Dispersion metamaterial lens design method based on nanostructure phase expansion matching

Abstract

The invention provides a dispersion metamaterial lens design method based on nanostructure phase expansion matching, and relates to the technical field of metasurface structures.The method comprises the steps that a unit structure phase response database is established; the unit structure phase response database comprises phase responses of different unit structures under different design wavelengths; presetting a plurality of design wavelengths to obtain a target phase at each position on the surface of the metamaterial lens under different design wavelengths; matching the target phase with the phase response in the unit structure phase response database, periodically adjusting the phase response of the unit structure under each design wavelength by using light waves, so that the difference value between the phase response of each position and the corresponding target phase is within the light wave period range, and generating geometric parameters of the unit structure of each position; and obtaining the surface structure of the super-structure lens. Phase matching of a plurality of design wavelengths is carried out based on the light wave period, the problem that the dispersion range is small is solved, and regulation and control of phases of all positions of the super-structure lens are achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of super surface structures, and in particular to a dispersion meta-lens design method based on nanostructure phase expansion matching. Background Art

[0002] Since metasurfaces have the ability to control the phase of incident light waves at subwavelength scales, they are widely used in the field of modern optics, providing a new approach to the design and functional realization of optical components. The construction of metasurfaces is based on a series of ingeniously designed subwavelength unit structures. The subwavelength unit structures are arranged in an orderly manner according to specific rules to form metasurfaces with specific functions. By adjusting different arrangement parameters, the metasurface can achieve the control of light wave amplitude, phase, polarization and other characteristics in the plane. With the rapid development of optical sensing systems, the demand for miniaturized and lightweight optical systems is also growing. Traditional optical lenses usually rely on sufficient accumulation of optical path difference to meet the control of light waves, which greatly limits the size of traditional lens groups, making the optical system huge and bulky.

[0003] As a special form of metasurface, metalens has powerful focusing ability. Unlike traditional lenses that rely on the refractive index gradient of the material to achieve focusing, metalens achieves focusing by regulating the phase distribution of incident light in a plane. It can achieve the regulation of incident light in an extremely thin plane. This method significantly reduces the volume and weight of the optical system, making it easier to integrate it on other optical components, and provides the possibility for miniaturization and lightweighting of the optical system.

[0004] Currently, researchers have made significant progress in the dispersion control of metalens. They usually use a fixed design wavelength to design a dispersive metalens, and then determine the phase distribution curve. The phase distribution curve is used to determine the unit structure parameters at each position of the metalens, thereby achieving the elimination of dispersion and the control of the dispersion range.

[0005] Metalenses rely on phase design to achieve different functions, and different positions have different phase requirements. The focusing principle of dispersive metalenses is as follows: Figure 1 As shown in Figure 1, in the design process of meta-lens, the meta-lens is usually designed with a fixed design wavelength. Figure 2 The phase distribution curve of the meta-lens is shown when the design wavelength is 600nm and the design focal length is 1mm. After the required phase distribution curve is established, the geometric parameters of the unit structure at each position on the surface of the meta-lens are determined.

[0006] However, due to the dispersion effect of the meta-lens itself, at locations deviating from the design wavelength, such as Figure 2As shown, the phase will deviate from the ideal profile; as a result, light of different wavelengths will be focused at different positions at a fixed design wavelength, resulting in a relatively small dispersion range provided by the meta-lens itself, generally tens of microns; and thus the dispersion cannot be well regulated and utilized to achieve specific optical functions. Summary of the invention

[0007] The present invention provides a method for designing a dispersion meta-lens based on nanostructure phase expansion matching, which is used to solve the problem of a small dispersion range caused by the current design of a dispersion meta-lens using a single fixed design wavelength.

[0008] The present invention provides a method for designing a dispersion meta-lens based on nanostructure phase expansion matching, the method comprising: Establishing a unit structure phase response database; the unit structure phase response database includes phase responses of different unit structures at different design wavelengths; Preset multiple design wavelengths to obtain the target phase at each position on the meta-lens surface at different design wavelengths; The target phase is matched with the phase response in the unit structure phase response database, and the phase response of the unit structure at each design wavelength is adjusted periodically using light waves, so that the difference between the phase response at each position and the corresponding target phase is within the light wave period range, and the geometric parameters of the unit structure at each position are generated to obtain the surface structure of the meta-lens.

[0009] Furthermore, the matching formula includes: ; in, The design wavelength is The target phase required when Indicates the number of preset design wavelengths; Represents the phase response of the unit structure at different design wavelengths; represents the design wavelength; It represents the constant related to the design wavelength and phase response. The same unit structure has different phase response at different design wavelengths. represents the phase response after adjustment of the light wave period; represents the difference between the target phase and the adjusted phase response, .

[0010] Furthermore, the matching also includes: determining the unit structure at each position by comparing the mean square error of different unit structures at each position.

[0011] Furthermore, the mean square error formula is: ; in, represents the difference between the target phase and the adjusted phase response, ; Indicates the number of unit structures.

[0012] Furthermore, the target phase The design formula is: ; in, represents the design wavelength; , Represents the position coordinates of the unit structure on the metalens; The meta-lens is The design focal length is as follows.

[0013] Furthermore, the aperture of the designed meta-lens is N A =20um, the plane wave of 500~700nm can be converged to the predetermined focus on the axis, while keeping the dispersion range within 250um.

[0014] Furthermore, the designed meta-lens includes unit structures of different sizes and shapes.

[0015] Furthermore, the unit structure includes a nanocolumn and a substrate; wherein the shape of the nanocolumn is a symmetrical structure.

[0016] Furthermore, the height of the nanocolumns is 700-1000 nm; and the substrate period of the silicon dioxide substrate is 400-600 nm.

[0017] Furthermore, the geometric parameters of the metasurface unit structures of different shapes are scanned and optimized by using the simulation software FDTD solution to establish the unit structure phase response database.

[0018] In general, the present invention provides a method for designing a dispersion meta-lens based on nanostructure phase expansion matching. The technical solution conceived by the present invention can achieve the following beneficial effects compared with the prior art: The present invention uses the light wave period for phase matching and adjusts the phase response of the unit structure at each design wavelength, so that the difference between the phase response at each position and the corresponding target phase is within the light wave period, and the matching effect is better. Compared with the single-wavelength design, the present invention performs phase matching of multiple design wavelengths based on the light wave period, which solves the problem of a small dispersion range caused by the current design of a dispersion meta-lens using a single fixed design wavelength, can better realize the regulation of the phase of each position of the meta-lens, and can converge a plane wave of 500-700nm to a predetermined focus on the axis, while keeping the dispersion range controlled within a bandwidth of 250um. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0020] Figure 1 It is a schematic diagram of the focusing effect of a dispersion meta-lens provided by the present invention, according to a dispersion meta-lens design method based on nanostructure phase expansion matching; Figure 2 It is a schematic diagram of phase distribution at different wavelengths under a fixed design wavelength in a dispersion meta-lens design method based on nanostructure phase expansion matching provided by the present invention; Figure 3 It is a schematic diagram of the focusing principle of a dispersion meta-lens according to a dispersion meta-lens design method based on nanostructure phase expansion matching provided by the present invention; Figure 4 It is a schematic diagram of a method for designing a dispersion meta-lens based on nanostructure phase expansion matching provided by the present invention; Figure 5 It is a schematic diagram of a unit structure of a dispersion meta-lens design method based on nanostructure phase expansion matching provided by the present invention; Figure 6 It is a schematic diagram of the processing of a unit structure of a dispersion meta-lens design method based on nanostructure phase expansion matching provided by the present invention, in which the nano-column height is 900nm and the silicon dioxide substrate period is 500nm; Figure 7 It is a schematic diagram of a unit structure of different nanocolumn shapes of a dispersion meta-lens design method based on nanostructure phase expansion matching provided by the present invention; Figure 8 It is a phase matching schematic diagram of a dispersion meta-lens design method based on nanostructure phase expansion matching provided by the present invention; Fig. 9 It is a schematic diagram of the overall and local structures of a meta-lens enlarged in a method for designing a dispersion meta-lens based on nanostructure phase expansion matching provided by the present invention; Fig.10 It is a schematic diagram of phase matching results of multiple design wavelengths at various wavelengths of a dispersion meta-lens design method based on nanostructure phase expansion matching provided by the present invention; Fig.11 It is a schematic diagram of the phase matching results of a single fixed design wavelength at each wavelength; Fig.12 It is a schematic diagram of simulation results of the focal length direction of a meta-lens according to a dispersion meta-lens design method based on nanostructure phase expansion matching provided by the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings and embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention.

[0022] It should be noted that, in the description of the embodiments of the present invention, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a method, step or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such method, step or device. In the absence of further restrictions, the elements defined by the sentence "include a ..." do not exclude the existence of other identical elements in the method, step or device including the elements.

[0023] In order to solve the problem of small dispersion range caused by the current design of dispersive meta-lenses using a single fixed design wavelength and to manipulate the dispersion range of the meta-lens, it is necessary to design different design wavelengths and design independent phase profiles at all design wavelengths. In other words, Figure 3 As shown, it is necessary to focus light of different wavelengths at the same design wavelength to their respective focal points. In this way, at the same design wavelength, light of each wavelength has its own design focal length. The unit structure shape parameters required for each position of the meta-lens are then determined through phase matching, so that the phase will be in the ideal profile even at different wavelengths, thereby increasing the dispersion range.

[0024] The present invention provides a design of a dispersion meta-lens based on multi-wavelength phase matching of light wave periods, such as Figure 4 Specifically, the method includes: S101: Establishing a unit structure phase response database, wherein the unit structure phase response database includes phase responses of different unit structures at different design wavelengths.

[0025] As an embodiment, the geometric parameters of the metasurface unit structures of different shapes can be scanned and optimized by simulation software FDTD solution to establish a unit structure phase response database. The unit structure phase response database records the phase response characteristics of unit structures of different shapes at different design wavelengths.

[0026] It should be noted that the unit structure includes a nanocolumn and a substrate.

[0027] Since silicon nitride material has high transmittance and refractive index in the visible light band, light loss is small, and silicon nitride material has mature processing technology and is easy to process. Therefore, as a preferred embodiment of the present invention, Figure 5 As shown, the nanorods are preferably made of silicon nitride material (Si3N4); and the substrate is preferably made of silicon dioxide material (SiO2).

[0028] In order to provide sufficient phase difference design requirements, as an embodiment, the present invention selects a nanocolumn height range of 700~1000nm to increase the control ability of the unit structure; and selects a substrate period of the silicon dioxide substrate of 400~600nm to ensure the phase requirements and nanocolumn processing accuracy.

[0029] Although increasing the height of the nanopillars can improve the controllability of the structure, the increase in height will increase the aspect ratio of the unit structure, making the processing more difficult and possibly affecting the surface morphology and verticality of the final meta-lens. Figure 6 As shown, the present invention preferably has a unit structure in which the height H of the nanocolumns is 900 nm and the base period P is preferably 500 nm to ensure the processing morphology and verticality of the nanocolumns.

[0030] Transmission-type phase is achieved by phase control through the optical path difference generated when light propagates. The specific method is to adjust the shape and geometric parameters of each unit structure to change the equivalent refractive index of the unit structure, thereby achieving the function of phase control.

[0031] In order to ensure the polarization-insensitive property of the meta-lens, the shape of the nanorods of the present invention is preferably a symmetrical structure, such as Figure 7 As shown, the shape of the nanorod can be various symmetrical structures such as a cylinder, a cuboid, a cross, a torus, a square torus, etc.

[0032] By changing the geometric parameters of the shape of the unit structure, the wavelength and phase relationship curve of each unit structure is generated, and the phase response of different unit structures at different design wavelengths is obtained, thereby establishing a unit structure phase response database.

[0033] For example, the unit structure of each shape is simulated using the finite difference time domain method through the software FDTD solution. During the simulation, periodic boundary conditions are set in the x and y directions, and a perfectly matched layer boundary condition is applied along the z direction.

[0034] S102: Preset multiple design wavelengths to obtain a target phase at each position on the surface of the meta-lens at different design wavelengths.

[0035] After establishing the unit structure phase response database, it is also necessary to determine the target phase required for each position of the meta-lens at different design wavelengths. In other words, multiple design wavelengths correspond to multiple target phases at each position.

[0036] As an example, the target phase The design formula is: ; in, represents the design wavelength; , Represents the position coordinates of the unit structure on the metalens; The meta-lens is The design focal length is as follows.

[0037] S103: Match the target phase with the phase response in the unit structure phase response database, and use the light wave periodically to adjust the phase response of the unit structure at each design wavelength, so that the difference between the phase response at each position and the corresponding target phase is within the light wave period, generate the unit structure geometric parameters at each position, and obtain the surface structure of the meta-lens.

[0038] The present invention achieves control over the phase of the metalens by matching multiple target phases obtained at each position of the metalens with the phase responses recorded in a unit structure database.

[0039] Furthermore, the matching formula includes: ; in, The design wavelength is The target phase required when Indicates the number of preset design wavelengths; Represents the phase response of the unit structure at different design wavelengths; represents the design wavelength; It represents the constant related to the design wavelength and phase response. The same unit structure has different phase response at different design wavelengths. represents the phase response after adjustment of the light wave period; represents the difference between the target phase and the adjusted phase response, .

[0040] Since each unit structure will have an error with the target phase at the corresponding position at different design wavelengths after matching, the matching also includes: determining the unit structure at each position by comparing the mean square error of different unit structures at each position.

[0041] As an embodiment, the mean square error formula is: ; in, represents the difference between the target phase and the adjusted phase response, ; Indicates the number of unit structures.

[0042] Thus, the unit structure required for each position of the meta-lens can be determined. The meta-lens designed in the present invention can include unit structures of different sizes and shapes. A =20um, the plane wave of 500~700nm can be converged to the predetermined focus on the axis, while keeping the dispersion range within 250um.

[0043] In order to verify the matching effect of the present invention, Figure 8 As shown in the figure, the design wavelengths of the meta-lenses are: , , ; The corresponding design focal lengths are: , , ; Target phase when the radius of the meta-lens is 20um With the adjusted phase response The target phase has a good matching effect with the phase response in the unit structure phase response database. The unit structure geometric parameters at each position are generated by phase matching, and then the following are obtained: Fig. 9 The meta-lens surface structure shown.

[0044] In addition, the present invention also compares the phase matching results of multiple design wavelengths of the present invention under the same conditions with those of a single fixed design wavelength at each wavelength, such as Fig.10 and 11As shown, it is a comparison diagram of the target phase and the simulation results. The simulation results show that the phase of the meta-lens surface designed by the present invention meets the design requirements. Compared with the single fixed design wavelength design, the present invention can better realize the phase control of each position of the meta-lens.

[0045] Fig.12 Focal lengths designed for different wavelengths , , The schematic diagram of the simulation results in the focal length direction is shown below. It can be seen that the simulation results are focused near the designed focal length, which meets the requirements.

[0046] In summary, the present invention performs phase matching based on the light wave period, and uses the light wave periodicity to adjust the phase response of the unit structure at each design wavelength, so that the difference between the phase response at each position and the corresponding target phase is within the light wave period, and the matching effect is better; compared with the single wavelength design, the present invention performs phase matching of multiple design wavelengths based on the light wave period, which solves the problem of small dispersion range caused by the current design of dispersion meta-lens using a single fixed design wavelength, can better realize the regulation of the phase of each position of the meta-lens, and can converge the plane wave of 500~700nm to the predetermined focus on the axis, while keeping the dispersion range controlled within the bandwidth of 250um.

[0047] It should be noted that, for the above-mentioned various embodiments, for the sake of simplicity of description, they are all expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the described order of actions, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0048] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0049] In the several embodiments provided in this application, it should be understood that the disclosed method or system can be implemented in other ways. For example, the above-described embodiments are only schematic, and the division of the units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0050] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0051] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0052] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or the whole or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a memory, including a number of instructions for a computer device (which can be a personal computer, a server or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application.

[0053] Those skilled in the art will appreciate that all or part of the various circuits in the above embodiments may be completed by entering a program to instruct related hardware, and the program may be stored in a computer-readable memory, which may include: a flash drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, etc.

[0054] The above is only an exemplary embodiment of the present disclosure, and the scope of the present disclosure cannot be limited thereto. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. After considering the specification and practicing the disclosure here, those skilled in the art will easily think of the implementation scheme of the present disclosure. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary technical means in the technical field not recorded in the present disclosure. The description and examples are regarded as exemplary only, and the scope and spirit of the present disclosure are defined by the claims.

[0055] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. As long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0056] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for designing a dispersion meta-lens based on nanostructure phase expansion matching, characterized in that: The method comprises: Establishing a unit structure phase response database; the unit structure phase response database includes phase responses of different unit structures at different design wavelengths; Preset multiple design wavelengths to obtain the target phase at each position on the surface of the meta-lens at different design wavelengths; The target phase is matched with the phase response in the unit structure phase response database, and the phase response of the unit structure at each design wavelength is adjusted periodically using light waves, so that the difference between the phase response at each position and the corresponding target phase is within the light wave period range, and the geometric parameters of the unit structure at each position are generated to obtain the surface structure of the meta-lens.

2. The method for designing a dispersion meta-lens based on nanostructure phase expansion matching according to claim 1, characterized in that: The matching formula includes: ； in, The design wavelength is The target phase required when Indicates the number of preset design wavelengths; Represents the phase response of the unit structure at different design wavelengths; represents the design wavelength; It represents the constant related to the design wavelength and phase response. The same unit structure has different design wavelengths. represents the phase response after adjustment of the light wave period; represents the difference between the target phase and the adjusted phase response, .

3. A method for designing a dispersion meta-lens based on nanostructure phase expansion matching according to claim 1 or 2, characterized in that: The matching further includes: determining the unit structure at each position by comparing the mean square errors of different unit structures at each position.

4. The method for designing a dispersion meta-lens based on nanostructure phase expansion matching according to claim 3, characterized in that: The mean square error formula is: ； in, represents the difference between the target phase and the adjusted phase response, ; Indicates the number of unit structures.

5. The method for designing a dispersion meta-lens based on nanostructure phase expansion matching according to claim 2, characterized in that: The target phase The design formula is: ； in, represents the design wavelength; , Represents the position coordinates of the unit structure on the metalens; The meta-lens is The design focal length below.

6. The method for designing a dispersion meta-lens based on nanostructure phase expansion matching according to claim 1, characterized in that: The designed aperture of the meta-lens is N A =20um, the plane wave of 500~700nm can be converged to the predetermined focus on the axis, while keeping the dispersion range within 250um.

7. The method for designing a dispersion meta-lens based on nanostructure phase expansion matching according to claim 1, characterized in that: The designed meta-lens includes unit structures of different sizes and shapes.

8. The method for designing a dispersion meta-lens based on nanostructure phase expansion matching according to claim 1, characterized in that: The unit structure includes a nanocolumn and a substrate; wherein the shape of the nanocolumn is a symmetrical structure.

9. The method for designing a dispersion meta-lens based on nanostructure phase expansion matching according to claim 8, characterized in that: The height of the nanocolumns is 700-1000 nm; the substrate period of the substrate is 400-600 nm.

10. The method for designing a dispersion meta-lens based on nanostructure phase expansion matching according to claim 1, characterized in that: The geometric parameter scanning and optimization of metasurface unit structures of different shapes are performed by simulation software FDTD solution to establish the unit structure phase response database.

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