A design method of visible waveband achromatic superlens based on spatial multiplexing

Abstract

The application discloses a visible light waveband achromatic superlens design method based on spatial multiplexing, and steps of the method comprise the following steps: S1, setting a simulation mode and simulation conditions of the superlens; S2, setting the simulation mode and simulation conditions of the superlens; S3, calculating ideal phases of each nanometer column; S4, filling the superlens with single-wavelength lens nanometer columns based on a Fresnel waveband spatial multiplexing method; and S5, using a two-dimensional particle swarm algorithm to obtain an optimal solution of a parameter C. The method uses the double-wavelength Fresnel waveband spatial multiplexing method, realizes achromatism of double wavelengths, realizes achromatism of the entire wavelength range, and has the advantages of simple superlens design, large bandwidth range and polarization insensitivity based on transmission phase design, and provides a reference for design of other super surface devices.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of super surface technology super lens design, and particularly relates to a visible light wave band achromatic super lens design method based on spatial multiplexing. BACKGROUND

[0002] Super surface is a structure composed of a series of sub-wavelength units, which has strong light field control ability. By fine design of the size, rotation angle, etc. of the unit structure, the phase, amplitude and polarization of electromagnetic waves are changed; therefore, the super surface can flexibly control the wave front and control the size of the optical device to sub-wavelength level, and is rapidly developed in various fields and widely used in lenses, holograms, wave plates, vortex light and other fields. As one of the important applications of super surface, super lens breaks the constraints of traditional lens, and focuses light on a point through continuous light path accumulation of each light path; at the same time, the size of super lens is controlled to sub-wavelength level, which provides the possibility for miniaturization, microfabrication and integration of optical systems. However, super lens will be affected by chromatic aberration, that is, the focal length becomes smaller as the incident wavelength increases; and the influence of chromatic aberration causes the lens to be unable to focus light of different wavelengths on the same plane, thereby causing imaging blur and color distortion, and correcting chromatic aberration in a wide band is the basis for realizing full-color imaging. Since it is difficult to construct phase profiles of different wavelengths on a single super surface, it is a great challenge to design an achromatic lens that can produce a single focal length within a certain bandwidth.

[0003] At present, there are methods for eliminating chromatic aberration, such as spatial multiplexing, combination of propagation phase and geometric phase, and use of dielectric coupling resonance. In 2019, Ren Jielin et al. used GaN nanoantennas to realize a 400-640nm achromatic super lens array to capture light field information and realize a full optical camera. The use of a 60x60 super lens array makes it have different focal points, which can reconstruct the spatial scene and restore objects under different depths of field. In 2019, Zhi-Bin Fan et al. realized a wide wave band achromatic lens in the 430-780nm wave band. By using a variety of different shapes of silicon nitride, 10 structures with the required linear change of phase and frequency were found out by linear fitting, so that the effective refractive index does not change with frequency. Finally, a wide wave band achromatic lens is realized, and a 60x60 lens array is established for white light imaging. However, this method of constructing a large phase library uses a variety of unit structures, which brings challenges to processing and preparation. In 2020, Feng Tang et al. used silicon nanocolumns to realize double-wavelength focusing under long-wave infrared conditions through multiplexing, and by interlacing 8um and 12um wavelength unit structures, a double-wavelength achromatic lens and a double-focus lens with a diameter of 0.4mm were constructed. However, this method only realizes focusing of three wavelengths.

[0004] BAEK S et al. proposed a multi-wavelength metal lens by spatial multiplexing of visible wavelengths, which arranges TiO2 unit structure by two methods of spatial stagger method and symmetric linear array method; wherein, the spatial stagger arrangement method is to place the nanostructures corresponding to three wavelengths alternately to meet the requirements of three-wavelength achromatism; the symmetric linear array arrangement method is to place the unit structures corresponding to different wavelengths in each row and symmetrically in the center. Three wavelengths of achromatism are achieved by using the two methods. However, this method only realizes the focusing of three wavelengths.

[0005] LI Y et al. proposed a single-layer multi-task vortex metal lens for super-miniature two-photon excitation STED microscopic imaging, which is composed of nanocolumns with c-Si material and hexagonal bases with SiO2 material, and divides the superlens area into 36 sectors, wherein the blue sector corresponds to the structure corresponding to 1050nm pump light, and the orange sector corresponds to the unit structure corresponding to 599nm depletion light (vortex light). Finally, both wavelengths are focused to 10um. However, this method only realizes the focusing of two wavelengths.

[0006] FAN Z B et al. proposed a broadband achromatic metal array for visible light imaging, which is designed to achieve achromatism from the principle of realizing zero material dispersion; to achieve achromatism, i.e. zero material dispersion, the effective refractive index of different wavelengths is a constant value; therefore, by selecting appropriate structures, the effective refractive index is a constant value, the phase increases linearly with frequency at the same position, and the effective refractive index is a constant value; and then after linear fitting, the effective refractive index and the corresponding structure parameters are obtained, and finally 10 different silicon nitride structures are selected to realize the achromatism of 430-780nm. However, this method uses a variety of different nanostructures, which brings challenges to processing and preparation.

[0007] LIANG YU et al. proposed a polarization-insensitive achromatic superlens design, which uses transmission phase method and particle swarm optimization algorithm to design a reflective achromatic superlens based on titanium dioxide nanocolumn unit, which realizes constant focusing between 500-550nm. However, this method realizes a narrow bandwidth range of 500-550nm.

[0008] In summary, in the above-mentioned schemes for realizing achromatism of superlens, there are problems of complex lens structure, use of multiple different structures, which brings challenges to processing and preparation, and if only titanium dioxide nanocolumns are used, it will lead to high preparation cost and narrow bandwidth range. Therefore, based on the defects still existing in the above-mentioned prior art, it is necessary to propose a new design scheme of achromatic superlens. SUMMARY

[0009] The purpose of this invention is to provide a spatially multiplexed visible light band achromatic superlens design method for realizing dual-wavelength focusing superlens design in the visible light range.

[0010] Therefore, the technical solution of the present invention is as follows:

[0011] A design method for achromatic superlens in the visible light band based on spatial multiplexing, comprising the following steps:

[0012] S1. Set the structural parameters and simulation methods and conditions of the superlens;

[0013] S2, Design in λ 起 to λ 止 The unit structure of the achromatic superlens within the range will affect the entire λ band. 起 ~λ 止 The band is divided into two regions, namely the blue region and the red region, with λ1 and λ2 being self-selected wavelengths from the blue and red regions, respectively. The phase transition curves and transmittance curves of nanopillars with different diameters at the two incident wavelengths λ1 and λ2 are obtained through simulation, and a nanopillar diameter-phase library with high transmittance characteristics is constructed. The unit structure of the superlens consists of a cubic silicon dioxide substrate and a cylindrical silicon nitride nanopillar vertically fixed at the center of the top surface of the substrate. The height of the nanopillar and the period of the unit structure satisfy the following: within a specified diameter range, the nanopillars cover at least one phase period within a set incident wavelength range.

[0014] S3. Discretize the several nanopillars in the superlens in a plane to calculate the ideal phase of each nanopillar; the formula for calculating the ideal phase is:

[0015]

[0016] In the formula, The theoretical phase; (x,y) are the position coordinates of the center of the nanopillar; λ i Where λ is the wavelength of the incident light, i = 1 or 2; f is the focal length of the superlens; C(λ) i () is a constant whose value depends only on the incident wavelength;

[0017] S4. Single-wavelength lens nanopillar filling of superlenses based on Fresnel dual-wavelength spatial multiplexing method;

[0018] S5. Using the two-dimensional particle swarm optimization algorithm, calculate the parameter C(λ). i The optimal solution.

[0019] Furthermore, in step S1, the superlens is simulated using the finite-time difference method.

[0020] Further, in step S1, the simulation of the superlens is simulated by using the finite time domain difference method; the simulation conditions are set as follows: ① the simulation light source is set as: the x-polarized plane light is incident from the unit structure of the superlens; ② the boundary condition is set as: the upper and lower layers in the unit structure are perfect matched layers to prevent light reflection; the four sides of the unit structure are set as periodic boundaries; ③ the monitor is set as: the z-plane monitor and the point monitor are placed above the unit structure of the superlens to monitor the transmittance change and the phase change of the unit structure of the superlens, respectively.

[0021] Further, the specific implementation steps of step S2 are as follows:

[0022] S201, designing a unit structure of a superlens and determining the height H, diameter D and period P of the unit structure; wherein the value range of P is P < λ / 2NA, and the wavelength of the incident light < P < the wavelength of the incident light, NA is the numerical aperture,

[0023] S202, respectively, simulate the phase response curve and the transmittance response curve corresponding to the nanometer column of different diameters under the two incident wavelengths λ1 and λ2, and construct a nanometer column diameter-phase library;

[0024] Further, the specific implementation steps of step S4 are as follows:

[0025] S401, dividing the superlens into several regions along the radial direction from the center of the base plane, and alternately setting each region as the structure region corresponding to λ1 and the structure region corresponding to λ2;

[0026] S402, for each nanometer column in the λ1 region, selecting the D corresponding to the minimum phase deviation from the ideal phase in the phase library as the diameter of the nanometer column; for each nanometer column in the λ2 region, selecting the D corresponding to the minimum phase deviation from the ideal phase in the phase library as the diameter of the nanometer column; and further determining the composition of the superlens.

[0027] Further, in step S401, the superlens is divided into four regions along the radial direction from the center of the base plane, and the ratio of the radius of the center circular region to the width of the remaining three annular regions from the inside to the outside is R1:R2:R3:R4.

[0028] Further, the specific implementation steps of step S5 are as follows:

[0029] S501, initializing to obtain a two-dimensional particle swarm;

[0030] S502, sequentially extracting the current position of each two-dimensional particle as a constant C(λ i ​​), and sequentially substitute into step S3 and step S4 to obtain the fitness function value Δ, and determine the individual optimal fitness function value and the group optimal fitness function value in all fitness functions;

[0031] S503, updating the two-dimensional particle swarm according to the speed updating formula and the position updating formula, and repeating step S502;

[0032] v j+1 = w x v j + c1 x rand x (p best - x j ) + c2 x rand x (g best - x j ),

[0033] x j+1 = x j + v j ,

[0034] In the formula, v j is the current speed of the particle, x j is the current position of the particle, rand is a random number in (0, 1), w is an inertia factor, c1 and c2 are acceleration factors, p best is the position corresponding to the individual optimal fitness function value, and g best is the position corresponding to the group optimal fitness function value.

[0035] S504, repeating step S503, and the super lens constructed in the last iteration process is the super lens meeting the design requirements.

[0036] Further, in step S502, the calculation formula of the fitness function value Δ is:

[0037]

[0038] In the formula, is the target phase calculated according to the formula; is the actual phase obtained by the light passing through the nano structure; and the total phase error is the sum of the absolute values of the two wavelength phase errors.

[0039] Compared with the prior art, the visible light wave band achromatic super lens design method based on spatial multiplexing utilizes the method of double-wavelength Fresnel wave band spatial multiplexing, not only realizes the achromatism of λ1 and λ2 double wavelengths, but also realizes the achromatism of the entire wavelength range λ 起 - λ 止achromatism, and the designed superlens has simple design, wide bandwidth range and polarization insensitivity based on transmission phase design; the method can indeed realize achromatic lens design of target focal length through design practice. In specific implementation, achromatic design of a wide waveband of 470-700nm is realized, the focusing change is 7.2566%, the average focusing efficiency is 31.71%, and the focusing efficiency at 700nm reaches 47.1275%. The method is not only suitable for visible light waveband, but also can be used for achromatic design of other wavebands and provides a reference. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 a flowchart of the visible light waveband achromatic superlens design method based on spatial multiplexing of the application;

[0041] Fig. 2(a) is a schematic diagram of a unit structure of a superlens in the visible light waveband achromatic superlens design method based on spatial multiplexing of the application;

[0042] Fig. 2(b) is a partial top view of a superlens in the visible light waveband achromatic superlens design method based on spatial multiplexing of the application;

[0043] Fig. 2(c) is a schematic diagram of phase and transmittance response curves corresponding to changes in nanocolumn diameter when the incident wave is 488nm in an embodiment of the application;

[0044] Fig. 2(d) is a schematic diagram of phase and transmittance response curves corresponding to changes in nanocolumn diameter when the incident wave is 632.8nm in an embodiment of the application;

[0045] Fig. 3(a) is an XY plane view of a superlens structure obtained through step S401 in the visible light waveband achromatic superlens design method based on spatial multiplexing of the application;

[0046] Fig. 3(b) is a three-dimensional schematic diagram of a superlens structure obtained through step S401 in the visible light waveband achromatic superlens design method based on spatial multiplexing of the application;

[0047] Figure 4 Fig. 4 is a flowchart of step S5 of using a particle swarm algorithm in the visible light waveband achromatic superlens design method based on spatial multiplexing of the application;

[0048] Fig. 5(a) is a normalized light intensity diagram in the XZ plane obtained when the incident light is 488nm in an embodiment of the application;

[0049] Fig. 5(b) is a normalized light intensity diagram in the XZ plane obtained when the incident light is 632.8nm in an embodiment of the application;

[0050] Figure 5(c) is a normalized XY focal plane intensity plot for the embodiment of the present application for 488 nm light;

[0051] Figure 5(d) is a normalized XY focal plane intensity plot for the embodiment of the present application for 632.8 nm light;

[0052] Figure 5(e) is a normalized focal spot intensity field plot at the X-axis intersection with the focal plane for the embodiment of the present application for 488 nm light;

[0053] Figure 5(f) is a normalized focal spot intensity field plot at the X-axis intersection with the focal plane for the embodiment of the present application for 632.8 nm light;

[0054] Figure 6(a) is a normalized XZ plane intensity plot for the embodiment of the present application for 470 nm light;

[0055] Figure 6(b) is a normalized XZ plane intensity plot for the embodiment of the present application for 488 nm light;

[0056] Figure 6(c) is a normalized XZ plane intensity plot for the embodiment of the present application for 540 nm light;

[0057] Figure 6(d) is a normalized XZ plane intensity plot for the embodiment of the present application for 632.8 nm light;

[0058] Figure 6(e) is a normalized XZ plane intensity plot for the embodiment of the present application for 700 nm light;

[0059] Figure 7(a) is a normalized XY focal plane intensity plot for the embodiment of the present application for 470 nm light;

[0060] Figure 7(b) is a normalized XY focal plane intensity plot for the embodiment of the present application for 488 nm light;

[0061] Figure 7(c) is a normalized XY focal plane intensity plot for the embodiment of the present application for 540 nm light;

[0062] Figure 7(d) is a normalized XY focal plane intensity plot for the embodiment of the present application for 632.8 nm light;

[0063] Figure 7(e) is a normalized XY focal plane intensity plot for the embodiment of the present application for 700 nm light;

[0064] Figure 8(a) is a normalized focal spot intensity field plot at the X-axis intersection with the focal plane for the embodiment of the present application for 470 nm light;

[0065] Fig. 8(b) is a normalized focal spot intensity field diagram at the intersection of the X axis and the focal plane obtained when the 488 nm light is incident in the embodiment of the present application;

[0066] Fig. 8(c) is a normalized focal spot intensity field diagram at the intersection of the X axis and the focal plane obtained when the 540 nm light is incident in the embodiment of the present application;

[0067] Fig. 8(d) is a normalized focal spot intensity field diagram at the intersection of the X axis and the focal plane obtained when the 632.8 nm light is incident in the embodiment of the present application;

[0068] Fig. 8(e) is a normalized focal spot intensity field diagram at the intersection of the X axis and the focal plane obtained when the 700 nm light is incident in the embodiment of the present application;

[0069] Fig. 9(a) is a focal length distribution diagram corresponding to different wavelengths in the visible light range of 470-700 nm in the achromatic superlens in the embodiment of the present application;

[0070] Fig. 9(b) is a focal length distribution diagram corresponding to different wavelengths in the visible light range of 470-700 nm in the chromatic superlens in the embodiment of the present application. DETAILED DESCRIPTION

[0071] The present application will be further described below in conjunction with the drawings and specific embodiments, but the following embodiments are by no means limiting to the present application. Referring to Fig. 1, the design method of the visible light waveband achromatic superlens based on spatial multiplexing is as follows: Figure 1

[0072] S1, setting the structure parameters of the superlens and the simulation mode:

[0073] In this embodiment, the structure parameters of the superlens are as follows: the diameter d of the superlens is 14 um, the focal length f is 20 um, and the numerical aperture NA is 0.33, so as to achieve achromatism in the range of 470-700 nm;

[0074] The superlens simulation design is simulated by using the finite time domain difference method, specifically,

[0075] ① The simulation light source is set to be x-polarized plane light incident from the unit structure of the superlens;

[0076] ② The boundary condition is set as follows: the upper and lower layers in the unit structure are perfect matching layers to prevent light reflection; the four sides of the unit structure are set as periodic boundaries;

[0077] ③ The monitor is set as follows: the z plane monitor and the point monitor are placed above the unit structure of the superlens to monitor the transmittance change and the phase change of the unit structure of the superlens, respectively;

[0078] ​S2, design the unit structure of the superlens, and construct the nanorod diameter-phase library according to the phase response curves and transmittance response curves of the nanorods with different diameters obtained through simulation;

[0079] S201, design the unit structure of the superlens, and the parameters of the unit structure must be designed finely to achieve phase coverage of at least one period; meanwhile, according to the Nyquist sampling theorem, the period P of the unit structure should satisfy P < λ / 2NA;

[0080] Referring to FIGS. 2(a) and 2(b), the superlens is composed of a plurality of silicon nitride nanorods arranged in an array on a silicon dioxide substrate; the superlens can be regarded as being composed of a plurality of unit structures; each unit structure is composed of a silicon dioxide substrate at the lower layer and a silicon nitride nanorod at the upper layer; the silicon dioxide substrate is a cubic structure, and the silicon nitride nanorod is a cylindrical structure, which is vertically arranged and fixed in the center on the top surface of the silicon dioxide substrate; the height H of the silicon nitride nanorod is 1.3 um, the period (i.e., the center distance between adjacent silicon nitride nanorods) P is 380 nm, and the diameter D ranges from 50 nm to 380 nm.

[0081] S202, divide 470 nm to 700 nm into two regions, i.e., a blue region and a red region; select 488 nm as the wavelength in the blue region and 632.8 nm as the wavelength in the red region; based on the simulation conditions set in step S1, simulate to obtain the phase response curves and transmittance response curves of the nanorods with different diameters under the wavelengths of 488 nm and 632.8 nm;

[0082] Specifically, based on the diameter D ranging from 50 nm to 380 nm, a plurality of sampling points are selected at equal intervals in the diameter range, and the nanorods with diameters corresponding to the sampling points are simulated and scanned under the two incident wavelengths of 488 nm and 632.8 nm, respectively, to obtain the phase and transmittance of the nanorods with different diameters under the two wavelengths of 488 nm and 632.8 nm, and the phase response curves and transmittance response curves are drawn, respectively.

[0083] As shown in FIG. 2(c), it is a schematic diagram of the phase and transmittance response curves corresponding to the change of the diameter of the nanorod when the incident wave is 488 nm; as can be seen from the figure, when the incident wave is 488 nm, the phase change from -π to π is realized with the change of the diameter of the nanorod, while the high transmittance is maintained;

[0084] As shown in FIG. 2(d), it is a schematic diagram of the phase and transmittance response curves corresponding to the change of the diameter of the nanorod when the incident wave is 632.8 nm; as can be seen from the figure, when the incident wave is 632.8 nm, the phase change from -π to π is realized; as can be seen from the transmittance curve, the high transmittance is maintained under most diameters;

[0085] S203, constructing a diameter-phase library according to the simulation result of step S202; specifically, the phase library is composed of several groups of diameter-wavelength data with high transmittance, each group of data is composed of a diameter D, and three elements;

[0086] S3, plane-dispersing several nanometer pillars in the superlens to calculate the ideal phase of each nanometer pillar;

[0087] S301, dispersing several nanometer pillars in the superlens into several coordinate points on the substrate plane;

[0088] According to the design diameter of the superlens and the unit structure period P determined in step S1, the centers of the nanometer pillars on the superlens are dispersed into several coordinate points (x, y) on the substrate plane (top surface), wherein the center point of the superlens plane is (0, 0);

[0089] S302, calculating the ideal phase required by each nanometer pillar at two different incident wavelengths according to the coordinate points of each nanometer pillar;

[0090] wherein the calculation formula of the ideal phase is:

[0091]

[0092] In the formula, is the theoretical phase; (x, y) is the position coordinate of the center of the nanometer pillar; λ i is the wavelength of the incident light, i = 1 or 2, when i = 1, λ1= 488 nm, when i = 2, λ2= 632.8 nm; f is the focal length of the superlens; C(λ i ) is a constant, whose value is only related to the incident wavelength; At the same time, C(λ i ) is also a value used for optimization in the design of the present application;

[0093] S4, single-wavelength lens nanometer pillar filling of the superlens based on the Fresnel band space multiplexing method;

[0094] The superlens is divided into four regions, region I, region II, region III and region IV, along the radial direction from the center on the plane according to the Fresnel band method, except that region I at the center is a circular region, the remaining regions II, III and IV are annular regions; wherein the ratio of the radius R1 of region I, the width R2 of region II, the width R3 of region III and the width R4 of region IV is 3:2:1:1. Region I and region III are 488 nm corresponding nanometer pillars, and the ideal phase deviation minimum in the phase library is selected in turn D is the diameter of the nanocolumn; the nanocolumns corresponding to region II and region IV are 632.8 nm, and the nanocolumns corresponding to region III and region V are 1064 nm D is the diameter of the nanocolumn; the nanocolumns corresponding to region II and region IV are 632.8 nm, and the nanocolumns corresponding to region III and region V are 1064 nm

[0095] Fig. 3(a) is an XY plane view of the superlens structure obtained after the step S401; Fig. 3(b) is a three-dimensional schematic view of the superlens structure obtained after the step S401;

[0096] S5, using a two-dimensional particle swarm algorithm, to obtain the optimal solution of the parameter C(λ i );

[0097] Specifically, as shown in Figure 4 ,

[0098] S501, initializing to obtain a two-dimensional particle swarm;

[0099] Specifically, each two-dimensional particle includes a current speed and a current position;

[0100] S502, taking the current position of each two-dimensional particle as a constant C(λ i ) and substituting it into the steps S3 and S4 to obtain the fitness function value Δ, and determining the individual optimal fitness function value and the group optimal value and the group optimal fitness function value in all fitness functions;

[0101] Specifically, the specific implementation of this step is as follows:

[0102] Step 1: taking the current position of each two-dimensional particle as a constant C(λ i ) and substituting it into the step S302 to calculate the ideal phase of each nanocolumn and constructing a superlens using the nanocolumn filling mode determined in the step S4;

[0103] Step 2: based on the superlens constructed in step 2, calculating its fitness function value Δ: In the formula, is the target phase calculated according to the formula; is the actual phase of light passing through the nanometer structure (i.e. the actual phase determined from the phase library); the total phase error is the sum of the absolute values of the phase errors of the two wavelengths;

[0104] Step 3: Among all the calculated fitness function values Δ, the minimum value of all the fitness function values Δ of each particle from the beginning of iteration to the current iteration process is selected as the individual optimal fitness function value, and the minimum value of all the fitness function values Δ of all particles from the beginning of iteration to the current iteration process is selected as the group optimal fitness function value;

[0105] S503, updating the two-dimensional particle swarm, and repeating step S502;

[0106] Specifically, the velocity update formula and the position update formula of each particle in the particle swarm are as follows:

[0107] v j+1 = w × v j + c1 × rand × (p best - x j ) + c2 × rand × (g best - x j ),

[0108] x j+1 = x j + v j ,

[0109] wherein v j is the current velocity of the particle, x j is the current position of the particle, rand is a random number in (0, 1), w is an inertia factor, which is a non-negative number, and is usually a number between 0 and 1. c1 and c2 are acceleration factors, which are usually numbers between 1.5 and 2.5. p best is the position corresponding to the individual optimal fitness function value, and g best is the position corresponding to the group optimal fitness function value;

[0110] S504, repeating step S503 until the current position of the particle is the optimal solution of the constant C, at which time the constructed superlens is the superlens meeting the design requirements.

[0111] Further, simulation experiments are performed on the final superlens design result of the embodiment to verify whether the design result meets the design requirements.

[0112] (I) By obtaining the far-field information in the monitor, the focusing condition of the superlens is analyzed:

[0113] Figure 5(a) shows the normalized light intensity in the XZ plane when the light of 488 nm is incident; Figure 5(b) shows the normalized light intensity in the XZ plane when the light of 632.8 nm is incident; from the above-mentioned XZ plane light field intensity diagrams, it can be concluded that the light of 488 nm and 632 nm is focused at 20.28 um and 20.82 um respectively, and the average error of the distance from the design focal length 20 um is 2.25%, which meets the requirement of achromatism of dual-wavelength;

[0114] Figure 5(c) shows the normalized XY focal plane light intensity diagram when the light of 488 nm is incident; Figure 5(d) shows the normalized XY focal plane light intensity diagram when the light of 632.8 nm is incident; from the above-mentioned normalized XY focal plane light intensity diagrams, it can be seen that the focal points of different wavelengths are a Gaussian distributed circular point.

[0115] Figure 5(e) shows the normalized focal spot light intensity field diagram at the intersection of the X axis and the focal plane when the light of 488 nm is incident; Figure 5(f) shows the normalized focal spot light intensity field diagram at the intersection of the X axis and the focal plane when the light of 632.8 nm is incident. Specifically, referring to Figure 5(e), when the light of 488 nm is incident, the full width at half maximum (FWHM) of the light spot is 603 nm; referring to Figure 5(f), when the light of 632.8 nm is incident, the FWHM of the superlens is 904 nm, and the diffraction limit is 958.78 nm, with a small difference; the focusing efficiency is defined as the ratio of the corresponding light field energy in the light spot range with a radius of 3 times the FWHM to the total incident energy. The focusing efficiency of the superlens corresponding to the incidence of 488 nm and 632.8 nm is 31% and 40% respectively.

[0116] (ii) After the above analysis of dual-wavelength focusing, the focusing of the superlens in the entire waveband is further analyzed:

[0117] In the waveband of 470-700 nm, the focusing effect of the superlens when the light of 470 nm, 540 nm, 632.8 nm and 700 nm is incident is analyzed in detail. Figure 6(a) shows the normalized light intensity in the XZ plane when the light of 470 nm is incident; Figure 6(b) shows the normalized light intensity in the XZ plane when the light of 488 nm is incident; Figure 6(c) shows the normalized light intensity in the XZ plane when the light of 540 nm is incident; Figure 6(d) shows the normalized light intensity in the XZ plane when the light of 632.8 nm is incident; Figure 6(e) shows the normalized light intensity in the XZ plane when the light of 700 nm is incident; from the five diagrams, it can be seen that the superlens has the function of achromatism in the entire waveband.

[0118] Figure 7(a) shows the normalized XY focal plane light intensity diagram obtained when 470 nm light is incident; Figure 7(b) shows the normalized XY focal plane light intensity diagram obtained when 488 nm light is incident; Figure 7(c) shows the normalized XY focal plane light intensity diagram obtained when 540 nm light is incident; Figure 7(d) shows the normalized XY focal plane light intensity diagram obtained when 632.8 nm light is incident; and Figure 7(e) shows the normalized XY focal plane light intensity diagram obtained when 700 nm light is incident. As can be seen from the five diagrams, the superlens has a symmetrical circular spot in the entire waveband, and the focusing quality is good.

[0119] Figure 8(a) shows the normalized focal spot light intensity field diagram at the position where the X axis intersects the focal plane when 470 nm light is incident; Figure 8(b) shows the normalized focal spot light intensity field diagram at the position where the X axis intersects the focal plane when 488 nm light is incident; Figure 8(c) shows the normalized focal spot light intensity field diagram at the position where the X axis intersects the focal plane when 540 nm light is incident; Figure 8(d) shows the normalized focal spot light intensity field diagram at the position where the X axis intersects the focal plane when 632.8 nm light is incident; and Figure 8(e) shows the normalized focal spot light intensity field diagram at the position where the X axis intersects the focal plane when 700 nm light is incident. As can be seen from the five diagrams, the sidelobe intensity of the superlens is small, and does not affect the focusing quality.

[0120] As a comparison, we designed a chromatic aberration superlens with a design wavelength of 488 nm, and divided the 470-700 nm waveband into 470 nm, 488 nm, 500 nm, 520 nm, 540 nm, 560 nm, 580 nm, 600 nm, 632.8 nm, 650 nm, 680 nm and 700 nm, a total of 12 wavelengths. Figure 9(a) shows the focal length distribution diagram of the achromatic superlens corresponding to different wavelengths in the visible light 470-700 nm range, which is plotted based on the corresponding focal point positions of the 12 incident wavelengths. Figure 9(b) shows the focal length distribution diagram of the chromatic aberration superlens corresponding to different wavelengths in the visible light 470-700 nm range, which is plotted based on the corresponding focal point positions of the 12 incident wavelengths. For the achromatic superlens, the focal length hardly changes when the incident light changes in the entire waveband; for the chromatic aberration superlens, the corresponding focal length changes in a large range when the incident light changes. In which, we write the focal length change of the achromatic superlens as:

[0121]

[0122] In the formula, max(f) is the maximum focal length, min(f) is the minimum focal length, and mean(f) is the average focal length.

[0123] Accordingly, the focal length change is 7.2566%, and the average focusing efficiency of 12 wavelengths is 31.71%; wherein the focusing efficiency corresponding to 700nm wavelength is the highest, which is 47.1275%.

[0124] In summary, the dual-wavelength achromatic superlens design method in the visible light region of the application utilizes the transmission phase principle, adopts silicon nitride nanocolumns, and focuses 488nm and 632.8nm at the designed focal length through the method of Fresnel band space multiplexing, and the average focusing efficiency reaches 35.5%; at the same time, it has achromatic effect in the 470-700nm visible light band range, the focal length change is 7.2566%, the average focusing efficiency is 31.71%, and the focusing efficiency corresponding to 700nm wavelength is the highest, which is 47.1275%; it can be seen that the design method adopted has simple structure, polarization insensitivity, easy implementation and preparation, and can provide a reference for the design of other metasurface devices, and is further used in endoscopes, microscopic imaging and other fields. At the same time, in other wavelength ranges, this method can also be used for design.

Claims

1. A method for designing a spatial multiplexing based achromatic metalens in visible waveband, characterized in that, The steps are as follows: S1, setting the structure parameters of the superlens and the simulation mode, simulation conditions; S2, design in λ 起 to λ 止 achromatic superlens unit structure, the entire wavelength range λ 起 ~ λ 止 into two regions, namely the blue region and the red region, λ1 and λ2 are respectively selected from the blue region and the red region; the phase transition curve and the transmittance curve of the nanometer column with different diameters under the two incident wavelengths λ1 and λ2 are obtained by simulation, and a nanometer column diameter-phase library with high transmittance characteristics is constructed; wherein the unit structure of the superlens is composed of a silicon dioxide substrate with a cubic structure and a silicon nitride nanometer column with a cylindrical structure vertically fixed at the center of the top surface of the substrate, and the height of the nanometer column and the period of the unit structure satisfy: the nanometer column with a specified diameter range has at least one phase period covering in the set incident wavelength range; S3, plane discrete is performed on a plurality of nanometer columns in the superlens to calculate ideal phases of the nanometer columns; wherein, a calculation formula of the ideal phase is: wherein is the theoretical phase; (x, y) is the position coordinate of the center of the nanopillar; λ i is the wavelength of the incident light, i = 1 or 2; f is the focal length of the superlens; C(λ i ) is a constant whose value is only related to the incident wavelength; S4, based on the Fresnel two-wavelength spatial multiplexing method, the superlens is filled with nanometer columns of a single-wavelength lens; S401, the superlens is divided into a plurality of regions along a radial direction from a center of a circle on a base plane, and each region is defined as a region corresponding to λ1 and a region corresponding to λ2 in an alternating manner; S402、for each nanorod in the region λ1, sequentially select the one with the minimum deviation from the ideal phase in the phase library corresponding to D as the diameter of the nanorod; for each nanorod in the region λ2, sequentially select the one with the minimum deviation from the ideal phase in the phase library corresponding to D as the diameter of the nanorod; and determine the composition of the superlens S5, using two-dimensional particle swarm algorithm, the optimal solution of parameter C(λ i ) is obtained, the ideal phase of each nanopillar is calculated, and the superlens is constructed by using the nanopillar filling mode determined in step S4.

2. The spatial multiplexing based visible waveband achromatic superlens design method according to claim 1, wherein, In step S1, the simulation mode of the superlens is simulated by using the finite time domain difference method. 3.The spatial multiplexing based visible waveband achromatic superlens design method according to claim 1, wherein, The specific implementation steps of step S2 are as follows: S201, designing a unit structure of the superlens and determining a nanometer column height H, a diameter D and a unit structure period P; S202, simulation is performed to obtain phase response curves and transmittance response curves corresponding to nanometer columns with different diameters under two incident wavelengths λ1 and λ2, respectively, to construct a nanometer column diameter-phase library.

4. The spatial multiplexing based visible waveband achromatic superlens design method of claim 1, wherein, In step S401, the superlens is divided into four regions along a radial direction from a center of a circle on a base plane, and a ratio of a radius of the central circular region to widths of the remaining three annular regions from inside to outside is R1:R2:R3:R4.

5. The spatial multiplexing based visible waveband achromatic superlens design method of claim 1, wherein, The specific implementation steps of step S5 are as follows: S501, initialization is performed to obtain a two-dimensional particle swarm; S502, extract the current position of each two-dimensional particle as a constant C(λ i ), and substitute it into step S3 and step S4 to obtain the fitness function value Δ, and determine the individual optimal fitness function value and the group optimal value and the group optimal fitness function value in all fitness functions; S503, the two-dimensional particle swarm is updated according to a speed updating formula and a position updating formula, and step S502 is repeated; v j+1 = w x v j + c1 x rand x (p best - x j ) + c2 x rand x (g best - x j ), x j+1 = x j + v j , where v j is the current velocity of the particle, x j is the current position of the particle, rand is a random number in (0, 1), w is an inertia factor, c1, c2 are acceleration factors, p best is the position corresponding to the individual best fitness function value, g best is the position corresponding to the group best fitness function value; S504, repeat step S503, in the last iteration, the current position of the particle is the optimal solution of the constant C (λ i ) and the constructed superlens is the superlens that meets the design requirements.

6. The spatial multiplexing based visible waveband achromatic superlens design method of claim 1, wherein, In step S501, each two-dimensional particle includes a current speed and a current position.

7. The spatial multiplexing based visible waveband achatnatic superlens design method of claim 1, wherein, In step S502, a calculation formula of the fitness function value Δ is: wherein is the target phase calculated according to the formula is the actual phase obtained by light passing through the nanostructure; the total phase error is the sum of the absolute values of the two wavelength phase errors.

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