Self-focusing perovskite laser with micro-nano cavity structure and design method

By constructing a concentric ring structure on a perovskite thin film and combining it with a metasurface, the miniaturization and optical loss problems of micro/nano lasers were solved, realizing a low-cost, low-size self-focusing laser that is easy to integrate on a chip.

CN116683287BActive Publication Date: 2026-06-26SHANDONG NORMAL UNIV

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
SHANDONG NORMAL UNIV
Filing Date
2023-06-20
Publication Date
2026-06-26

AI Technical Summary

Technical Problem

Existing micro/nano lasers face challenges in miniaturization, including difficulties in mode matching, high optical loss, low actual output power, and high cost. In particular, the operation is difficult when coupling optical signals between micro/nano devices, making true micro/nano miniaturization impossible.

Method used

By combining a BIC micro/nano laser fabricated from halide perovskite with a metasurface that enables focusing, a self-focusing perovskite laser is constructed by setting multiple concentric ring micro/nano structural units on the perovskite thin film, achieving autonomous focusing of the laser beam without the need for a focusing lens.

Benefits of technology

It reduces optical loss, improves the quality factor, and the laser size is only about 10 micrometers, which is convenient for on-chip integration, and realizes autonomous focusing of laser beam and low-cost micro-nano miniaturization.

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Abstract

The application provides a micro-nano cavity structure self-focusing perovskite laser and a design method, relates to the technical field of lasers, and specifically includes the following steps: an ultrathin film with a plurality of concentric ring structures is provided, the ultrathin film is provided with micro-nano structure units along a ring path on a perovskite thin film, air holes are arranged at the centers of the micro-nano structure units, the regularly arranged micro-nano structure units form a BIC resonant cavity, the BIC resonant cavity is used to obtain laser with gain under excitation of pump light, and the BIC resonant cavity is used to focus a light beam to a target focusing position, the BIC micro-nano laser prepared from a perovskite halide is combined with an ultrathin film capable of realizing a focusing function, the focusing of the laser light beam can be realized autonomously, a focusing lens is not needed to be added, the size of the laser is only about 10 microns, and on-chip integration can be easily realized.
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Description

Technical Field

[0001] This invention belongs to the field of laser technology, and particularly relates to a self-focusing perovskite laser with a micro / nano cavity structure and its design method. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] For half a century, the semiconductor technology industry has largely followed Moore's Law. However, with the further development of information technology and the rise of emerging fields such as cloud computing, the Internet of Things, and artificial intelligence, higher demands have been placed on semiconductor technology. High integration, low power consumption, and high speed have become the mainstream development direction of the modern information technology industry. More and more people believe that Moore's Law will no longer be able to predict the further development of modern semiconductor information technology. To address these issues, people are actively exploring and trying various solutions. Among them, optoelectronic integration, which combines the advantages of photonics and electronics, is considered one of the most promising directions. Combining microelectronics and optoelectronics, integrating photonic and electronic devices on the same chip, and fully leveraging the advanced and mature process technology of microelectronics and the advantages of photonics such as high bandwidth, high speed, and anti-interference, makes optoelectronic integrated chips highly competitive in the field of device development in the post-Moore's Law era.

[0004] As an on-chip light source, the miniaturization of lasers is a crucial step in achieving optoelectronic integration. While advancements in nanofabrication and other technologies have significantly improved the miniaturization of semiconductor lasers, practical applications still face challenges with micro / nano lasers. These challenges include small device size, difficulties in mode matching, high optical loss, relatively low actual output power, and stringent requirements for materials such as gain media, leading to high costs. In systems composed of micro / nano laser devices, especially for the coupling of optical signals between various micro / nano devices, diffraction devices such as metalenses made of metasurfaces are often used to further improve integration. However, in practical applications, the fabrication, assembly, and packaging of micro / nano lasers and metasurface devices require alignment at the micrometer or submicrometer scale, which is extremely difficult and prevents true micro / nano miniaturization from being achieved. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention provides a self-focusing perovskite laser with a micro-nano cavity structure and a design method. By combining a BIC micro-nano laser made of halide perovskite with a metasurface that can achieve focusing, the laser beam can be focused autonomously without the need for a focusing lens. The laser size is only about 10 micrometers, which is convenient for on-chip integration.

[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0007] The first aspect of the present invention provides a self-focusing perovskite laser with a micro / nano cavity structure.

[0008] A self-focusing perovskite laser with a micro / nano cavity structure includes a metasurface with multiple concentric ring structures, wherein the metasurface is formed by continuously arranging micro / nano structural units along a ring path on a perovskite thin film.

[0009] The micro / nano structure unit has an air hole at its center. The regularly arranged micro / nano structure units form a BIC resonant cavity, which is used to obtain a laser beam with gain under pump light excitation and to focus the beam at the target focusing position.

[0010] Based on the target resonant frequency and target focusing position, the distance between each ring and the center and the parameter values ​​of the micro / nano structure units are set to ensure that all micro / nano structure units have the same resonant frequency and that the parameter values ​​of the micro / nano structure units on the same ring are the same. The parameters of the micro / nano structure units include the air hole size and the micro / nano structure unit size.

[0011] Furthermore, the perovskite film is prepared by synthesizing perovskite material using thermal evaporation or solution methods.

[0012] Preferably, the thickness of the perovskite film is set to 650 nm.

[0013] Preferably, the metasurface is provided with four concentric rings;

[0014] The distances between the ring and the center, from the inner ring to the outer ring, are 2.3 μm, 4.0 μm, 5.4 μm, and 7.5 μm, respectively.

[0015] The dimensions of the air holes, from the inner ring to the outer ring, are 120nm, 102nm, 84nm, and 52nm, respectively.

[0016] The dimensions of the micro / nano structure units, from the inner ring to the outer ring, are 500nm, 472nm, 431nm, and 203nm, respectively.

[0017] The target focusing position is 50 micrometers away from the metasurface from the beam focal point.

[0018] Furthermore, it also includes a pump source and an isolation layer, wherein the pump source is used to generate pump light and the isolation layer serves as a substrate for the metasurface, providing support.

[0019] A second aspect of the present invention provides a design method for a self-focusing perovskite laser with a micro / nano cavity structure.

[0020] A design method for a self-focusing perovskite laser with a micro / nano cavity structure includes:

[0021] Obtain the target resonant frequency, target focusing position, and thickness of the prepared perovskite film;

[0022] Based on the target resonant frequency and the target focusing position, the distance between each ring and the center and the parameter values ​​of the micro / nano structure units are calculated to ensure that all micro / nano structure units have the same resonant frequency and that the parameter values ​​of the micro / nano structure units on the same ring are the same. The parameters of the micro / nano structure units include the air hole size and the micro / nano structure unit size.

[0023] Based on the solution results, micro / nano structural units were continuously arranged along a circular path on the prepared perovskite thin film.

[0024] Furthermore, the specific steps for determining the distance between each annulus and its center, as well as the parameter values ​​of the micro / nano structure units, are as follows:

[0025] Based on the thickness of the perovskite thin film, the resonant frequencies of micro / nano structural units with different parameter values ​​were calculated.

[0026] Select micro / nano structure units with a resonant frequency equal to the target resonant frequency;

[0027] Based on the target focusing position and the target resonant frequency, calculate all Fresnel half-wave zones up to the target focusing position, select the Fresnel half-wave zones that can accommodate an integer number of selected micro / nano structure units as rings, and obtain the distance from each ring to the center of the ring;

[0028] Based on the position of each ring and the parameter values ​​of the micro / nano structure units that meet the conditions for resonant frequency, micro / nano structure units are selected for each ring.

[0029] Furthermore, the calculation of the resonant frequency of the micro / nano structure unit with different parameter values ​​is specifically as follows:

[0030] Using finite element analysis and time-domain finite difference method, the relationship between different parameter values ​​and resonant frequency is obtained; based on the relationship, the resonant frequency of different parameter values ​​is calculated.

[0031] Furthermore, the distance from each annulus to the center is obtained as follows:

[0032] Based on the optical path length from different positions on the perovskite thin film to the target focusing position, the wavelength of light corresponding to the target focusing position and the target resonant frequency, the position of each ring, i.e. the distance from the ring to the center, is calculated.

[0033] Furthermore, the selection of micro / nano structural units for each ring specifically involves:

[0034] The optical phase values ​​from the ring at different positions to the target focusing position are calculated. The optical phase values ​​at different positions are matched with micro / nano structural units whose resonant frequencies meet the conditions. The positions are discretized to obtain the specific position of each micro / nano structural unit on each ring.

[0035] The above one or more technical solutions have the following beneficial effects:

[0036] Compared with the materials used in existing designs, most existing micro / nano lasers use second- or third-generation semiconductors, which have high manufacturing costs. This invention uses halide perovskite to synthesize perovskite thin films through solution or thermal deposition methods as BIC micro / nano lasers. On the perovskite thin film, specific micro / nano structural units are selected to construct a metasurface structure with focusing function, resulting in a self-focusing perovskite laser. The steps are simple and the cost is low.

[0037] Compared with existing designs, this invention employs a preferred metasurface structure design and parameters, which reduces optical loss and achieves a quality factor of 1200, representing a 42.5% improvement in quality factor compared with other BIC perovskite lasers.

[0038] Compared with existing application devices, this invention combines a BIC micro / nano laser with a metasurface that can achieve focusing, enabling the laser beam to be focused autonomously without the need for a focusing lens. The laser size is only about 10 micrometers, making it easy to achieve on-chip integration.

[0039] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0040] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0041] Figure 1 This is a structural diagram of the laser in the first embodiment.

[0042] Figure 2 This is a top view of the micro / nano structure unit of the first embodiment.

[0043] Figure 3 This is a front view of the micro / nano structure unit of the first embodiment.

[0044] Figure 4 This is a method structure diagram of the second embodiment. Detailed Implementation

[0045] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0046] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0047] Example 1

[0048] In one or more embodiments, a self-focusing perovskite laser with a micro / nano cavity structure is disclosed, such as Figure 1 As shown, it includes a pump source, an isolation layer, and a metasurface with multiple concentric ring structures. The pump source is used to generate pump light, and the isolation layer serves as the substrate of the metasurface, providing support. The metasurface is formed by continuously setting micro- and nano-structure units along a ring path on a perovskite thin film.

[0049] The micro-nano structure unit has an air hole at its center. The regularly arranged micro-nano structure units form a BIC resonant cavity, which is used to obtain a laser beam with gain under pump light excitation and to focus the beam at the target focusing position.

[0050] Based on the target resonant frequency and target focusing position, the distance between each ring and the center and the parameter values ​​of the micro / nano structure units are set to ensure that all micro / nano structure units have the same resonant frequency and that the parameter values ​​of the micro / nano structure units on the same ring are the same. The parameters of the micro / nano structure units include the air hole size and the micro / nano structure unit size.

[0051] The following is a detailed description of a self-focusing perovskite laser with a micro-nano cavity structure according to this embodiment.

[0052] Traditional lasers typically consist of three main components: a pump source, a laser gain medium, and a resonant cavity source. In this embodiment, a metasurface is used instead of the laser gain medium and the resonant cavity source to achieve optical gain and beam focusing.

[0053] The metasurface in this embodiment is actually a micro / nano laser resonator based on continuous domain bound states. By superimposing phase-tuned micro / nano structural units on a perovskite thin film, a perovskite micro / nano laser with beam focusing function is realized.

[0054] Perovskite CsPbBr3 thin films synthesized by thermal evaporation or solution method are used as the gain medium. Meanwhile, an optical resonant cavity is realized by fabricating micro-nano structural units on the thin film. Pump light enters the cavity through optical fiber or spatial light, and optical gain is realized through the continuous domain bound state principle, and finally 532nm laser output is output.

[0055] Bound states in the continuous (BIC) are special states that remain localized and non-radiative within a continuous body. Since the refractive index of perovskite CsPbBr3 thin films is 2.3, a high refractive index difference can be formed at the material-air interface. The fabricated resonant cavity is sufficient to provide adequate feedback. Therefore, under ideal conditions, micro / nano lasers based on BICs can achieve a very high quality factor, solving the problems of high optical loss and low output power.

[0056] This invention selects micro-nano structural units with specific parameters to construct a metasurface structure with focusing function, thereby achieving laser beam focusing without the need for additional focusing lenses, and effectively reducing the size of the device while ensuring laser intensity.

[0057] The micro / nano structure unit is centered around an air pore. Figure 2 This is a top view of a micro / nano structure unit. Figure 3 This is a front view of a micro / nano structure unit, where a is the size of the micro / nano structure unit, d is the diameter of the air pore, and h is the thickness of the perovskite film.

[0058] Specifically, taking advantage of the excellent optical gain characteristics of perovskite materials, this embodiment designs a periodic air-hole crystal array to realize BIC laser and modulate it. During the design, the BIC mode is made to be in the gain range of 500-550nm of the perovskite thin film. The periodic air-hole crystal array here is a ring composed of micro and nano structure units.

[0059] In this embodiment, both the thin film and the micro / nano structure units are perovskite planar photonic crystals synthesized from perovskite materials using thermal evaporation or solution methods. Four micro / nano structure units with the same resonant frequency were selected: a = 500 nm, r = 120 nm, a = 472 nm, r = 102 nm, a = 431 nm, r = 84 nm, and a = 203 nm, r = 52 nm, where r is the radius of the air hole and a represents the size of the micro / nano structure unit. The phase corresponding to each unit was calculated, and the phase delay value at different positions was obtained based on the phase distribution information at different positions. The phase delay values ​​at different positions were matched with the micro / nano structure units that met the conditions, and the positions were discretized to complete the design of a metasurface with beam focusing function.

[0060] Based on four micro / nano structural units with the same resonant frequency, the designed metasurface has a four-layer concentric ring structure, with equally spaced air holes arranged on each ring. The radii from the center of the concentric rings to the four ring structures are 2.3 μm, 4.0 μm, 5.4 μm, and 7.5 μm, respectively. From the inner ring to the outer ring, the spacing between the air holes on each ring corresponds to the 'a' values ​​of the four unit structures, which are 500 nm, 472 nm, 431 nm, and 203 nm, respectively, with 28, 57, 78, and 231 air holes, respectively. From the inner ring to the outer ring, the radii of the air holes on each ring are 120 nm, 102 nm, 84 nm, and 52 nm, respectively.

[0061] Based on the parameters mentioned above, the laser beam is finally focused at the target focal position 50 micrometers away from the metasurface.

[0062] Example 2

[0063] In one or more embodiments, a design method for a self-focusing perovskite laser with a micro / nano cavity structure is disclosed, such as Figure 4 As shown, it includes:

[0064] Step S1: Obtain the target resonant frequency, target focusing position, and thickness of the prepared perovskite film.

[0065] Perovskite thin films are prepared by synthesizing perovskite materials using thermal evaporation or solution methods.

[0066] Step S2: Based on the target resonant frequency and target focusing position, calculate the distance between each ring and its center, as well as the parameter values ​​of the micro / nano structure units, ensuring that all micro / nano structure units have the same resonant frequency and that the parameter values ​​of the micro / nano structure units on the same ring are identical. The parameters of the micro / nano structure units include the air hole size and the micro / nano structure unit size. The specific steps are as follows:

[0067] (1) Based on the thickness of the perovskite film, the resonant frequency of the micro / nano structure unit with different parameter values ​​is calculated.

[0068] Using finite element analysis and time-domain finite difference method, the relationship between different parameter values ​​and resonant frequency is obtained; based on the relationship, the resonant frequency of different parameter values ​​is calculated.

[0069] Specifically, the structural parameters of the perovskite planar photonic crystal were calculated using finite element analysis (FEM) and the finite-difference time-domain method (FDTD): lattice size a = 576.3 nm, air hole radius r = 160 nm, perovskite film thickness h = 650 nm, and resonant wavelength 532 nm. That is, the resonant wavelength was calculated based on the air hole size, the micro / nano structure unit size, and the perovskite film thickness.

[0070] (2) Select micro / nano structure units with a resonant frequency equal to the target resonant frequency.

[0071] (3) Based on the target focusing position and the target resonant frequency, calculate the radius of different Fresnel half-wave zones to the target focusing position. The optical path difference between each adjacent Fresnel half-wave zone to the target focusing position is required to be λ / 2 or the phase difference is π. The lens phase matching of the laser at the target resonant frequency is achieved to generate focusing at the target focusing position. Select Fresnel half-wave zones that can arrange an integer number of selected micro / nano structure units as rings and obtain the distance from each ring to the center of the ring. Here, λ represents the light wavelength corresponding to the target resonant frequency.

[0072] The selection criteria for the Fresnel half-wave zone are: an integer number of structural units can be arranged on the Fresnel half-wave zone according to the parameters of the micro-nano structural units, and the micro-nano structural units arranged between two adjacent rings will not overlap.

[0073] Based on the optical path length l from different positions on the perovskite thin film to the target focusing position n Calculate the position of each Fresnel half-wave zone ring (i.e., the distance r from the ring to the center) based on the target focusing position f and the light wavelength λ corresponding to the target resonant frequency. n .

[0074] The position of the first ring should be l1 = f, and the optical path length of each subsequent ring should be l. n Available optical path Let r represent the distance from the center of each level of the ring. n , and l n There should be a relation between them. Substituting further, we can obtain the calculation formula. Where n represents the series.

[0075] (4) Select micro-nano structure units for each ring based on the position of each ring and the parameter values ​​of the micro-nano structure units that meet the conditions of the resonant frequency.

[0076] Based on the radius r of the Fresnel half-wave zone rings of different orders n Calculate the circumference of the rings and the spacing between adjacent rings; calculate the optical phase values ​​from the rings at different positions to the target focusing position, and match the optical phase values ​​at different positions with micro / nano structural units that meet the resonant frequency requirements. It is necessary to find an integer number of structural units on the half-wave zone rings that can be arranged according to the micro / nano structural unit parameters, ensuring that the micro / nano structural units arranged between adjacent rings do not overlap; discretize the positions to finally obtain the specific position of each micro / nano structural unit on each ring.

[0077] Step S3: Based on the solution results, micro / nano structural units are continuously set along a circular path on the prepared perovskite thin film.

[0078] Through the above three steps, the distance between each ring and the center, the size of the air hole, and the size of the micro / nano structure unit are obtained. Based on these parameters, micro / nano structure units are continuously set along the ring path on the prepared perovskite film to obtain a metasurface. Thus, the metasurface with the focusing delay phase function is combined with the BIC laser to realize the laser output focused beam.

[0079] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A self-focusing perovskite laser with a micro / nano cavity structure, characterized in that, The metasurface includes a multi-concentric ring structure, wherein micro-nano structural units are continuously arranged on a perovskite thin film along a ring path; The micro-nano structure unit has an air hole at its center. The regularly arranged micro-nano structure units form a BIC resonant cavity, which is used to obtain a laser beam with gain under pump light excitation and to focus the beam at the target focusing position. Specifically, based on the target resonant frequency and the target focusing position, the distance between each ring and the center and the parameter values ​​of the micro / nano structure units are set to ensure that all micro / nano structure units have the same resonant frequency and that the parameter values ​​of the micro / nano structure units on the same ring are the same. The parameters of the micro / nano structure units include the air hole size and the micro / nano structure unit size. By combining BIC micro / nano lasers made from halide perovskites with a metasurface that enables focusing, laser beams can be focused autonomously without the need for a focusing lens.

2. The self-focusing perovskite laser with a micro / nano cavity structure as described in claim 1, characterized in that, The perovskite thin film is prepared by thermal evaporation or solution synthesis of perovskite material.

3. The self-focusing perovskite laser with a micro / nano cavity structure as described in claim 1, characterized in that, The thickness of the perovskite film was set to 650 nm.

4. A self-focusing perovskite laser with a micro / nano cavity structure as described in claim 1, characterized in that, The metasurface is provided with four concentric rings; The distances between the ring and the center, from the inner ring to the outer ring, are 2.3 μm, 4.0 μm, 5.4 μm, and 7.5 μm, respectively. The dimensions of the air holes, from the inner ring to the outer ring, are 120nm, 102nm, 84nm, and 52nm, respectively. The dimensions of the micro / nano structure units, from the inner ring to the outer ring, are 500nm, 472nm, 431nm, and 203nm, respectively. The target focusing position is 50 micrometers away from the metasurface from the beam focal point.

5. A self-focusing perovskite laser with a micro / nano cavity structure as described in claim 1, characterized in that, It also includes a pump source and an isolation layer, wherein the pump source is used to generate pump light and the isolation layer serves as a substrate for the metasurface and provides support.

6. A design method for a self-focusing perovskite laser with a micro / nano cavity structure, characterized in that, Obtain the target resonant frequency, target focusing position, and thickness of the prepared perovskite film; The micro-nano structure unit has an air hole at its center. The regularly arranged micro-nano structure units form a BIC resonant cavity, which is used to obtain a laser beam with gain under pump light excitation and to focus the beam at the target focusing position. Based on the target resonant frequency and the target focusing position, the distance between each ring and the center and the parameter values ​​of the micro / nano structure units are calculated to ensure that all micro / nano structure units have the same resonant frequency and that the parameter values ​​of the micro / nano structure units on the same ring are the same. The parameters of the micro / nano structure units include the air hole size and the micro / nano structure unit size. Based on the solution results, micro-nano structural units were continuously set along a circular path on the prepared perovskite thin film; By combining BIC micro / nano lasers made from halide perovskites with a metasurface that enables focusing, laser beams can be focused autonomously without the need for a focusing lens.

7. The design method of a self-focusing perovskite laser with a micro / nano cavity structure as described in claim 6, characterized in that, The specific steps for determining the distance between each annulus and its center, as well as the parameter values ​​of the micro / nano structure units, are as follows: Based on the thickness of the perovskite thin film, the resonant frequencies of micro / nano structural units with different parameter values ​​were calculated. Select micro / nano structure units with a resonant frequency equal to the target resonant frequency; Based on the target focusing position and the target resonant frequency, calculate all Fresnel half-wave zones up to the target focusing position, select the Fresnel half-wave zones that can accommodate an integer number of selected micro / nano structure units as rings, and obtain the distance from each ring to the center of the ring; Based on the position of each ring and the parameter values ​​of the micro / nano structure units that meet the conditions for resonant frequency, micro / nano structure units are selected for each ring.

8. The design method of a self-focusing perovskite laser with a micro / nano cavity structure as described in claim 7, characterized in that, The calculation of the resonant frequency of the micro / nano structure unit with different parameter values ​​is specifically as follows: Using finite element analysis and time-domain finite difference method, the relationship between different parameter values ​​and resonant frequency is obtained; based on the relationship, the resonant frequency of different parameter values ​​is calculated.

9. The design method of a self-focusing perovskite laser with a micro / nano cavity structure as described in claim 7, characterized in that, The distance from each annulus to the center is obtained as follows: Based on the optical path length from different positions on the perovskite thin film to the target focusing position, the wavelength of light corresponding to the target focusing position and the target resonant frequency, the position of each ring, i.e. the distance from the ring to the center, is calculated.

10. The design method of a self-focusing perovskite laser with a micro / nano cavity structure as described in claim 7, characterized in that, The selection of micro / nano structural units for each ring is specifically as follows: The optical phase values ​​from the ring at different positions to the target focusing position are calculated. The optical phase values ​​at different positions are matched with micro / nano structural units whose resonant frequencies meet the conditions. The positions are discretized to obtain the specific position of each micro / nano structural unit on each ring.