High-Q-value chiral metasurface design method based on topological optimization

Abstract

The invention discloses a high-Q-value chiral metasurface design method based on topological optimization, and belongs to the field of polarized optical metamaterials. The metasurface with the quasi-BIC function serves as an initial structure of topological optimization, the chiral metasurface with the high Q value is optimized, and the problem that the chiral metasurface with the high Q value is difficult to optimize is solved. The high-Q-value chiral metasurface device can obviously enhance CD signals, so that the detection sensitivity of chiral molecules is greatly improved. In addition, the metasurface device can also be used as a polarization device, the polarization state of the circularly polarized light can be accurately regulated and controlled, and generation and detection of the circularly polarized light are facilitated. The high-Q-value chiral metasurface based on topological optimization also has the capability of multi-dimensionally regulating and controlling the phase, the amplitude and the polarization state of a light field. According to the method, the high Q value chirality is used as an optimization target, and the superatom structure is reversely optimized; compared with a traditional numerical calculation method, the method has the advantages that the optimization efficiency of the high-Q-value chiral metasurface can be improved, and the problem of structural limitation is solved.

Description

Technical Field

[0001] The present invention relates to a method for designing a high-Q chiral metasurface based on topological optimization, and particularly to an inverse design method for metasurface patterns with high Q values and high CDs, belonging to the field of polarization optical metamaterials. Background Art

[0002] Chirality is a fundamental physical property in nature, which describes that an object cannot be completely coincident with its mirror image through any continuous rotation and translation operations. This unique asymmetry appears commonly in many different fields, including chemistry, biology, materials science, and optics. In optics, the chirality of a substance can be described by the difference in spectra when right-handed circularly polarized (RCP) and left-handed circularly polarized (LCP) waves are incident, i.e., the circular dichroism (CD) spectrum. Due to their optical chirality and small volume, the development of natural chiral materials in the field of optical devices is limited. Artificial nanostructures represented by two-dimensional metasurfaces can control the light field at the sub-wavelength scale, greatly enhancing the interaction between light and matter. With the proposal and development of optical metasurfaces, chiral metasurfaces have attracted extensive attention. Traditional chiral metasurfaces rely on the local response of unit cells, resulting in a low Q factor. Planar chiral metasurfaces with a high Q factor can achieve a strong chiral field enhancement, which is beneficial to many applications such as chiral sensing and chiral emission. To overcome this limitation and improve the Q factor while maintaining chirality, introducing bound states in the continuum (BICs) provides an effective solution. When a perturbation is introduced into the BIC system, such as breaking the structural symmetry or changing the incident angle, the BIC transforms into a quasi-BIC, and its Q factor is inversely proportional to the square of the asymmetry parameter. Chiral BIC metasurfaces can effectively solve the low Q factor defect in planar chiral metasurfaces.

[0003] Designing chiral BIC metasurfaces usually requires extensive parameter scanning, which is not only time-consuming but also computationally expensive. In addition, traditional numerical simulation methods are only optimized for regular structures, restricting the design flexibility and performance of metasurface structures. For this reason, researchers have proposed various inverse designs to solve the design limitation problems of metasurfaces, such as genetic algorithm-based, topological optimization algorithm-based, deep learning method-based, etc. Inverse design methods can design free-form metasurfaces by specifying the target response rather than the structure of the metasurface itself. So far, the application of inverse design methods has been extended to the optimization of various functional metasurfaces. However, the method of optimizing chiral BIC metasurfaces with high Q values using inverse design methods has not been studied. Summary of the Invention

[0004] To meet the requirements of inverse design for optimizing chiral BIC metasurfaces with high Q values, one of the objectives of the present invention is to provide a design method for high-Q chiral metasurfaces based on topological optimization. Aiming at the design requirements of high Q values and large CD, an ultra-atomic structure with corresponding functions is inversely designed at a predetermined wavelength target in the near-infrared band, improving the structural degrees of freedom and design efficiency.

[0005] Another objective of the present invention is to provide a preparation method for high-Q chiral metasurfaces based on topological optimization, which prepares the optimized metasurface with high degrees of freedom and improves the preparation accuracy of the metasurface with high degrees of freedom.

[0006] The objectives of the present invention are achieved through the following technical solutions:

[0007] A design method for high-Q chiral metasurfaces based on topological optimization disclosed by the present invention adopts inverse design and includes the following steps:

[0008] Step 1: The unit structure of the metasurface to be designed is a pixel-based topological planar two-dimensional structure, and the height of the pixel-based topological planar two-dimensional structure is 220 - 350 nm, and the design wavelength range is the near-infrared band of 1100 - 1400 nm.

[0009] Step 2: Using the rigorous coupled-wave analysis (RCWA) numerical algorithm for simulating the interaction between electromagnetic waves and periodic optical structures, an ultra-atomic structure with BIC function at the target wavelength is constructed.

[0010] Step 3: Taking the ultra-atomic structure designed in Step 2 as the initial structure, by breaking the in-plane symmetry of the initial structure, an ultra-atomic structure with an x-polarized reflectivity of 1, a y-polarized reflectivity of 0 at the target wavelength and having a quasi-BIC function at the target wavelength is realized.

[0011] Step 4: Based on the reflectivity matrix, using topological optimization inverse design and the RCWA algorithm, the figure of merit (FoM) in the topological optimization process is defined, and an inverse design method from the target function to the unit structure of the metasurface is constructed. In the inverse design method, the difference between the element R β*α and other elements in the reflection matrix is set as FoM, and the form is as follows:

[0012] FoM = R β*α - R α*α - R α * β - R β*β (1)

[0013] where α and β are the polarization states of incidence and reflection respectively, and the reflectivity matrix is obtained from the inner product of the reflection Jones matrix.

[0014]

[0015] Where R ji = |r ji | 2 , the Jones matrix is

[0016]

[0017] Step Five: Set the optimization goal. The meta-atom has a high-Q chiral quasi-BIC function. Using the meta-atom structure designed in Step Three as the initial structure for inverse design, and adopting the inverse design method in Step Four, the optimal meta-atom structural unit under the target conditions is obtained.

[0018] Step Six: In Step Five, the manufacturability of the high-Q chiral metasurface based on topology optimization needs to be considered. To eliminate small features that appear during the optimization process and improve the manufacturability of the optimized structure, the initial structure and the meta-atom structure before each iteration are blurred. The cells of the initial structure are divided into m×n pixels. The structure of the pixel at position r is represented by a density distribution ρ(r) ranging from 0 to 1, corresponding to the range from ε Air to ε Si . Therefore, the dielectric constant at position r is ε(r) = ρ(r)ε Si + (1 - ρ(r))ε Ai , and then the pattern ρ is blurred by convolution with a Gaussian distribution.

[0019]

[0020] where r0 is the blurring radius and A is the normalization factor. To optimize the actual metasurface device, the value ρ must be pushed to 0 or 1, so the binary push function is applied:

[0021]

[0022]

[0023] where β is a binarization factor that increases with iteration, and η is the midpoint of the binary push function, defined as:

[0024]

[0025] where: σ is the edge deviation value, resulting in erosion, intermediate, or dilation devices.

[0026] Step Seven: Periodically expand the meta-atom structure optimized in Step Five to obtain a metasurface device with the target function.

[0027] Step 8: Based on the optimal superatom structure obtained in Step 6, the fabricated high-Q metasurface device can significantly enhance the CD signal, thereby improving the detection sensitivity for chiral molecules, and is applied in chiral sensing and the detection of biomolecules; this metasurface device serves as a polarization device and can precisely control the polarization state of circularly polarized light, providing a method for the generation and detection of circularly polarized light; the high-Q chiral metasurface based on topology optimization can perform multi-dimensional control over the phase, amplitude, and polarization state of the light field.

[0028] The present invention also discloses a preparation method of a high-Q chiral metasurface based on topology optimization. Based on a high-Q chiral metasurface designed according to the present invention, the superatoms in this metasurface have a high degree of freedom and a small pixel size. Based on the above problems, a preparation method for a high-Q chiral metasurface with a high degree of freedom and a small pixel size structure is proposed. The preparation method of the high-Q chiral metasurface based on topology optimization disclosed by the present invention includes the following steps:

[0029] Preparation Step 1: Deposit a layer of amorphous silicon thin film with a target thickness on a cleaned glass substrate by inductively coupled plasma chemical vapor deposition (ICPCVD).

[0030] Preparation Step 2: Use electron beam lithography (EBL) to transfer the pattern of the high-Q metasurface after topology optimization onto the electron beam positive resist evenly coated on the surface of the amorphous silicon thin film. After developing and fixing, a photoresist mask with the complementary pattern of the metasurface after topology optimization is obtained.

[0031] Preparation Step 3: Evaporate a hard mask with a predetermined thickness on the sample after Preparation Step 2 using an electron beam evaporation system. After stripping the photoresist with dimethylacetamide (ZDMAC), a hard mask with the pattern of the metasurface after topology optimization is obtained.

[0032] Preparation Step 4: Perform reactive ion etching (RIE) with SF6 and O2 and remove the excess hard mask to obtain a high-Q chiral metasurface.

[0033] Beneficial effects:

[0034] 1. A design method of a high-Q chiral metasurface based on topology optimization disclosed by the present invention uses a metasurface with a quasi-BIC function as the initial structure for topology optimization, and optimizes a high-Q chiral metasurface, solving the problem of difficult optimization of high-Q chiral metasurfaces. The high-Q chiral metasurface device can significantly enhance the CD signal, thereby greatly improving the detection sensitivity for chiral molecules, and can be widely applied in the fields of chiral sensing and biomolecule detection. In addition, this metasurface device can also serve as a polarization device and can precisely control the polarization state of circularly polarized light, providing a new technical means for the generation and detection of circularly polarized light. The high-Q chiral metasurface based on topology optimization also has the ability to perform multi-dimensional control over the phase, amplitude, and polarization state of the light field.

[0035] 2. A design method of a high-Q chiral metasurface based on topology optimization according to the present invention takes high-Q chirality as the optimization target and reversely optimizes the meta-atom structure. Compared with traditional numerical calculation methods, it can improve the optimization efficiency of the high-Q chiral metasurface and solve the problem of structural limitations.

[0036] 3. A preparation method of a high-Q chiral metasurface based on topology optimization according to the present invention uses inductively coupled plasma chemical vapor deposition (ICPCVD) to deposit a target-thickness amorphous silicon thin film on a cleaned glass substrate; uses electron beam lithography (EBL) to transfer the pattern of the topology-optimized high-Q metasurface to the electron beam positive photoresist evenly coated on the surface of the amorphous silicon thin film; uses an electron beam evaporation system to evaporate a predetermined thickness of hard mask on the sample, and after stripping the photoresist with dimethylacetamide (ZDMAC), a hard mask with the topology-optimized metasurface pattern is obtained. After performing reactive ion etching (RIE) with SF6 and O2 and removing the excess hard mask, a high-Q chiral metasurface is obtained. The present invention can alleviate the error caused by processing accuracy during the processing of the topology-optimized metasurface. Description of the Drawings

[0037] Figure 1 A schematic diagram of a high-Q chiral metasurface designed according to the present invention. (a) Transformation diagram of BIC structure, quasi-BIC structure and topology-optimized meta-atoms; (b) Schematic diagram of the topology optimization algorithm flow; (c) Functional diagram of the high-Q chiral metasurface device.

[0038] Figure 2 Simulation data of a high-Q chiral metasurface device designed using the present invention. (a) Reflection spectra of the BIC metasurface and quasi-BIC metasurface before optimization; (b) Curve of the figure of merit (FoM) change during the iteration process; (c) Reflection spectra of the meta-atom structure after the 100th, 200th, 300th, and 400th iterations during the topology optimization process.

[0039] Figure 3 Experimental data of a high-Q chiral metasurface device designed using the present invention. (a) Experimental optical path diagram; (b) Transmission spectra of the BIC metasurface and quasi-BIC metasurface before optimization; (c) Chiral metasurface after optimization; (d) CD curve after optimization.

[0040] Figure 4 Using this method, 2 chiral metasurface devices were designed and fabricated in the range of 1200 - 1400 nm.

[0041] Figure 5 This is an extended application of the present invention, which can realize a metasurface device covering the entire Poincaré sphere.

[0042] Figure 6Flow chart of a design and preparation method of a high-Q chiral metasurface based on topology optimization disclosed in the present invention. Detailed implementation manners

[0043] To better illustrate the purpose and advantages of the present invention, the following further describes the content of the invention with reference to the drawings and examples.

[0044] Example 1:

[0045] As Figure 1 shown in Figure 2 The example discloses a design method of a high-Q chiral metasurface based on topology optimization disclosed in the present invention, which adopts reverse design and includes the following steps:

[0046] Step 1: The unit structure of the metasurface to be designed is a pixel-based topological planar two-dimensional structure, the structure type is a double rectangular column, the height of the pixel-based topological planar two-dimensional structure is 220-350 nm, and the design wavelength range is the near-infrared band of 1100-1400 nm.

[0047] Step 2: Using the rigorous coupled-wave analysis (RCWA) numerical algorithm for simulating the interaction between electromagnetic waves and periodic optical structures, by simultaneously adjusting the length and width of the rectangular column, a meta-atom structure with BIC function at the target wavelength is constructed.

[0048] Step 3: Taking the meta-atom structure designed in Step 2 as the initial structure, by breaking the in-plane symmetry of the initial structure, that is, changing the L and W of one of the rectangular columns, a meta-atom structure with an x-polarized reflectivity of 1, a y-polarized reflectivity of 0 at the target wavelength and a quasi-BIC function at the target wavelength is realized.

[0049] Step 4: Based on the reflectivity matrix, using topology optimization reverse design and the RCWA algorithm, define the figure of merit (FoM) of the optimization process in topology optimization, and construct a reverse design method from the target function to the unit structure of the metasurface. In the reverse design method, set the difference between the element R β*α and other elements in the reflection matrix as FoM, and the form is as follows:

[0050] FoM = R β*α - R α*α - R α*β - R β*β (1)

[0051] where α and β are the polarization states of incidence and reflection respectively, and the reflectivity matrix is obtained from the inner product of the reflection Jones matrix

[0052]

[0053] where R ji = |r ji |2 , the Jones matrix is

[0054]

[0055] Step 5: Set the optimization goal. The superatom has a high-Q chiral quasi-BIC function. Using the superatom structure designed in Step 3 as the initial structure for inverse design, and adopting the inverse design method in Step 4, the optimal superatom structure unit under the target conditions is obtained.

[0056] Step 6: In Step 5, to ensure the manufacturability of the high-Q chiral metasurface based on topology optimization, the optimization process needs to be improved. Specifically, to eliminate the small features that appear in the optimization process and improve the manufacturability of the optimized structure, this method performs blurring and binarization processing on both the initial structure and the superatom structure before each iteration. At the same time, a dynamic adjuster is introduced to dynamically adjust the learning rate in the hyperparameters, with a set step size of 0.08 and a multiplication factor of 0.992. As Figure 2 shown, taking the quasi-BIC structure as the initial structure for topology optimization, as the number of iterations increases, the superatom structure gradually approaches binarization, and the parameters in the optimization function also gradually approach the target values. In addition, to ensure the efficiency and stability of the optimization process, the maximum number of iterations is set to 400 times, and the minimum blurring radius is set to 10 nm. During the optimization process, the cells of the initial structure are divided into m×n pixels. The structure of the pixel at position r is represented by the density distribution ρ(r) from 0 to 1, corresponding to the range from ε Air to ε Si . Therefore, the dielectric constant at position r is ε(r) = ρ(r)ε Si +(1 - ρ(r))ε Ai , and then the pattern ρ is blurred by convolution with a Gaussian distribution.

[0057]

[0058] where r0 is the blurring radius and A is the normalization factor. To optimize the actual metasurface device, the value ρ must be pushed to 0 or 1, so the binary push function is applied:

[0059]

[0060] α1 = 1 - ρ blur (r) / η (6)

[0061]

[0062] where β is a binarization factor that increases with iteration, and η is the midpoint of the binary push function, defined as:

[0063]

[0064] Where: σ is the edge deviation value, resulting in an erosion, intermediate or dilation device.

[0065] Step Seven: Periodically expand the optimized superatom structure in Step Five to obtain a metasurface device with the target function.

[0066] Step Eight: According to Steps One to Seven, the optimal superatom structure is obtained, as Figure 3 shown. The initial structure maintains the quasi-BIC characteristic in the experiment, and the structure after topological optimization has a high-Q chiral function and a relatively high CD. Figure 4 To prove the universality of the algorithm, two chiral metasurface devices were designed and fabricated in the range of 1200 - 1400 nm. Similarly, they have high-Q and high-CD performances at their respective target wavelengths.

[0067] Step Nine: As Figure 5 shown, in addition to designing chiral metasurfaces, the design method of high-Q chiral metasurfaces based on topological optimization can be further extended to optimize metasurfaces that can cover the entire Poincaré sphere. Such a metasurface allows preferential reflection of the polarization state α(2ψ, 2χ) and completely transmits its orthogonal state β(2(ψ - 90°), -2χ).

[0068] Step Ten: As Figure 6 shown, based on the optimal superatom structure obtained according to the above steps, the fabricated high-Q metasurface device can significantly enhance the CD signal, thereby improving the detection sensitivity for chiral molecules and finding applications in chiral sensing and the detection of biomolecules; this metasurface device serves as a polarization device and can precisely control the polarization state of circularly polarized light, providing a method for the generation and detection of circularly polarized light; the high-Q chiral metasurface based on topological optimization can perform multi-dimensional regulation of the phase, amplitude, and polarization state of the light field.

[0069] This embodiment also discloses a preparation method of a high-Q chiral metasurface based on topological optimization. Based on a high-Q chiral metasurface designed according to the present invention, the superatom in this metasurface has a high degree of freedom and a small pixel size. Based on the above problems, a preparation method of a high-Q chiral metasurface with a high degree of freedom and a small pixel size structure is proposed. The preparation method of the high-Q chiral metasurface based on topological optimization disclosed in this embodiment includes the following steps:

[0070] Preparation Step One: Immerse the glass substrate in acetone, isopropyl alcohol, and deionized water in sequence and ultrasonically clean for 10 minutes, then place the glass substrate in a plasma asher and clean it again with oxygen for 5 minutes to remove surface impurities.

[0071] Preparation Step Two: Using inductively coupled plasma chemical vapor deposition method, deposit a layer of amorphous silicon thin film with a thickness of 220 - 350 nm on the cleaned glass substrate using deposition gas (5% silane in helium).

[0072] Preparation Step Three: Spin-coat a layer of ZEP520A electron beam positive photoresist with a thickness of 120 nm, and spin-coat a layer of AR-PC5092.02 conductive adhesive with a thickness of 50 nm to avoid the accumulation of charging effects.

[0073] Preparation Step Four: Use electron beam lithography process to transfer the topologically optimized metasurface pattern onto the electron beam positive photoresist. After removing the conductive adhesive with deionized water, use amyl acetate as the developer and isopropyl alcohol as the fixer. After fixing, obtain a photoresist mask with the complementary pattern of the topologically optimized metasurface, and use RIE to remove the residual photoresist on the sample surface.

[0074] Preparation Step Five: Use an electron beam evaporation system to deposit a 40-nm-thick chromium mask on the sample after Preparation Step Four. After stripping the photoresist with ZDMAC, obtain a chromium mask with the topologically optimized metasurface pattern.

[0075] Preparation Step Six: Perform plasma etching with SF6 and O2 at room temperature, and remove the excess chromium mask with ammonium cerium nitrate solution to obtain a high-Q chiral metasurface.

[0076] The above specific description further elaborates on the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A high-Q chiral metasurface design method based on topology optimization, characterized by: The reverse design includes the following steps: Step 1: The metasurface unit structure to be designed is a pixel-type topological plane two-dimensional structure, the height of the pixel-type topological plane two-dimensional structure is 220-350nm, and the design wavelength range is the near-infrared band of 1100-1400nm; Step 2: Use the rigorous coupled wave analysis (RCWA) numerical algorithm for simulating the interaction between electromagnetic waves and periodic optical structures to construct a meta-atomic structure with BIC function at the target wavelength; Step 3: Using the super-atom structure designed in step 2 as the initial structure, breaking the in-plane symmetry of the initial structure to achieve a super-atom structure with an x-polarization reflectivity of 1 and a y-polarization reflectivity of 0 at the target wavelength and a quasi-BIC function at the target wavelength; Step 4: Based on the reflectivity matrix, the topology optimization inverse design and RCWA algorithm are used to define the optimization function FoM in the topology optimization process and construct a reverse design method from the target function to the metasurface unit structure. In the reverse design method, the element R β*α The difference with other elements in the reflection matrix is ​​set to FoM, which is as follows: FoM=R β*α -R α*α -R α*β -R β*β (1) Where α and β are the polarization states of the incident and reflected polarizations, respectively. The reflectivity matrix is ​​obtained by the inner product of the reflected Jones matrix: Where R ji =|r ji | 2 , the Jones matrix is Step 5: Set the optimization target superatom to have a high-Q chiral quasi-BIC function, use the superatom structure designed in step 3 as the initial structure for reverse design, and use the reverse design method of step 4 to obtain the optimal superatom structure unit under the target conditions; Step 6: In step 5, the manufacturability of the high-Q chiral metasurface based on topology optimization needs to be considered, and the initial structure and the meta-atom structure before each iteration are blurred; The cells of the initial structure are divided into m×n pixels; the structure of the pixel at position r is represented by the density distribution ρ(r) from 0 to 1, corresponding to the distribution from ε Air to ε Si range; therefore, the dielectric constant at position r is ε(r)=ρ(r)ε Si +(1-ρ(r))ε Ai , blur the pattern ρ by convolution with Gaussian distribution; Where r0 is the blur radius and A is the normalization factor; the value ρ is pushed to 0 or 1 in order to apply a binary push function: Where β is a binarization factor that increases with iteration, and η is the midpoint of the binary push function, defined as: Where: σ is the edge deviation value, resulting in erosion, intermediate or dilation device; Step 7: Periodically unfold the meta-atomic structure optimized in step 5 to obtain a metasurface device with target functions.

2. The method for designing a high-Q chiral metasurface based on topology optimization according to claim 1, characterized in that: It also includes step eight: according to the optimal super-atom structure obtained in step six, a high-Q metasurface device is manufactured, which can significantly enhance the CD signal, thereby improving the detection sensitivity of chiral molecules, and is applied to chiral sensing and detection of biomolecules; the metasurface device acts as a polarization device and can precisely control the polarization state of circularly polarized light; the high-Q chiral metasurface based on topology optimization can perform multi-dimensional control of the phase, amplitude and polarization state of the light field.

3. A method for preparing a high-Q chiral metasurface based on topology optimization, which is used to prepare a high-Q chiral metasurface designed by a high-Q chiral metasurface design method based on topology optimization as claimed in claim 1 or 2, characterized in that: The following steps are included: Preparation step 1: using inductively coupled plasma chemical vapor deposition (ICPCVD) to deposit a layer of amorphous silicon film of target thickness on a cleaned glass substrate; Preparation step 2: using electron beam exposure process EBL to transfer the topology optimized high Q value metasurface pattern to the electron beam positive photoresist uniformly formed on the surface of the amorphous silicon film, and after development and fixing, a photoresist mask having a topology optimized metasurface complementary pattern is obtained; Preparation step three: using an electron beam evaporation system to evaporate a hard mask of a predetermined thickness on the sample after preparation step two, and using dimethylacetamide ZDMAC to strip the photoresist to obtain a hard mask having a topology-optimized metasurface pattern; Preparation step 4: After using SF6 and O2 for reactive ion etching (RIE) and removing the redundant hard mask, a chiral metasurface with a high Q value is obtained.

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