An Airy beam generation method and device

Abstract

An Airy beam generation method and device, the method comprising: S1, determination of working frequency and device construction; S2, establishing the corresponding relationship of leaky wave unit geometric parameters and leaky wave phase, amplitude; S3, solving one-dimensional Airy beam complex amplitude distribution; S4, backstepping unit geometric parameters to realize target complex amplitude regulation; S5, constructing a super surface complex amplitude regulation device based on one-way electromagnetic mode. The application realizes the complex amplitude regulation of transmission wave in free space by independently regulating the size of metal block and the thickness of air medium layer; the super surface device is simple in structure design, high in efficiency, easy to integrate and reconfigurable, and can replace the spatial light modulator through the one-way waveguide phase regulation function, reduce the system cost and improve the integration, and is suitable for on-chip integrated high-efficiency free-space wavefront control applications.

Description

Technical Field

[0001] This invention belongs to the technical field of combining unidirectional waveguides with electromagnetic metasurfaces, specifically relating to an Airy beam generation method and device. Background Technology

[0002] In the fields of modern electromagnetics and photonics, the efficient, precise, and flexible control of electromagnetic waves has always been a core research objective. Electromagnetic metasurfaces, as artificial two-dimensional structures with a thickness much smaller than the wavelength, can locally control the phase, amplitude, polarization, and propagation direction of electromagnetic waves through the arrangement of "artificial atoms" at the subwavelength scale, showing great potential in stealth, antennas, microwave / terahertz devices, and integrated photonic systems. However, traditional metasurfaces generally rely on external free-space optical excitation and resonant artificial atoms, which not only results in narrow bandwidth and high loss but also severely restricts their application in on-chip integrated photonic systems. Furthermore, due to the inherent limitations of the resonance mechanism, traditional structures struggle to achieve arbitrary wavefront synthesis at the subwavelength scale, especially in scenarios requiring precise control of complex amplitudes to generate complex optical fields (such as Airy beams).

[0003] Controlling an Airy beam requires not only phase control but also amplitude control. Furthermore, the amplitude and phase of the Airy beam need to satisfy specific complex functions, which are complex to implement and require complex equipment with low precision, as well as complex calculations and high costs.

[0004] While Chinese patent publication CN119376114A can generate Airy beams, its controllability is limited to phase. All its units are cylindrical nanopillars of fixed height, and their geometric parameters (radii) are only used to achieve phase control, without introducing amplitude control degrees of freedom. The generated beam is a phase approximation of an "elliptical Airy beam," with the amplitude determined by the natural attenuation of the incident Gaussian light. Its intensity distribution is limited by the incident light, making precise control of the amplitude envelope impossible. The system lacks backscattering resistance, and the beam trajectory is easily disturbed. This scheme requires an external excitation source for beam control, resulting in a complex system structure that is difficult to integrate on a single chip, thus limiting its potential application as a static device in integrated photonic systems.

[0005] To achieve high-precision complex amplitude control, existing technologies face two major technical bottlenecks: First, traditional metasurfaces based on discretized "artificial atom" libraries (such as Chinese patent publication CN114839772A) suffer from inherent coupling between phase and amplitude. Limited complex amplitude control can only be indirectly achieved through large-scale parameter scanning and approximate matching algorithms. This method is not only computationally expensive and inefficient, but also relies on discrete unit combinations, making continuous and precise wavefront control difficult and unable to meet the practical requirements for generating arbitrarily complex light fields. Second,

[0006] While some cutting-edge research has achieved complex amplitude modulation of evanescent waves at deep subwavelength scales using unidirectional surface magnetic plasmons (USMPs), this approach has two limitations: in principle, its design goals and physical mechanisms are entirely focused on the near field, failing to extend the ability to modulate complex amplitudes to the free-space radiation field; in terms of implementation, its unit size is too small, making it difficult and costly to manufacture, and thus difficult to put into practical use in conventional optical or microwave systems.

[0007] Meanwhile, Airy beams, as a special type of diffraction-free beam, have attracted widespread attention in fundamental and applied physics research since their theoretical proposal due to their self-acceleration, diffraction-free, and self-healing properties. In optics, the self-acceleration characteristic of Airy beams allows them to propagate along a parabolic path in free space, breaking through the traditional linear propagation mode of light; the diffraction-free characteristic ensures the stability of the beam's transverse intensity profile during long-distance transmission, thereby improving the spatial resolution of energy transfer; and the self-healing characteristic allows the beam to recover its original shape after encountering obstacles, significantly enhancing its robustness in complex media environments. In electronics, Airy beams have also been applied to electron beam imaging and manipulation. However, when extending their application to other fields (such as neutronics), the efficient and low-cost generation of Airy beams remains a pressing technical challenge. Summary of the Invention

[0008] To address the aforementioned problems, this invention proposes an Airy beam generation method and device that can easily perform phase and complex amplitude decoupling control, generate far-field transmission waves (such as Airy beams), and has high precision, high stability, and non-reciprocity. At the same time, it has a simple structure, low cost, and is easy to integrate.

[0009] In a first aspect, the present invention proposes an Airy beam generating device, comprising a gyromagnetic material layer 3 extending along a unidirectional waveguide transmission direction on a horizontal plane, wherein the unidirectional waveguide transmission direction is defined as the x-axis, the direction perpendicular to the x-axis on the horizontal plane is defined as the y-axis, and the direction perpendicular to the horizontal plane is defined as the z-axis; a metal block array is arranged above the gyromagnetic material layer 3 along the x-axis, the metal block array being composed of equidistantly arranged metal blocks 1, wherein the cross-section of the metal block 1 is T-shaped, and is composed of a first rectangular body 11 in the horizontal direction and a second rectangular body 12 in the vertical direction, the second rectangular body 12 being connected to the middle of the first rectangular body 11 and extending vertically downward; the length of the first rectangular body 11 along the x-axis is defined as the length of the metal block 1. ;

[0010] An air dielectric layer 2 separates the metal block 1 and the gyromagnetic material 3; the metal block 1, the air dielectric layer 2, and the gyromagnetic material layer 3 below them constitute a leakage wave unit; the remanent magnetization direction of the gyromagnetic material layer 3 is the y-axis direction;

[0011] Air dielectric layer thickness required for leakage wave unit Length of metal block 1 It consists of three sets of mapping relationships ( → , → , → The thickness of the air dielectric layer 2 in the first leakage wave unit is determined by calculation. Its phase Mapping; thickness of the air medium layer 2 in the middle of any adjacent unit pair Phase difference Mapping; length of metal block 1 With leakage wave amplitude The mapping.

[0012] Preferably, the thickness of the gyromagnetic material 3 is t = 50 mm, and the dielectric constant is... Magnetic permeability is ,in , Its permeability is in tensor form.

[0013] Preferably, the spacing between adjacent T-shaped metal sheets is p=16mm; the x-axis direction is defined as the length direction, the y-axis direction as the width direction, and the z-axis direction as the thickness direction; wherein the first rectangular body 11 extends along the x-axis with a width of w=8 mm and a thickness of h=0.5mm; the second rectangular body 12 extends along the z-axis with a length of l=1 mm and a width of w=8mm.

[0014] More specifically, the leakage units of metasurface devices are subwavelength scale, supporting unidirectional propagation of magnetic surface plasmon polaritons, allowing electromagnetic waves to leak out from the slits, and the complex amplitude of the transmitted wave can be controlled in free space by independently adjusting the size of the metal block and the thickness of the air dielectric layer.

[0015] Preferably, the operating center frequency of the metasurface device is 8.5 GHz.

[0016] More specifically, the gyromagnetic material layer 3 generates a permeability tensor under the action of an external magnetic field perpendicular to the waveguide propagation direction, causing the magnetic surface plasmons to exhibit non-reciprocal propagation characteristics, and the electromagnetic field propagates only in a single direction.

[0017] This structure supports a unidirectional electromagnetic mode (magnetic surface plasmon resonance). During the propagation of the magnetic surface plasmon resonance, electromagnetic waves leak out through the slits between the T-shaped metal sheets; simultaneously, the wave vector in the leakage unit... Determined by the thickness of the air medium layer The decision is made, and then the air medium layers of different thicknesses are passed through. The phases accumulated by the unit structures are different, and at the same time, the amplitude of the electromagnetic wave is determined by the length of the T-shaped metal block. It is determined that the longer the metal block is, the smaller the gap between adjacent metal blocks, and the smaller the amplitude of the leaked electromagnetic wave. Therefore, the thickness of the air dielectric layer in each unit structure is designed accordingly. and T-shaped metal sheet length This allows for the control of the phase and amplitude of the electromagnetic waves leaking out at each local location, ultimately enabling the presentation of the Airy beam.

[0018] Secondly, this invention proposes an Airy beam generation method, comprising the following steps:

[0019] S1. Determination of operating frequency and device construction;

[0020] Based on the conventional dispersion relation derivation method for waveguides with a metal block / air / gyromagnetic material structure, the dispersion characteristics of the waveguide with this structure are obtained, and its unidirectional transmission frequency range is determined accordingly. Based on this, the operating frequency is selected, and a metasurface device is constructed. The metasurface device includes a gyromagnetic material layer 3 extending along the unidirectional waveguide transmission direction on a horizontal plane. The unidirectional waveguide transmission direction is defined as the x-axis, the horizontal plane perpendicular to the x-axis is defined as the y-axis, and the horizontal plane perpendicular to the z-axis is defined as the z-axis. One end of the metasurface device in the x-axis direction is... At the light incident end, a queue of several metal blocks 1 arranged at equal intervals along the x-axis is provided above the gyromagnetic material layer 3. Each metal block 1 is composed of a first rectangular body 11 in the horizontal direction and a second rectangular body 12 in the vertical direction. The second rectangular body 12 is connected to the middle of the first rectangular body 11 and extends downward. The spacing between adjacent metal blocks 1 is defined as p. An air medium layer 2 separates the metal blocks 1 from the gyromagnetic material layer 3. A combination of a single metal block 1, the air medium layer flush with it above and below, and the gyromagnetic material layer below it is defined as a leakage wave unit.

[0021] S2. Establish the correspondence between the geometric parameters of the leakage wave unit and the leakage wave phase and amplitude;

[0022] Change the thickness of the air dielectric layer 2 of the first leaky wave unit from the incident end Obtain the phase of the leaky wave unit. and The correspondence; adjust the thickness of the air dielectric layer 2 of the second leaky wave unit furthest from the incident end in any pair of adjacent leaky wave units on the x-axis. Obtain the phase difference of this pair of leaky wave elements. and The corresponding relationship; then, adjust the length of metal block 1 of any leaky wave unit. Based on the effect of its changes on the amplitude of the leakage wave, the leakage wave amplitude is obtained. Length of metal block 1 The correspondence is then established; the obtained correspondence is extended to all leaky wave elements, thereby establishing the following three sets of mapping relationships:

[0023] The first leaky wave unit has an air dielectric layer thickness of 2. Its phase Mapping; thickness of the air dielectric layer 2 in the second leaky cell of any adjacent leaky cell pair Phase difference Mapping; length of metal block 1 With leakage wave amplitude The mapping relationships described above are not limited to a specific unit, but are universally applicable to all leaky wave units. This is mainly because: 1) the electromagnetic response of each leaky wave unit is primarily determined by its own parameters, not by its absolute position; 2) the operating frequency is fixed within the single-mode range, preventing the introduction of additional modal coupling; 3) the arrangement of leaky wave units is periodic, thus possessing local equivalent characteristics. Under these conditions, the phase modulation of each unit depends on the thickness of its air dielectric layer. Amplitude modulation depends on the length of the metal block. ,thus → , → as well as → The mapping relationship holds true for all leaky wave elements.

[0024] S3. Solve for the complex amplitude distribution of a one-dimensional Airy beam;

[0025] Based on the finite-energy Airy solution of the paraxial diffraction equation, the complex amplitude distribution of the target Airy beam is obtained, and the target distribution is discretized into multiple sampling points to determine the target phase at each position. and amplitude ;

[0026] S4. Inversely calculate the element geometric parameters to achieve target complex amplitude control;

[0027] Based on the three sets of mapping relationships established in step S2 ( → , → , → The required air dielectric layer thickness for each leakage wave element is calculated. With the length of the metal block ;

[0028] S5. Construct a metasurface complex amplitude modulation device based on unidirectional electromagnetic mode;

[0029] Based on the air dielectric layer thickness and metal block length of each leaking wave unit obtained in step S4, adjust the air dielectric layer thickness and metal block length of the leaking wave unit on the metasurface device; inject light along the x-axis from the light incident end to generate the target Airy beam.

[0030] Preferably, the target Airy beam is a one-dimensional finite-energy Airy beam, whose propagation is based on the finite-energy Airy solution of the paraxial diffraction equation:

[0031]

[0032] in, As the normalization factor, The attenuation coefficient is... For wave vector, For the Airy function;

[0033] The innovation of this invention is:

[0034] 1. Decoupling and Direct Control of Complex Amplitude Based on Magnetic Surface Plasmon Polaritons: This invention creatively combines a gyromagnetic material layer with a periodic T-shaped metal block structure to construct a waveguide-driven leaky wave metasurface supporting unidirectional propagation of magnetic surface plasmon polaritons. This structure exhibits non-reciprocal transport characteristics under an external magnetic field, fundamentally suppressing backscattering and improving system robustness. More importantly, by introducing the geometrical degree of freedom of the T-shaped metal block, this invention overcomes the limitation of existing unidirectional metasurfaces that can only control the phase, achieving independent and decoupled control of phase and amplitude on a unidirectional leaky wave platform: the phase is continuously adjusted by the air layer thickness, and the amplitude is independently controlled by the horizontal arm length of the T-shaped metal block. Therefore, the complex amplitude of free-space propagating waves can be arbitrarily controlled, providing a physical basis for the generation of complex wavefronts (such as Airy beams and flat-top beams).

[0035] 2. Independent and decoupled phase and amplitude control is achieved, eliminating the need for complex coupling parameter search algorithms: This invention introduces an independent amplitude control dimension on a unidirectional waveguide platform. By establishing a direct mapping relationship between structural parameters and electromagnetic response, complex amplitude control is physically separated into two independent structural parameters: phase is determined by the thickness of the air dielectric layer. Independent control; amplitude determined by the horizontal length of the T-shaped metal block. Independent control. This invention only needs to determine the two parameters of each element according to the target complex amplitude distribution through mapping relationship, avoiding cumbersome global optimization and realizing true decoupled control capability of complex amplitude.

[0036] 3. Application and Extension from Near-Field Evanescent Wave Manipulation to Free-Space Radiation Fields: Unlike cutting-edge research focusing on deep subwavelength near-field sub-diffraction focusing (requiring evanescent wave excitation), this invention addresses the generation of complex optical fields in far-field free space, where the spectrum of the target wavefront (such as an Airy beam) lies entirely within the transmission wave range. This invention proposes a novel leaky metasurface structure based on T-shaped metal units, achieving efficient manipulation of the free-space radiation field. This design overcomes the limitations of existing USMP and other schemes, which are limited to near-field evanescent wave manipulation, successfully extending the complex amplitude manipulation capability from the local evanescent field to far-field radiation waves. It is suitable for practical applications such as wireless communication and radar imaging, possessing both engineering feasibility and system practicality.

[0037] 4. A high-performance, easily integrated on-chip Airy beam generation solution is provided: Compared with pure phase solutions that rely on external light sources and mechanical tuning, this invention eliminates the need for free-space incident light, spatial light modulators (SLMs), and rotation mechanisms, providing an on-chip solution that can replace SLMs. This solution is based on an integrated device of unidirectional waveguides and metasurfaces, featuring a compact structure, no moving parts, and advantages of high stability, high integration, and low cost. It is suitable for applications with stringent requirements for system robustness, power consumption, and size (such as spaceborne communication, automotive radar, and wearable sensing), filling the gap in existing technologies for integrating complex wavefront generators.

[0038] In summary, this invention constructs a non-reciprocal leaky metasurface supporting decoupled manipulation of complex amplitudes based on the unidirectional transport mechanism of magnetic surface plasmon resonances. Through the structural design of a gyromagnetic material layer and T-shaped metal block units, independent control of phase and amplitude at the physical level is achieved, establishing a direct, decoupled complex amplitude mapping relationship. This design not only eliminates the reliance on traditional complex optimization algorithms but also overcomes the limitations of near-field manipulation, effectively extending the ability to manipulate arbitrary complex amplitudes to far-field radiation systems. Furthermore, this invention successfully integrates the generation function of high-performance complex wavefronts (such as Airy beams) onto a single chip, providing a key technological foundation for compact and robust novel optoelectronic systems.

[0039] The working principle of this invention is to construct a leaky metasurface that supports unidirectional propagation of magnetic surface plasmon resonances by combining a gyromagnetic material layer with a periodically arranged T-shaped metal block structure. This structure exhibits non-reciprocal transport characteristics under the influence of an external magnetic field, allowing electromagnetic waves to propagate only in a single direction. Electromagnetic energy is radiated into free space through subwavelength slits between the metal blocks, forming a leaky wave. The thickness of the air dielectric layer in each leaky wave unit can be independently adjusted (…). ) and the length of the metal block ( The phase and amplitude of the leaked wave can be flexibly controlled. Phase control originates from the change in wave propagation constant caused by different air layer thicknesses, thus accumulating different phase delays; amplitude control is achieved by adjusting the slit size by changing the length of the metal block. The longer the metal block and the smaller the slit, the smaller the amplitude. In this invention, a metasurface based on a unidirectional electromagnetic mode can achieve arbitrary control of complex amplitude without the need for external free-space light incidence, ultimately generating a target wavefront with a specific complex amplitude distribution in free space.

[0040] The advantages of this invention are:

[0041] 1. Overcoming the limitations of phase modulation in unidirectional leaky metasurfaces to achieve decoupled modulation of complex amplitude of free-space propagating waves: This invention establishes... → , → as well as → For the first time, three sets of mapping relationships allow for independent decoupling and control of phase and amplitude on a unidirectional leaky metasurface platform. This advantage stems from the reduction of the length of the T-shaped metal block ( ) is used as the amplitude control parameter, and the thickness of the air medium layer ( This innovative design of phase control parameters overcomes the limitation of the original technology (Comparative Document 1), which states that unidirectional leaky metasurfaces can only control the phase. Building upon this, the present invention further overcomes the fundamental defect of traditional metasurfaces proposed in Comparative Document 2, which require large-scale parameter scanning and approximate matching algorithms due to phase-amplitude parameter coupling. By establishing a direct mapping relationship between structural parameters and electromagnetic response, it achieves direct and precise complex amplitude control without global optimization, providing a key technological foundation for the generation of high-fidelity complex wavefronts such as Airy beams.

[0042] 2. Specifically designed for generating complex optical fields in far-field free space, this invention extends functionality from near-field manipulation of evanescent waves to far-field manipulation of propagating waves: For typical far-field optical fields such as Airy beams, whose complex amplitude spectrum lies entirely within the propagating wave range, there is no need to excite evanescent waves. This invention utilizes subwavelength slits between T-shaped metal blocks to achieve efficient energy radiation and wavefront shaping. Optical field manipulation is expanded from localized evanescent field manipulation to complex amplitude manipulation of free-space radiated waves, providing a new technical approach for far-field wavefront manipulation applications such as wireless communication and radar imaging.

[0043] 3. Simple structure, low cost, and easy on-chip integration: Compared with traditional systems that rely on external light sources and dynamic control mechanisms (such as spatial light modulators SLM), this invention uses a metasurface driven by unidirectional electromagnetic modes, which does not require external free space light incidence and has good on-chip integration potential. It significantly reduces manufacturing costs and system complexity, laying a solid foundation for realizing a high-performance, easily integrated on-chip wavefront control system.

[0044] 4. Endowing the generated beam with unique properties of high precision, high stability, and non-reciprocity: This invention benefits from the aforementioned three sets of mapping relationships ( → , → as well as → The flexible complex amplitude control provided by the waveguide, along with the inherent immune backscattering characteristics of the unidirectional magnetic surface plasma waveguide, significantly enhances the overall performance of the generated Airy beam. In terms of accuracy, independent control of the complex amplitude ensures that the beam's transverse intensity distribution closely matches theoretical expectations; in terms of stability, the non-reciprocal transport mechanism effectively suppresses environmental reflections and interference, guaranteeing the reliability and controllability of the beam trajectory. Attached Figure Description

[0045] Figure 1 This is a structural diagram of the metasurface complex amplitude control device based on unidirectional electromagnetic mode of the present invention.

[0046] Figure 2 This is a top view of the metasurface complex amplitude control device based on unidirectional electromagnetic mode according to the present invention.

[0047] Figure 3 This is a bottom view of the metasurface complex amplitude control device based on unidirectional electromagnetic mode according to the present invention.

[0048] Figure 4 This is a front view of the metasurface complex amplitude control device based on unidirectional electromagnetic mode according to the present invention.

[0049] Figure 5 This is a side view of the metasurface complex amplitude control device based on unidirectional electromagnetic mode according to the present invention.

[0050] Figure 6 This is a detailed diagram of the leakage wave unit of the metasurface complex amplitude control device based on unidirectional electromagnetic mode of the present invention.

[0051] Figure 7 This is the dispersion relation curve of the waveguide structure of the "metal sheet / air / magnetic material" of the present invention.

[0052] Figure 8 This is a simulation of the "metal sheet / air / gyromagnetic material" waveguide structure of the present invention at an operating frequency of 8.5 GHz. Field distribution.

[0053] Figure 9 This is a schematic diagram of the periodic leaky metasurface unit structure designed based on the unique dispersion characteristics of the "metal sheet / air / magnetic material" waveguide structure of the present invention.

[0054] Figure 10 This is a schematic diagram of the leakage principle of the metasurface complex amplitude control device based on unidirectional electromagnetic mode of the present invention.

[0055] Figure 11 This is the initial phase of the present invention. With air medium layer thickness The relationship.

[0056] Figure 12 The phase difference of the present invention With air medium layer thickness The relationship.

[0057] Figure 13 This is the line of the present invention Directional Airy beam phase distribution.

[0058] Figure 14 This is the line of the present invention Directional Airy beam amplitude distribution.

[0059] Figure 15a This is a diagram illustrating the effect of the Airy beam characterization in Embodiment 1 of the present invention.

[0060] Figure 15b This is a characterization effect diagram of the self-healing verification of the Airy beam in Embodiment 2 of the present invention. Detailed Implementation

[0061] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.

[0062] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0063] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0064] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a connection that allows communication between them; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0065] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0066] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0067] The present invention will now be described in detail with reference to the accompanying drawings and exemplary embodiments.

[0068] Example 1

[0069] This embodiment relates to an Airy beam generation method, including the following steps:

[0070] S1. Determination of operating frequency and device construction;

[0071] Based on the conventional dispersion relation derivation method for waveguides with a bulk metal / air / gyromagnetic material structure, the dispersive characteristics (e.g., ...) of waveguides with a bulk metal / air / gyromagnetic material structure are obtained. Figure 7 The unidirectional transmission frequency range is determined based on this; the operating frequency is selected based on this, and a metasurface device is constructed; the metasurface device includes a gyromagnetic material layer 3 extending along the unidirectional waveguide transmission direction on a horizontal plane, the unidirectional waveguide transmission direction is defined as the x-axis, the horizontal plane perpendicular to the x-axis is the y-axis, and the horizontal plane perpendicular to the z-axis is the z-axis, and one end of the metasurface device in the x-axis direction is the light incident end; above the gyromagnetic material layer 3 is a queue composed of several metal blocks 1 arranged at equal intervals along the x-axis direction, the metal blocks 1 are composed of a first rectangular body 11 in the horizontal direction and a second rectangular body 12 in the vertical direction, the second rectangular body 12 is connected to the middle of the first rectangular body 11 and extends downward; the spacing between adjacent metal blocks 1 is defined as p; an air dielectric layer 2 separates the metal blocks 1 and the gyromagnetic material layer 3; a combination of a single metal block 1, the air dielectric layer flush with it above and below, and the gyromagnetic material layer below it is defined as a leakage wave unit (e.g. Figure 9 );

[0072] S2. Establish the correspondence between the geometric parameters of the leakage wave unit and the leakage wave phase and amplitude;

[0073] Change the thickness of the air dielectric layer 2 of the first leaky wave unit from the incident end Obtain the phase of the leaky wave unit. and The correspondence (e.g.) Figure 11 Adjust the thickness of the air dielectric layer 2 of the second leaky wave unit furthest from the incident end in any pair of adjacent leaky wave units on the x-axis. Obtain the phase difference of this pair of leaky wave elements. and The correspondence (e.g.) Figure 12 Then, adjust the length of metal block 1 of any leaky wave unit. Based on the effect of its changes on the amplitude of the leakage wave, the leakage wave amplitude is obtained. Length of metal block 1 The correspondence is then established; the obtained correspondence is extended to all leaky wave elements, thereby establishing the following three sets of mapping relationships:

[0074] The first leaky wave unit has an air dielectric layer thickness of 2. Its phase Mapping; thickness of the air dielectric layer 2 in the second leaky cell of any adjacent leaky cell pair Phase difference Mapping; length of metal block 1 With leakage wave amplitude Mapping;

[0075] The above three sets of mapping relationships are not limited to a specific unit, but are universally applicable to all leaky wave units. The main reasons are: 1) The electromagnetic response of each leaky wave unit is primarily determined by its own parameters, not by its absolute position; 2) The operating frequency is fixed within the single-mode range, preventing the introduction of additional modal coupling; 3) The arrangement of the leaky wave units is periodic, thus possessing local equivalent characteristics. Under these conditions, the phase modulation of each unit depends on the thickness of its air dielectric layer. Amplitude modulation depends on the length of the metal block. ,thus → , → as well as → The mapping relationship holds true for all leaky wave elements.

[0076] S3. Solve for the complex amplitude distribution of a one-dimensional Airy beam;

[0077] Based on the finite-energy Airy solution of the paraxial diffraction equation, the complex amplitude distribution of the target Airy beam is obtained, and the target distribution is discretized into multiple sampling points to determine the target phase at each position. and amplitude ;

[0078] S4. Inversely calculate the element geometric parameters to achieve target complex amplitude control;

[0079] Based on the three sets of mapping relationships established in step S2 ( → , → , → The required air dielectric layer thickness for each leakage wave element is calculated. With the length of the metal block ;

[0080] S5. Construct a metasurface complex amplitude modulation device based on unidirectional electromagnetic mode;

[0081] Based on the air dielectric layer thickness and metal block length of each leaking wave unit obtained in step S4, adjust the air dielectric layer thickness and metal block length of the leaking wave unit on the metasurface device; inject light along the x-axis from the light incident end to generate the target Airy beam.

[0082] Preferably, the target Airy beam is a one-dimensional finite-energy Airy beam, whose propagation is based on the finite-energy Airy solution of the paraxial diffraction equation:

[0083]

[0084] in, As the normalization factor, The attenuation coefficient is... For wave vector, For the Airy function;

[0085] Example 2

[0086] This embodiment, based on Embodiment 1 of the present invention, further characterizes the generated Airy beam, specifically including the following steps:

[0087] A1: Determination of geometric parameters for leakage wave unit

[0088] The metasurface complex amplitude modulation device model constructed in Example 1 is called, and the three sets of mapping relationships established in steps S2–S4 are used ( → , → , → First, the required complex amplitude distribution of the Airy beam is obtained through numerical solution. In the simulation, the complex amplitude (including amplitude and phase) of the target Airy beam is sampled at 16mm intervals along the x-axis, resulting in a total of 30 sampling points. Each sampling point corresponds to the design parameters of a drain element. Then, the air dielectric layer thickness and metal block length of the corresponding drain element are calculated based on the target complex amplitude of each sampling point. Finally, the air dielectric layer thickness and metal block length of all drain elements are compiled into Tables 1 and 2, providing numerical basis for simulation verification and device design, thereby ensuring that the metasurface device can realize the complex amplitude distribution of the entire target Airy beam.

[0089] A2: Acquisition and Verification of Complex Amplitude at the Slit of the Leakage Element

[0090] The complex amplitude modulation device model of the metasurface constructed in Example 1 was called in the electromagnetic simulation software to calculate the complex amplitude of the electromagnetic field at the slit between each leakage wave unit. The amplitude was obtained by line integration along the x-direction of the slit, and the phase was obtained by point calculation at the center point of the slit. Sampling was performed at 16mm intervals along the x-direction of the slit for numerical comparison between the simulation results and the theoretical Airy beam.

[0091] The simulation results of amplitude and phase at each sampling point are compared and analyzed with the complex amplitude of the theoretical Airy beam at the corresponding position, such as... Figure 13 and Figure 14 As shown in the figure, the theoretical distribution curve and simulation results are displayed simultaneously, and the degree of agreement between the transverse light intensity and phase distribution is analyzed.

[0092] The parameters of the ideal Airy beam are as follows: normalization factor 45mm; attenuation coefficient The value is 0.04, and the main lobe width is 106 mm;

[0093] Simulation results show that the main lobe width of 104 mm is highly consistent with the theoretical value; the generated Airy beam (such as...) Figure 15a The transverse light intensity conforms to the Airy function, exhibiting an asymmetric structure of a main lobe region (central bright spot) and a series of gradually decaying side lobes. Furthermore, the complex amplitude distribution matches the theoretical design, thus verifying that the device achieves precise control of the target complex amplitude.

[0094] A3: Verification of Airy Beam's Self-Healing Function

[0095] Based on the Airy beam generated in Example 1, an obstacle was added to the propagation path of the Airy beam. The obstacle was a metal plate with a length of 48 mm and a width of 32 mm, placed at the main lobe of the Airy beam, and characterized. The characterization results are as follows: Figure 15b As shown, when the main lobe is blocked, the energy of the side lobes (secondary bright spots) will refill the damaged area through diffraction and interference effects, thus restoring the overall profile of the beam. This result proves that the Airy beam generated by metasurface devices has self-healing properties.

[0096] Example 3

[0097] This embodiment provides an Airy beam generating device, the structure of which is as follows: Figures 1 to 6 As shown. Figure 1 As shown, the device includes a gyromagnetic material layer 3 extending along the unidirectional waveguide propagation direction on a horizontal plane. The unidirectional waveguide propagation direction is defined as the x-axis, the direction perpendicular to the x-axis on the horizontal plane is defined as the y-axis, and the direction perpendicular to the horizontal plane is defined as the z-axis. Above the gyromagnetic material layer 3, a metal block array is provided along the x-axis direction. The metal block array consists of metal blocks 1 arranged at equal intervals.

[0098] like Figure 2 and Figure 3 As shown, the metal block 1 has a T-shaped cross-section, consisting of a first rectangular body 11 in the horizontal direction and a second rectangular body 12 in the vertical direction. The second rectangular body 12 is connected to the middle of the first rectangular body 11 and extends vertically downward. The length of the first rectangular body 11 along the x-axis is defined as the length of the metal block 1. An air dielectric layer 2 separates the metal block 1 and the gyromagnetic material 3. The metal block 1, the air dielectric layer 2, and the gyromagnetic material layer 3 below them together form a leakage wave unit (e.g., ...). Figure 6 ).

[0099] Preferred, such as Figure 4 and Figure 5As shown, the spacing between adjacent T-shaped metal sheets is p = 16 mm; wherein, the first rectangular body 11 extends along the x-axis, with a width of w = 8 mm and a thickness of h = 0.5 mm; the second rectangular body 12 extends along the z-axis, with a length of l = 1 mm and a width of w = 8 mm. The thickness of the gyromagnetic material layer 3 is t = 50 mm, and its remanence direction is along the y-axis. Under the action of an external magnetic field perpendicular to the waveguide propagation direction, it generates a permeability tensor, causing the magnetic surface plasmon polaritons to exhibit non-reciprocal propagation characteristics, thereby ensuring that the electromagnetic field propagates only in a single direction (e.g., Figure 8 ).

[0100] In this structure, the thickness of the air dielectric layer 2 required for the leakage wave unit and the length of the metal block 1 are respectively determined by three sets of mapping relationships ( → , → , → The calculations determine the following: the mapping between the thickness and phase of the air dielectric layer in the first leaking wave unit; the mapping between the thickness and phase difference of the air dielectric layer in the next unit after centering any adjacent unit; and the mapping between the length of metal block 1 and the leakage wave amplitude. By independently designing the thickness of the air dielectric layer and the length of the metal block, the phase and amplitude of the electromagnetic wave leaking out at each local location can be flexibly controlled.

[0101] The operating center frequency of the device described in this embodiment is 8.5 GHz. In practical applications, the leakage units of the metasurface device are subwavelength scale, supporting the unidirectional propagation of magnetic surface plasmon resonances (MSPs) and leaking into free space through the slits between the T-shaped metal blocks (e.g., Figure 10 Because each leaky wave unit has different geometric parameters, the leaky wave electromagnetic wave is precisely controlled in amplitude and phase, ultimately generating the required complex amplitude distribution in free space.

[0102] This embodiment demonstrates that the device of the present invention can not only replace the traditional spatial light modulator to achieve wavefront complex amplitude modulation, but also has the advantages of simple structure, easy integration and low cost, providing a reliable device basis for efficient wavefront modulation and Airy beam generation based on metasurfaces.

[0103] Table 1: Designed Devices Distribution map (unit: millimeters)

[0104]

[0105] Table 2: Designed Devices Distribution map (unit: millimeters)

[0106]

[0107] Example 4

[0108] This embodiment relates to an Airy beam generating device, including a gyromagnetic material layer 3 extending along the unidirectional waveguide transmission direction on a horizontal plane. The unidirectional waveguide transmission direction is defined as the x-axis, the direction perpendicular to the x-axis on the horizontal plane is defined as the y-axis, and the direction perpendicular to the horizontal plane is defined as the z-axis. A metal block array is arranged above the gyromagnetic material layer 3 along the x-axis. The metal block array consists of equidistantly arranged metal blocks 1. The cross-section of each metal block 1 is T-shaped and consists of a first rectangular body 11 in the horizontal direction and a second rectangular body 12 in the vertical direction. The second rectangular body 12 is connected to the middle of the first rectangular body 11 and extends vertically downward. The length of the first rectangular body 11 along the x-axis is defined as the length of the metal block 1. ;

[0109] An air dielectric layer 2 separates the metal block 1 and the gyromagnetic material 3; the metal block 1, the air dielectric layer 2, and the gyromagnetic material layer 3 below them constitute a leakage wave unit; the remanent magnetization direction of the gyromagnetic material layer 3 is the y-axis direction;

[0110] Air dielectric layer thickness required for leakage wave unit Length of metal block 1 It consists of three sets of mapping relationships ( → , → , → The thickness of the air dielectric layer 2 in the first leakage wave unit is determined by calculation. Its phase Mapping; thickness of the air medium layer 2 in the middle of any adjacent unit pair Phase difference Mapping; length of metal block 1 With leakage wave amplitude The mapping. Preferably, the thickness of the gyromagnetic material 3 is t=50 mm, and the dielectric constant is... Magnetic permeability is ,in , Its permeability is in tensor form.

[0111] The spacing between adjacent T-shaped metal sheets is p=16mm; the x-axis direction is defined as the length direction, the y-axis direction as the width direction, and the z-axis direction as the thickness direction; wherein the first rectangular body 11 extends along the x-axis, with a width of w=8 mm and a thickness of h=0.5mm; the second rectangular body 12 extends along the z-axis direction, with a length of l=1 mm and a width of w=8mm.

[0112] More specifically, the leakage units of metasurface devices are subwavelength scale, supporting unidirectional propagation of magnetic surface plasmon polaritons, allowing electromagnetic waves to leak out from the slits, and the complex amplitude of the transmitted wave can be controlled in free space by independently adjusting the size of the metal block and the thickness of the air dielectric layer.

[0113] The operating center frequency of the metasurface device is 8.5 GHz.

[0114] More specifically, the gyromagnetic material layer 3 generates a permeability tensor under the action of an external magnetic field perpendicular to the waveguide propagation direction, causing the magnetic surface plasmons to exhibit non-reciprocal propagation characteristics, and the electromagnetic field propagates only in a single direction.

[0115] This structure supports a unidirectional electromagnetic mode (magnetic surface plasmon resonance). During the propagation of the magnetic surface plasmon resonance, electromagnetic waves leak out through the slits between the T-shaped metal sheets; simultaneously, the wave vector in the leakage unit... Determined by the thickness of the air medium layer The decision is made, and then the air medium layers of different thicknesses are passed through. The phases accumulated by the unit structures are different, and at the same time, the amplitude of the electromagnetic wave is determined by the length of the T-shaped metal block. It is determined that the longer the metal block is, the smaller the gap between adjacent metal blocks, and the smaller the amplitude of the leaked electromagnetic wave. Therefore, the thickness of the air dielectric layer in each unit structure is designed accordingly. and T-shaped metal sheet length This allows for the control of the phase and amplitude of the electromagnetic waves leaking out at each local location, ultimately enabling the presentation of the Airy beam.

Claims

1. An Airy beam generating device, characterized in that: it includes a gyromagnetic material layer (3) extending along the unidirectional waveguide transmission direction on a horizontal plane, the unidirectional waveguide transmission direction is defined as the x-axis, one end of the x-axis is the incident end, the direction perpendicular to the x-axis on the horizontal plane is the y-axis, and the direction perpendicular to the horizontal plane is the z-axis; a metal block array is provided above the gyromagnetic material layer (3) along the x-axis direction, the metal block array is composed of metal blocks (1) arranged at equal intervals, the cross-section of the metal block (1) is T-shaped, and it is composed of a first rectangular body in the horizontal direction and a second rectangular body in the vertical direction, the second rectangular body is connected to the middle of the first rectangular body and extends vertically downward; the length of the first rectangular body on the x-axis is defined as the length of the metal block (1). ; An air medium layer (2) separates the metal block (1) and the gyromagnetic material layer (3); the metal block (1), the air medium layer (2) and the gyromagnetic material layer (3) below it form a leakage wave unit; the remanent magnetization direction of the gyromagnetic material layer (3) is the y-axis direction; The distance between the bottom of the second rectangular body and the gyromagnetic material layer (3) is defined as the thickness of the air dielectric layer (2). The thickness of the air medium layer (2) Length of metal block (1) Three sets of mapping relationships ( → , → , → The thickness of the air dielectric layer (2) of the first leakage wave unit is determined by calculation. Its phase Mapping; thickness of the air medium layer (2) in the middle of any adjacent unit pair Phase difference Mapping; length of metal block (1) With leakage wave amplitude The mapping.

2. The Airy beam generating device according to claim 1, characterized in that: The thickness of the gyromagnetic material layer (3) is t=50 mm, and the dielectric constant is Magnetic permeability is ,in , ; It is the operating angular frequency; Its permeability It is in tensor form.

3. The Airy beam generating device according to claim 1, characterized in that: The spacing between adjacent metal blocks is p=16mm; the x-axis direction is defined as the length direction, the y-axis direction as the width direction, and the z-axis direction as the thickness direction; the first rectangular body (11) extends along the x-axis with a width of w=8 mm and a thickness of h=0.5mm; the second rectangular body (12) extends along the z-axis with a length of l=1 mm and a width of w=8mm.

4. A method for generating Airy beams, comprising the following steps: S1. Determination of operating frequency and device construction; Based on the conventional dispersion relation derivation method of waveguides with metal block / air / gyromagnetic material structure, the dispersion characteristics of waveguides with metal block / air / gyromagnetic material structure are obtained, and their unidirectional transmission frequency range is determined accordingly; on this basis, the operating frequency is selected, and a metasurface device is constructed; the metasurface device includes a gyromagnetic material layer (3) extending along the unidirectional waveguide transmission direction on the horizontal plane, the unidirectional waveguide transmission direction is defined as the x-axis, the horizontal plane perpendicular to the x-axis is the y-axis, and the horizontal plane perpendicular to the z-axis is the z-axis, and one end of the metasurface device in the x-axis direction is the light incident end; Above the gyromagnetic material layer (3) is a queue of several metal blocks (1) arranged at equal intervals along the x-axis. Each metal block (1) is composed of a first rectangular body (11) in the horizontal direction and a second rectangular body (12) in the vertical direction. The second rectangular body (12) is connected to the middle of the first rectangular body (11) and extends downward. The spacing between adjacent metal blocks (1) is defined as p. An air medium layer (2) separates the metal blocks (1) and the gyromagnetic material layer (3). The metal blocks (1), the air medium layer (2) and the gyromagnetic material layer (3) below them form a leakage wave unit. S2. Establish the correspondence between the geometric parameters of the leakage wave unit and the leakage wave phase and amplitude; The distance between the bottom of the second rectangular body and the gyromagnetic material layer (3) is defined as the thickness of the air dielectric layer (2). ; Change the thickness of the air dielectric layer (2) of the first leaky wave unit from the incident end Obtain the phase of the leaky wave unit. and The correspondence; adjust the thickness of the air dielectric layer (2) of the second leaky wave unit furthest from the incident end in any pair of adjacent leaky wave units on the x-axis. Obtain the phase difference of this pair of leaky wave elements. and The correspondence; then, adjust the length of the metal block (1) of any leaky wave unit. Based on the effect of its changes on the amplitude of the leakage wave, the leakage wave amplitude is obtained. Length of metal block (1) The correspondence is then established; the obtained correspondence is extended to all leaky wave elements, thereby establishing the following three sets of mapping relationships: The thickness of the first leaky wave unit air dielectric layer (2) Its phase Mapping; thickness of the air dielectric layer (2) of the second leaky cell in any adjacent leaky cell pair Phase difference Mapping; length of metal block (1) With leakage wave amplitude Mapping; S3. Solve for the complex amplitude distribution of a one-dimensional Airy beam; Based on the finite-energy Airy solution of the paraxial diffraction equation, the complex amplitude distribution of the target Airy beam is obtained, and the target distribution is discretized into several sampling points on the metasurface device to determine the target phase corresponding to each position. and amplitude ; S4. Inversely calculate the element geometric parameters to achieve target complex amplitude control; Based on the three sets of mapping relationships established in step S2 ( → , → , → The required air dielectric layer (2) thickness for each leakage wave unit was calculated. Length of metal block (1) ; S5. Construct a metasurface complex amplitude modulation device based on unidirectional electromagnetic mode; Based on the thickness of the air dielectric layer (2) and the length of the metal block (1) of each leaking wave unit obtained in step S4, adjust the thickness of the air dielectric layer (2) and the length of the metal block (1) of the leaking wave unit on the metasurface device; inject light along the x-axis from the light incident end to generate the target Airy beam.

5. The Airy beam generation method according to claim 4, characterized in that: The target Airy beam is a one-dimensional finite-energy Airy beam, and its propagation is based on the finite-energy Airy solution of the paraxial diffraction equation: in, These are the coordinates on the x-axis; These are the coordinates on the z-axis; As the normalization factor, The attenuation coefficient is... For wave vector, This is the Airy function.

6. The Airy beam generation method according to claim 4, characterized in that, The process of obtaining the dispersion characteristics of a unidirectional waveguide with a metal block / air / gyromagnetic material structure in S1 is as follows: Under an applied bias magnetic field, the dispersion relation of the waveguide composed of the metal block / air dielectric layer / gyromagnetic material is derived based on Maxwell's equations and boundary conditions, and the dispersion relation indicates the frequency range of the waveguide composed of the metal block / air dielectric layer / gyromagnetic material with unidirectional transmission characteristics.

7. The Airy beam generation method according to claim 4, characterized in that: The waveguide, which is composed of a metal block / air dielectric layer / magnetic material, has a frequency range of 7.5 GHz to 10 GHz with unidirectional transmission characteristics.

8. The Airy beam generation method according to claim 7, characterized in that: The operating frequency selected within the frequency range with unidirectional transmission characteristics is 8.5 GHz.

9. The Airy beam generation method according to claim 4, characterized in that: The specific process of step S2 is as follows: Change the thickness of the air dielectric layer (2) of the first leaky wave unit from the incident end. Electromagnetic simulation software was used to calculate different thickness values. Phase of the slit between the lower element and the second leaky element ,by The air dielectric layer (2) thickness of the first leaky wave unit is established by fitting a function to the independent variable. Its phase The first mapping relationship; Adjust the thickness of the air dielectric layer (2) of any pair of adjacent leaky wave elements on the x-axis, specifically the leaky wave element furthest from the incident end. Meanwhile, keeping the geometric parameters of the leakage wave element near the incident end constant, electromagnetic simulation software was used to calculate different thickness values. The phase difference between the slits of the adjacent leaky wave element pairs ,by To establish the air dielectric layer thickness of the second leaky wave unit, a function is fitted to the independent variable. Phase difference The second mapping relationship; Adjust the length of the metal block in any leaky wave unit Electromagnetic simulation software was used to calculate different length values. The leakage amplitude of the leakage element ,by The length of the metal block (1) was obtained by fitting a function to the independent variable. With leakage wave amplitude The third mapping relationship.

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