Design method of multi-focal superlens with controllable focal energy

Abstract

The application relates to a design method of a multi-focal superlens with controllable focal point energy. The method comprises the following steps: designing a basic super atom: determining the number of phase division levels of the superlens and corresponding parameters of the basic super atom; designing a phase distribution of the multi-focal superlens: according to a superlens phase distribution formula, the number of focal lengths, the size of the focal length, the size of the super atom array, and the energy proportion of the multi-focal length, the phase distribution of the multi-focal superlens is designed; and arranging the basic super atom: the multi-focal superlens is designed according to the phase distribution of the multi-focal superlens and the arrangement of the basic super atom. According to the designed focal point energy proportion, the phase information of the corresponding focal point is alternately obtained, the obtained phase information is arranged by using a ring algorithm, the phase distribution of the multi-focal superlens is obtained, the basic super atom is arranged, and the multi-focal superlens is designed. Meanwhile, the focusing ability of the focal points with different focal lengths can be controlled by controlling the focal point energy proportion.

Description

Technical Field

[0001] This invention relates to the fields of micro-nano optics and novel display devices, and in particular to a design method for a multifocal length superlens with controllable focal energy. Background Technology

[0002] Lenses are widely used in optical devices such as medical imaging, 3D display devices, CCDs, and projectors. Traditional lenses have only one focal length, making it impossible to simultaneously and clearly capture information about different depths of an object in display systems like medical imaging and 3D displays. Common methods for traditional lenses to simultaneously and clearly capture information about different depths include: First, splitting a single-layer microlens array into a complementary symmetric double-layer microlens array, with each layer being half the size of the original array and responsible for focusing on a central depth plane. While this method can capture information about different depths simultaneously, the display resolution is halved because each layer is half the size of the original single-layer array. Second, using high-precision, high-speed displacement equipment to move the microlens array, allowing the system to capture multiple central depth planes. This method relies on the high-speed movement of the displacement equipment, requiring high precision and incurring high costs. Third, post-processing the images acquired by the microlens array to clearly display information about different depths. This method requires high image processing capabilities and a high-performance image processor.

[0003] Superlenses are novel display devices with subwavelength dimensions, possessing advantages such as high design freedom, ease of integration, and wide application range, making them a significant contributor to information display. The phase distribution of a superlens can be freely controlled, allowing a single lens to have multiple focal points. Many methods exist for designing multifocal / multi-focus superlenses, such as the dynamic multifocal superlens of CN109270606A. This involves using multilayer graphene in the substrate to construct a reflective focusing lens and dynamically adjusting the focal point position by changing the Fermi level of the graphene. While this achieves dynamic control, the subwavelength structure of the superlens results in a very small size. The multilayer graphene structure requires high processing precision and relies on adjusting the Fermi level of the graphene substrate, limiting the range of superlens materials that can be selected. While CN115542437A can achieve vertical dual focal points, its basic superatom structural units use a 1:1 embedded ratio, increasing the processing difficulty. Summary of the Invention

[0004] The purpose of this invention is to provide a design method for a multifocal length superlens with controllable focal energy. This method involves alternately acquiring the phase information of corresponding focal points based on a designed focal energy ratio, and then arranging the acquired phase information using a ring algorithm to obtain the phase distribution of the multifocal length superlens. The multifocal length superlens can then be designed by arranging basic metaatoms based on the obtained phase distribution. Furthermore, the focusing capability of focal points at different focal lengths can be controlled by adjusting the focal energy ratio. This invention's multifocal length superlens has no specific material requirements, does not have a multilayer structure, and has a relatively simple design process and manufacturing process.

[0005] To achieve the above objectives, the technical solution of the present invention is: a design method for a multifocal length superlens with controllable focal energy, wherein the multifocal length superlens simultaneously has n focal points, and the energy of each focal point is controlled by the arrangement of superatoms. The design method of the multifocal length superlens includes the following steps:

[0006] (1) Design of basic superatoms: Determine the number of levels of phase division of the superlens and the corresponding basic superatoms, including cell period, cross-sectional shape, size, and material parameters;

[0007] (2) Design the phase distribution of the multifocal superlens: Based on the superlens phase distribution formula and the number of focal lengths, focal lengths, size of the superatomic array, and energy ratio of the multifocal superlens, design the phase distribution of the multifocal superlens.

[0008] (3) Arrange basic superatoms: Arrange basic superatoms according to the phase distribution of the multifocal superlens to form a superatomic array to obtain a multifocal superlens.

[0009] In one embodiment of the present invention, the phase distribution design of the multifocal length superlens is as follows:

[0010] 1) Determine the number of focal points n and the corresponding focal lengths f1 to f2. n The focal energy ratio E1:E2:…:E n The number of rows and columns of the superatomic array; where n, E1, E2, ..., E n All are positive integers; the number of rows and columns of the superatomic array are the same, and the value is N, where N is a non-zero positive even number;

[0011] 2) When all n focal lengths are unequal, the phase distribution Φ of these n focal points is calculated using the superlens phase distribution formula (1). n :

[0012]

[0013] Where, λ d f is the center wavelength at which a single-focus superlens operates. n For the focal length of a single-focus superlens, rn f is the distance from a point in the nth monofocal superlens to the center of the monofocal superlens, where n is a positive integer; when n is different, f n They are also different, and satisfy f1>f2>...>f n ;

[0014] 3) with (E1+E2+…+E n The process involves periodically acquiring the phases corresponding to n foci, and then using a circular algorithm to reorder these phases based on the foci energy ratios E1:E2:…:E n By rearranging the elements, the phase distribution of the multifocal superlens can be obtained.

[0015] In one embodiment of the present invention, the number of levels of phase division of the superlens refers to the number of levels into which the superlens divides the angle (0° to 360°) of incident light deflection into incident light, with each level corresponding to a basic superatom.

[0016] In one embodiment of the present invention, the period p of the basic superatomic unit cell should satisfy formula (2):

[0017]

[0018] Where p is the cell period of the superatom, λ d NA is the center wavelength at which the single-focus superlens operates, and NA is the numerical aperture of the superlens; the superatomic size should be smaller than the cell period p.

[0019] In one embodiment of the present invention, the shape of the basic superatomic cross-section is circular, elliptical, square, rectangular, or irregular; the material of the superatomic includes silicon, silicon dioxide, silicon nitride, titanium dioxide, graphene, etc.

[0020] In one embodiment of the present invention, in the phase distribution of the multifocal superlens, the number of focal points n and the number of rows and columns of the superatomic array must maintain a predetermined constraint relationship, that is, these n focal points respectively require at least n1×n1, n2×n2, ..., n n ×n n Only a superatomic array can achieve a phase distribution with a single phase period, therefore the size of N should be: N≥(n1+n2+...+n n ).

[0021] In one embodiment of the present invention, in the phase distribution of the multifocal superlens, alternately acquiring the phases corresponding to n focal points means, according to the focal energy ratio E1:E2:…:E n Sequentially, acquire the E1 ring data of the focal phase distribution from 1 to E1 for focal length f1, the E2 ring data of the focal phase distribution from (1+E1) to (E1+E2) for focal length f2, and so on, for focal length f...n The focal phase distribution is (1+E1+E2+…+E) n-1 )~(E1+E2+…+E n E n A ring of data;

[0022] The ring data refers to the decomposition of the phase distribution of the superlens into an N×N matrix with a cell period of p. The phase corresponding to each element can be represented by the phase level of the basic unit closest to that described in claim 3. The first ring consists of the first row, the Nth column, the Nth row, and the first column of the phase distribution. The second ring consists of the second row, the (N-1)th column, the (N-1)th row, and the second column of the phase distribution, removing the parts that are the same as the first ring. The third ring consists of the third row, the (N-2)th column, the (N-2)th row, and the third column of the phase distribution, removing the parts that are the same as the first and second rings. ... The N / 2th ring consists of the N / 2th row, the (1+N / 2)th column, the (1+N / 2)th row, and the N / 2th column of the phase distribution, removing the parts that are the same as the first, second, ..., ((N / 2)-1)th rings.

[0023] In one embodiment of the present invention, the phase distribution of the multifocal superlens is achieved by using a ring algorithm to alternately acquire the phases corresponding to n focal points according to the focal energy ratio E1:E2:…:E n Rearrangement refers to using a ring algorithm to quickly rearrange the E1 ring data of the focal phase distribution with focal length f1 (1 to E1), the E2 ring data of the focal phase distribution with focal length f2 (1+E1) to (E1+E2), ..., and the ring data with focal length f n The focal phase distribution is (1+E1+E2+…+E) n-1 )~(E1+E2+…+E n E n The ring data are arranged sequentially as the E1 ring data of the phase of the multifocal telescope from E1 to E1, the E2 ring data of (1+E1) to (E1+E2), ..., the E1 ring data of (1+E1+E2+...+E1)-E2 ... n-1 )~(E1+E2+…+E n E n A ring of data, thus, based on the focal energy ratio E1:E2:…:E n Rearrange these n focal lengths from f1 to f n The corresponding phase of the superlens.

[0024] In one embodiment of the present invention, the phase distribution of the multifocal superlens is such that (E1+E2+…+E…) n The period refers to the process of using a circular algorithm to alternately acquire the phases corresponding to n focal points according to the focal energy ratio E1:E2:…:E nRearranged as f1~f n After the corresponding phase of the superlens, the remaining N / 2 - (E1 + E2 + ... + E n The ring data will continue in (E1+E2+…+E) n The phase distribution of claim 8 is arranged in a periodic repeating pattern, thereby obtaining the phase distribution of the multifocal superlens.

[0025] In one embodiment of the present invention, the arrangement of basic superatoms refers to arranging the basic superatoms that divide the phase of the superlens into corresponding phase levels according to claim 9 in the phase distribution of the multifocal superlens, thereby designing a multifocal superlens.

[0026] Compared to existing technologies, this invention offers the following advantages: This invention only requires alternating acquisition of phase information of corresponding focal points based on the designed focal energy ratio, and then using a ring algorithm to arrange the obtained phase information to obtain the phase distribution of the multifocal length superlens. Based on the obtained phase distribution of the multifocal length superlens, basic superatoms can be arranged to design the multifocal length superlens. Simultaneously, by controlling the focal energy ratio, the focusing capability of focal points at different focal lengths can be controlled. The multifocal length superlens of this invention has no specific material requirements, does not have a multilayer structure, and its design process and manufacturing process are relatively simple. Attached Figure Description

[0027] Figure 1 These are schematic diagrams of the superatomic structures of the first, second, and third embodiments provided by the present invention;

[0028] Figure 2 These are schematic diagrams of the 18 basic superatoms in the first, second, and third embodiments provided by this invention;

[0029] Figure 3 These are phase distribution diagrams of a single-focus superlens with f1 = 10 μm provided in the first, second, and third embodiments of the present invention;

[0030] Figure 4 These are phase distribution diagrams of a single-focus superlens with f2 = 5μm provided in the first, second, and third embodiments of the present invention;

[0031] Figure 5 This is a phase distribution diagram of a multifocal superlens provided in the first embodiment of the present invention;

[0032] Figure 6 This is a schematic diagram of a multifocal superlens according to the first embodiment of the present invention;

[0033] Figure 7 This is a focal electric field intensity distribution diagram of the first embodiment provided by the present invention;

[0034] Figure 8 This is a phase distribution diagram of a multifocal superlens provided in the second embodiment of the present invention;

[0035] Figure 9 This is a schematic diagram of a multifocal superlens according to the second embodiment of the present invention;

[0036] Figure 10 This is a focal electric field intensity distribution diagram of the second embodiment provided by the present invention;

[0037] Figure 11 This is a phase distribution diagram of a multifocal superlens provided in the third embodiment of the present invention;

[0038] Figure 12 This is a schematic diagram of a multifocal superlens according to the third embodiment of the present invention;

[0039] Figure 13 This is a focal electric field intensity distribution diagram of the third embodiment provided by the present invention.

[0040] Figure 14 This is a flowchart of the method of the present invention. Detailed Implementation

[0041] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0042] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below through specific embodiments and related drawings. Here, the reference figures are schematic diagrams of idealized embodiments of the invention. The embodiments of the invention should not be considered limited to the specific shapes of the regions shown in the figures, but rather include the obtained shapes, such as those caused by manufacturing deviations. In this embodiment, superatomic cross-sections are represented by rectangles. The representations in the figures are schematic and should not be considered as limiting the scope of the invention. The size of the superatomic pattern in this embodiment has a certain range. In actual production, the size of the superatomic pattern can be designed according to actual needs. The values ​​of parameters such as the period, length, width, and height of the superatomic unit cell, and the proportion of the phase distribution of multiple alternating single foci in the embodiment are only schematic values ​​and should not be considered as limiting the scope of the invention.

[0043] like Figure 14 As shown, this invention provides a design method for a multifocal-length superlens with controllable focal energy. The multifocal-length superlens simultaneously has n focal points, and the energy of each focal point is controlled by the arrangement of superatoms. The design method of the multifocal-length superlens includes the following steps:

[0044] (1) Design of basic superatoms: Determine the number of levels of phase division of the superlens and the corresponding basic superatoms, such as cell period, cross-sectional shape, size, and material parameters;

[0045] (2) Design the phase distribution of the multifocal superlens: Based on the superlens phase distribution formula and the number of focal lengths, focal lengths, size of the superatomic array, and energy ratio of the multifocal superlens, design the phase distribution of the multifocal superlens.

[0046] (3) Arrangement of basic superatoms: Based on the phase distribution of the multifocal superlens, basic superatoms are arranged to form a superatom array, which can be used to design a multifocal superlens.

[0047] The phase distribution of the multifocal length superlens mentioned above refers to:

[0048] 1) Determine the number of focal points n and the corresponding focal lengths f1 to f2. n The focal energy ratio E1:E2:…:E n The number of rows and columns of the superatomic array is N. Where n, E1, E2, ..., E... n All are positive integers; the number of rows and columns of the superatomic array is the same, and the value is N, where N is a non-zero positive even number.

[0049] 2) When all n focal lengths are unequal, the phase distribution Φ of these n focal points is calculated using the superlens phase distribution formula (formula (1)). n .

[0050]

[0051] Where, λ d f is the center wavelength at which a single-focus superlens operates. n For the focal length of a single-focus superlens, r n f is the distance from a point on the nth monofocal superlens to the center of the monofocal superlens, where n is a positive integer; when n is different, f n They are also different, and satisfy f1>f2>...>f n .

[0052] 3) with (E1+E2+…+E n The process involves periodically acquiring the phases corresponding to n foci, and then using a circular algorithm to transfer these phases according to the foci energy ratios E1:E2:…:E n By rearranging the elements, the phase distribution of the multifocal superlens can be obtained.

[0053] The number of levels of phase division of the superlens refers to the number of levels into which the superlens divides the angle (0° to 360°) of incident light deflection into incident light. Each level corresponds to a basic superatom.

[0054] The superatomic cell period p should satisfy formula (2):

[0055]

[0056] Where p is the cell period of the superatom, λ d NA is the center wavelength at which the superlens operates, and NA is the numerical aperture of the superlens.

[0057] The superatomic size should be smaller than the cell period p.

[0058] The shape of the superatomic cross section can be circular, elliptical, square, rectangular, or irregular; the material of the superatom can be silicon, silicon dioxide, silicon nitride, titanium dioxide, graphene, etc.

[0059] The phase distribution of the multifocal superlens described herein requires a certain constraint relationship between the number of focal points n and the number of rows and columns N of the superatomic array. For example, these n focal points must respectively require at least n1×n1, n2×n2, ..., n n ×n n Only superatomic arrays can achieve a phase distribution with a single phase period, therefore the size of N should be: N≥(n1+n2+...+n n ).

[0060] The phase distribution of the multifocal superlens design, wherein alternatingly acquiring the phase corresponding to n focal points means, according to the focal energy ratio E1:E2:…:E n Sequentially, acquire the E1 ring data of the focal phase distribution from 1 to E1 for focal length f1, the E2 ring data of the focal phase distribution from (1+E1) to (E1+E2) for focal length f2, and so on, for focal length f... n The focal phase distribution is (1+E1+E2+…+E) n-1 )~(E1+E2+…+E n E n A ring of data.

[0061] The aforementioned ring data refers to the decomposition of the phase distribution of the superlens into an N×N matrix with a cell period of p. The phase corresponding to each element can be represented by the phase level of the basic unit closest to that described in claim 3. The first ring consists of the first row + the Nth column + the Nth row + the first column of the phase distribution. The second ring consists of the second row + the (N-1)th column + the (N-1)th row + the second column of the phase distribution (removing the part that is the same as the first ring). The third ring consists of the third row + the (N-2)th column + the (N-2)th row + the third column of the phase distribution (removing the part that is the same as the first and second rings). ... The N / 2th ring consists of the N / 2th row + the (1+N / 2)th column + the (1+N / 2)th row + the N / 2th column of the phase distribution (removing the part that is the same as the first, second, ..., ((N / 2)-1)th rings).

[0062] The phase distribution of the multifocal superlens described herein is wherein these phases are determined according to the focal energy ratio E1:E2:…:E n Rearrangement refers to using a circular algorithm to quickly rearrange the obtained circular data of focal length f1 (1 to E1), focal length f2 (1+E1) to (E1+E2), and so on, until the focal length is f... n The focal phase distribution is (1+E1+E2+…+E) n-1 )~(E1+E2+…+E n E n The ring data are arranged sequentially as the E1 ring data of the phase of the multifocal telescope from E1 to E1, the E2 ring data of (1+E1) to (E1+E2), ..., the E1 ring data of (1+E1+E2+...+E1)-E2 ... n-1 )~(E1+E2+…+E n E n A ring of data, thus, based on the focal energy ratio E1:E2:…:E n Rearrange these n focal lengths from f1 to f n The corresponding phase of the superlens.

[0063] The phase distribution of the multifocal superlens design is described, wherein (E1+E2+…+E n The period refers to the periodicity of the energy distribution according to the focal energy ratio E1:E2:…:E. n Rearrange these n focal lengths from f1 to f n After the corresponding phase of the superlens, the remaining N / 2 - (E1 + E2 + ... + E n The ring data will continue in (E1+E2+…+E) n The phase distribution of claim 8 is arranged in a periodic repeating pattern, thereby obtaining the phase distribution of the multifocal superlens.

[0064] The aforementioned arrangement of basic superatoms refers to arranging the basic superatoms of corresponding phase levels according to the phase distribution of the multifocal superlens, thereby designing a multifocal superlens.

[0065] Example 1:

[0066] like Figure 1The diagram below shows the superatom structure of Example 1. In this example, the number of phase division levels of the superlens is first set to 18. Then, the cross-sectional shape of the superatom is designed to be rectangular, and 18 basic superatoms responsible for different phase levels are obtained by rotating the superatom. Next, the number of multifocal distances is set to 2, and the phase distribution of the bifocal superlens is designed using a ring algorithm. Finally, the 18 basic superatoms of phase levels are arranged according to the phase distribution of the bifocal superlens to obtain the bifocal superlens.

[0067] The following is a further description of the first embodiment of the present invention, a multifocal length superlens with controllable focal energy and its design method;

[0068] A design method for a multifocal length superlens with controllable focal energy includes the following steps:

[0069] (S11) Design of basic superatoms

[0070] First, the angle (0° to 360°) at which the incident light rays are deflected by the superlens is divided into 18 levels: (0°, 20°], (20°, 40°], (40°, 60°], (60°, 80°], (80°, 100°], (100°, 120°], (120°, 140°], (140°, 160°], (160°, 180°], (180°, 200°], (200°, 220°], (220°, 240°], (240°, 260°], (260°, 280°], (280°, 300°], (300°, 320°], (320°, 340°], and (340°, 360°).

[0071] Then, the superatomic material was selected as α-Si, and the substrate material was selected as fused silica, such as... Figure 1 The diagram shows a superatomic structure. The superatomic cross-section is rectangular, the cell period is p = 200 nm, the substrate height is h = 20 nm, and the superatomic height is h1 = 300 nm, width is w = 35 nm, and length is l = 135 nm.

[0072] Finally, by rotating superatoms, as shown in the figure Figure 2The 18 basic superatoms shown are numbered from "17" to "0". According to the geometric phase shift principle, the angle at which a superatom deflects the incident light is twice the angle at which the superatom rotates. For example, if a superlens needs to deflect the incident light by 20°, it is only necessary to rotate the superatom by 10°. Thus, the superatoms numbered "17" to "0" are obtained by rotating the original superatoms by 5°, 15°, 25°, 35°, 45°, 55°, 65°, 75°, 85°, 95°, 105°, 115°, 125°, 135°, 145°, 155°, 165°, and 175°, respectively. They can deflect the incident light by 10°, 30°, 50°, 70°, 90°, 110°, 130°, 150°, 170°, 190°, 210°, 230°, 250°, 270°, 290°, 310°, 330°, and 350°, respectively, and are responsible for the 18 levels of incident light deflection to be achieved.

[0073] (S12) Design the phase distribution of a multifocal superlens

[0074] This embodiment designs a bifocal superlens with n=2, focal lengths f1=10μm and f2=5μm respectively, focal energy ratio E1:E2:=1:1, and N=46.

[0075] First, substitute f1 = 10 μm and f2 = 5 μm into the superlens phase distribution formula, respectively; then, decompose the superlens phase distribution into a 46×46 matrix with a cell period of p = 200 nm. The phase corresponding to each element is represented by the phase level of the closest basic unit as described in (S11), resulting in the following... Figure 3 The phase distribution code diagram of a single-focus superlens with f1 = 10μm is shown below. Figure 4 The diagram shows the phase distribution code of a single-focus superlens with f2 = 5μm. Finally, based on the focal energy ratio E1:E2: = 1:1, the phase information of rings 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, and 23 of f1 = 10μm and the phase information of rings 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, and 22 (divisible by (1+1)) of f2 = 5μm are alternately acquired. The phase of the bifocal superlens is then arranged using a ring algorithm to obtain the following... Figure 5 The phase distribution diagram of the bifocal superlens is shown.

[0076] (S13) Arrangement of basic superatoms

[0077] The phase distribution diagram of the bifocal superlens obtained from (S12) is arranged with superatoms "17" to "0", which can then be used to obtain the following... Figure 6 The superatom array shown is illustrated. Simulations yielded the focal section of the bifocal superlens in the xy direction and the point spread function of the bifocal superlens, as shown below. Figure 7 As shown. In this embodiment, when the energy ratio of the dual focal points E1:E2:=1:1 is controlled, the maximum energy values ​​of the focal points f1=10μm and f2=5μm are 2.7V / m and 4.9V / m, respectively. The maximum electric field strength of the f1=10μm focal point is smaller than that of the f2=5μm focal point.

[0078] Thus, a multifocal length superlens with controllable focal energy and its design method have been formed.

[0079] Example 2:

[0080] like Figure 1 The diagram below shows the superatom structure of Example 1. In this example, the number of phase division levels of the superlens is first set to 18. Then, the cross-sectional shape of the superatom is designed to be rectangular, and 18 basic superatoms responsible for different phase levels are obtained by rotating the superatom. Next, the number of multifocal distances is set to 2, and the phase distribution of the bifocal superlens is designed using a ring algorithm. Finally, the 18 basic superatoms of phase levels are arranged according to the phase distribution of the bifocal superlens to obtain the bifocal superlens.

[0081] The following is a further description of the first embodiment of the present invention, a multifocal length superlens with controllable focal energy and its design method;

[0082] A design method for a multifocal length superlens with controllable focal energy includes the following steps:

[0083] (S21) Design of basic superatoms

[0084] First, the angle (0° to 360°) at which the incident light rays are deflected by the superlens is divided into 18 levels: (0°, 20°], (20°, 40°], (40°, 60°], (60°, 80°], (80°, 100°], (100°, 120°], (120°, 140°], (140°, 160°], (160°, 180°], (180°, 200°], (200°, 220°], (220°, 240°], (240°, 260°], (260°, 280°], (280°, 300°], (300°, 320°], (320°, 340°], and (340°, 360°).

[0085] Then, the superatomic material was selected as α-Si, and the substrate material was selected as fused silica, such as... Figure 1 The diagram shows a superatomic structure. The superatomic cross-section is rectangular, the cell period is p = 200 nm, the substrate height is h = 20 nm, and the superatomic height is h1 = 300 nm, width is w = 35 nm, and length is l = 135 nm.

[0086] Finally, by rotating superatoms, as shown in the figure Figure 2 The 18 basic superatoms shown are numbered from "17" to "0". According to the geometric phase shift principle, the angle at which a superatom deflects the incident light is twice the angle at which the superatom rotates. For example, if a superlens needs to deflect the incident light by 20°, it is only necessary to rotate the superatom by 10°. Thus, the superatoms numbered "17" to "0" are obtained by rotating the original superatoms by 5°, 15°, 25°, 35°, 45°, 55°, 65°, 75°, 85°, 95°, 105°, 115°, 125°, 135°, 145°, 155°, 165°, and 175°, respectively. They can deflect the incident light by 10°, 30°, 50°, 70°, 90°, 110°, 130°, 150°, 170°, 190°, 210°, 230°, 250°, 270°, 290°, 310°, 330°, and 350°, respectively, and are responsible for the 18 levels of incident light deflection to be achieved.

[0087] (S22) Design the phase distribution of a multifocal superlens

[0088] This embodiment designs a bifocal superlens with n=2, focal lengths f1=10μm and f2=5μm respectively, focal energy ratio E1:E2:=2:1, and N=46.

[0089] First, substitute f1 = 10 μm and f2 = 5 μm into the superlens phase distribution formula, respectively; then, decompose the superlens phase distribution into a 46×46 matrix with a cell period of p = 200 nm. The phase corresponding to each element is represented by the phase level of the closest basic unit as described in (S11), resulting in the following... Figure 3 The phase distribution code diagram of a single-focus superlens with f1 = 10μm is shown below. Figure 4 The diagram shows the phase distribution code of a single-focus superlens with f2 = 5μm. Finally, based on the focal energy ratio E1:E2: = 2:1, the phase information of rings 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, and 23 of f1 = 10μm and the phase information of rings 3, 6, 9, 12, 15, 18, and 21 (divisible by (2+1)) of f2 = 5μm are alternately obtained. The phase of the bifocal superlens is then arranged using a ring algorithm to obtain the following... Figure 8 The phase distribution diagram of the bifocal superlens is shown.

[0090] (S23) Arrangement of basic superatoms

[0091] The phase distribution diagram of the bifocal superlens obtained from (S22) is arranged with superatoms "17" to "0", which can then be used to obtain the following... Figure 9The superatom array shown is illustrated. Simulations yielded the focal section of the bifocal superlens in the xy direction and the point spread function of the bifocal superlens, as shown below. Figure 10 As shown. In this embodiment, when the energy ratio of the dual focal points E1:E2:=2:1 is controlled, the maximum energy values ​​of the focal points f1=10μm and f2=5μm are 3.5V / m and 3.9V / m, respectively. The maximum electric field strength of the f1=10μm focal point is approximately the same as that of the f2=5μm focal point.

[0092] Thus, a multifocal length superlens with controllable focal energy and its design method have been formed.

[0093] Example 3:

[0094] like Figure 1 The diagram below shows the superatom structure of Example 1. In this example, the number of phase division levels of the superlens is first set to 18. Then, the cross-sectional shape of the superatom is designed to be rectangular, and 18 basic superatoms responsible for different phase levels are obtained by rotating the superatom. Next, the number of multifocal distances is set to 2, and the phase distribution of the bifocal superlens is designed using a ring algorithm. Finally, the 18 basic superatoms of phase levels are arranged according to the phase distribution of the bifocal superlens to obtain the bifocal superlens.

[0095] The following is a further description of the first embodiment of the present invention, a multifocal length superlens with controllable focal energy and its design method;

[0096] A design method for a multifocal length superlens with controllable focal energy includes the following steps:

[0097] (S31) Design of basic superatoms

[0098] First, the angle (0° to 360°) at which the incident light rays are deflected by the superlens is divided into 18 levels: (0°, 20°], (20°, 40°], (40°, 60°], (60°, 80°], (80°, 100°], (100°, 120°], (120°, 140°], (140°, 160°], (160°, 180°], (180°, 200°], (200°, 220°], (220°, 240°], (240°, 260°], (260°, 280°], (280°, 300°], (300°, 320°], (320°, 340°], and (340°, 360°).

[0099] Then, the superatomic material was selected as α-Si, and the substrate material was selected as fused silica, such as... Figure 1The diagram shows a superatomic structure. The superatomic cross-section is rectangular, the cell period is p = 200 nm, the substrate height is h = 20 nm, and the superatomic height is h1 = 300 nm, width is w = 35 nm, and length is l = 135 nm.

[0100] Finally, by rotating superatoms, as shown in the figure Figure 2 The 18 basic superatoms shown are numbered from "17" to "0". According to the geometric phase shift principle, the angle at which a superatom deflects the incident light is twice the angle at which the superatom rotates. For example, if a superlens needs to deflect the incident light by 20°, it is only necessary to rotate the superatom by 10°. Thus, the superatoms numbered "17" to "0" are obtained by rotating the original superatoms by 5°, 15°, 25°, 35°, 45°, 55°, 65°, 75°, 85°, 95°, 105°, 115°, 125°, 135°, 145°, 155°, 165°, and 175°, respectively. They can deflect the incident light by 10°, 30°, 50°, 70°, 90°, 110°, 130°, 150°, 170°, 190°, 210°, 230°, 250°, 270°, 290°, 310°, 330°, and 350°, respectively, and are responsible for the 18 levels of incident light deflection to be achieved.

[0101] (S32) Design the phase distribution of a multifocal superlens

[0102] This embodiment designs a bifocal superlens with n=2, focal lengths f1=10μm and f2=5μm respectively, focal energy ratio E1:E2:=3:1, and N=46.

[0103] First, substitute f1 = 10 μm and f2 = 5 μm into the superlens phase distribution formula, respectively; then, decompose the superlens phase distribution into a 46×46 matrix with a cell period of p = 200 nm. The phase corresponding to each element is represented by the phase level of the closest basic unit as described in (S11), resulting in the following... Figure 3 The phase distribution code diagram of a single-focus superlens with f1 = 10μm is shown below. Figure 4 The diagram shows the phase distribution code of a single-focus superlens with f2 = 5μm. Finally, based on the focal energy ratio E1:E2: = 3:1, the phase information of rings 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, and 23 of f1 = 10μm and the phase information of rings 4, 8, 12, 16, and 20 (divisible by (3+1)) of f2 = 5μm are alternately obtained. The phase of the bifocal superlens is then arranged using a ring algorithm to obtain the following... Figure 11 The phase distribution diagram of the bifocal superlens is shown.

[0104] (S33) Arrangement of basic superatoms

[0105] The phase distribution diagram of the bifocal superlens obtained from (S32) is arranged with superatoms numbered "17" to "0", which yields the following result: Figure 12 The superatom array shown is illustrated. Simulations yielded the focal section of the bifocal superlens in the xy direction and the point spread function of the bifocal superlens, as shown below. Figure 13 As shown. In this embodiment, when the energy ratio of the dual focal points E1:E2:=3:1 is controlled, the maximum focusing energy of the focal points f1=10μm and f2=5μm are 4.4V / m and 2.6V / m, respectively, and the maximum electric field strength of the f1=10μm focal point is greater than that of the f2=5μm focal point.

[0106] Thus, a multifocal length superlens with controllable focal energy and its design method have been formed.

[0107] The multifocal length superlens with controllable focal energy and its design method provided by the present invention are not limited to the above embodiments. The above preferred embodiments further illustrate the purpose, technical solution and advantages of the present invention. It should be understood 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, improvements, etc. made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for a multifocal length superlens with controllable focal energy, characterized in that, The multifocal-length superlens has n focal points, and the energy of each focal point is controlled by the arrangement of superatoms. The design method of the multifocal-length superlens includes the following steps: (1) Design of basic superatoms: Determine the number of levels of phase division for the superlens and their corresponding basic superatoms, including cell period, cross-sectional shape, size, and material parameters; specifically, The phase angle of the incident light from the superlens is divided into M phase levels from 0° to 360°, where M is an integer ≥ 2. A basic superatom is designed for each phase level, and the cell period p, cross-sectional shape, cross-sectional size and height of each basic superatom are determined. in , λ d The central operating wavelength is NA, where NA is the numerical aperture of the superlens, and the basic superatom occupies a size smaller than p. (2) Design of the phase distribution of the multifocal superlens: Based on the superlens phase distribution formula and the number of focal lengths, focal lengths, size of the superatomic array, and energy ratio of the multifocal superlens, the phase distribution of the multifocal superlens is designed; specifically, Determine the number of focal points n and their corresponding focal lengths f1 to f2. n Focal energy ratio E1:E2:…:E n The number of rows and columns of the superatomic array; Where n, E1, E2, ..., E n All are positive integers; the number of rows and columns of the superatomic array are the same, and the value is N, where N is a non-zero positive even number; When all n focal lengths are unequal, the phase distribution Φ of these n focal points can be calculated using the superlens phase distribution formula (1). n : （1） Among them, f n For the focal length of a single-focus superlens, r n f is the distance from a point in the nth monofocal superlens to the center of the monofocal superlens, where n is a positive integer; when n is different, f n They are also different, and satisfy... ; The phase distribution of each focus is quantized to the M phase levels of step (1) to obtain the quantized phase distribution of each focus; Each quantized phase distribution is decomposed into ring data from the first ring to the N / 2th ring using an N×N matrix, and elements that are repeated with the inner ring are removed. With (E1+E2+ … +E n The period is defined by the focal energy ratio E1:E2:…:E n Sequentially, acquire the E1th ring data of the focal phase distribution with focal length f1 (1 to E1), the E2th ring data of the focal phase distribution with focal length f2 (1+E1) to (E1+E2), and so on, until the focal length is f n The focal phase distribution is (1 + E1 + E2 + ... + E) n-1 )~ (E1+E2+…+E n E n The data is collected in a ring, and a ring algorithm is used to alternately acquire the phases corresponding to n focal points according to the focal energy ratio E1:E2:…:E n By rearranging the elements, the phase distribution of the multifocal superlens can be obtained. (3) Arrangement of basic superatoms: Based on the phase distribution of the multifocal superlens, basic superatoms are arranged to form a superatom array to obtain a multifocal superlens; specifically, The quantized phase level corresponding to each array unit in the multi-focal phase distribution obtained in step (2) is mapped to the basic superatoms of the corresponding phase level in step (1), and arranged according to the position of the phase distribution to form a basic superatomic array, forming an array with n foci, and the energies of each foci are in the order E1:E2:…:E n Controlled multifocal distance superlens.

2. The design method of a multifocal length superlens with controllable focal energy according to claim 1, characterized in that, The basic superatomic cross-section has a circular, elliptical, square, rectangular, or irregular shape; the superatomic material includes silicon, silicon dioxide, silicon nitride, titanium dioxide, or graphene.

3. The design method of a multifocal length superlens with controllable focal energy according to claim 1, characterized in that, In the phase distribution of the multifocal superlens, the number of focal points n and the number of rows and columns of the superatomic array must maintain a predetermined constraint relationship, that is, these n focal points must respectively require at least n1×n1, n2×n2, ..., n n ×n n Only a superatomic array can achieve a phase distribution with a single phase period, so the size of N should be: .

4. The design method of a multifocal length superlens with controllable focal energy according to claim 1, characterized in that, The ring data refers to the decomposition of the phase distribution of the superlens into an N × N matrix with a cell period of p. The phase corresponding to each element is represented by the closest phase level. The first ring consists of the first row, the Nth column, the Nth row, and the first column of the phase distribution. The second ring consists of the second row, the (N-1)th column, the (N-1)th row, and the second column of the phase distribution, removing the parts that are the same as the first ring. The third ring consists of the third row, the (N-2)th column, the (N-2)th row, and the third column of the phase distribution, removing the parts that are the same as the first and second rings. ... The N / 2th ring consists of the N / 2th row, the (1+N / 2)th column, the (1+N / 2)th row, and the N / 2th column of the phase distribution, removing the parts that are the same as the first, second, ..., and ((N / 2)-1)th rings.

5. The design method of a multifocal length superlens with controllable focal energy according to claim 4, characterized in that, In the phase distribution of the multifocal superlens, a ring algorithm is used to alternately acquire the phases corresponding to n focal points according to the focal energy ratio E1:E2:…:E n Rearrangement refers to using a circular algorithm to quickly rearrange the obtained circular data of focal length f1 (1 to E1), focal length f2 (1+E1) to (E1+E2), and so on, until the focal length is f... n The focal phase distribution is (1 + E1 + E2 + ... + E) n-1 )~ (E1+E2+…+E n E n The ring data are arranged sequentially as the E1 ring data of the phase of the multifocal length superlens from E1 to E1, the E2 ring data of (1+E1) to (E1+E2), ..., the E1 ring data of (1+E1+E2+...+E1) to E2. n-1 ) ~ (E1+E2+…+E n E n A ring of data, therefore, based on the focal energy ratio E1:E2:…:E n Rearrange these n focal lengths to f1 ~ f n The corresponding phase of the superlens.

6. The design method of a multifocal length superlens with controllable focal energy according to claim 5, characterized in that, In the phase distribution of the multifocal superlens, (E1+E2+…+E…) n The period refers to the process of alternately acquiring the phases corresponding to n focal points using a circular algorithm, based on the focal energy ratio E1:E2:…:E… n Rearranged as f1 ~ f n After the corresponding phase of the superlens, the remaining N / 2 - (E1 + E2 + ... + E n The ring data will continue in (E1+E2+…+E) n The phase distribution of the multifocal lens is arranged in a periodic repeating pattern, thereby obtaining the phase distribution of the multifocal lens.

7. The design method of a multifocal length superlens with controllable focal energy according to claim 6, characterized in that, The arrangement of basic superatoms refers to arranging the basic superatoms corresponding to the phase levels of the superlens according to the phase distribution of the multifocal superlens, thereby designing a multifocal superlens.

8. The design method of a multifocal length superlens with controllable focal energy according to claim 1, characterized in that, Among the M phase levels, the phase interval between adjacent levels is 360° / M, and the phase coverage is continuous.

9. A design method for a multifocal length superlens with controllable focal energy according to claim 1 or 8, characterized in that, The M phase levels are 18 levels, and each level corresponds to a phase range of 20°.

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