when VO2 is in the metallic state in the embodiment of the present invention; Figure 6(b) shows the relationship between the imaginary part of the intrinsic values ​​and the frequency.

[0045] Figure 7(a) shows the cross-polarization component r of the unit structure at the operating frequency when VO2 is in the metallic state in the embodiment of the present invention. +- The relationship between amplitude and parameter variation is shown in Figure 7(b); Figure 7(b) shows the cross-polarization component r. -+ The relationship between amplitude and parameter changes;

[0046] Figure 8(a) shows the cross-polarization components of the unit structure at the operating frequency when VO2 is in the metallic state in the embodiment of the present invention. Figure 8(b) shows the relationship between phase and parameter variations; Figure 8(b) shows the cross-polarization components. A graph showing the relationship between phase and parameter changes;

[0047] Figure 9(a) shows the cross-polarization component r of the unit structure at the operating frequency when VO2 is in an insulating state in an embodiment of the present invention. +- The relationship between amplitude and parameter variation is shown in Figure 9(b); Figure 9(b) shows the cross-polarization component r. -+ The relationship between amplitude and parameter changes;

[0048] Figure 10(a) shows the cross-polarization components of the unit structure at the operating frequency when VO2 is in an insulating state in an embodiment of the present invention. The relationship between phase and parameter variation is shown in Figure 10(b); Figure 10(b) shows the cross-polarization components. A graph showing the relationship between phase and parameter changes;

[0049] Figure 11 In this embodiment of the invention, the GS algorithm is used to process the holographic image I. A The generated phase arrangement diagram;

[0050] Figure 12(a) is the target hologram of an embodiment of the present invention; Figure 12(b) is the restored image I generated by the GS algorithm. A ;

[0051] Figure 13 In this embodiment of the invention, the GS algorithm is used to process the holographic image I. B The generated phase arrangement diagram;

[0052] Figure 14(a) is the target hologram of an embodiment of the present invention; Figure 14(b) is the restored image I generated by the GS algorithm. B. Detailed Implementation

[0053] The present invention will be further described below with reference to the accompanying drawings and embodiments, but the scope of protection of the present invention is not limited to the scope described.

[0054] A method for designing reconfigurable non-Hermitian metasurfaces based on singular point phase characteristics includes the following steps:

[0055] The non-Hermitian metasurface provided by the present invention comprises, from top to bottom: a metal and phase change material composite structure layer, a dielectric substrate layer, and a metal reflective layer.

[0056] First, a nanostructure unit is constructed, as shown in Figures 1(a) and 1(b). The optimized structural parameters include: the nanostructure unit consists of a combination of Au nanobricks 4 and VO2 nanobricks 3, a SiO2 dielectric substrate 2, and an Au metal reflective layer 1. An xoy coordinate system is established with the right-angled sides of the structural unit as the x-axis and y-axis. In the structure, the side length of the Au nanobrick 4 along the y-axis is L1, and the width along the x-axis is W1. The VO2 nanobricks 3 are placed close to the gold nanobricks, with the side length along the x-axis being L2 and the width along the y-axis being W2. At the selected operating frequency, the parameters are optimized using electromagnetic simulation software to find the EP. The optimized structural parameters include: the periodic side length P of the structural unit, the thickness h1 of the Au metal reflective layer 1, the thickness h2 of the SiO2 dielectric substrate 2, and the side lengths L1 and L2, widths W1 and W2, and height h3 of the combination of Au nanobricks 4 and VO2 nanobricks 3, and the positional change Δy of the VO2 nanobricks 3 along the y-axis. The optimized structural parameters are as follows: the length and width of Au nanobrick 4 are L1 = 150 μm and W1 = 20 μm; the length and width of VO2 nanobrick 3 are L2 = 65 μm and W2 = 40 μm; the thickness is h1 = 50 μm, h2 = 40 μm and h3 = 80 μm; the unit structure period is P = 250 μm; the position change of VO2 nanobrick 3 along the y-axis is Δy = 21 μm.

[0057] When VO2 nanobricks 3 are in an insulating state, VO2 nanobricks 3 have little effect on the nanostructure. Figure 2 The reflection amplitude diagram shows only slight deviations between the two cross-polarizations. For example... Figure 3 As shown, changing the rotation angle of the nanostructure at the operating frequency results in two cross-polarization phase changes that conform to the relationship of twice the rotation angle, indicating that it conforms to the PB phase.

[0058] When VO2 is in the metallic state, from Figure 4 The reflection amplitude diagram shows that one cross-polarization is 0, while the other cross-polarization is not 0, consistent with singularity characteristics. For example... Figure 5As shown, changing the rotation angle of the nanostructure at the operating frequency, the phase changes of the two cross-polarizations conform to the relationship of twice the rotation angle, indicating that they conform to the PB phase. To verify that it is a singularity, the relationship between the real and imaginary parts of the eigenvalues ​​and the frequency is calculated. As can be seen from Figures 6(a) and 6(b), the real and imaginary parts of the eigenvalues ​​are degenerate at the operating frequency. Keeping other parameters constant, changing the length L2 of the VO2 nanobrick 3 and the position Δy along the y-axis, we obtain the two amplitude distribution diagrams in Figures 7(a) and 7(b) and the two phase distribution diagrams in Figures 8(a) and 8(b). It can be seen that only one cross-polarization has a zero point in amplitude and has a 2π phase change around the zero point, while the amplitude and phase of the other cross-polarization do not change much.

[0059] Next, we investigated the effect of parameter changes on the nanostructure when the VO2 nanobrick 3 is in an insulating state. Similarly, we changed the length L2 and the vertical position Δy along the y-axis of the VO2 nanobrick 3, obtaining two amplitude distribution diagrams in Figures 9(a) and 9(b) and two phase distribution diagrams in Figures 10(a) and 10(b). As can be seen from Figures 9(a) and 9(b), and Figures 10(a) and 10(b), when the VO2 nanobrick 3 is in an insulating state, the parameter changes do not have a significant impact on the amplitude and phase characteristics of the Au nanobrick.

[0060] Further searching for structures satisfying the sixteen-step gradient phase yielded sixteen optimized VO2 nanobricks with the following parameters: First type: L2 = 50 μm, Δy = 23 μm; Second type: L2 = 53 μm, Δy = 50 μm; Third type: L2 = 60 μm, Δy = 46 μm; Fourth type: L2 = 68 μm, Δy = 50 μm; Fifth type: L2 = 75 μm, Δy = 50 μm; Sixth type: L2 = 85 μm, Δy = 55 μm; Seventh type: L2 = 94 μm, Δy = 55 μm; Eighth type: ... L2 = 104 μm, Δy = 50 μm; Ninth type L2 = 110 μm, Δy = 40 μm; Tenth type L2 = 108 μm, Δy = 30 μm; Eleventh type L2 = 100 μm, Δy = 21 μm; Twelfth type L2 = 90 μm, Δy = 14 μm; Thirteenth type L2 = 82 μm, Δy = 6 μm; Fourteenth type L2 = 66 μm, Δy = 0 μm; Fifteenth type L2 = 50 μm, Δy = 4 μm; Sixteenth type L2 = 50 μm, Δy = 15 μm.

[0061] As shown in Figures 12(a) and 14(a), two holographic images with a pixel size of 100×100 are used as target images. The GS algorithm is then used to obtain... Figure 11 and Figure 13 The two phase images shown represent the restoration of holographic information from the phases of the sixteen optimized structures using Fourier transform. These images are then compared with the target hologram to calculate the error. The error function is defined as follows:

[0062]

[0063] Where I is the target image, I′ is the image restored by the algorithm, and i and j represent the row and column numbers of the pixels, respectively.

[0064] The array of arranged nanostructures was observed. When the VO2 nanobricks 3 were in an insulating state, circularly polarized light was incident, and the first "frog" hologram I, as shown in Figure 12(b), was displayed. A When the VO2 nanobrick 3 is in the metallic state, the entire metasurface achieves phase reconstruction. Using right-handed circularly polarized light with frequency f as incident, a second "raven" hologram I is displayed as shown in Figure 14(b). B Since the singularity is related to the operating frequency and the circular polarization state, hologram I can only be seen by incident with right-handed circularly polarized light at frequency f. B Since the PB phase is widespread, hologram I can be seen using circularly polarized light incident over a wide wavelength range. A .

[0065] The embodiments described in this specification are merely examples of implementations of the inventive concept. The scope of protection of this invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of this invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A reconfigurable non-Hermite super surface design method based on singularity point phase characteristics, characterized in that, The phase characteristics of singular points in a non-Hermite super surface and a phase change material VO2 are used, and when the VO2 changes from an insulating state to a metal state, the phase of the super surface is reconfigured, and the function is switched. The method comprises the following steps: 1) constructing a nano structure unit: the nano structure unit comprises three layers, a bottom layer of a metal reflection layer, a middle layer of a dielectric substrate, and a periodic arrangement of a combination of metal nano bricks and VO2 nano bricks with different length-width and rotation angles placed on the upper layer of the substrate; an xoy coordinate system is established with the right-angle side of the nano structure unit as the x and y axes, the length of the metal nano brick along the y axis is L1, and the width along the x axis is W1; the VO2 nano brick is placed close to the metal nano brick, wherein the length along the x axis is L2, and the width along the y axis is W2; At a selected working frequency, sixteen different size nano structures are optimized by an electromagnetic simulation software, and the optimized structure parameters include: the period length P of the nano structure unit, the thickness h1 of the metal reflection layer, the thickness h2 of the substrate layer, and the length L1 and L2, the width W1 and W2, the height h3 of the combination of the metal nano brick and the VO2 nano brick, and the position change Ay of the VO2 nano brick along the y axis; 2) determining the parameters of the metal nano brick when the VO2 is in an insulating state: by optimizing the length-width L1 and W1 of the metal nano brick, the CST simulation is used to determine that it can realize good polarization conversion function in a wide wave band range; 3) optimizing the singular point of the nano structure when the VO2 is in a metal state: based on the metal nano brick optimized in step 2), the length L2 of the VO2 nano brick and the position Ay moving up and down along the y axis are changed, and the CST simulation is used to determine the singular point; 4) changing the parameters around the singular point optimized in step 3), optimizing sixteen nano structures to meet the phase change of 2π; 5) Determining the phase distribution of two holographic images I A and I B : Based on the principle of computer holography, the GS algorithm is used to operate on two target images with pattern I A and pattern I B respectively, and two phase distribution matrices are obtained, wherein the phase distribution of I A is continuous phase, and the phase distribution of I B is sixteen-step gradient phase; 6) Arranging the nanostructure array: First, change the corner of the metal nano-brick, use PB phase to meet the continuous phase distribution of I A ; use the optimized sixteen nanostructures to change the phase distribution of the entire super surface array to meet the sixteen-step phase distribution of I B ; 7) Observe the nanometer array arranged in step 6, when VO2 is in the insulating state, the circularly polarized light with frequency f is vertically incident on the metasurface, and the first holographic image I can be reproduced in the nanometer brick array A ; change the temperature to make VO2 change from insulating state to metallic state, realize the phase reconstruction of the whole array, when the right circularly polarized light with frequency f is vertically incident on the metasurface, the second holographic image I can be reproduced in the nanometer brick array B .

2. The design method of reconfigurable non-Hermite super surface based on singularity point phase characteristics according to claim 1, characterized in that In step 1), the three layers of different materials are the bottom metal reflection layer, the SiO2 substrate layer, and the combination of the metal nano brick and the VO2 nano brick structure layer, and the metal material is Au material.

3. The design method of reconfigurable non-Hermite super surface based on singularity point phase characteristics according to claim 1, characterized in that, In step 4), the sixteen nano structures contained in the nano structure array have different phase responses: when the right-handed circularly polarized light with a frequency of f is vertically incident on the super surface along the z axis, the phases of the sixteen nano structures are "179.516°", "157.975°", "135.051°", "111.558°", "89.857°", "66.649°", "46.193°", "23.247°", "0.697°", "-23.176°", "-46.102°", "-66.571°", "-91.430°", "-112.881°", "-134.458°", "-158.693°".

4. The reconfigurable non-Hermite super surface based on the phase characteristics of singular points according to claim 1, characterized in that, In step 5), the GS algorithm optimization process is calculated by matlab software, in which the target holographic image I A and I B is input as the optimization target of the algorithm, the function of optimization is set as the error between the restored holographic information and the target holographic image, and the error function is defined as: where I is the target image, I' is the image restored by the algorithm, i and j represent the row number and column number of the pixel point respectively; the output is two holographic images I A and I B ; By reasonably arranging the types of nano structures corresponding to each pixel area, the phase reconfiguration of the nano structure array can be realized after the phase change of VO2.

5. The reconfigurable non-Hermite super surface based on the phase characteristics of singular points according to claim 1, characterized in that, In step 5), pattern I A and pattern I B are both 100 x 100 pixels.

Images