A single-layer zoom metalens and its design method

Abstract

The present invention belongs to the field of metalenses technology and provides a single-layer variable-focus metalense and a design method thereof. The single-layer variable-focus metalense design method comprises calculating the transmittance corresponding to a phase-change material unit at different heights, and determining the height corresponding to the maximum transmittance as the height of the phase-change material unit; randomly generating an initial radius distribution of multiple phase-change material units; constructing an optimization index based on focal plane focusing efficiency and optical axis zoom, and optimizing the initial radius distribution according to the optimization index until the radius distribution of the multiple phase-change material units meets a preset optimization termination condition, thereby obtaining a final radius distribution of the multiple phase-change material units; and designing a single-layer variable-focus metalense based on the height and the final radius distribution. The present invention can improve the focusing effect of the variable-focus metalense.

Description

Technical Field

[0001] The present invention relates to the field of metalens technology, and in particular to a single-layer variable-focus metalens and a design method thereof. Background Art

[0002] Compared to traditional refractive and diffractive optical devices, dielectric metalenses not only offer the advantages of a more compact size and higher-resolution imaging, but also possess superior light manipulation capabilities. Therefore, metalenses can achieve a number of special functions, such as generating polarization-encrypted composite vortex light, metalenses optical tweezers for three-dimensional capture, and 4D imaging. Among them, reconfigurable zoom metalenses have attracted much attention. Zoom lens systems can focus light on focal planes with different focal lengths, which means they can better meet the functional requirements of more optical systems. However, traditional zoom is achieved through the use of many lenses, and such combinations are often bulky and complex. At the same time, they use mechanical focusing mechanisms, which are prone to introducing more potential errors. In view of this, the idea of ​​using tunable active materials to prepare metalenses has been proposed. Metalenses prepared using tunable active materials can adjust the focal length by simply irradiating the metalenses with a laser, or applying voltage and heating the metalenses, without mechanically changing the incident light or the lens position angle.

[0003] Specifically, tunable active materials include liquid crystal materials and phase change materials. Liquid crystal materials and phase change materials each have their own characteristics. When combined with liquid crystals, an electrically braked zoom metalens can be designed. When combined with phase change materials, an adjustable focal length can be achieved by regulating the phase change. Technicians in related fields have proposed using sulfide phase change materials Sb2S3 to design zoom metalens. This is because this material not only has a non-volatile phase change, but also has ultra-low light absorption loss and a high two-state refractive index gap in the near-infrared band. It is one of the most promising materials for designing reconfigurable zoom metalens. Not only that, the degree of crystallinity of Sb2S3 can also be controlled by multi-pulse femtosecond laser irradiation or heating pulses. Different degrees of crystallinity will also result in different optical properties, creating a wider adjustable space for the Sb2S3 zoom metalens.

[0004] However, the focusing effect of the zoom superlens designed by the traditional zoom superlens design method based on sulfide phase change material Sb2S3 is poor and it is difficult to meet the needs of practical applications. Summary of the Invention

[0005] The technical problem solved by the present invention is to provide a single-layer zoom metalens and a design method thereof to improve the focusing effect of the zoom metalens.

[0006] In a first aspect, the present invention provides a single-layer zoom metalens design method, which is applied to the single-layer zoom metalens provided by the present invention. The single-layer zoom metalens includes multiple phase change material units. The single-layer zoom metalens design method provided by the present invention includes the following steps:

[0007] Calculating the transmittances of the phase change material units at different heights respectively, and determining the height corresponding to the maximum transmittance as the height of the phase change material units;

[0008] Dividing a plurality of phase change material units into a plurality of unit groups, and randomly generating an initial radius distribution of the plurality of phase change material units; wherein the phase change material units belonging to the same unit group have the same distance from the center of the single-layer variable focus metalens, the phase change material units belonging to different unit groups have different distances from the center of the single-layer variable focus metalens, and the radius of each phase change material unit in the same unit group is the same;

[0009] An optimization index is constructed based on the focal plane focusing efficiency and the optical axis zoom. The initial radius distribution is optimized according to the optimization index until the radius distribution of the multiple phase change material units meets the preset optimization termination condition, thereby obtaining the final radius distribution of the multiple phase change material units. The focal plane focusing efficiency is used to measure the light energy loss, and the optical axis zoom represents the zoom capability of the single-layer zoom metalens.

[0010] Design of single-layer variable-focus metalenses based on the height and final radius distribution.

[0011] Optionally, an optimization index is constructed based on the focal plane focusing efficiency and the zoom in the optical axis direction, and the initial radius distribution is optimized according to the optimization index until the radius distribution of the multiple phase change material units meets a preset optimization termination condition, thereby obtaining a final radius distribution of the multiple phase change material units, including:

[0012] For each cell group, perform the following steps:

[0013] Step I: updating the initial radius of each phase change material unit in the unit group to obtain a first updated radius, calculating a first optimization index corresponding to the first updated radius, and if the first optimization index meets a preset standard, using the first updated radius as the first radius of each phase change material unit in the unit group and executing step II; otherwise, using the initial radius as the first radius of each phase change material unit in the unit group and executing step II; wherein the initial radius is determined by the initial radius distribution, and the first optimization index is used to evaluate the shape similarity between the one-dimensional light intensity distribution in the focal plane and the ideal first-order point spread function;

[0014] Step II: constructing a second optimization index based on the focal plane focusing efficiency, updating the first radius to obtain a second updated radius, and calculating a second optimization index corresponding to the second updated radius. If the second optimization index meets the preset standard, the second updated radius is used as the second radius of each phase change material unit in the unit group, and step III is executed; otherwise, the first radius is used as the second radius, and step III is executed; the second optimization index is used to evaluate the shape similarity between the one-dimensional light intensity distribution on the focal plane and the ideal first-order point spread function and the focusing efficiency of the focal plane;

[0015] Step III: constructing a third optimization index based on the zoom in the optical axis direction, updating the second radius to obtain the third updated radius, and calculating the third optimization index corresponding to the third updated radius. If the third optimization index meets the preset standard, the third updated radius is used as the final radius of each phase change material unit in the unit group; otherwise, the second radius is used as the final radius. The process of updating the radius of each phase change material unit in steps I, II, and III is the same. The third optimization index is used to evaluate the shape similarity between the one-dimensional light intensity distribution of the focal plane and the ideal first-order point spread function, the focusing efficiency of the focal plane, and the ratio of the variable focal length to the design target zoom length.

[0016] According to the final radius, a final radius distribution is obtained.

[0017] Optionally, the expression for updating the radius of each phase change material unit is r′=Δr×(N r -1); where r′ represents the updated radius, Δr represents the radius change interval, and N r A random integer between 1 and 31.

[0018] Optionally, the expression of the first optimization indicator is:

[0019] FOM=(FOM crys +FOM amor ) / 2

[0020] FOM crys or FOM amor =μ-10×ε

[0021]

[0022] Among them, FOM represents the first optimization index, FOM crys Indicates the FOM value of the crystal lens focusing calculation, FOM amorrepresents the FOM value of the amorphous state calculation, μ is the factor describing the similarity, which is the shape similarity between the one-dimensional light intensity distribution on the focal plane and the ideal first-order point spread function, ε is the factor describing the difference, which is the shape difference between the one-dimensional light intensity distribution on the focal plane and the ideal first-order point spread function, I(x) represents the one-dimensional light intensity distribution along the x-axis on the target focal plane, T(x) represents the one-dimensional Gaussian function with diffraction-limited FWHM, FWHM is the width of the Gaussian beam intensity distribution curve at half the maximum value, x max Indicates the maximum x-axis value of the focal plane, x min Indicates the minimum x-axis value of the focal plane.

[0023] Optionally, the expression of the second optimization index is as follows: FOM′ crys orFOM′ amor =(μ-10×ε)+γ; where γ is used to evaluate the focusing efficiency of the metalens in the optimization, E far is the energy within a circular mask with a diameter of three times the FWHM at the target focal plane in the far field, E near is the near-field energy at the monitor position.

[0024] Optionally, the expression of the third optimization index is as follows: FOM′=FOM′ crys +FOM′ amor +dfl; dfl is used to evaluate the degree of zoom optimization. Δfl represents the focal length difference of the phase change material unit in different states, Δfl target The focal length difference set for the target.

[0025] Optionally, the preset standard is that the value of the optimization indicator is greater than or equal to a preset indicator threshold;

[0026] The preset optimization termination condition is that the first optimization indicator, the second optimization indicator, and the third optimization indicator all meet the preset standards.

[0027] In a second aspect, the present invention provides a single-layer variable focus metalens, which includes a plurality of phase change material units arranged in a periodic manner, and the plurality of phase change material units are arranged coplanarly.

[0028] Optionally, the material of the phase change material unit is Sb2S3.

[0029] Optionally, the phase change material unit is cylindrical in shape, and the heights of the multiple phase change material units are the same.

[0030] The beneficial effects of the present invention are:

[0031] The single-layer zoom metalens design method provided by the present invention calculates the transmittance corresponding to multiple phase change material units at different heights respectively, and determines the height corresponding to the maximum transmittance as the height of the multiple phase change material units. The single-layer zoom metalens designed in this way has the optimal transmittance, which is beneficial to improving the focusing effect of the zoom metalens; an optimization index is constructed based on the focal plane focusing efficiency and the zoom in the optical axis direction, and the initial radius distribution is optimized according to the optimization index until the radius distribution of the multiple phase change material units meets the preset optimization termination condition, thereby obtaining the final radius distribution of the multiple phase change material units. The final radius distribution obtained by the optimization process can enable the zoom metalens to have a diffraction-limited focusing half-maximum width, enhance the focused light intensity, and improve the focusing effect of the zoom metalens. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a schematic diagram of the transformation characteristics of the Sb2S3 intermediate phase in one embodiment of the present application;

[0033] Figure 2 This is a schematic structural diagram of a phase change material unit in one embodiment of the present application;

[0034] Figure 3 This is a flow chart of a method for designing a single-layer variable-focus metalens in one embodiment of the present application;

[0035] Figure 4a This is a schematic diagram of the transmittance of a phase change material unit in a crystalline state and an amorphous state with a period of 0.5 microns in one embodiment of the present application;

[0036] Figure 4b Schematic diagram of phase control of a phase change material unit in a crystalline state and an amorphous state with a period of 0.5 microns in one embodiment of the present application;

[0037] Figure 4c This is a schematic diagram of calculation results of average transmittance of a phase change material unit at various heights in one embodiment of the present application;

[0038] Figure 4d This is a phase transmittance modulation diagram of a phase change material unit in a crystalline state when the period is 0.5 microns and the height is 0.56 microns in one embodiment of the present application;

[0039] Figure 4e This is a phase transmittance modulation diagram of the amorphous state of the phase change material unit in one embodiment of the present application when the period is 0.5 microns and the height is 0.56 microns;

[0040] Figure 5a Schematic diagram of the light intensity distribution on the xz plane of a single-layer variable focus metalens designed based on the first radius obtained based on the first optimization index in one embodiment of the present application;

[0041] Figure 5b Schematic diagram of the normalized light intensity distribution along the x-axis of a single-layer variable-focus metalens designed based on the first radius obtained based on the first optimization index in one embodiment of the present application;

[0042] Figure 6a Schematic diagram of the two-dimensional intensity distribution of the crystalline and amorphous dual-focus zoom lens along the light propagation direction in Example 1 of the present application;

[0043] Figure 6b Schematic diagram of the normalized light intensity distribution along the x-axis for the crystalline and amorphous dual-focus zoom lens in Example 1 of the present application;

[0044] Figure 7a Schematic diagram of the intensity distribution of the transmitted wave in the xz plane of the dual-focus variable metalens in the crystalline state and the amorphous state in Example 2 of the present application;

[0045] Figure 7b Schematic diagram of the light intensity distribution of the dual-focus variable metalens in the crystalline state and the amorphous state in the focal plane in Example 2 of the present application;

[0046] Figure 8a This is the optical force curve of the single-layer variable focus metalens in the crystalline state in Example 3 of this application;

[0047] Figure 8b This is the optical force curve of the single-layer variable focus metalens in the amorphous state in Example 3 of this application;

[0048] Figure 8c Schematic diagram of the calculation results of the optical potential well U along the x-axis, y-axis and z-axis normalized by kBT in Example 3 of the present application;

[0049] Figure 9a Schematic diagram of the focusing result of the continuous zoom metalens in the fourth embodiment of the present application on the xz plane;

[0050] Figure 9b This is a focusing effect of the continuous zoom metalens at the focal plane in the fourth embodiment of the present application;

[0051] Figure 9c This is another focusing effect of the continuous zoom metalens at the focal plane in Example 4 of the present application;

[0052] Figure 9d Schematic diagram of one-dimensional light intensity distribution of the continuous zoom metalens in Example 4 of the present application when the focus is in the crystalline state;

[0053] Figure 9e Schematic diagram of one-dimensional light intensity distribution of the continuous zoom metalens in Example 4 of the present application when the focus is in an intermediate state with a phase change degree of 0.5;

[0054] Figure 9f Schematic diagram of one-dimensional light intensity distribution of the continuous zoom metalens in Example 4 of the present application when the focus is in the amorphous state;

[0055] Figure 10a Schematic diagram of the two-dimensional xz plane light intensity distribution of the continuous zoom metalens in multiple phase transition states in Example 4 of the present application;

[0056] Figure 10b Schematic diagram of one-dimensional z-axis light intensity distribution of the continuous zoom metalens in multiple phase transition states in Example 4 of the present application;

[0057] Figure 10c Schematic diagram of the focal length change of the continuous zoom metalens in multiple phase transition states in Example 4 of the present application;

[0058] Figure 10d This is a diagram showing the FWHM change of the continuously variable focus metalens in Example 4 of the present application. DETAILED DESCRIPTION

[0059] The present invention discloses a single-layer zoom metalens and a design method thereof.

[0060] For ease of explanation, the single-layer variable focus metalens provided by the present invention is first described.

[0061] In the current design of superlens based on Sb2S3, studies have shown that continuous focusing can be achieved by utilizing the characteristics of the intermediate phase transformation of Sb2S3. Figure 1 As shown, the principle is to apply uniform energy along the optical axis to the lens (heating, applying voltage or using pulsed laser irradiation), so that the temperature of the Sb2S3 atoms reaches the critical value of phase change, so that it is in a state of coexistence of crystal and amorphous solid. At this time, it can focus on planes at different distances. Not only that, due to the non-volatility of Sb2S3 atoms, the superlens based on Sb2S3 will be able to be stably controlled. In addition, the phase change material Sb2S3 has ultra-low light absorption loss and a higher two-state refractive index difference in the near-infrared band. Based on the above advantages, the material of the traditional zoom superlens is mainly the phase change material Sb2S3, but the traditional zoom superlens adopts a double-layer superlens structure, which currently has greater process difficulties. In this regard, the present invention has been improved and a single-layer superlens structure is adopted. The single-layer zoom superlens includes a plurality of phase change material units arranged in a periodic manner. The material of the phase change material unit is Sb2S3, such as Figure 2As shown, the phase change material unit is cylindrical in shape, and multiple phase change material units are arranged in the same plane, and the height of each phase change material unit is the same. Among them, the cylindrical phase change material unit has the advantage of polarization insensitivity, and the same height of multiple phase change material units can ensure that the phase change degree (PCD, Phase change degree, the ratio of the depth of amorphization to the total thickness) of each part of the single-layer zoom metalens is equal. On the one hand, the single-layer metalens structure has a low process difficulty. On the other hand, it can conveniently and uniformly control the phase change degree of the entire zoom metalens, thereby achieving multi-level control of the focusing conditions of different focal planes.

[0062] The following is a detailed description of the single-layer zoom metalens design method provided by the present invention.

[0063] like Figure 3 As shown, the single-layer zoom metalens design method provided by the present invention includes the following steps:

[0064] Step 31 : calculating the transmittances of the phase change material units at different heights respectively, and determining the height corresponding to the maximum transmittance as the height of the phase change material units.

[0065] For example, in one embodiment of the present invention, taking a 50×50 array with a period of 0.5 microns as an example, the phase change material units under this period are scanned, and the diameter range is set to 0.1 microns to 0.4 microns, the height range is set to 0.5 microns to 0.6 microns, and the scanning interval is 0.01 microns. Figure 4a The transmittance of the phase change material unit in the crystalline and amorphous states with a period of 0.5 microns is shown. Figure 4b The phase control of the phase change material unit in the crystalline and amorphous states at a period of 0.5 microns is shown. Figure 4c The average transmittance calculation results at each height are shown, where Figure 4a 、 Figure 4b The horizontal axis represents the radius of the phase change material unit in micrometers. Figure 4a 、 Figure 4b The vertical axis represents the height of the phase change material unit in micrometers. Figure 4c The horizontal axis represents the height of the phase change material unit in micrometers. Figure 4c The vertical axis represents the transmittance, Average T C Average T represents the average transmittance of crystalline atoms. A represents the average transmittance of the amorphous state, and Average T of 2states represents the average of the average transmittance of the crystalline atoms and the average transmittance of the amorphous state, which is given by Figure 4c It can be seen that the height corresponding to the maximum transmittance (0.56 μm) is selected as the height of the phase change material unit. Figure 4dThe phase transmittance modulation diagram of the crystalline state of the phase change material unit is shown when the period is 0.5 microns and the height is 0.56 microns. Figure 4e The phase transmittance modulation diagram of the amorphous phase change material unit is shown when the period is 0.5 microns and the height is 0.56 microns. Figure 4d 、 Figure 4e The horizontal axis represents the radius of the phase change material unit in micrometers. Figure 4d 、 Figure 4e The vertical axis represents the phase and transmittance.

[0066] It should be understood that transmittance is the ratio of the intensity of light passing through the metalens to the intensity of the incident light. The transmittance corresponding to multiple phase change material units at different heights can be calculated using a conventional transmittance calculation formula, which will not be described in detail here.

[0067] Step 32: Divide the plurality of phase change material units into a plurality of unit groups, and randomly generate an initial radius distribution of the plurality of phase change material units.

[0068] Among them, the phase change material units belonging to the same unit group are at the same distance from the center of the single-layer zoom metal lens, the phase change material units belonging to different unit groups are at different distances from the center of the single-layer zoom metal lens, and the radius of each phase change material unit in the same unit group is the same.

[0069] The calculation formula for the above center distance can use Euclidean distance. It is worth mentioning that setting the center distance of the phase change material unit of the same unit group and the single-layer zoom metalens to be the same takes into account the circular symmetry of light focusing, which can reduce the number of optimizations and reduce the loss of computing resources.

[0070] It should be noted that the initial radius distribution of the randomly generated multiple phase change material units is based on groups. For example, in one embodiment of the present invention, there are 5 unit groups, among which unit group 1 includes 4 phase change material units with a radius of 0.1 micron; unit group 2 includes 8 phase change material units with a radius of 0.12 micron; unit group 3 includes 4 phase change material units with a radius of 0.09 micron; unit group 4 includes 8 phase change material units with a radius of 0.13 micron; unit group 5 includes 4 phase change material units with a radius of 0.11 micron.

[0071] Step 33 : constructing an optimization index based on the focal plane focusing efficiency and the optical axis zoom, and optimizing the initial radius distribution according to the optimization index until the radius distribution of the multiple phase change material units meets the preset optimization termination condition, thereby obtaining the final radius distribution of the multiple phase change material units.

[0072] The focal plane focusing efficiency is used to measure the light energy loss, and the zoom along the optical axis represents the zoom capability of the single-layer zoom metalens.

[0073] Specifically, for each unit group, perform the following steps:

[0074] Step 33.1: Update the initial radius of each phase change material unit in the unit group to obtain the radius after the first update, and calculate the first optimization index corresponding to the radius after the first update. If the first optimization index meets the preset standard, the radius after the first update is used as the first radius of each phase change material unit in the unit group, and execute step 33.2; otherwise, the initial radius is used as the first radius of each phase change material unit in the unit group, and execute step 33.2.

[0075] The initial radius is determined by the initial radius distribution, and the first optimization index is used to evaluate the shape similarity between the one-dimensional light intensity distribution in the focal plane and the ideal first-order point spread function.

[0076] The above expression for updating the initial radius of each phase change material unit in the unit group is r′=Δr×(N r -1); where r′ represents the updated radius, Δr represents the radius change interval, and N r is a random integer between 1 and 31. The preset standard is set to the value of the optimization indicator being greater than or equal to the preset indicator threshold. The preset optimization termination condition is that all optimization indicators meet the preset standard.

[0077] The expression of the first optimization indicator is:

[0078] FOM=(FOM crys +FOM amor ) / 2

[0079] FOM crys orFOM amor =μ-10×ε

[0080]

[0081] Among them, FOM represents the first optimization index, FOM crys Indicates the FOM value of the crystal lens focusing calculation, FOM amor represents the FOM value of the amorphous state calculation, μ is the factor describing the similarity, which is the shape similarity between the one-dimensional light intensity distribution on the focal plane and the ideal first-order point spread function, ε is the factor describing the difference, which is the shape difference between the one-dimensional light intensity distribution on the focal plane and the ideal first-order point spread function, I(x) represents the one-dimensional light intensity distribution along the x-axis on the target focal plane, T(x) represents the one-dimensional Gaussian function with diffraction-limited FWHM, FWHM is the width of the Gaussian beam intensity distribution curve at half the maximum value, x max Indicates the maximum x-axis value of the focal plane, x min Indicates the minimum x-axis value of the focal plane.

[0082] It should be noted that traditional zoom metalens design methods mostly use the first optimization index to design a single-layer zoom metalens.

[0083] Figure 5a The light intensity distribution of the single-layer zoom metalens designed based on the first radius obtained by the first optimization index on the xz plane is shown. Figure 5b The normalized light intensity distribution along the x-axis of the single-layer zoom metalens designed based on the first radius obtained based on the first optimization index is shown. Figure 5a The horizontal axis represents the x-coordinate (horizontal direction), Figure 5a The vertical coordinate represents the z coordinate (optical axis direction), Figure 5b Normalized intensity represents the regularized intensity, the red dotted line Target gaussian curve represents the target function (Gaussian function), the blue solid line Simulated represents the simulated value, c-Sb2S3 represents crystalline Sb2S3, a-Sb2S3 represents amorphous Sb2S3, and the meanings of c-Sb2S3 and a-Sb2S3 in other figures are the same as above. Figure 5a and Figure 5b It can be seen that although the focusing result matches the target Gaussian function well in terms of one-dimensional light intensity distribution, the focusing intensity of this single-layer zoom metalens is far from ideal. The present invention further optimizes it by constructing optimization indicators based on the focal plane focusing efficiency and the zoom along the optical axis.

[0084] Step 33.2: Construct a second optimization index based on the focal plane focusing efficiency, update the first radius to obtain the second updated radius, and calculate the second optimization index corresponding to the second updated radius. If the second optimization index meets the preset standard, the second updated radius is used as the second radius of each phase change material unit in the unit group, and step 33.3 is executed; otherwise, the first radius is used as the second radius, and step 33.3 is executed.

[0085] The second optimization index is used to evaluate the shape similarity between the one-dimensional light intensity distribution on the focal plane and the ideal first-order point spread function and the focusing efficiency of the focal plane.

[0086] Specifically, the expression of the second optimization index is as follows: FOM′ crys or FOM′ amor =(μ-10×ε)+γ. γ is used to evaluate the focusing efficiency of the metalens in the optimization. E far is the energy within a circular mask with a diameter of three times the FWHM at the target focal plane in the far field, E nearis the near-field energy at the monitor position. It should be understood that a monitor is a function setting in simulation software (such as Lumerical FDTD) that allows you to view light field parameters within a specific area. The near-field energy at the monitor position refers to the near-field simulation results of the metalens. The near-field is the space one wavelength away after light passes through the lens.

[0087] Step 33.3, construct a third optimization index based on the zoom in the optical axis direction, update the second radius, obtain the radius after the third update, and calculate the third optimization index corresponding to the radius after the third update. If the third optimization index meets the preset standard, the radius after the third update is used as the final radius of each phase change material unit in the unit group; otherwise, the second radius is used as the final radius.

[0088] Specifically, the expression of the third optimization index is as follows: FOM′=FOM′ crys +FOM′ amor +dfl; dfl is used to evaluate the degree of zoom optimization. Δfl represents the focal length difference of the phase change material unit in different states, Δfl target The focal length difference set for the target.

[0089] In an embodiment of the present invention, the process of updating the radius of each phase change material unit in step 33.1, step 33.2 and step 33.3 is the same, and the third optimization index is used to evaluate the shape similarity between the one-dimensional light intensity distribution on the focal plane and the ideal first-order point spread function, the focusing efficiency of the focal plane, and the ratio of the variable focal length to the design target zoom length.

[0090] It should be noted that, in one embodiment of the present invention, the ideal maximum value of μ-10×ε is approximately 0.7073, and the ideal maximum values ​​of γ and dfl are 1, so there is no need to introduce excessive adjustments to the balance factor when optimizing (μ-10×ε), γ, and dfl.

[0091] Step 33.4, obtaining a final radius distribution based on the final radius.

[0092] After executing steps 33.1 to 33.3, the final radius of each unit group is obtained, and the final radius distribution of all phase change material units in the single-layer variable focus metalens is obtained from the final radius of each unit group.

[0093] Step 34, designing a single-layer variable focus metalens based on the height and final radius distribution.

[0094] In actual implementation, after executing the above steps, the height and final radius of each phase change material unit are obtained. When the period is pre-set, the height and final radius of each Sb2S3 cylinder in the single-layer zoom metalens can be adjusted according to the height and final radius.

[0095] In order to further verify the effectiveness of the single-layer zoom metalens and its design method provided by the present invention, the present invention designed several different single-layer zoom metalens based on the single-layer zoom metalens design method, which are described below.

[0096] Example 1

[0097] In this embodiment, a dual-focus zoom lens was designed according to the single-layer zoom metalens design method provided by the present invention. The optimization target was to focus the lens at 20 microns in the amorphous state and 40 microns in the crystalline state. Specifically, the dual-focus zoom lens had an aperture of 25 microns, an operating wavelength of 1064 nm, numerical apertures of 0.3024 and 0.5230 in the crystalline and amorphous states, respectively, and the amplitude of the light source was set to 1.

[0098] Figure 6a The two-dimensional intensity distribution of the dual-focus zoom lens in the crystalline and amorphous states along the light propagation direction is shown. Figure 6b The normalized light intensity distribution along the x-axis for the crystalline and amorphous dual-focus variable focus lens is shown. The results show that the dual-focus variable focus lens focuses at 20 microns in the amorphous and crystalline states, respectively, essentially matching the optimization target. The calculated focusing efficiencies are 48.23% and 48.38%, respectively. Furthermore, when focusing at 20.67 microns, the FWHM is 1.0550 microns, while the diffraction-limited FWHM is 1.0039 microns. When focusing at 39.40 microns, the FWHM is 1.7592 microns, while the diffraction-limited FWHM is 1.7460 microns. This shows that the FWHM of the single-layer variable focus metalens in both the crystalline and amorphous states is very close to the diffraction limit. Regardless of the crystalline or amorphous state, the normalized light intensity distribution in the focal plane closely coincides with a Gaussian function with a diffraction-limited FWHM.

[0099] Combine Figure 5a 、 Figure 5b 、 Figure 6a and Figure 6b It can be seen that the maximum light intensity of the focal spot of the dual-focus zoom lens designed according to the single-layer zoom metalens design method provided by the present invention is about 6 or 7 times that of the traditional design method, which proves the effectiveness and superiority of the single-layer zoom metalens design method provided by the present invention.

[0100] Example 2

[0101] In this embodiment, a dual-focus variable superlens with a high NA value is designed according to the single-layer zoom superlens design method provided by the present invention. Metal optical tweezers with high NA have been proven to be a new type of optical tweezers for capturing microscopic particles, and play an important role in biology, physics, micro-nano optics and other fields. Some schemes have been proposed to create tweezers with more adjustable functions. However, polarization-insensitive dual-focus variable superlens optical tweezers have not yet been designed. For example, the focal length targets of the high NA superlens are set to 9μm (crystalline) and 8μm (amorphous), respectively. The resulting focal lengths of the dual-focus variable superlens with a high NA value are 8.4μm (crystalline) and 7.2μm (amorphous), and the resulting NA variation range is 0.8331 to 0.8641. Figure 7a The intensity distribution of the transmitted wave in the xz plane of the dual-focus variable metalens in the crystalline state and the amorphous state is shown. Figure 7b The light intensity distribution of the dual-focus variable metalens in the crystalline and amorphous states at the focal plane is shown. Calculated focusing efficiencies of the dual-focus variable metalens in the crystalline and amorphous states are 52.61% and 52.80%, respectively. These results demonstrate that the high-NA dual-focus variable metalens designed using the single-layer variable focus metalens design method provided by the present invention offers promising focusing results for particle capture.

[0102] Example 3

[0103] In this example, the optical forces and potential wells around the focal region of a single-layer variable-focus metalens were calculated after implementing the design method for a single-layer variable-focus metalens provided by the present invention. The incident light power was set to 100 mW. The particles were silicon dioxide with a radius of 375 nm, and the medium was air. It is worth noting that the particle radius is determined by the minimum half-width of the focal spot in the two states: 752 nm for the crystalline state and 790 nm for the amorphous state. Figure 8a and Figure 8b The optical force curves of the single-layer variable focus metalens in the crystalline and amorphous states are shown respectively. Figure 8a The horizontal coordinates from left to right are the positions of force analysis, Figure 8a The vertical axis is the magnitude of the force in the force analysis, and Potential Depth represents the depth of the potential well. Figure 8a and Figure 8bIt can be seen that all force curve distributions contain positive and negative parts, which means that the optical force changes direction when the particle moves along the corresponding axis. It should be noted that the original positions of the particles are set to (0, 0, 8.4μm) and (0, 0, 7.2μm), that is, at the focal length. At this time, the particle moves along the x or y axis without changing its position in the z direction, and the maximum optical forces in the two directions along the z axis are 18.87pN and -1.59pN (crystalline state), and 14.07pN and -0.60pN (amorphous state). There is a significant difference in the maximum force in the positive and negative directions, which is normal and can be explained by the fact that the intensity distribution at the focus is usually uneven.

[0104] Based on the above optical force analysis, the optical trap stiffnesses of the x-axis, y-axis and z-axis are calculated. For the crystalline state, they are 631.97 pN / (μm·W), 555.90 pN / (μm·W) and 99.37 pN / (μm·W), respectively; for the amorphous state, they are 529.41 pN / (μm·W), 443.11 pN / (μm·W) and 89.09 pN / (μm·W), respectively.

[0105] The optical potential well U can be calculated as the integrated displacement of the optical force along its trapping direction, along which K B The results of the normalized x-axis, y-axis, and z-axis are as follows Figure 8c As shown. Among them, K B is the Boltzmann constant. T is the ambient temperature, which is set to 293K. In order to obtain a stable optical trap, a trap potential depth greater than 10kBT is usually required to overcome the interference of thermal effects. Figure 8c It can be seen that the optical potential well curves Ux and Uy clearly form a well with a value greater than 10 kBT, so the particle can be trapped in two dimensions under the dual-focus variable metal optical tweezers. In contrast, the equilibrium point of Uz (maximum value of the potential well) is not so obvious. However, after zooming in, it can be seen that the equilibrium point in the z direction differs by hundreds of times K B T, indicating the formation of a potential well. In summary, the dual-focus variable metal optical tweezers designed using the single-layer variable focus metal lens design method provided by the present invention can achieve three-dimensional capture of SiO2 particles with a radius of 375nm. The equilibrium points of capture are 9.75μm (crystalline state) and 8.38μm (amorphous state), respectively. This means that the variable focus metal lens optical tweezers can capture particles in the crystalline state and stabilize them at 9.75μm, and when the phase transition occurs to the amorphous state, it changes to about 8.38μm.

[0106] Example 4

[0107] In this embodiment, a continuously variable-focus metalens was designed according to the single-layer variable-focus metalens design method provided by the present invention. The optimization targets were set to focus at 30 microns in the amorphous state and 36 microns in the crystalline state. Furthermore, when the lens's phase-change material layer was in an intermediate state with a phase transition degree of 0.5, the optimization target was set to focus at 33 microns. Figure 9a The focusing result of the continuous zoom metalens in the xz plane is shown. Figure 9a It can be seen that the continuous zoom metalens focuses at 30 microns in the amorphous state and at 36 microns in the crystalline state. In the intermediate state with a phase transition degree of 0.5, the lens focuses at 32.7 microns. Figure 9b 、 Figure 9c The focusing effect of the continuous zoom metalens at the focal plane is shown. Figure 9d 、 Figure 9e 、 Figure 9f The one-dimensional light intensity distribution corresponding to multiple states of the continuously variable zoom metalens in the focal plane (corresponding to the crystal state, the intermediate state with a phase transition degree of 0.5, and the amorphous state) is shown. The red dotted line is the one-dimensional Gaussian function with the diffraction limit of the focal length, and the blue solid line is the simulation result of the continuously variable zoom metalens. Normalized intensity represents the normalized intensity, which is represented by Figure 9d 、 Figure 9e 、 Figure 9f It can be seen that the continuous zoom metalens basically matches the optimization target. The results show that when the amorphous state is focused, the FWHM value of the diffraction limit is 1.3832 microns, and the FWHM of the continuous zoom metalens is 1.4188 microns. When the crystalline state is focused, the FWHM value of the diffraction limit is 1.6215 microns, and the FWHM of the continuous zoom metalens is 1.6792 microns. When PCD=0.5, the diffraction limit is 1.4915 microns, and the FWHM of the continuous zoom metalens is 1.5516. Obviously, the continuous zoom metalens designed based on the single-layer zoom metalens design method provided by the present invention has a diffraction-limited focusing half-height width and has a good focusing effect.

[0108] The phase change material unit of the continuously variable focus metalens is constructed into different degrees of phase change, which can continuously adjust the lens. In this embodiment, when the PCD gradually changes from 0 to 1, the focal length gradually changes from 36 microns to 30 microns. Figure 10a The two-dimensional xz plane light intensity distribution of the continuous zoom metalens in multiple phase transition states is shown. Figure 10b The one-dimensional z-axis light intensity distribution of the continuously variable focal length metalens in multiple phase transition states is shown. Normalized light intensity represents the normalized light intensity. Figure 10c The figure shows the focal length changes of the continuous zoom metalens in multiple phase transition states, where Focal length represents the focal length. Figure 10a 、 Figure 10b 、 Figure 10c It can be seen that the continuously variable focus metalens changes continuously under multiple phase transition states. After calculation, the continuously variable focus metalens maintains a certain focusing efficiency, with an average focusing efficiency of 55%. Figure 10d The FWHM of the continuously zooming metalens is shown. The diffraction limit (green circle) represents the diffraction limit, and the red circle represents the simulated diffraction limit. Figure 10d It can be seen that the FWHM focused by the continuous zoom metalens is relatively close to the diffraction limit. This continuous zoom metalens proves that the single-layer zoom metalens designed by the single-layer zoom metalens design method provided by the present invention can achieve the function of continuous zoom.

[0109] In summary, the single-layer zoom metalens design method provided by the present invention calculates the transmittance corresponding to multiple phase change material units at different heights respectively, and determines the height corresponding to the maximum transmittance as the height of multiple phase change material units. The single-layer zoom metalens designed in this way has the optimal transmittance, which is beneficial to improving the focusing effect of the zoom metalens; an optimization index is constructed based on the focal plane focusing efficiency and the zoom in the optical axis direction, and the initial radius distribution is optimized according to the optimization index until the radius distribution of the multiple phase change material units meets the preset optimization termination condition, and the final radius distribution of the multiple phase change material units is obtained. The final radius distribution obtained by the optimization process can enable the zoom metalens to have a diffraction-limited focusing half-maximum width, enhance the focused light intensity, and improve the focusing effect of the zoom metalens.

[0110] Those skilled in the art should understand that the discussion of any of the above embodiments is merely illustrative and is not intended to imply that the scope of protection of the present application is limited to these examples. In line with the present application, the technical features in the above embodiments or different embodiments may be combined, the steps may be implemented in any order, and there are many other variations of different aspects of one or more embodiments of the present application as described above, which are not provided in detail for the sake of simplicity.

[0111] The one or more embodiments of this application are intended to encompass all such substitutions, modifications, and variations that fall within the broad scope of this application. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of one or more embodiments of this application should be included in the scope of protection of this application.

Claims

1. A method for designing a single-layer zoom metalens, characterized in that: Applied to a single-layer variable-focus metalens, the single-layer variable-focus metalens includes multiple phase-change material units, and the single-layer variable-focus metalens design method includes: respectively calculating the transmittances of the plurality of phase change material units at different heights, and determining the height corresponding to the maximum transmittance as the height of the plurality of phase change material units; Dividing the plurality of phase-change material units into a plurality of unit groups, and randomly generating an initial radius distribution of the plurality of phase-change material units in units of groups; wherein the phase-change material units belonging to the same unit group have the same center distance from the single-layer variable-focus metalens, the phase-change material units belonging to different unit groups have different center distances from the single-layer variable-focus metalens, and the radii of the phase-change material units in the same unit group are the same; An optimization index is constructed based on the focal plane focusing efficiency and the optical axis zoom, and the initial radius distribution of each unit group is optimized according to the optimization index until the radius distribution of the multiple phase change material units meets the preset optimization termination condition, thereby obtaining the final radius of each unit group, and obtaining the final radius distribution of the multiple phase change material units from the final radius of each unit group; the focal plane focusing efficiency is used to measure the light energy loss, the optical axis zoom represents the zoom capability of the single-layer zoom metalens, and the preset optimization termination condition is that all optimization indicators meet the preset standard; The single-layer variable focus metalens is designed according to the height and the final radius distribution.

2. The method for designing a single-layer variable focus metalens according to claim 1, wherein: The method includes constructing an optimization index based on the focal plane focusing efficiency and the optical axis direction zoom, and optimizing the initial radius distribution according to the optimization index until the radius distribution of the multiple phase change material units meets a preset optimization termination condition, thereby obtaining a final radius distribution of the multiple phase change material units, including: For each cell group, perform the following steps: Step I: updating the initial radius of each phase change material unit in the unit group to obtain a first updated radius, calculating a first optimization index corresponding to the first updated radius, and if the first optimization index meets a preset standard, using the first updated radius as the first radius of each phase change material unit in the unit group and executing step II; otherwise, using the initial radius as the first radius of each phase change material unit in the unit group and executing step II; wherein the initial radius is determined by the initial radius distribution, and the first optimization index is used to evaluate the shape similarity between the one-dimensional light intensity distribution in the focal plane and the ideal first-order point spread function; Step II: constructing a second optimization index based on the focal plane focusing efficiency, updating the first radius to obtain a second updated radius, and calculating a second optimization index corresponding to the second updated radius. If the second optimization index meets the preset standard, the second updated radius is used as the second radius of each phase change material unit in the unit group, and step III is executed; otherwise, the first radius is used as the second radius, and step III is executed; the second optimization index is used to evaluate the shape similarity between the one-dimensional light intensity distribution on the focal plane and the ideal first-order point spread function and the focusing efficiency of the focal plane; Step III: constructing a third optimization index based on zoom in the optical axis direction, updating the second radius to obtain a third updated radius, and calculating a third optimization index corresponding to the third updated radius. If the third optimization index meets the preset standard, the third updated radius is used as the final radius of each phase change material unit in the unit group; otherwise, the second radius is used as the final radius. The process of updating the radius of each phase change material unit in Step I, Step II, and Step III is the same. The third optimization index is used to evaluate the shape similarity between the one-dimensional light intensity distribution of the focal plane and the ideal first-order point spread function, the focusing efficiency of the focal plane, and the ratio of the variable focal length to the design target zoom length. The final radius distribution is obtained according to the final radius.

3. The method for designing a single-layer variable focus metalens according to claim 2, wherein: The expression for updating the radius of each phase change material unit is: ;in, represents the updated radius, Indicates the radius change interval, A random integer between 1 and 31.

4. The method for designing a single-layer variable focus metalens according to claim 2, wherein: The expression of the first optimization index is: in, represents the first optimization index, Represents the focusing calculation of the crystal lens value, Represents amorphous calculation value, is a factor describing the similarity between the shape of the one-dimensional light intensity distribution in the focal plane and the ideal first-order point spread function, is a factor describing the difference between the shape of the one-dimensional light intensity distribution in the focal plane and the ideal first-order point spread function, Indicates the target focal plane along One-dimensional light intensity distribution along the axis, represents a one-dimensional Gaussian function with diffraction-limited FWHM, where FWHM is the width of the Gaussian beam intensity distribution curve at half its maximum value. Represents the focal plane Axis maximum value, Represents the focal plane Axis minimum value.

5. The method for designing a single-layer variable focus metalens according to claim 4, wherein: The expression of the second optimization index is as follows: ;in, Used to evaluate the focusing efficiency of the metalens during optimization, , is the energy within a circular mask with a diameter of three times the FWHM at the target focal plane in the far field, is the near-field energy at the monitor position.

6. The method for designing a single-layer variable focus metalens according to claim 5, wherein: The expression of the third optimization index is as follows: ;in, Used to evaluate the degree of zoom optimization, , represents the focal length difference of the phase change material unit in different states, The focal length difference set for the target.

7. The method for designing a single-layer variable focus metalens according to claim 2, wherein: The preset standard is that the value of the optimization index is greater than or equal to the preset index threshold; The preset optimization termination condition is that the first optimization indicator, the second optimization indicator, and the third optimization indicator all meet the preset standard.

8. A single-layer zoom metalens, implemented based on the single-layer zoom metalens design method according to any one of claims 1 to 7, characterized in that: The single-layer variable focus metalens includes a plurality of phase change material units arranged in a periodic manner, and the plurality of phase change material units are arranged in a coplanar manner.

9. The single-layer variable focus metalens according to claim 8, wherein The material of the phase change material unit is .

10. The single-layer variable focus metalens according to claim 9, wherein: The phase change material unit is cylindrical in shape, and the plurality of phase change material units have the same height.

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