Metasurface and Method for Generating Orbital Angular Momentum Vortex Beam Arrays

Abstract

This invention discloses a metasurface and method for generating an orbital angular momentum vortex beam array. The metasurface includes a central region and N edge regions, which are symmetrically arranged along the central region. Each edge region comprises a unit structure with a gradually changing arrangement from the center to the edge. The edge regions deflect vertically incident linearly polarized light toward the central region. The deflection angle θ and the change in the unit structure size satisfy the generalized Snell's law. The method involves incident an expanded linearly polarized laser onto the metasurface, which, after transmission through the central region, is deflected and transformed into left-handed circularly polarized light (LCP) or right-handed circularly polarized light (RCP). The N edge regions, after transmission, generate a polarization angle θ toward the central region. The deflected beams interfere with the central beam to form a vortex beam array. The metasurface is composed of subwavelength structural units arranged periodically, with a size on the order of tens to hundreds of wavelengths, facilitating chip integration and producing a stable vortex array.

Description

Technical Field

[0001] This invention belongs to the field of metasurface technology, specifically relating to a metasurface for generating orbital angular momentum vortex beam arrays. Background Technology

[0002] Orbital angular momentum (OAM) vortex beams, with their hollow intensity distribution and helical phase wavefronts, hold significant potential for applications in high-capacity optical communication, super-resolution optical imaging, micromanipulation, and quantum information, making them a current research hotspot. OAM vortex beam arrays, composed of vortex beams with identical intensity distribution and helical topological cores arranged according to a specific pattern, hold even broader application prospects in areas such as micro-etching, micro-optomechanical pumping, and parallel quantum information processing. Methods for generating OAM vortex beam arrays include spatial light modulators, spatial multi-aperture wavefront interferometry, and multi-grating diffraction. However, these methods either involve large component sizes, hindering integration, or suffer from insufficient stability. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a metasurface for generating orbital angular momentum vortex beam arrays, which facilitates chip integration and produces stable vortex arrays.

[0004] The specific plan is as follows:

[0005] A metasurface for generating an array of orbital angular momentum vortex beams is provided. The metasurface includes a central region and N edge regions, where N is a positive integer. The N edge regions are symmetrically arranged along the central region and are all fixedly connected to the central region. Each edge region includes a unit structure arranged in a gradually changing pattern from the center to the edge. The edge regions deflect vertically incident linearly polarized light toward the central region by an angle θ. The angle θ and the change in the unit structure size satisfy the generalized Snell's law.

[0006] The central region is composed of periodically arranged dielectric pillars, and the unit structure is a dielectric pillar, which is silicon or titanium dioxide.

[0007] The dielectric pillars in the central region are elliptical dielectric pillars, and the arrangement of the elliptical dielectric pillars in two-dimensional space is a square lattice or a hexagonal lattice. The dielectric pillars in the edge region are any one of circular dielectric pillars, square dielectric pillars, or trapezoidal dielectric pillars.

[0008] The central angle corresponding to each edge region is 2π / N.

[0009] The expanded linearly polarized laser beam is incident on the metasurface. After transmission through the central region, it is deflected and transformed into left-handed circularly polarized light (LCP) or right-handed circularly polarized light (RCP). After transmission through the N edge regions, it generates a polarization angle θ towards the central region. The deflected beams meet and interfere with the central beam to form a vortex beam array, wherein the central beam is either left-handed circularly polarized light (LCP) or right-handed circularly polarized light (RCP).

[0010] This invention discloses a metasurface and method for generating orbital angular momentum vortex beam arrays. The metasurface structure generates an interference vortex beam array by controlling the polarization conversion of the central beam and the deflection direction of the surrounding symmetrical beams. The metasurface is composed of subwavelength structural units arranged in a periodic manner, with a size of only tens to hundreds of wavelengths, which is convenient for chip integration, and the generated vortex array is stable. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of a metasurface structure.

[0012] Figure 2 This is a structural diagram of the central and peripheral regions.

[0013] Figure 3 It is an optical path diagram of a vortex optical array generated using metasurfaces.

[0014] Figure 4 This is a schematic diagram of the structure by which light is deflected at the edge region of a metasurface.

[0015] Figure 5 This is a schematic diagram of a polarized light coordinate system.

[0016] Figure 6 These are the XY plane light intensity distribution diagrams and the corresponding three-dimensional vortex light field distribution diagrams obtained when the center beam is RCP and the polarization angles are 0 and 0.25π.

[0017] Figure 7 These are the XY plane light intensity distribution diagrams and the corresponding three-dimensional vortex light field distribution diagrams obtained when the center beam is RCP and the polarization angles are 0.5π and 0.75π.

[0018] Among them, 1. central region, 2. edge region, 3. elliptical dielectric column, 4. circular dielectric column, 5. expanded linearly polarized laser, 6.

[0019] 7. Metasurface, 8. Linear polarized light, 9. Circular polarized light, 10. Vortex array. Detailed Implementation

[0020] The technical solutions in the embodiments of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the implementation of the present invention, and not all of it. 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.

[0021] like Figures 1 to 2 As shown, a metasurface that generates an orbital angular momentum vortex beam array is described. The metasurface includes a central region 1 and N edge regions 2, where N is a positive integer. The N edge regions 2 are symmetrically arranged along the central region 1, and all N edge regions 2 are fixedly connected to the central region 1. The edge regions 2 include unit structures arranged in a gradually changing pattern from the center to the edge. The edge regions 2 deflect vertically incident linearly polarized light toward the central region 1 at an angle of θ. The angle of deflection θ and the change in the unit structure size satisfy the generalized Snell's law.

[0022] The central region 1 is a periodically arranged dielectric pillar, and the unit structure is a dielectric pillar, which is silicon or titanium dioxide.

[0023] The dielectric pillars in the central region 1 are elliptical dielectric pillars 3, which are arranged in a two-dimensional space as either a square lattice or a hexagonal lattice. The dielectric pillars in the edge region 2 are any one of circular, square, or trapezoidal dielectric pillars. In this embodiment, the edge region 2 is preferably composed of circular dielectric pillars 4.

[0024] Each edge region 2 corresponds to a central angle of 2π / N.

[0025] like Figure 2 As shown, the central region 1 is formed by elliptical dielectric pillars 3 arranged periodically against an air background. These pillars can be made of silicon or high-dielectric-constant materials such as titanium dioxide. The elliptical dielectric pillars 3 are arranged in a two-dimensional space using either a square or hexagonal lattice. Vertically incident linearly polarized light passes through... Figure 2 The central region 1 is then converted into circularly polarized light of transmitted RCP or LCP.

[0026] The edge region 2 consists of circular dielectric pillars 4 whose size gradually changes from the center to the edge. The circular dielectric pillars 4 are arranged in a certain pattern, which can deflect vertically incident linearly polarized light towards the center at a certain angle θ. The deflection angle θ and the change in the unit structure size satisfy the generalized Snell's law.

[0027] The size of the dielectric column determines the effective refractive index and optical path length at that location, and the optical path difference between two locations determines the deflection angle. The arrangement of circular dielectric columns follows this pattern: Assuming the spacing between two adjacent columns is *a*, their radii are *r1* and *r2*, and the column length is *L*, the relationship between the dielectric column and the deflection angle θ is as follows: Where n is the refractive index of the dielectric pillar material, silicon or titanium dioxide.

[0028] like Figures 3 to 5 As shown, the method of generating an orbital angular momentum vortex beam array using the metasurface 6 involves incident an expanded linearly polarized laser 5 onto the metasurface. After transmission through the central region 1, the laser beam is deflected and transformed into circularly polarized light 8, which includes left-handed circularly polarized light LCP or right-handed circularly polarized light RCP. After transmission through N edge regions 2, linearly polarized light 7 is generated towards the central region 1, with a polarization angle θ. The deflected beams interfere with the central beam to form a vortex beam array 9, where the central beam is either left-handed circularly polarized light LCP or right-handed circularly polarized light RCP.

[0029] like Figure 4 As shown, normally light incident perpendicularly to a normal refractive surface will not change direction and will be refracted perpendicularly. However, due to phase abrupt changes at different positions, light incident perpendicularly to the metasurface in this embodiment will be deflected.

[0030] like Figure 4 As shown, the phase difference between light rays L1 and L2 after passing through metasurface 6 is... Where λ is the wavelength and θ is the deflection angle;

[0031] For those skilled in the art, phase difference = 2π / wavelength * optical path difference. The optical path difference is the segment BC that is cut off from the starting point A of one ray to another ray by drawing a perpendicular line AC.

[0032] Assuming AB is a tiny scale change dx on the metasurface, the phase change is expressed as: Therefore, the relationship between the phase change per unit size of the metasurface and the deflection angle is: Assuming the period of the transverse unit structure is 'a', then the phase difference between two adjacent unit structures is: This allows for the design of the dimensions of each unit structure.

[0033] coordinate system such as Figure 5 As shown, where θ is the deflection angle. Let z be the polarization angle in the x′-y′-z′ coordinate system. In the x′-y′-z′ coordinate system, z′ is related to the wave vector k. m The directions are the same, E m Let K be the electric field of beam m, and let the direction of the electric field of beam m be the same as the wave vector k. m The direction is perpendicular, which is also the wave vector k. m The polarization direction.

[0034] The electric field of the central beam "0" after transmission is E0=A0Exp(ik0·r)e0;

[0035] The electric fields of the transmitted edge beam m are Em =A m Exp(ik m ·r)e m ,

[0036] in,

[0037] A0 is the amplitude of the central beam, A m Let m be the amplitude of the edge beam.

[0038] k0 is the wave vector of the central beam, k m The wave vector of the edge beam.

[0039] r = xi + yj + zk is a coordinate vector.

[0040] e0 is the vector of the central beam in the polarization direction. m This is the vector of the edge beam in the polarization direction.

[0041] The wave vector of the central beam is represented as k0 = 2π / λ0,0,1).

[0042] The wave vector of the edge beam is represented as k m =2π / λsinθcosφ m ,sinθsinφ m (cosθ)

[0043] Where, φ m =2π(m-1) / N, φ m This represents the angle between the wave vector component in the xy plane and the x-axis;

[0044] polarization direction is Where ± represents LCP and RCP polarized light, and i represents the imaginary unit;

[0045] e m =R m ·J m ,

[0046] Where the rotation matrix Jones Vector Rm represents the rotation matrix of the m-th beam, and Jm represents the Jones vector of the m-th beam.

[0047] The intensity of the transmitted multi-beam interference light is Both i and j represent beam numbers, and both i and j are positive integers.

[0048] When N=6, A m =A0=1, Polarization angle The vortex beam array xy-plane light field and the corresponding three-dimensional asymmetric vortex light field distribution obtained when taking different values ​​are as follows: Figures 6 to 7 As shown. In Figure 6 and Figure 7 The values ​​on the x-axis, y-axis, and z-axis are all spatial coordinates, and the unit is micrometers.

[0049] Figure 6 Polarization angle Time, polarization angle At that time, the light field distribution diagram of the vortex beam array in the xy plane, and the corresponding three-dimensional asymmetric vortex light field distribution diagram;

[0050] Figure 7 Polarization angle Time, polarization angle The diagram shows the light field distribution of the vortex beam array in the xy plane, as well as the corresponding three-dimensional asymmetric vortex light field distribution.

[0051] from Figures 6 to 7 The distribution of the light field along the xy direction is clearly visible, showing a hexagonal lattice semi-circular asymmetric array and a vortex array distribution along the z direction.

[0052] This invention discloses a metasurface and method for generating orbital angular momentum vortex beam arrays. The metasurface structure generates an interference vortex beam array by controlling the polarization conversion of the central beam and the deflection direction of the surrounding symmetrical beams. The metasurface is composed of subwavelength structural units arranged in a periodic manner, with a size of only tens to hundreds of wavelengths, which is convenient for chip integration, and the generated vortex array is stable.

[0053] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications are also considered within the scope of protection of this invention.

Claims

1. A metasurface for generating an array of orbital angular momentum vortex beams, characterized in that: The metasurface includes a central region (1) and N edge regions (2), where N is a positive integer. The N edge regions (2) are symmetrically arranged along the central region (1), and all N edge regions (2) are fixedly connected to the central region (1). The edge regions (2) include unit structures arranged in a gradually changing pattern from the center to the edge. The edge regions (2) deflect vertically incident linearly polarized light toward the central region (1) at an angle of θ. The angle of deflection θ and the change in the unit structure size satisfy the generalized Snell's law.

2. The metasurface for generating orbital angular momentum vortex beam arrays according to claim 1, characterized in that: The central region (1) is a periodically arranged dielectric column, the unit structure is a dielectric column, and the dielectric column is silicon or titanium dioxide.

3. The metasurface for generating orbital angular momentum vortex beam arrays according to claim 2, characterized in that: The dielectric pillars in the central region (1) are elliptical dielectric pillars (3), and the elliptical dielectric pillars (3) are arranged in a two-dimensional space as a square lattice or a hexagonal lattice. The dielectric pillars in the edge region (2) are any one of circular dielectric pillars, square dielectric pillars or trapezoidal dielectric pillars.

4. The metasurface for generating orbital angular momentum vortex beam arrays according to claim 1, characterized in that: Each edge region (2) corresponds to a central angle of 2π / N.

5. A method for generating an orbital angular momentum vortex beam array using a metasurface as described in any one of claims 1 to 3, characterized in that: The expanded linearly polarized laser beam is incident on the supersurface and is deflected after being transmitted through the central region (1) into left-hand circularly polarized light LCP or right-hand circularly polarized light RCP; after being transmitted through the N edge regions (2), it generates a polarization angle θ towards the central region (1); the deflected beams meet and interfere with the central beam to form a vortex beam array, wherein the central beam is left-hand circularly polarized light LCP or right-hand circularly polarized light RCP.

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