Polarization-independent metasurface design method and metasurface lens based on dielectric structure

Abstract

The present invention relates to the field of micro-nano optics and optical chip integration, and in particular to a polarization-independent metasurface design method based on a dielectric structure and a metasurface lens comprising the metasurface structure; the metasurface design method comprises the following steps: S1, constructing a unit structure database corresponding to multiple wavelengths and capable of covering a transmission phase of 0 to 2π, and obtaining transmission phase data; S2, calculating the ideal phase distribution of the metasurface structure by the superposition principle of holograms; S3, matching the ideal phase distribution obtained in step S2 with the transmission phase data obtained in step S1, optimizing the difference between the phases as a target evaluation function, and arranging the metasurface structure with the finally obtained structural parameters; the metasurface structure of the present invention can realize array multi-wavelength multiplexing in the same field of view, and compared with the splicing of multiple super lenses, it avoids the influence of incident light splitting and multi-wavelength chromatic aberration, and has great application prospects.

Description

Technical Field

[0001] The present invention relates to the field of micro-nano optics and optical chip integration, and in particular to a polarization-independent metasurface design method based on a dielectric structure and a metasurface lens comprising the metasurface structure. Background Art

[0002] Array beams have the advantages of fast, parallel and simultaneous processing, and are widely used in imaging and optical communications. In the field of communications, array vortex beams can not only improve the security of information, but also increase the capacity of information; the topological charge carried by orbital angular momentum and the annular light intensity distribution can provide torsional torque and gradient force to tiny particles, which can be used for the manipulation of microscopic particles, while the array vortex beam can capture more particles at the same time, and change the distribution and pattern of captured particles by loading functions such as wavelength multiplexing; in the field of imaging, multiplexed focused beams make it easier for us to control and compare beams in different channels, which is of great significance for simplifying imaging systems.

[0003] At present, the generation of array beams mainly uses beam splitters, lens arrays, diffractive optical elements, etc. to divide the incident light beam into multiple beams, which are widely used in imaging and optical communications. However, the manufacturing process of optical elements is usually very complicated, and the corresponding optical system is also relatively large, which brings difficulties to the miniaturization of the structure and limits its application in the field of integrated optics. At the same time, for some complex application fields, the non-modulation of optical elements also limits the flexibility of their application. In recent years, research based on the field of metasurfaces has attracted the attention of a large number of researchers.

[0004] Metasurfaces are periodic or non-periodic arrays composed of subwavelength structures. They control the geometric parameters of the cell structure to obtain the corresponding optical response, thereby achieving control over the incident electromagnetic wave. Compared with traditional optical lenses, metasurfaces introduce abrupt phase changes and no longer rely on phase accumulation during the propagation process. Metasurfaces also have the advantages of miniaturization and ease of manipulation. Currently, they have successively realized functions such as planar lenses, structured beam generators, optical holography, and polarization control.

[0005] In order to realize the function of array beams, in 2016, MQMehmood et al. used spatial multiplexing to generate multi-focused vortex beams. In 2019, HAORAN LV et al. proposed an optical metasurface superlens with multi-focus metal subwavelength gratings. However, the realization of most metasurface array beams still relies on geometric phase structures based on polarized light. In order to further improve energy efficiency and simplify optical systems, especially for non-polarized light sources, we need to design a polarization-independent holographic metasurface. For example, single-molecule detection technology of fluorescent labels, especially research on multi-color single-molecule fluorescence arrays and biomolecular chirality, has a significant demand for multi-color non-polarized array focused beams. In addition, optical communications, optical particle manipulation, etc. require high-energy-density vortex beams, and polarization-independent holographic vortex light array beams will have significant advantages. Summary of the invention

[0006] In order to solve the above problems, the present invention provides a polarization-independent multi-wavelength multi-focus metasurface design method based on a dielectric structure.

[0007] The present invention provides a polarization-independent metasurface design method based on a dielectric structure, and the metasurface design method comprises the following steps:

[0008] S1. Construct a unit structure database corresponding to multiple wavelengths and capable of covering 0-2π transmission phases to obtain transmission phase data;

[0009] S2. Through the superposition principle of holograms, the ideal phase distribution of the metasurface structure is calculated as follows:

[0010] Φ(x,y,λ)=arg(E(x,y,λ));

[0011] Φ(x, y, λ) represents the ideal phase of the holographic metasurface at different wavelengths, x, y represent the position coordinates of the unit structure on the metalens, E represents the amplitude distribution after interference, and λ represents the wavelength;

[0012] S3. Match the ideal phase distribution obtained in step S2 with the transmission phase data obtained in step S1, optimize the difference between the phases as the target evaluation function, and use the final structural parameters to form a metasurface structure.

[0013] Preferably, in S2, the formula for the complex amplitude distribution of the focused light beam array superimposed together by the superposition principle of the hologram is:

[0014]

[0015] (x m ,y n ) represents the horizontal and vertical coordinates of each focal spot relative to the center of the lens, f represents the axial distance of the focal plane relative to the lens, Amn Represents the amplitude distribution of the corresponding focal spot.

[0016] Preferably, in S2, the formula for the complex amplitude distribution of the focused vortex beam array superimposed together by the superposition principle of holograms is:

[0017]

[0018] (x m ,y n ) represents the horizontal and vertical coordinates of each focal spot relative to the center of the lens, f represents the axial distance of the focal plane relative to the lens, A mn represents the amplitude distribution of the corresponding focal spot, and e represents the exponent.

[0019] Preferably, the wavelength difference between each wavelength in the multiple wavelengths is not less than 100 nm.

[0020] Preferably, the construction of a unit structure database corresponding to multiple wavelengths and capable of covering 0-2π transmission phases includes scanning unit structures of different radius values ​​by linearly polarized light in any direction to obtain transmission phase data of the unit structures.

[0021] Preferably, the wavelength range of the linearly polarized light scanning is 80 nm to 310 nm.

[0022] Preferably, the unit structure comprises an upper structure and a lower structure, the upper structure is a dielectric nanocolumn, and the lower structure is a dielectric substrate; the dielectric nanocolumn is a cylindrical structure; and the dielectric substrate is a cubic structure.

[0023] Preferably, the matching of the ideal phase distribution obtained in step S2 with the transmission phase data obtained in step S1 is achieved by a genetic algorithm.

[0024] Preferably, the calculation formula of the objective evaluation function is as follows:

[0025]

[0026] represents the actual phase randomly selected from the database, represents the ideal phase calculated by the formula in step S2, It represents the sum of the phase fitting differences of each wavelength, β represents the weight factor for adjusting the objective function of different wavelengths based on the simulation results; C(λ) represents a constant phase that is only related to the wavelength.

[0027] The present invention also provides a supersurface lens, which includes a supersurface structure, and the supersurface structure is designed by the above-mentioned supersurface design method.

[0028] The present invention combines a genetic algorithm with a phase-type computational holographic method to provide a wavelength-multiplexed multi-channel array beam generator, which can achieve array beam reconstruction by adjusting the wavelength of the incident light, and by utilizing the transmission phase of the structure itself, the structure has the characteristic of polarization insensitivity. The metasurface structure designed by the design method of the present invention can realize array multi-wavelength multiplexing in the same field of view, and compared with the splicing of multiple super lenses, it avoids the impact of incident light splitting and multi-wavelength chromatic aberration, etc., and has great application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a phase distribution diagram of the unit structure under three wavelengths of RGB in one embodiment of the present invention;

[0030] Figure 2 This is a schematic diagram of a unit structure in a metasurface lens in an embodiment of the present invention;

[0031] Figure 3 is a normalized light intensity distribution of a focused light beam array representing the focal planes of three wavelengths B, G, and R in one embodiment of the present invention;

[0032] Figure 4 is a top view of a metasurface lens structure in one embodiment of the present invention;

[0033] Figure 5 is a normalized light intensity distribution of a focused vortex beam array representing three wavelength focal planes of B, G, and R in another embodiment of the present invention;

[0034] Figure 6 1 is a top view of a metasurface lens structure in another embodiment of the present invention. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0036] A specific embodiment of the present invention provides a polarization-independent metasurface design method based on a dielectric structure, and the metasurface design method comprises the following steps:

[0037] S1. Construct a unit structure database corresponding to multiple wavelengths and capable of covering 0-2π transmission phases to obtain transmission phase data;

[0038] S2. Through the superposition principle of holograms, the ideal phase distribution of the metasurface structure is calculated as follows:

[0039] Ф(x,y,λ)=arg(E(x,y,λ));

[0040] Φ(x, y, λ) represents the ideal phase of the holographic metasurface at different wavelengths, x, y represent the position coordinates of the unit structure on the metalens, E represents the amplitude distribution after interference, and λ represents the wavelength;

[0041] In a specific implementation, the superposition principle of the hologram mainly refers to treating each focus on the focal plane as a luminous spherical wave, interfering on the superlens, extracting the phase of the field after interference, and E is the amplitude distribution after this interference.

[0042] S3. Match the ideal phase distribution obtained in step S2 with the transmission phase data obtained in step S1, optimize the difference between the phases as the target evaluation function, and use the final structural parameters to form a metasurface structure.

[0043] In a specific implementation manner, Figure 2 As shown in FIG. 1 , a schematic diagram of a unit structure in a metasurface lens in an embodiment of the present invention is shown. From the figure, it can be seen that the structure arrangement of the designed metasurface lens is that the unit structure includes an upper structure and a lower structure. The upper structure is a dielectric nanocolumn 2, and the lower structure is a dielectric substrate 1, that is, from bottom to top, it includes a dielectric substrate 1 and a dielectric nanocolumn 2. In a specific implementation, the dielectric substrate 1 adopts a cubic structure. The material of the dielectric substrate 1 can be silicon dioxide, silicon, sapphire, gallium arsenide and other dielectric materials with low loss in the visible light wavelength. In a specific implementation, nano-SiO 2 For example, the side length is P, that is, the period p of the unit structure. The period p is the sampling frequency of the phase profile and must satisfy the Nyquist sampling condition, that is, p<λ / 2NA, where λ is the wavelength and NA is the numerical aperture of the lens. By setting the p value to be smaller than all wavelengths in the free space, the waveguide mode resonance can be stimulated to produce an abnormal phase response and achieve the purpose of suppressing high-order diffraction orders.

[0044] In a specific embodiment, the dielectric nanorod 2 is a cylindrical structure. The material of the dielectric nanorod 2 can be titanium dioxide, gallium nitride, silicon nitride and other high refractive index, low loss materials. In a specific embodiment, nano-TiO 2 For example, the diameter of the cylinder is D, the height is H, the cylinder diameter D is smaller than the period p, and the larger the height H is, the wider the phase coverage is; by selecting the nanocolumns with cylindrical structures, the polarization insensitivity of the unit structure can be better realized, and the unit structure is a rotationally symmetric structure, which also makes the transmittance more uniform; in a specific implementation, when the unit structure period is 320nm, the nano-TiO 2 The minimum value of the diameter D of the cylindrical structure is selected as 80nm, and the maximum value is selected as 310nm, that is, when scanning the dielectric nanocolumns with different radius values, the scanning range is 80nm to 310nm; nano-TiO 2The height H of the cylindrical structure can be selected to be 600 nm.

[0045] In a specific implementation, we first obtain the relationship between the unit structure with different radius values ​​and the transmission phase in order to match and fit with the ideal phase of different wavelengths; specifically, the unit structure with different radius values ​​is scanned by linearly polarized light in any direction to obtain the transmission phase data of the unit structure, thereby constructing a unit structure database corresponding to multiple wavelengths and capable of covering 0 to 2π transmission phases to obtain the transmission phase data.

[0046] In a specific implementation, three wavelengths (486nm, 587nm, 656nm) that can represent the three primary colors of visible light are selected for design. The unit structure period is 320nm, the upper structure is a titanium dioxide cylinder, and the lower structure is a silicon dioxide cube. With the help of the simulation software FDTD, we obtain the transmission phase data of the unit structure by scanning the dielectric nanocolumns of different radius values, and the scanning range is 80nm to 310nm; then use these geometric parameters and the phase data calculated by the software to establish the structure-phase database required for the next step.

[0047] Due to the complete symmetry of the cylindrical structure, it is insensitive to light waves polarized in different directions. Specifically, the following analysis is based on light waves polarized in the x direction. Because the scanning range is large, the phase response coverage obtained by simulation is very large. In the design process, only the phase coverage of 0 to 2π is required to meet the conditions. Figure 1 From the phase distribution diagram of the unit structure at three wavelengths of RGB, it can be seen that the designed phase meets the basic requirements.

[0048] In a specific implementation, a metasurface with an aperture of 16um and a focal length of 10um is designed, and the entire metasurface is discretized into 100*100 pixels. The ideal phase value of each pixel can be obtained according to the ideal phase formula.

[0049] In a specific implementation, the ideal phase distribution of the metasurface structure is as shown in formula (1):

[0050] Φ(x,y,λ)=arg(E(x,y,λ)) (1)

[0051] Φ(x, y, λ) represents the ideal phase of the holographic metasurface at different wavelengths, x, y represent the position coordinates of the unit structure on the metalens, E represents the amplitude distribution after interference, and λ represents the wavelength;

[0052] The formula (2) for the complex amplitude distribution of the focused beam array superimposed together by the superposition principle of the hologram is:

[0053]

[0054] (x m ,y n ) represents the horizontal and vertical coordinates of each focal spot relative to the center of the lens, f represents the axial distance of the focal plane relative to the lens, A mn represents the amplitude distribution of the corresponding focal spot, and e represents the exponent.

[0055] At this time, the previously calculated transmission phase database is called again. In order to find the most suitable structural arrangement, it is also necessary to find a transmission phase that matches the ideal phase of different wavelengths to generate the metasurface structure. The process of finding the transmission phase can quickly find a structure that meets the requirements by solving the minimum value through a genetic algorithm.

[0056] In a specific implementation, a genetic algorithm is used to match the ideal phase distribution with the transmission phase data. When matching, the difference between the phases can be used as a target evaluation function for optimization. Specifically, the target evaluation function is shown in formula (3):

[0057]

[0058] in, represents the actual phase randomly selected from the database, represents the ideal phase calculated by formula (1) or formula (2), It represents the sum of the phase fitting differences of each wavelength; Iterative optimization is performed to ultimately achieve a certain degree of matching between the actual phase in the phase database and the ideal phase between different wavelengths.

[0059] The present invention also provides a metasurface lens, wherein the metasurface lens comprises a metasurface structure, wherein the metasurface structure is designed by the above-mentioned metasurface design method; the simulation result of the metasurface lens is as follows: Figure 3 As shown, the first three figures from left to right in the figure represent the normalized light intensity distribution of the focused beam array of the three wavelength focal planes B, G, and R. Figure 4 is a top view of the metasurface lens structure in this specific implementation manner, from Figure 3 and Figure 4 It can be seen that the position arrangement of the focal spot is consistent with the theoretical design, 4 microns away from the origin, in a hexagonal shape, with a maximum position error of only about 0.31λ, and small side lobes, more concentrated energy, and the energy efficiency of different spots at the same wavelength is basically equal. The corresponding values ​​are shown in Table 1.

[0060] Table 1 Focal position, efficiency, and full width at half maximum of metasurface lenses

[0061]

[0062] The data in Table 1 show that the metasurface lens provided by the present invention can realize the function of generating different array light beams when different wavelengths are incident.

[0063] In order to better understand the present invention, the specific implementation of the design method of the present invention is further described in detail below through specific embodiments.

[0064] In other specific embodiments, since the interference amplitude is inconsistent when a focused beam or a vortex beam is generated and superimposed, in order to prove the universality of the polarization-independent metasurface design method based on the dielectric structure provided by the present invention, a wavelength multiplexing vortex beam array generator based on the metasurface structure is designed. In this embodiment, the formula (3) for the complex amplitude distribution of the focused vortex beam array superimposed together by the superposition principle of the hologram is:

[0065]

[0066] (x m ,y n ) represents the horizontal and vertical coordinates of each focal spot relative to the center of the lens, f represents the axial distance of the focal plane relative to the lens, A mn Represents the amplitude distribution of the corresponding focal spot; Similar to the previous embodiment, the corresponding simulation results are obtained as follows Figure 5 As shown, the first three figures from left to right in the figure represent the normalized light intensity distribution of the focused vortex beam array at the three wavelength focal planes of B, G, and R. Figure 6 is a top view of the metasurface lens structure in this specific implementation manner, from Figure 5 and Figure 6 It can be seen that under the irradiation of light waves of different wavelengths, the metasurface emits different vortex arrays, and the topological charge of the vortex array is spatially variable, which proves the universality of the polarization-independent metasurface design method based on dielectric structure provided by the present invention.

[0067] The present invention combines a genetic algorithm with a phase-type computational holographic method to provide a wavelength-multiplexed multi-channel array beam generator, which can achieve array beam reconstruction by adjusting the wavelength of the incident light, and by utilizing the transmission phase of the structure itself, the structure has the characteristic of polarization insensitivity. The metasurface structure designed by the design method of the present invention can realize array multi-wavelength multiplexing in the same field of view, and compared with the splicing of multiple super lenses, it avoids the impact of incident light splitting and multi-wavelength chromatic aberration, etc., and has great application prospects.

[0068] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present invention. Those skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

[0069] The above specific implementations of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A polarization-independent metasurface design method based on dielectric structure, characterized in that: The super surface design method comprises the steps of: S1, build corresponding to multiple wavelengths and can cover 0~ A unit structure database of the transmission phase, to obtain the transmission phase data; S2. Through the superposition principle of holograms, the ideal phase distribution of the metasurface structure is calculated as follows: ； represents the ideal phase of the holographic metasurface at different wavelengths, x,y represents the position coordinates of the unit structure on the metalens, E represents the amplitude distribution after interference, Indicates wavelength; The unit structure comprises an upper structure and a lower structure, wherein the upper structure is a dielectric nanocolumn and the lower structure is a dielectric substrate; the dielectric nanocolumn is a cylindrical structure; and the dielectric substrate is a cube structure; S3, matching the ideal phase distribution obtained in step S2 with the transmission phase data obtained in step S1, optimizing the difference between the phases as the target evaluation function, and arranging the metasurface structure with the finally obtained structural parameters.

2. The super surface design method according to claim 1, characterized in that: In S2, the formula for the complex amplitude distribution of the focused beam array superimposed together by the superposition principle of the hologram is: ； Represents the horizontal and vertical coordinates of each focal spot relative to the center of the lens, represents the axial distance of the focal plane relative to the lens, represents the amplitude distribution of the corresponding focal spot, and e represents the exponent.

3. The super surface design method according to claim 1, characterized in that: In S2, the formula for the complex amplitude distribution of the focused vortex beam array superimposed together by the superposition principle of holograms is: ； Represents the horizontal and vertical coordinates of each focal spot relative to the center of the lens, represents the axial distance of the focal plane relative to the lens, Represents the amplitude distribution of the corresponding focal spot.

4. The super surface design method according to claim 1, characterized in that: The wavelength difference between each wavelength in the plurality of wavelengths is not less than 100 nm.

5. The super surface design method according to claim 1, characterized in that: The construction corresponds to multiple wavelengths and can cover 0~ The unit structure database of the transmission phase includes scanning unit structures with different radius values ​​by linear polarized light in any direction to obtain the transmission phase data of the unit structure.

6. The super surface design method according to claim 5, characterized in that: The wavelength range of the linear polarized light scanning is 80nm~310nm.

7. The super surface design method according to claim 1, characterized in that: The matching of the ideal phase distribution obtained in step S2 with the transmission phase data obtained in step S1 is achieved through a genetic algorithm.

8. The super surface design method according to claim 7, characterized in that: The calculation formula of the objective evaluation function is as follows: ； represents the actual phase randomly selected from the database, represents the ideal phase calculated by the formula in step S2, represents the sum of the phase fitting differences for each wavelength, represents the weight factor for adjusting the objective function of different wavelengths based on the simulation results; represents a constant phase that depends only on the wavelength.

9. A metasurface lens, characterized in that: The metasurface lens comprises a metasurface structure, and the metasurface structure is designed by the metasurface design method according to any one of claims 1 to 8.

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