Sinusoidal amplitude grating based on metasurface and performance verification method

Abstract

The invention provides a metasurface-based sinusoidal amplitude grating and a performance verification method, and belongs to the field of micro-nano optics, and the metasurface-based sinusoidal amplitude grating comprises a plurality of substrate units and resonators arranged on the substrate units; the substrate units of the sub-wavelength unit structure are arranged on a one-dimensional plane according to a rectangular array; in a polar coordinate system with a central point as an original point, a plurality of grating periods are included in any radial direction, and each grating period is composed of a preset number of substrate units; in the grating period, the rotation angles of the substrate units and the corresponding resonance bodies change according to a preset sequence. The metasurface novel technology is applied to the sinusoidal amplitude grating, the flexibility and the freedom degree of the sinusoidal amplitude grating are greatly improved, and the sinusoidal amplitude grating which is difficult to achieve through a traditional process is obtained. Furthermore, the rotation angle of the resonance body in the radial direction is set through polar coordinates, and the rotation angle of the resonance body can control the transmittance and the phase, so that a sinusoidal amplitude grating distributed in the radial direction is formed.

Description

Technical Field

[0001] This invention relates to the field of micro-nano optics technology, specifically to a sinusoidal amplitude grating based on a metasurface and a performance verification method. Background Technology

[0002] Currently, optical elements composed of a large number (thousands or even tens of thousands) of slits of equal width and spacing are called diffraction gratings. However, modern gratings come in many varieties, and the diffraction units of some gratings are no longer slits in the conventional sense. To include these gratings in the definition of diffraction gratings, a grating is defined as an optical element that can periodically spatially modulate the amplitude or phase, or both, of incident light. Gratings can be classified according to their modulation effect on incident light into amplitude gratings and phase gratings.

[0003] Amplitude gratings, limited by traditional manufacturing capabilities, typically only have a binary distribution of transmittance between "0" and "1," and are often referred to as black-and-white gratings. However, in many situations, the amplitude distribution required by the amplitude grating is continuous, and a simple binary distribution is insufficient. For example, for sinusoidal amplitude gratings, traditional optical processing methods can achieve this by photographically recording the interference fringes of two plane waves with a certain angle between their propagation directions. However, for sinusoidal amplitude gratings distributed radially, where the amplitude distribution must be sinusoidal in the radial direction, it is difficult to manufacture using traditional optical methods. Summary of the Invention

[0004] In view of this, it is necessary to provide a sinusoidal amplitude grating based on metasurface and a performance verification method to solve the technical problem of sinusoidal amplitude gratings that are difficult to achieve by traditional processes.

[0005] To address the aforementioned technical problems, in a first aspect, the present invention provides a sinusoidal amplitude grating based on a metasurface, comprising: Multiple subwavelength unit structures are arranged in a rectangular array on a two-dimensional plane. The subwavelength unit structure includes a substrate unit and a resonator disposed on the substrate unit. In a polar coordinate system with the center point as the origin, any radial direction contains multiple grating periods, and the grating period is composed of a predetermined number of the subwavelength unit structures; During the grating period, the rotation angle of the subwavelength unit structure changes in a preset order, and the rotation angle is the angle between the base unit and the corresponding resonator.

[0006] In one possible implementation, the subwavelength unit structures with the same polar diameter have the same rotation angle.

[0007] In one possible implementation, the preset order in the grating period is the order of changes of a sine function.

[0008] In one possible implementation, the resonator is a rounded rectangular prism.

[0009] In one possible implementation, the transmittance distribution function in polar coordinates is:

[0010] Where m is the amplitude fluctuation coefficient of the grating, r is the longitudinal coordinate, R is the total radius of each of the resonators, and f0 is the spatial frequency constant.

[0011] In one possible implementation, as the rotation angle changes from 0° to 45°, the transmittance of the subwavelength unit structure changes continuously from 0 to its maximum value, and the relationship between the phase of the subwavelength unit structure and the rotation angle conforms to |sin(2θ)|; where θ is the rotation angle.

[0012] Secondly, the present invention also provides a performance verification method for a metasurface-based sinusoidal amplitude grating, applied to the aforementioned metasurface-based sinusoidal amplitude grating, wherein the method: The polarization directions of the incident light and the probe light are determined, and the diffraction field distribution of the metasurface-based sinusoidal amplitude grating is determined based on the incident light and the probe light. Based on the diffraction field distribution, determine whether the sinusoidal amplitude grating based on the metasurface meets the design performance requirements.

[0013] In one possible implementation, determining the polarization directions of the incident light and the probe light includes: A rectangular coordinate system is established on the plane of the subwavelength unit structure with the vertical direction as the x-axis. The incident light is polarized along the x-axis and incident perpendicularly to the substrate, and the probe light is polarized along the y-axis to form a diffraction field distribution.

[0014] In one possible implementation, the diffraction field is distributed in a ring shape with a bright spot at the center.

[0015] In one possible implementation, determining whether the metasurface-based sinusoidal amplitude grating meets the design performance requirements based on the diffraction field distribution includes: The theoretical diffraction field distribution is obtained by deriving the transmittance distribution function in polar coordinates, combined with Fourier transform theory and numerical simulation. The theoretical diffraction field distribution is compared with the actual diffraction field distribution to verify whether it meets the design performance requirements.

[0016] The beneficial effects of this invention are as follows: The sinusoidal amplitude grating based on a metasurface provided by this invention has multiple subwavelength unit structures arranged in a rectangular array on a one-dimensional plane. Each subwavelength unit structure includes a substrate unit and a resonator disposed on the substrate unit. In a polar coordinate system with the center point as the origin, any radial direction contains multiple grating periods, each grating period consisting of a predetermined number of subwavelength unit structures. Within the grating period, the rotation angles of the subwavelength unit structures change in a predetermined order, and the rotation angle is the angle between the substrate unit and the corresponding resonator. Applying this novel metasurface technology to the design and fabrication of sinusoidal amplitude gratings greatly enhances the flexibility and freedom of sinusoidal amplitude gratings, achieving sinusoidal amplitude gratings that are difficult to achieve using traditional processes. Furthermore, this invention sets the rotation angle of the resonator in the radial direction using polar coordinates, because the rotation angle of the resonator can control the transmittance and phase, forming a radially distributed sinusoidal amplitude grating. Attached Figure Description To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A schematic diagram of an embodiment of the sinusoidal amplitude grating based on metasurface provided by the present invention; Figure 2 A partial structural schematic diagram of a sinusoidal amplitude grating based on a metasurface provided by the present invention; Figure 3 The simulation results show the electric field distribution. Figure 4 A partial structural schematic diagram of a sinusoidal amplitude grating based on a metasurface provided by the present invention; Figure 5 A schematic flowchart of an embodiment of the verification method for the sinusoidal amplitude grating based on metasurface provided by the present invention; Figure 6 A partial structural schematic diagram of a verification method for incident light onto a sinusoidal amplitude grating based on a metasurface; Figure 7 For the present invention Figure 6 A schematic diagram of an embodiment of S602; Figure 8 This represents the theoretical calculation results of the electric field distribution.

[0018] In the diagram: 100 - resonator, 101 - subwavelength structural unit. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0020] In the description of the embodiments of the present invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0021] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0022] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0023] Before demonstrating the embodiments, the following terms will be explained.

[0024] Metamaterials are a class of man-made materials with special properties that do not exist in nature. They possess unique properties, such as the ability to alter the normal properties of light and electromagnetic waves, effects that are impossible with conventional materials. Metamaterials are not particularly special in terms of composition; their extraordinary properties stem from their intricate geometry and size. Their microstructures, smaller than the wavelength of light they interact with, allow them to influence waves.

[0025] Metasurfaces: Also known as two-dimensional metamaterials, metasurfaces are typically composed of basic structural units at the subwavelength scale and possess the ability to manipulate the amplitude, phase, and polarization state of electromagnetic waves. Metasurface technology provides new solutions for designing ultrathin optical devices, including the most basic optical component, the lens.

[0026] Sinusoidal amplitude grating: A grating whose transmission coefficient varies according to a cosine or sine function is called a sinusoidal (amplitude) grating. The intensity distribution function of a two-beam interference pattern has a cosine function form; therefore, after "linearly developing" a film recording two-beam interference fringes, its transmission coefficient distribution will have a cosine form, and such a film is a sinusoidal grating. The diffraction pattern of a sinusoidal grating contains only the zeroth and ±1st order spectral lines.

[0027] This invention provides a sinusoidal amplitude grating based on metasurface and a performance verification method, which are described below.

[0028] Figure 1 A schematic diagram of an embodiment of the sinusoidal amplitude grating based on a metasurface provided by the present invention is shown below. Figure 1 As shown, the sinusoidal amplitude grating based on a metasurface includes: multiple subwavelength unit structures arranged in a rectangular array on a two-dimensional plane, each subwavelength unit structure including a substrate unit and a resonator disposed on the substrate unit; in a polar coordinate system with the center point as the origin, an arbitrary radial direction contains multiple grating periods, each grating period consisting of a preset number of subwavelength unit structures; in the grating period, the rotation angle of the subwavelength unit structure changes in a preset order, and the rotation angle is the angle between the substrate unit and the corresponding resonator.

[0029] Figure 1 This is a schematic diagram of the sinusoidal amplitude grating structure based on a metasurface. Figure 1 Using the center of the circle O polar coordinate system with origin (r,θ) The position of each subwavelength unit structure is determined by its polar coordinates. (rᵢ,θⱼ) Each subwavelength unit structure 101 includes a base unit and a resonator 100 disposed on the base unit, and the angle between the base unit and the corresponding resonator 100 is a rotation angle; the overall structure achieves amplitude modulation along the radial direction r, and along the angle... θ Symmetrical replication is achieved in the direction of the grating, with multiple grating periods contained in any radial direction. Each grating period consists of a preset number of subwavelength unit structures 101, and the rotation angle of the subwavelength unit structures 101 in each grating period is different. The subwavelength unit structures 101 with different rotation angles are arranged along... r The directions are arranged periodically.

[0030] The sinusoidal amplitude grating based on metasurface is composed of a subwavelength unit structure 101 consisting of a series of resonators 100 arranged radially. The resonators 100 exhibit a periodic distribution in the radial direction, and the overall structure has obvious symmetry and regularity. From the center to the periphery, the resonators 100 are arranged closely and orderly, forming a pattern similar to a radial shape.

[0031] It should be noted that: such as Figure 2 As shown, (a) is a subwavelength unit cell structure, where P is the period of the subwavelength unit cell structure. a, b, h (a) shows the width, length, and height of the resonator, respectively; (b) shows a partial cross-sectional view of the resonator. Since the effective refractive index is different in the two symmetry axes of the resonator, the resonator can be regarded as having a fast axis and a slow axis. That is, the two symmetry axes can be regarded as the fast axis and the slow axis. The rotation angle θ is the angle between the slow axis and the x-axis. A rectangular coordinate system with the horizontal direction as the x-axis and the y-axis as the vertical direction is established on the plane of the subwavelength unit structure.

[0032] In some embodiments of the present invention, the subwavelength unit structures with the same polar diameter have the same rotation angle.

[0033] The overall subwavelength unit structure achieves multiple grating periodic repeats along the radial direction r, and along the angle θ Symmetrical replication is achieved in the direction of the grating. The resonator is repeatedly rotated radially, altering the structural symmetry and optical properties of the grating. This is because the rotation angle of the resonator at different radial positions affects the phase and polarization modulation effects when light interacts with the grating. When light is incident on the grating after this rotation, diffraction occurs due to the altered grating structure. Unlike the diffracted beams of ordinary gratings, a special diffracted beam is output here. This special diffracted beam may have a unique intensity distribution, polarization state, or propagation direction. This application can be applied across the entire electromagnetic spectrum, including ultraviolet, visible, infrared, terahertz, and microwaves. Furthermore, it can be applied to acoustic waves, mechanical waves, and other fields. In this embodiment, a sinusoidal amplitude grating designed in the terahertz band is used as an example.

[0034] In some embodiments of the present invention, the material of the subwavelength unit structure is silicon. Specifically, by selecting other metamaterials and designing them in the same way, the desired radially distributed sinusoidal amplitude grating can also be obtained.

[0035] In this embodiment of the invention, resonators of a metasurface (such as nanopillars, open rings, etc.) are arranged radially on a substrate according to polar coordinate rules. This arrangement breaks through the limitations of traditional rectangular gratings, and by using the radial (radius) and angular (angle) parameters of polar coordinates, non-uniform control of the phase distribution of the light wavefront can be achieved. The polar coordinate arrangement directly correlates the distribution of the resonators with the angular momentum of the light wave. For example, radial periodic changes can introduce a spiral phase, and angular periodic changes can achieve wavefront tilting, thus providing a structural basis for generating special light fields such as vortex beams and Bessel beams. Compared with the uniform arrangement of traditional gratings, polar coordinate design can more flexibly match the phase requirements of the light wave, reduce energy loss, and support more complex light field control (such as three-dimensional beam shaping).

[0036] In some embodiments of the present invention, the preset order in the grating period is the order of changes of a sine function.

[0037] Subwavelength unit structures with different rotation angles along r The orientations are periodically arranged, and the distance covered by each grating period is: Tᵣ =1 / f 0 =600 μm , f 0 represents the spatial frequency constant. Each subwavelength unit structure occupies one period. P =130 μm Therefore, approximately every 5 units constitute a complete grating cycle. Within each grating cycle, the rotation angle changes sinusoidally, that is, the rotation angle changes from 45 degrees to 0 degrees and then back to 45 degrees according to a sinusoidal function, and five units form a cycle that repeats in the radial direction.

[0038] In some embodiments of the present invention, when the rotation angle changes from 0° to 45°, the transmittance of the subwavelength unit structure continuously changes from 0 to its maximum value, and the relationship between the phase of the subwavelength unit structure and the rotation angle conforms to | sin(2θ) |; where θ is the rotation angle.

[0039] It is understandable that, such as Figure 2 As shown in (c), when the subwavelength unit structure rotates along an axis perpendicular to the substrate, the transmittance and phase of the subwavelength unit structure change with the rotation angle. θ The changing relationship. When the resonator of the subwavelength unit structure rotates along the axis perpendicular to the base, the rotation angle... θ Relationship with electromagnetic wave transmittance as follows Figure 2 As shown in (c), it can be seen that when the rotation angle changes from 0° to 45°, the transmittance of the subwavelength unit structure can continuously change from 0 to the maximum value (0.9), and the phase dependence of the subwavelength unit structure is shown in | sin(2θ) A direct proportional relationship, such as Figure 3 As shown, a sinusoidal amplitude grating based on a metasurface directly generates a ring-shaped light field with a central bright spot.

[0040] It should be noted that controlling the rotation of the resonator around an axis perpendicular to the substrate, and dynamically adjusting its response characteristics to incident light by changing the rotation angle (e.g., from 0° to 90°), affects the degree of matching between the resonator and the polarization direction of the incident light, thus altering the transmitted light intensity. For example, the transmittance is lowest when the slow axis of the resonator is at 45 degrees to the polarization direction of the incident light. The rotation angle introduces an additional phase delay through the phase. For example, when left-handed circularly polarized light is incident, the rotation angle... θ It will introduce 2 θThe phase change enables continuous and wide-bandgap phase control. By detecting transmittance and phase changes in real time, the rotation angle can be adjusted to achieve adaptive optimization of the light field control (such as achromatic aberration and efficient focusing).

[0041] In some embodiments of the present invention, the resonator is a rounded rectangular prism.

[0042] In some embodiments of the present invention, such as Figure 2 ,in, P =120 um , h =150 um , a =40 um , b =85 um , r =10 um Both the substrate and the resonator are made of silicon. A Cartesian coordinate system is established on the plane of the subwavelength unit structure, along... x Directionally polarized electromagnetic waves are incident perpendicularly to the substrate, and outgoing electromagnetic waves polarized along the y-direction are detected. Therefore, with proper configuration, this structure can function as a half-wave plate. This embodiment is based on 1... THz It operates at a specific frequency. In the subwavelength unit structure, the resonator's cross-section is a rounded rectangle, meaning the resonator is a rounded rectangular prism. This design takes into account practical manufacturing considerations. Based on past manufacturing experience, when the resonator is a cube, its sharp corners will have manufacturing errors, thus forming a rounded rectangle. Based on experience, a rounded rectangle... r The selection range is (0, 0.5a). In this embodiment, the selection is... r =10 μm .

[0043] In some embodiments of the present invention, the transmittance distribution function in polar coordinates is:

[0044] in, m The amplitude fluctuation coefficient of the grating. r For coordinates, R The total radius of each resonator. f 0 represents the spatial frequency constant.

[0045] This invention, through controlling the rotation angle of the subwavelength unit structure and repeating this operation radially, unlike traditional gratings where the structural parameters remain constant, achieves dynamic adjustability of the grating structure within a certain range. This allows for flexible adjustment of the subwavelength unit structure's rotation angle according to different application requirements, thereby altering the grating's optical properties, such as diffraction efficiency and diffraction angle, providing greater flexibility for grating applications in various optical systems. This method can generate special diffracted beams with unique properties, applicable to fields with specific beam characteristic requirements. For example, in optical imaging, special diffracted beams can improve image resolution and contrast; in optical communication, they can be used to achieve more efficient information encoding and transmission. Furthermore, the detection and analysis of these special diffracted beams can lead to in-depth research into the microscopic mechanisms of light-matter interaction, providing a theoretical basis for the design and development of novel optical devices.

[0046] To better implement the metasurface-based sinusoidal amplitude grating in the embodiments of the present invention, based on the performance of the metasurface-based sinusoidal amplitude grating, correspondingly, as follows: Figure 5 As shown, this embodiment of the invention also provides a verification method for a sinusoidal amplitude grating based on a metasurface. The verification method for a sinusoidal amplitude grating based on a metasurface includes: S501. Determine the polarization directions of the incident light and the probe light, and determine the diffraction field distribution of the sinusoidal amplitude grating based on the metasurface based on the incident light and the probe light. S502. Determine whether the sinusoidal amplitude grating based on the metasurface meets the design performance requirements based on the diffraction field distribution.

[0047] The diffraction characteristics of sinusoidal amplitude gratings based on metasurfaces are highly sensitive to the polarization direction of the incident light. Therefore, the polarization direction needs to be optimized according to the target diffraction field distribution (e.g., energy concentration at the ±1st order, elimination of the zeroth order, etc.). When the polarization direction is perpendicular to the substrate, the grating achieves the highest amplitude modulation efficiency for the incident light, concentrating energy in the ±1st order diffracted light, while significantly suppressing the zeroth order intensity. When the polarization direction is parallel to the substrate, the modulation effect of the grating on the incident light weakens, the zeroth order intensity is enhanced, and the ±1st order intensity is reduced, making it suitable for scenarios where the zeroth order light needs to be preserved.

[0048] The polarization direction of the probe light must match the polarization state of the diffracted light to maximize detection efficiency. By rotating the polarization direction of the probe light, diffracted light with different polarization states can be separated. For example, in a cascaded metasurface system, the diffraction order can be dynamically switched by controlling the relative displacement of the two metasurfaces. In this case, the polarization direction of the probe light must be consistent with the polarization state of the diffracted light after the switch to ensure signal strength.

[0049] In this embodiment, an optical experimental platform was built, and a laser, polarizer, metasurface sample, and detector were used to measure the intensity distribution of diffracted light under different polarization directions. During the experiment, the polarization direction of the incident light needed to be controlled (e.g., by rotating a half-wave plate), and the diffraction pattern received by the detector was recorded. The accuracy of the diffraction field distribution was verified by comparing the theoretical and experimental results.

[0050] In some embodiments of the present invention, step S501 includes: A rectangular coordinate system is established on the plane of the subwavelength unit structure with the vertical direction as the x-axis. The incident light is polarized along the x-axis and incident perpendicularly to the substrate, while the probe light is polarized along the y-axis to form a diffraction field distribution. The diffraction field distribution is a ring shape with a bright spot at the center.

[0051] It should be noted that, Figure 6 This diagram illustrates incident light onto a sinusoidal amplitude grating. A Cartesian coordinate system is established on the plane of the subwavelength unit structure, with the vertical direction as the x-axis and the horizontal direction as the y-axis. Ein Indicates the polarization direction of the incident light. Edetect This indicates the polarization direction of the probe light; the light field distribution of the light passing through the grating is as follows: Figure 3 As shown, the transmitted light has a central bright spot in a ring shape. The x and y polarization components (or different diffraction orders) interfere in the far field, forming a ring distribution with a central bright spot. The central bright spot corresponds to zero-order diffraction (unmodulated light), and the ring corresponds to the superposition of first-order interference. By using the anisotropic structure of a sinusoidal amplitude grating (such as subwavelength metal / dielectric nanostripes), the coupling of amplitude modulation and polarization conversion is achieved. The geometric parameters of the grating (rotation angle, polar coordinates) simultaneously control the amplitude, phase, and polarization state of the transmitted light, breaking through the limitation of a single modulation dimension.

[0052] In some embodiments of the present invention, such as Figure 7 As shown, step S703 includes: S701. The theoretical diffraction field distribution is obtained by deriving the transmittance distribution function in polar coordinates and combining Fourier transform theory and numerical simulation. S702. Compare the theoretical diffraction field distribution with the actual diffraction field distribution to verify whether the design performance requirements are met.

[0053] The transmittance function describes the transmission characteristics of the grating or metasurface to incident light and is a position-dependent function. Based on the transmittance function distribution, the position of each resonator in the polar coordinate system is determined. t(r,θ) For example, if the transmittance function in certain specific... r and θGiven specific values, the resonator is placed at corresponding positions to achieve the desired optical properties. The transmittance function is mathematically derived in polar coordinates to analyze its properties and characteristics. For the transmittance function of a metasurface, Fourier transform can convert it from the polar coordinate space domain to the corresponding frequency domain, thus analyzing the modulation effect of the metasurface structure on light of different spatial frequency components. In diffraction problems, Fourier transform helps to understand the diffraction characteristics of light after passing through a metasurface, such as diffraction order and diffraction angle.

[0054] In some embodiments of the present invention, the subwavelength unit structure is as follows: Figure 4 As shown in (a). P =130 um , h =150 um , a =48 um , b =115 um Both the substrate and the resonator are made of silicon. This embodiment operates at a frequency of 1 THz. Theoretical derivation is performed based on known information: The transmittance function of a radially distributed sinusoidal amplitude grating in polar coordinates can be expressed as:

[0055] in, m The amplitude fluctuation coefficient of the sinusoidal amplitude grating. r For spatial location, R The total radius of the radially distributed grating. f 0 is the spatial frequency constant corresponding to the grating constant of the radially distributed grating.

[0056] The Fourier transform yields...

[0057] in fr For spatial frequency, we can simplify to obtain:

[0058] Furthermore, due to:

[0059] Only two diffraction orders remain: the zeroth order and the first order.

[0060] The diffraction field distribution is as follows:

[0061] After processing, the final diffraction field distribution is an analytical solution:

[0062] In the embodiment, let f 0 = 1 / 600, m = 1, R = 5.2 mm.

[0063] Based on theoretical analysis, the field distribution of the grating in space can be obtained as follows: Figure 8 As shown, Figure 8 As shown, (a) is the theoretical calculation result of the electric field distribution of the sinusoidal amplitude grating along the propagation direction; (b) is the theoretical calculation result of the electric field distribution of the sinusoidal amplitude grating in the far field. Clear 0th and 1st order diffraction at the center can be seen; this result represents the theoretically obtained diffraction field distribution.

[0064] On the other hand, by utilizing Figure 4 The subwavelength unit structures of the metasurface are mapped to corresponding positions based on the transmittance function, ultimately combining to form a radially distributed sinusoidal metasurface amplitude grating metasurface. The structure of the central region is as follows: Figure 1 As shown. By utilizing Rayleigh-Sommerfeld diffraction formula, the diffraction field distribution results obtained using metasurface structures can be simulated, such as... Figure 8 As shown. Figure 3 and Figure 8 The comparison shows that the simulation results match the theoretical results well, and the positions of level 0 and level 1 coincide exactly, which demonstrates the correctness of the design.

[0065] Radially distributed sinusoidal amplitude gratings are almost impossible to achieve using traditional processes. By utilizing metasurface technology, this novel technology is applied to the design and fabrication of special gratings, greatly enhancing the flexibility and freedom of these gratings. Radially distributed sinusoidal amplitude gratings can be designed and fabricated relatively easily, thus making the practical application of these special gratings possible.

[0066] This invention achieves refined design of metasurface structures by precisely setting the polar coordinate position of the resonator according to the transmittance function distribution. This performance verification method can more accurately control the light transmission characteristics of the metasurface, thereby achieving precise control of the light field. The transmittance function derivation, Fourier transform theory application, and numerical simulation are performed in a polar coordinate system, fully leveraging the advantages of polar coordinates in handling problems with rotational symmetry or radial distribution characteristics. This combined approach can more effectively analyze the optical properties of metasurface structures, especially when dealing with complex light field distributions and diffraction phenomena, providing more accurate and comprehensive results. Simultaneously, numerical simulation provides a means for verifying and optimizing theoretical analysis, accelerating the design and development process of metasurface structures.

[0067] The foregoing has provided a detailed description of the sinusoidal amplitude grating based on metasurface and the performance verification method provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A sinusoidal amplitude grating based on a metasurface, characterized in that, include: Multiple subwavelength unit structures are arranged in a rectangular array on a two-dimensional plane. The subwavelength unit structure includes a substrate unit and a resonator disposed on the substrate unit. In a polar coordinate system with the center point as the origin, any radial direction contains multiple grating periods, and the grating period is composed of a predetermined number of the subwavelength unit structures; During the grating period, the rotation angle of the subwavelength unit structure changes in a preset order, and the rotation angle is the angle between the base unit and the corresponding resonator.

2. The sinusoidal amplitude grating based on a metasurface as described in claim 1, characterized in that, The subwavelength unit structures with the same polar diameter have the same rotation angle.

3. The sinusoidal amplitude grating based on a metasurface as described in claim 1, characterized in that, In the grating period, the preset order is the sequence of changes of a sine function.

4. The sinusoidal amplitude grating based on a metasurface as described in claim 1, characterized in that, The resonator is a rounded rectangular prism.

5. The sinusoidal amplitude grating based on a metasurface as described in claim 1, characterized in that, The transmittance distribution function in polar coordinates is: Where m is the amplitude fluctuation coefficient of the grating, r is the longitudinal coordinate, R is the total radius of each of the resonators, and f0 is the spatial frequency constant.

6. The sinusoidal amplitude grating based on a metasurface as described in claim 1, characterized in that, When the rotation angle changes from 0° to 45°, the transmittance of the subwavelength unit structure changes continuously from 0 to the maximum value. The relationship between the phase of the subwavelength unit structure and the rotation angle conforms to |sin(2θ)|, where θ is the rotation angle.

7. A performance verification method for a sinusoidal amplitude grating based on a metasurface, characterized in that, The method, applied to a metasurface-based sinusoidal amplitude grating as described in any one of claims 1 to 6, comprises: The polarization directions of the incident light and the probe light are determined, and the diffraction field distribution of the metasurface-based sinusoidal amplitude grating is determined based on the incident light and the probe light. Based on the diffraction field distribution, determine whether the sinusoidal amplitude grating based on the metasurface meets the design performance requirements.

8. The performance verification method for the sinusoidal amplitude grating based on metasurface as described in claim 7, characterized in that, Determining the polarization directions of the incident light and the probe light includes: A rectangular coordinate system is established on the plane of the subwavelength unit structure with the vertical direction as the x-axis. The incident light is polarized along the x-axis and incident perpendicularly to the substrate, and the probe light is polarized along the y-axis to form a diffraction field distribution.

9. The performance verification method for the sinusoidal amplitude grating based on metasurface as described in claim 8, characterized in that, The diffraction field is distributed in a ring shape with a bright spot at the center.

10. The performance verification method for the sinusoidal amplitude grating based on metasurface as described in claim 7, characterized in that, Determining whether the sinusoidal amplitude grating based on the metasurface meets the design performance requirements based on the diffraction field distribution includes: The theoretical diffraction field distribution is obtained by deriving the transmittance distribution function in polar coordinates, combined with Fourier transform theory and numerical simulation. The theoretical diffraction field distribution is compared with the actual diffraction field distribution to verify whether it meets the design performance requirements.

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