A label-based metasurface vortex light generator and a design method thereof

Abstract

The application belongs to the technical field of micro-nano optics, and discloses a super-surface-based vortex light generator with a label and a design method thereof.The design method of the super-surface-based vortex light generator with a label provided by the application not only considers how to realize the function of the vortex light generator, but also considers how to directly display the topological charge number, selects and arranges the nano-brick structure units in combination with a binary image for displaying the topological charge number, and obtains the super-surface-based vortex light generator with a label.Under the premise of maintaining the function of the vortex light generator, the topological charge number of the vortex light generated by the vortex light generator can be directly displayed in a microscopic optical path, and the problem that it is difficult to directly obtain the topological charge number of the vortex light in the prior art is solved.The super-surface-based vortex light generator with a label provided by the application is compact in structure, and the topological charge number of the vortex light is easy to judge while the vortex light is generated.

Description

Technical Field

[0001] This invention belongs to the field of micro-nano optics technology, and more specifically, relates to a labeled vortex light generator based on metasurface and its design method. Background Technology

[0002] Vortex light, also known as optical vortex or optical singularity, is a type of light beam with a unique phase structure. A key characteristic of vortex light is the presence of a phase singularity along its propagation direction, resulting in a spiral-shaped phase distribution in its optical field, resembling a vortex or whirlpool. It possesses unique spin angular momentum properties and has broad application potential in fields such as optical communication, optical manipulation, optical microscopy, and quantum optics. There are various methods for generating vortex light, the most common being: liquid crystal spatial light modulators, waveplates, wavefront modulators, optical interference, and hybrid beam converters. These methods all achieve vortex light generation by adjusting or transforming the phase of the light.

[0003] Metasurfaces are novel micro / nano optical components, two-dimensional or three-dimensional surfaces with micro / nano structures, used for the efficient manipulation and control of light waves. The design and fabrication of metasurfaces can be achieved using computational methods, nanofabrication techniques, and optical measurement methods. The applications of metasurfaces are wide-ranging, encompassing optical imaging, communication, sensing, and optical computing, providing new possibilities and potential for optical technologies and devices. Although there have been studies on generating vortex light using metasurfaces, it is difficult to directly determine the topological charge from the vortex light generated after the metasurface has been fabricated. Summary of the Invention

[0004] This invention provides a labeled metasurface-based vortex light generator and its design method, solving the problem in the prior art where it is difficult to directly determine the topological charge of the vortex light generated by metasurface-based vortex light generators.

[0005] This invention provides a design method for a labeled vortex light generator based on metasurfaces, comprising the following steps:

[0006] Step 1: Construct the basic structure of the metasurface for realizing the function of the vortex light generator. The basic structure includes a substrate and an array of nanobricks on the substrate. The substrate is divided into multiple unit structures of the same size. The array of nanobricks includes multiple nanobricks. Each unit structure and one nanobrick on its working surface constitute a nanobrick structure unit.

[0007] Step 2: Optimize the size parameters of the nanobrick structure unit at the working wavelength to obtain multiple groups of nanobrick structure units as candidates. The different groups of nanobrick structure units have different transmission phases.

[0008] Step 3: Based on the vortex light to be generated by the vortex light generator, calculate the phase distribution required by the metasurface; determine the topological charge of the vortex light generator, and determine a binary image for displaying the topological charge based on the topological charge; calculate the candidate values ​​of the orientation angle of the nanobricks in the nanobrick structure unit at each position of the metasurface based on the intensity distribution of the binary image; calculate the difference between the geometric phase corresponding to the orientation angle of the candidate nanobricks at each position and the phase distribution required by the metasurface, and take the candidate value of the orientation angle of the nanobrick corresponding to the minimum value of the difference as the final value of the orientation angle of the nanobrick; the minimum value of the difference calculated at each position corresponds to the required transmission phase at that position, and select the final group of nanobrick structure units from the multiple candidate groups of nanobrick structure units based on the required transmission phase; arrange the nanobrick array according to the determined group of nanobrick structure units and the orientation angle of the nanobricks to obtain a labeled vortex light generator based on the metasurface.

[0009] When light of the operating wavelength is incident on the labeled metasurface-based vortex light generator, the emitted light is a vortex light with a designed topological charge. When the labeled metasurface-based vortex light generator is placed in a microscopic optical path, linearly polarized light formed by a polarizer is incident on it, and a binary image displaying the topological charge can be observed using an analyzer.

[0010] Preferably, the function of the nanobrick structural unit is equivalent to a micro / nano half-wave plate, and the geometric phase of the nanobrick structural unit with an orientation angle of θ is... satisfy:

[0011] Preferably, the size parameter includes the side length L of the long side of the nanobrick. x The length of the shorter side L y The height H, and the side length C of the working surface of the unit structure; the side length L of the longer side. x and the length of the shorter side L y They are not equal; the height H of the nanobrick and the side length C of the working surface of the unit structure are the same in the multiple groups of nanobrick structural units obtained as candidates.

[0012] Preferably, two groups of nanobrick structure units are obtained as candidates, and the transmission phase of the two groups of nanobrick structure units is... They are respectively

[0013] Preferably, the required phase distribution for the metasurface is calculated using the following formula:

[0014]

[0015] In the formula, Let α be the required phase modulation at coordinates (x, y) on the metasurface, l be the topological charge, φ be the spatial azimuth angle of the metasurface, k be the wavenumber corresponding to the operating wavelength, and α be the phase modulation value. x Let α be the off-axis angle of the vortex light along the x-direction. y Let be the off-axis angle of the vortex light along the y-direction;

[0016] Off-axis angle α x and α y Satisfy the following formula:

[0017]

[0018] In the formula, λ is the working wavelength, C is the side length of the working surface of the unit structure, and min{} represents the function that takes the minimum value.

[0019] Preferably, after calculating the required phase distribution of the metasurface, the method further includes step quantization of the required phase distribution of the metasurface.

[0020] Preferably, the phase distribution required for the metasurface is quantized using an eight-step quantization method, and the quantized eight-step phase is as follows:

[0021] For the binary image, at pixel 1, the light intensity I1 is designed as follows: The alternative values ​​for the orientation angle of the nanobrick at pixel 1 are as follows:

[0022] For the binary image, at pixel 0, the light intensity I0 is designed as follows: The alternative values ​​for the orientation angle of the nanobrick at pixel 0 are as follows:

[0023] Preferred, quantized step phase Geometric phase and transmission phase The following equation applies between them:

[0024] Preferably, the transmission axis of the polarizer is perpendicular to the transmission axis of the analyzer.

[0025] On the other hand, the present invention provides a metasurface-based labeled vortex light generator, which is prepared by the above-described design method of the metasurface-based labeled vortex light generator.

[0026] One or more technical solutions provided in this invention have at least the following technical effects or advantages:

[0027] This invention provides a design method for a labeled vortex light generator based on metasurfaces. This method not only considers how to realize the function of the vortex light generator but also how to directly display the topological charge. By combining a binary image used to display the topological charge, the selection and arrangement of nanobrick structural units are performed, resulting in a labeled vortex light generator based on metasurfaces. While maintaining the functionality of the vortex light generator, this invention can directly display the topological charge of the generated vortex light in a microscopic optical path, solving the problem of difficulty in directly obtaining the topological charge of vortex light in existing technologies. The device provided by this invention has a compact structure and allows for easy determination of the topological charge of the vortex light while generating it. Attached Figure Description

[0028] Figure 1 A schematic diagram showing a binary image displaying the topological charge number when a labeled metasurface-based vortex light generator is placed in a microscopic optical path, as provided in an embodiment of the present invention.

[0029] Figure 2 This is a schematic diagram of the structure of a nanobrick structure unit in a labeled vortex light generator based on a metasurface, provided in an embodiment of the present invention.

[0030] Figure 3 This is a schematic diagram of a labeled vortex light generator based on a metasurface provided in an embodiment of the present invention;

[0031] Figure 4 These are the reflection response curves of two alternative groups of nanobrick structure units in the embodiments of the present invention;

[0032] Figure 5 This is a schematic diagram of the metasurface azimuth angle in an embodiment of the present invention;

[0033] Figure 6 This is a binary image used to display the topological charge number in an embodiment of the present invention;

[0034] Figure 7 This is a schematic diagram of the phase distribution required for the metasurface in an embodiment of the present invention;

[0035] Figure 8 This is a schematic diagram of the metasurface transport phase distribution in an embodiment of the present invention;

[0036] Figure 9 This is a schematic diagram of the orientation angle distribution of the nanobricks in an embodiment of the present invention;

[0037] Figure 10 This is a rendering of a binary image showing the topological charge number observed in an embodiment of the present invention;

[0038] Figure 11 This is a diffraction effect diagram of the metasurface emitted vortex light in an embodiment of the present invention. Detailed Implementation

[0039] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0040] Example 1:

[0041] Example 1 provides a design method for a labeled vortex light generator based on metasurfaces, see [link to example]. Figure 1 It includes the following steps:

[0042] Step 1: Construct the basic structure of the metasurface for realizing the function of a vortex light generator. The basic structure includes a substrate and an array of nanobricks on the substrate. The substrate is divided into multiple unit structures 202 of uniform size. The nanobrick array includes multiple nanobricks 201. Each unit structure 202 and one nanobrick 201 located on its working surface constitute a nanobrick structure unit. See [link to relevant documentation]. Figure 2 .

[0043] Step 2: Optimize the size parameters of the nanobrick structure unit at the working wavelength to obtain multiple groups of nanobrick structure units as candidates. The different groups of nanobrick structure units have different transmission phases.

[0044] Step 3: Based on the vortex light to be generated by the vortex light generator, calculate the phase distribution required by the metasurface; determine the topological charge of the vortex light generator, and determine the binary image used to display the topological charge based on the topological charge; calculate the candidate values ​​of the orientation angle of the nanobricks in the nanobrick structure unit at each position of the metasurface based on the intensity distribution of the binary image; calculate the difference between the geometric phase corresponding to the orientation angle of the candidate nanobricks at each position and the phase distribution required by the metasurface, and take the candidate value of the orientation angle of the nanobrick corresponding to the minimum value of the difference as the final value of the orientation angle of the nanobrick; the minimum value of the difference calculated at each position corresponds to the required transmission phase at that position, and select the final group of nanobrick structure units from the multiple candidate groups of nanobrick structure units based on the required transmission phase; arrange the nanobrick array according to the determined group of nanobrick structure units and the orientation angle of the nanobricks to obtain a labeled vortex light generator based on the metasurface.

[0045] When light of the operating wavelength is incident on the labeled metasurface-based vortex light generator 2, the emitted light wave is a vortex light 3 with the designed topological charge. When the labeled metasurface-based vortex light generator 2 is placed in a microscopic optical path, linearly polarized light generated by a polarizer is incident, and a binary image 4 displaying the topological charge can be observed using an analyzer. The transmission axis 5 of the polarizer is perpendicular to the transmission axis 6 of the analyzer. (See [reference]). Figure 1 .

[0046] The vortex light generator provided by this invention is composed of an array of anisotropic nanobrick structure units with different size parameters and different orientation angles.

[0047] The function of the nanobrick structural unit is equivalent to a micro / nano half-wave plate, and the geometric phase of the nanobrick structural unit with an orientation angle of θ is... satisfy:

[0048] Specifically, the operating wavelength is determined, and the dimensional parameters of the nanobrick structural units are optimized using electromagnetic simulation software. These dimensional parameters include the length L of the long side of the nanobrick. x The length of the shorter side L y The height H, and the side length C of the working surface of the unit structure; the side length L of the longer side. x and the length of the shorter side L y They are not equal; in the multiple candidate nanobrick structural units, the height H of the nanobrick and the side length C of the working surface of the unit structure are all the same. The orientation angle θ of the nanobrick is the side length L of the longer side of the nanobrick. x The angle between the x-axis and the x-axis.

[0049] For example, with an operating wavelength of 632.8 nm, the optimized transmission phase They are respectively The size parameters of the two groups of nanobrick structural units are as follows: L n =260nm, L y1 =125nm; L x2 =205nm, L y2 =105nm; the height H and working surface side length C of the two groups of nanobrick structure units are the same, both being: H = 220nm and C = 400nm. The response of the two groups of nanobrick structure units at the design wavelength is as follows: Figure 4 As shown, its function during reflection is equivalent to a micro / nano half-wave plate.

[0050] For example, if the topological charge of the vortex light generator is determined to be 1, a binary image Img1 displaying the topological charge is determined based on the topological charge, such as... Figure 6 As shown. The azimuth angle φ of the metasurface is as follows. Figure 5As shown, the azimuth angle φ of the metasurface is the angle between the line connecting point (x, y) and point (0, 0) in a two-dimensional Cartesian coordinate system and the positive x-axis. Let l = 1, α... x =5°, α y =5°, according to the formula The required phase distribution for the metasurface is calculated, such as... Figure 7 As shown. The final value of the orientation angle of the obtained nanobricks is as follows. Figure 9 As shown, the distribution of the transmission phase is as follows: Figure 8 As shown, the resulting metasurface after arrangement is as follows: Figure 3 As shown, the diffraction pattern of the metasurface emitted vortex light is as follows. Figure 11 As shown, the observed binary image displaying the topological charge number is as follows: Figure 10 As shown.

[0051] The present invention will now be further described.

[0052] The Jones matrix of the nanobrick structure unit, functionally equivalent to a micro / nano half-wave plate, is used to describe it. The Jones matrix G(θ) of the optimized anisotropic nanobrick unit structure at an orientation angle θ can be expressed as:

[0053]

[0054] Where R is the rotation matrix, G0 is the Jones matrix of the nanobrick structural unit along the x-axis, and A and B are the complex reflection (or transmission) coefficients along the long and short sides of the nanobrick, respectively.

[0055] When linearly polarized light passes through an anisotropic nanobrick unit structure and then through an analyzer, the Jones vector E of the reflected light wave is expressed as:

[0056]

[0057] In the formula, α1 is the angle between the vibration direction of the incident linearly polarized light and the x-axis, and α2 is the angle between the transmission axis of the analyzer and the x-axis.

[0058] When the intensity of the incident linearly polarized light is I0, the intensity I1 of the light emitted after passing through the anisotropic nanobrick unit structure and then through the analyzer is:

[0059]

[0060] When the nanobrick unit structure exhibits anisotropy, A≠B, and when the transmission axis of the polarizer is perpendicular to the transmission axis of the analyzer, i.e., α2=α1+π / 2:

[0061]

[0062] When the nanobrick unit structure functions as a micro / nano half-wave plate, A = 1, B = -1, therefore equation (4) can be simplified to:

[0063] I = I0cos 2 (2θ-2α²-π / 2) (5)

[0064] The normalized intensity I′ of the reflected light intensity is:

[0065] I′=cos2(2θ-2α2-π / 2) (6)

[0066] Let α1 = -π / 4, α2 = π / 4, then equation (6) is:

[0067] I′=cos 2 (2θ) (7)

[0068] For a binary image, at pixel 1, the light intensity I1 is designed as follows:

[0069]

[0070] The alternative values ​​for the orientation angle of the nanobrick corresponding to pixel 1 are as follows:

[0071]

[0072] For a binary image, at pixel 0, the light intensity I0 is designed as follows:

[0073]

[0074] The alternative values ​​for the orientation angle of the nanobrick corresponding to pixel 0 are as follows:

[0075]

[0076] For a design wavelength λ, with an orientation angle distribution of θ for the nanobricks, the complex amplitude of the reflected cross-polarized circularly polarized light when incident on circularly polarized light is... Modulation:

[0077]

[0078] When the nanobrick unit structure functions as a micro / nano half-wave plate, A = 1, B = -1, and equation (12) can be simplified to:

[0079]

[0080] Where σ=1 and σ=-1 represent that the polarization state of the light wave is left-handed circularly polarized light or right-handed circularly polarized light, respectively.

[0081] Therefore, the geometric phase of the nanobrick structural unit with orientation angle θ for:

[0082]

[0083] Without loss of generality, taking σ = 1, equation (14) can be simplified to:

[0084]

[0085] To reduce the technical requirements for micro / nano fabrication during metasurface preparation while maintaining the metasurface's phase modulation characteristics, it is preferable to perform eight-step quantization of the phase distribution. The quantized eight-step phase is as follows: When the transmission phase of the nanobrick structure unit They are respectively At that time, the phase modulation amount of the nanobrick corresponding to the alternative values ​​of different orientation angles. As shown in Table 1.

[0086] Table 1. Phase modulation amount of nanobricks corresponding to alternative orientation angles.

[0087]

[0088] It can be seen that at the positions with pixel values ​​of 0 and 1, the transmission phase is designed. Both groups of nanobrick structure units, through combination with the orientation angle of the nanobrick structure, can achieve eight-step phase modulation, ultimately resulting in the following phase distribution of the metasurface:

[0089]

[0090] In the formula, Let α be the required phase modulation at coordinates (x, y) on the metasurface, l be the topological charge, φ be the spatial azimuth angle of the metasurface, k be the wavenumber corresponding to the operating wavelength, and α be the phase modulation value. x Let α be the off-axis angle of the vortex light along the x-direction. y Let be the off-axis angle of the vortex light along the y-direction.

[0091] To ensure that the light waves emitted from the metasurface are traveling waves that can propagate forward, the off-axis angle design must meet the following requirements:

[0092] sin 2 α x +sin 2 α y <1 (17)

[0093] Meanwhile, according to the sampling theorem, the phase interpolation of two adjacent nanobrick structural units needs to be less than π, so the off-axis angle needs to satisfy:

[0094]

[0095] Where C is the side length of the working surface of the unit structure, and λ is the working wavelength.

[0096] Combining equations (17) and (18), we can obtain:

[0097]

[0098] Here, min{} represents the function that takes the minimum value.

[0099] Example 2:

[0100] Example 2 provides a labeled vortex light generator based on metasurfaces, which is prepared using the design method of labeled vortex light generator based on metasurfaces as described in Example 1.

[0101] The metasurface, i.e., the vortex light generator, is composed of an array of anisotropic nanobrick structure units with different dimensional parameters and orientation angles. The metasurface can be made of SOI (Silicon-On-Insulator) material. Based on the arrangement of the nanobrick array determined in Example 1, the metasurface is prepared by micro-nano fabrication methods such as projection lithography or electron beam direct writing.

[0102] Since the device provided in Example 2 corresponds to the design method provided in Example 1, the structure and function of the device can be understood by referring to Example 1, and will not be repeated here.

[0103] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A design method for a labeled vortex light generator based on metasurfaces, characterized in that, Includes the following steps: Step 1: Construct the basic structure of the metasurface for realizing the function of the vortex light generator. The basic structure includes a substrate and an array of nanobricks on the substrate. The substrate is divided into multiple unit structures of the same size. The array of nanobricks includes multiple nanobricks. Each unit structure and one nanobrick on its working surface constitute a nanobrick structure unit. Step 2: Optimize the size parameters of the nanobrick structure unit at the working wavelength to obtain multiple groups of nanobrick structure units as candidates. The different groups of nanobrick structure units have different transmission phases. Step 3: Based on the vortex light to be generated by the vortex light generator, calculate the phase distribution required by the metasurface; determine the topological charge of the vortex light generator, and determine a binary image for displaying the topological charge based on the topological charge; calculate the candidate values ​​of the orientation angle of the nanobricks in the nanobrick structure unit at each position of the metasurface based on the intensity distribution of the binary image; calculate the difference between the geometric phase corresponding to the orientation angle of the candidate nanobricks at each position and the phase distribution required by the metasurface, and take the candidate value of the orientation angle of the nanobrick corresponding to the minimum value of the difference as the final value of the orientation angle of the nanobrick; the minimum value of the difference calculated at each position corresponds to the required transmission phase at that position, and select the final group of nanobrick structure units from the multiple candidate groups of nanobrick structure units based on the required transmission phase; arrange the nanobrick array according to the determined group of nanobrick structure units and the orientation angle of the nanobricks to obtain a labeled vortex light generator based on the metasurface. When light of the operating wavelength is incident on the labeled metasurface-based vortex light generator, the emitted light is a vortex light with a designed topological charge. When the labeled metasurface-based vortex light generator is placed in a microscopic optical path, linearly polarized light formed by a polarizer is incident on it, and a binary image displaying the topological charge can be observed using an analyzer.

2. The design method of the labeled vortex light generator based on metasurface according to claim 1, characterized in that, The function of the nanobrick structural unit is equivalent to a micro / nano half-wave plate, and the geometric phase of the nanobrick structural unit with an orientation angle of θ is... satisfy:

3. The design method of the labeled vortex light generator based on metasurfaces according to claim 1, characterized in that, said size parameters include the long side length L x , the short side length L y , the height H, and the edge length C of the working surface of said unit structure; the long side length L x and the short side length L y are not equal; resulting in a plurality of groups of nano brick structures units in which the height H of the nano bricks and the edge length C of the working surface of said unit structure are the same as alternatives.

4. The design method of the labeled vortex light generator based on metasurface according to claim 1, characterized in that, Two groups of nanobrick structure units were obtained as candidates, and the transmission phases of the two groups of nanobrick structure units were obtained. They are respectively 5. The design method of a labeled vortex light generator based on metasurfaces according to claim 1, characterized in that, The required phase distribution for the metasurface is calculated using the following formula: In the formula, Let l be the required phase distribution at coordinates (x, y) on the metasurface, l be the topological charge, φ be the spatial azimuth angle of the metasurface, k be the wavenumber corresponding to the operating wavelength, and α be the wavenumber. x Let α be the off-axis angle of the vortex light along the x-direction. y Let be the off-axis angle of the vortex light along the y-direction; Off-axis angle α x and α y Satisfy the following formula: In the formula, λ is the working wavelength, C is the side length of the working surface of the unit structure, and min{} represents the function that takes the minimum value.

6. The design method of the labeled vortex light generator based on metasurface according to claim 1, characterized in that, After calculating the required phase distribution of the metasurface, the process further includes step quantization of the required phase distribution of the metasurface.

7. The design method of a labeled vortex light generator based on metasurfaces according to claim 6, characterized in that, The required phase distribution of the metasurface is quantized using an eight-step quantization process. The resulting eight-step phase is: For the binary image, at pixel 1, the light intensity I1 is designed as follows: The alternative values ​​for the orientation angle of the nanobrick at pixel 1 are as follows: For the binary image, at pixel 0, the light intensity I0 is designed as follows: The alternative values ​​for the orientation angle of the nanobrick at pixel 0 are as follows:

8. The design method of the labeled vortex light generator based on metasurface according to claim 6, characterized in that, Quantized step phase Geometric phase and transmission phase The following equation applies between them:

9. The design method of a labeled vortex light generator based on metasurfaces according to claim 1, characterized in that, The transmission axis of the polarizer is perpendicular to the transmission axis of the analyzer.

10. A labeled vortex light generator based on metasurfaces, characterized in that, It was prepared using the design method of the metasurface-based labeled vortex light generator as described in any one of claims 1-9.

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