Narrowband holographic device design method based on quasi-continuous domain bound state metastructure surface and device

Abstract

The invention discloses a narrow-band holographic device design method based on a quasi-continuous domain bound state metasurface, and the method comprises the steps: designing a metasurface compatible with geometric phase response quasi-continuous domain bound state resonance, quantifying the influence of spatial random disturbance on the continuous domain bound state resonance, and determining a random disturbance threshold value; in the computer-generated holographic optimization process, the phase difference of adjacent pixels in the generated phase distribution is reduced, and the phase distribution with the slowly changing characteristic is obtained in combination with the determined random disturbance threshold value; and loading the phase distribution with the slowly changing characteristic into the quasi-continuous domain bound state metasurface array to obtain a final device design. According to the method, narrow-band q-BIC resonance with geometric phase response is utilized, the designed metasurface can maintain the characteristic of narrow-band optical response when encoding specific gradient phase or slowly-varying phase distribution, the phase difference of adjacent pixels is reduced in the computer-generated holographic optimization process, phase distribution with the slowly-varying characteristic can be obtained, and the performance of the computer-generated holographic system is improved. And finally, a q-BIC-based narrowband holographic technology is realized.

Description

Technical Field

[0001] The present invention relates to the fields of nano-optics and holography, and in particular, to a design method and device of a narrowband holographic device based on a quasi-bound state in the continuum metasurface. Background Art

[0002] Metasurfaces are composed of ultrathin subwavelength nanostructures, which can achieve excellent optical field regulation and exhibit unprecedented functions beyond traditional optical devices. By utilizing various resonance mechanisms and phase encoding strategies, metasurfaces can precisely manipulate multiple optical parameters, including phase, spectrum, polarization, and orbital angular momentum. Generally, metasurfaces work based on local responses, that is, the modulation of the wavefront depends on the independent responses of each nanostructure. Based on this optical field regulation ability, spatially designed metasurfaces have been widely used in various functional applications, such as beam deflection, metasurface lenses, and holographic displays. In addition, the nonlocal effects generated by the cooperative interaction between multiple nanostructures further enhance the optical field regulation ability and achieve optical regulation with a high quality factor (Q-factor). Such nonlocal metasurfaces exhibit unique optical properties at a specific single resonance wavelength, while effectively suppressing the crosstalk of other spectral components. Although local metasurfaces can also achieve spectral selective responses, nonlocal metasurfaces usually utilize more superior high-Q resonances to achieve ultrathinband wavefront regulation, showing broad application prospects in multiple fields, such as augmented / virtual reality displays, optical sensing, signal processing, chiral luminescence, spectral selective imaging, and thermal radiation engineering. For example, quasi-bound states in the continuum (q-BIC) have been introduced into metasurfaces and combined with Pancharatnam-Berry (PB) phase to achieve high-Q wavefront regulation for beam deflection, focusing, chiral selective response, and directional optical / thermal radiation.

[0003] However, existing nonlocal metasurfaces still face significant challenges. Its fundamental limitation lies in the strong dependence of high-Q resonances on the collective array effect of large-area uniform nanostructures. When the variation of adjacent pixel structures increases, the ability of the metasurface to maintain nonlocal effects decreases, resulting in the weakening of high-Q resonances. Therefore, the current state-of-the-art nonlocal metasurfaces still lack the ability of arbitrary phase encoding required for complex optical field generation. On the one hand, traditional nonlocal metasurfaces are composed of uniform nanostructures, and their resonance modes can be used to achieve spectral regulation, diffraction grating effects, and vortex beam generation. On the other hand, by combining the PB phase to produce a slowly varying phase change, the q-BIC metasurface can achieve beam deflection or focusing functions, but it is difficult to construct metasurface holograms. This is because such complex optical functions require an arbitrary coding distribution with abrupt phase shifts, and the nonlocal characteristics are difficult to be compatible with this requirement due to their inherent high uniformity constraints. Summary of the Invention

[0004] To overcome the deficiencies of the above-mentioned prior art, the present invention provides a method for realizing narrowband metasurface holography based on quasi-bound states in the continuum, which utilizes narrowband q-BIC resonances with geometric phase responses. The designed metasurface can maintain the characteristics of narrowband optical responses when encoding specific gradient phases or slowly varying phase distributions. Further, by reducing the phase difference between adjacent pixels during the computational holography optimization process, a phase distribution with a slowly varying characteristic can be obtained, and finally, the narrowband holography technology based on q-BIC can be realized.

[0005] According to one aspect of the specification of the present invention, a method for designing a narrowband holographic device based on a metasurface of quasi-bound states in the continuum includes: Design a metasurface that is compatible with the quasi-bound state resonance of geometric phase response, and quantify the influence of spatial random perturbations on the quasi-bound state resonance in the continuum to determine the random perturbation threshold; During the computational holography optimization process, reduce the phase difference between adjacent pixels in the generated phase distribution, and combine the determined random perturbation threshold to obtain a phase distribution with a slowly varying characteristic; Load the phase distribution with a slowly varying characteristic into the metasurface array of quasi-bound states in the continuum to obtain the final device design.

[0006] As a further technical solution, during the computational holography optimization process, it further includes: Reduce the degree of two-dimensional random perturbations by reducing the phase difference between adjacent pixels in the generated phase distribution through a preset method, so that a preset proportion of perturbations are within the set threshold.

[0007] As a further technical solution, reducing the phase difference between adjacent pixels in the generated phase distribution through a preset method further includes: In the GS algorithm, mean filtering is introduced to reduce phase mutations, and linear interpolation is used to overall reduce the phase differences in the holographic phase arrangement to obtain a gradual change characteristic.

[0008] As a further technical solution, determining the random perturbation threshold further includes: By simulating and quantifying the relationship between the degree of random perturbation and the maintenance effect of the quasi-bound state resonance in the quasi-continuous domain metasurface when it is subjected to two-dimensional random spatial perturbation to generate a specific phase distribution, the perturbation threshold that can maintain the quasi-bound state resonance in the quasi-continuous domain is determined.

[0009] As a further technical solution, quantifying the influence of spatial random perturbation on the quasi-bound state resonance in the quasi-continuous domain further includes: Nanobricks with exactly the same structural parameters are used to form a square small unit cell, and the small unit cells are arranged into a supercell according to a specific random rotation angle. The rotation angle differences between adjacent small unit cells in the supercell are statistically analyzed to quantify the severity of the spatial perturbation received by the supercell.

[0010] According to one aspect of the specification of the present invention, a narrowband holographic device based on a quasi-bound state metasurface in a quasi-continuous domain is provided, which is designed by using the design method of the narrowband holographic device based on the quasi-bound state metasurface in a quasi-continuous domain described above.

[0011] As a further technical solution, the slowly varying holographic phase designed by the narrowband holographic device based on the quasi-bound state metasurface in a quasi-continuous domain is encoded to realize a narrowband holographic display function that inherits the high-Q characteristics of the quasi-bound state in the quasi-continuous domain.

[0012] As a further technical solution, the structure of the metasurface is a periodic unit structure of silicon nanobrick - silicon nitride thin film - substrate. The introduction of the silicon nitride layer is used to reduce the refractive index contrast between the nanobrick and the environment, so that the BIC mode can still be generated when the height of the nanobrick is relatively high; The narrowband quasi-bound state resonance in the quasi-continuous domain is obtained by applying size perturbations to two orthogonal square rectangular nanobricks; the quasi-bound state metasurface in the quasi-continuous domain can encode a geometric phase four times the rotation angle for the transmitted cross-polarized light when the nanobrick rotates.

[0013] Compared with the existing metasurface holography and non-local metasurface methods and components, the present invention has the following beneficial effects: (1) The present invention expands the simple light field encoding ability of the existing non-local metasurface, which can only encode vortex light, beam deflection and focusing, and can further encode complex holographic light fields with two-dimensional random characteristics.

[0014] (2) The holography encoded by the present invention can integrate the high-Q characteristics of the q-BIC resonance, and realizes a narrower-band holographic function compared with the traditional local metasurface. Description of the Drawings

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0016] Figure 1 is a schematic diagram of the unit structure of the metasurface provided by the embodiment of the present invention; Figure 2 is a simulation result diagram of the cross-polarization efficiency of the unit structure of the metasurface provided by the embodiment of the present invention; Figure 3 is a simulation result diagram of the geometric phase of the unit structure of the metasurface provided by the embodiment of the present invention; Figure 4 is a schematic diagram of constructing a supercell using the unit structure of the metasurface provided by the embodiment of the present invention; Figure 5 is a simulation result diagram of the cross-polarization efficiency of the supercell array loaded with different random perturbations provided by the embodiment of the present invention; Figure 6 is a schematic diagram of the holographic phase optimization process provided by the embodiment of the present invention; Figure 7 is an evolution result diagram of the phase mutation during the optimization process provided by the embodiment of the present invention; Figure 8 is a statistical result diagram of the corner difference of the designed q-BIC metasurface provided by the embodiment of the present invention; Figure 9 is an experimental measurement result diagram of the transmission spectrum of the q-BIC metasurface for narrowband holographic display provided by the embodiment of the present invention; Figure 10 is an experimental measurement result diagram of the transmission holographic image of the q-BIC metasurface for narrowband holographic display provided by the embodiment of the present invention; Figure 11 is a schematic diagram of the effect comparison between traditional metasurface holography and narrowband holography based on the q-BIC metasurface provided by the embodiment of the present invention. Detailed implementation manners

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention. Additionally, the technical features in each embodiment or individual embodiment provided by the present invention can be arbitrarily combined with each other to form a new technical solution. Such combination is not restricted by the order of steps and / or the structure composition mode, but must be based on the ability of those of ordinary skill in the art to implement. When the combination of technical solutions results in contradictions or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0018] On the one hand, the embodiments of the present invention provide a narrowband holographic technology based on a quasi-bound state in the continuum (hereinafter referred to as q-BIC) metasurface. By simulating and quantifying the relationship between the degree of random perturbation and the maintenance effect of q-BIC resonance when the q-BIC metasurface is subjected to a two-dimensional random spatial perturbation to generate a specific phase distribution, a perturbation threshold that can maintain a good q-BIC resonance is determined; during the computational holography optimization process, methods such as restricting the holographic angle, low-pass filtering, and interpolation are used to reduce the phase difference between adjacent pixels in the generated phase distribution to reduce the degree of two-dimensional random perturbation, so that most of the perturbations are within the set threshold; the optimized characteristic phase distribution is loaded into the q-BIC metasurface array to obtain the final device design, and the holography realized will be able to integrate the narrowband effect of q-BIC resonance.

[0019] On the other hand, the embodiments of the present invention provide a narrowband holographic device based on a q-BIC metasurface. The structure of the metasurface device is a periodic unit structure of silicon nanobricks - silicon nitride thin film - substrate. The introduction of the silicon nitride layer is used to reduce the refractive index contrast between the nanobricks and the environment, so that the BIC mode can still be generated when the height of the nanobricks is relatively high; the narrowband q-BIC resonance is obtained by applying size perturbations to two orthogonal square rectangular nanobricks; the q-BIC metasurface can encode the geometric phase four times the rotation angle for the transmitted cross-polarized polarized light when the nanobricks rotate.

[0020] In the embodiments of the present invention, a micro-nano structure compatible with the geometric phase response q-BIC resonance is designed, and the influence of spatial random perturbations on the q-BIC resonance is quantified. Furthermore, a random perturbation threshold with less influence on the q-BIC resonance is determined. Further, in the holographic phase optimization algorithm (such as the GS algorithm, gradient descent algorithm), low-pass filtering, interpolation, or introducing a phase mutation suppression parameter into the loss function is used to reduce phase mutations. Finally, a phase distribution with a gradual change characteristic is output to control the spatial random perturbations of the designed q-BIC metasurface within the threshold range, so as to achieve a narrowband holographic display function that can inherit the high-Q characteristics of the q-BIC resonance.

[0021] As Figure 1 , shown in FIGS. 2 and 3, the embodiments of the present invention provide a micro-nano structure design that supports the BIC resonance mode and can encode geometric phases. As Figure 1 shown, the structure of the metasurface device is a unit structure of silicon nanobricks - silicon nitride thin film - silica substrate, with heights of 360 nm, 190 nm, and 500 μm respectively, and a period of P x = 400 nm and P y = 200 nm. By introducing a symmetry-breaking factor L to a set of orthogonal nanobricks with side lengths of δ to make their lengths and widths different, a symmetry-protected BIC mode is supported. The introduction of the silicon nitride layer is used to reduce the refractive index contrast between the nanobricks and the environment, so that the BIC mode can still be supported when the height of the nanobricks is relatively high. The corresponding simulation results of the BIC mode are as Figure 2 shown. As the symmetry-breaking factor δ increases from 0, the resonance degenerates from the non-radiative BIC mode to the q-BIC mode, and the Q factor of the q-BIC mode gradually decreases. As Figure 3 shown, as the orthogonal nanobricks supporting the q-BIC resonance rotate, the resonance wavelength of the transmitted cross-polarized light remains almost unchanged, but its phase response shows a geometric phase that is 4 times the rotation angle, thus having the ability to realize the optical field encoding that inherits the narrowband characteristics of the q-BIC resonance.

[0022] As Figure 4 , shown in FIG. 5, the embodiments of the present invention provide the simulation test results of quantifying the ability of the q-BIC resonance to resist spatial random perturbations. As Figure 4 shown, two pairs of nanobricks with exactly the same structural parameters form a square unit cell. Further, the unit cells are arranged in a 4×4 supercell according to a specific random rotation angle. Among them, the severity of the spatial perturbations received by the supercell can be quantified by statistically analyzing the rotation angle differences between adjacent unit cells within the supercell. As Figure 5As shown, a total of four sets of supercells with different degrees of spatial perturbation and a set of homogeneous and non-perturbed supercells were generated by generating different random numbers. As the degree of perturbation increases, the transmission peak of the narrowband cross-polarization efficiency of the supercells in the simulation gradually decreases and finally disappears. According to the evolution process of this transmission peak, the threshold of spatial perturbation can be set such that the angular difference between the vast majority of adjacent small cells is less than 30°.

[0023] As Figure 6 , Figures 7 and 8 show that the embodiments of the present invention provide a design process for optimizing the phase distribution with a gradual change characteristic. As Figure 6 shown, we introduced mean filtering in the traditional GS algorithm to reduce excessive phase mutations, and linearly interpolated to overall reduce the phase difference in the holographic phase arrangement to obtain a gradual change characteristic. Figure 7 The statistical results of the phase differences of the phase arrangements output by the GS algorithm before and after introducing mean filtering and before and after introducing linear interpolation are provided. It can be seen that introducing mean filtering is beneficial to suppressing excessive phase mutations, and introducing linear interpolation can overall reduce the phase difference to obtain a gradual change holographic phase arrangement. As Figure 8 shown, finally, the angular difference of the q-BIC metasurface array designed according to the optimized phase arrangement is basically maintained below 15°.

[0024] As Figure 9 , Figure 10 shows the experimental measurement results of a set of q-BIC metasurfaces provided by the embodiments of the present invention for realizing the narrowband holographic display function. According to the designed phase arrangement, a q-BIC metasurface holographic sample with L = 110 nm, δ = 10 nm was finally fabricated. As Figure 9 shown, its measured transmission spectrum shows that diffraction order peaks corresponding to holography appear at positions deviating from the zero-order light. The holographic transmission spectrum calculated based on the intensity of the diffraction peaks shows that the resonance wavelength of the holographic transmission peak of this metasurface is 642.5 nm, and its Q factor is as high as 89.6. Further, the metasurface was irradiated with quasi-monochromatic light of different wavelengths with equivalent energy density, and the measured transmission holographic images are as Figure 10 shown. The holographic images show stronger light intensity near the resonance wavelength (640 nm and 645 nm), while the holographic intensity significantly decreases in the region far from the resonance wavelength, realizing the proposed narrowband holographic display function inheriting the high-Q characteristics of q-BIC. The comparison of the effects between traditional metasurface holography and narrowband holography based on q-BIC metasurfaces is as Figure 11 shown.

[0025] In summary, in the above embodiments, the present invention utilizes the narrowband q-BIC resonance with geometric phase response, and the designed metasurface can maintain the characteristic of narrowband optical response when encoding a specific gradient phase or a slowly varying phase distribution. Further, by reducing the phase difference between adjacent pixels during the computer-generated hologram optimization process, a phase distribution with a slow-varying characteristic can be obtained, and finally, the narrowband holographic technology based on q-BIC is realized.

[0026] Among them, for the narrowband holographic technology based on q-BIC, the relationship between the degree of random perturbation and the maintenance effect of q-BIC resonance is quantified by simulation when the q-BIC metasurface is applied with two-dimensional random spatial perturbations to generate a specific phase distribution, and a perturbation threshold that can maintain good q-BIC resonance is determined; during the computer-generated hologram optimization process, the phase difference between adjacent pixels in the generated phase distribution is reduced by methods such as restricting the holographic angle, low-pass filtering, and interpolation to reduce the degree of two-dimensional random perturbation, so that most of the perturbations are within the set threshold; the optimized characteristic phase distribution is loaded into the q-BIC metasurface array to obtain the final device design, and the realized hologram will be able to integrate the narrowband effect of q-BIC resonance.

[0027] For the narrowband holographic technology and device based on q-BIC metasurface, by designing a micro-nano structure compatible with the geometric phase response q-BIC resonance and quantifying the influence of spatial random perturbation on q-BIC resonance, a random perturbation threshold with less influence on q-BIC resonance is further determined. Further, in the holographic phase optimization algorithm (such as the GS algorithm, gradient descent algorithm), methods such as low-pass filtering, interpolation, or introducing a phase mutation suppression parameter in the loss function are used to reduce phase mutations, and finally a phase distribution with a gradual change characteristic is output to control the spatial random perturbation of the designed q-BIC metasurface within the threshold range, thus realizing for the first time the narrowband holographic display function that can inherit the high-Q characteristic of q-BIC resonance.

[0028] The present invention expands the simple optical field encoding ability of the existing non-local metasurface, which can only encode vortex light, beam deflection, and focusing, and can further encode a complex holographic optical field with two-dimensional random characteristics. The encoded hologram can integrate the high-Q characteristic of q-BIC resonance, realizing a narrower band holographic function compared with the traditional local metasurface.

[0029] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A narrowband holographic device design method based on a quasi-continuous domain bound state metasurface, characterized in that Including: Design a metasurface that is compatible with geometric phase response quasi-bound states in the continuum, quantify the influence of spatial random perturbations on quasi-bound states in the continuum resonance, and determine the random perturbation threshold; During the computational holography optimization process, reduce the phase difference between adjacent pixels in the generated phase distribution, and combine the determined random perturbation threshold to obtain a phase distribution with a slow-varying characteristic; Load the phase distribution with a slow-varying characteristic into the quasi-bound state metasurface array to obtain the final device design.

2. The narrowband holographic device design method based on the quasi-continuous domain bound state metasurface according to claim 1, wherein During the computational holography optimization process, it also includes: Reduce the phase difference between adjacent pixels in the generated phase distribution by a preset method to reduce the degree of two-dimensional random perturbation, so that a preset proportion of the perturbation is within the set threshold.

3. The design method of the narrowband holographic device based on the quasi-continuous domain bound state metasurface according to claim 2, wherein Reducing the phase difference between adjacent pixels in the generated phase distribution by a preset method also includes: Introduce mean filtering in the GS algorithm to reduce phase mutations, and globally reduce the phase difference in the holographic phase arrangement by linear interpolation to obtain a gradual change characteristic.

4. The narrowband holographic device design method based on the quasi-continuous domain bound state metasurface according to claim 1, wherein Determining the random perturbation threshold also includes: Quantify the relationship between the degree of random perturbation and the maintenance effect of quasi-bound states in the continuum resonance when the quasi-bound state metasurface in the continuum is subjected to two-dimensional random spatial perturbations to generate a specific phase distribution through simulation, and determine the perturbation threshold that can maintain the quasi-bound state resonance in the continuum.

5. The narrowband holographic device design method based on the quasi-continuous domain bound state metasurface according to claim 3, characterized in that Quantifying the influence of spatial random perturbations on quasi-bound states in the continuum resonance also includes: Construct square unit cells with nanobricks having exactly the same structural parameters, arrange the unit cells into a supercell according to specific random rotation angles, and statistically analyze the rotation angle differences between adjacent unit cells within the supercell to quantify the severity of the spatial perturbations received by the supercell.

6. The narrowband holographic device based on the quasi-continuous domain bound state metasurface is characterized in that, Designed by using the method described in any one of claims 1-5.

7. The narrowband holographic device based on the quasi-continuous domain bound state metasurface according to claim 6, characterized in that, The narrowband holographic device based on the quasi-bound state metasurface encodes the slow-varying holographic phase designed in any one of claims 1-5, and realizes the narrowband holographic display function that inherits the high-Q characteristics of the quasi-bound state in the continuum.

8. The narrowband holographic device based on the quasi-bound state in the continuum metasurface according to claim 6, characterized in that, The structure of the metasurface is a periodic unit structure of silicon nanobrick-silicon nitride thin film-substrate. The introduction of the silicon nitride layer is used to reduce the refractive index contrast between the nanobrick and the environment, so that the BIC mode can still be generated when the height of the nanobrick is relatively high; The narrowband quasi-bound state resonance in the continuum is obtained by applying size perturbations to two orthogonal square rectangular nanobricks; the quasi-bound state metasurface in the continuum can encode a geometric phase four times the rotation angle for the transmitted cross-polarized polarized light when the nanobrick rotates.

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