Supercontinuum variable-order perfect vortex beam generator based on metasurface

Abstract

The application discloses a super-surface-based continuous-order-variable perfect vortex beam generator, relates to the technical field of micro-nano optics, and aims at solving the problems of non-continuous multi-order variable order and complex variable order mode in the prior art.The generator comprises a forwardly arranged super-surface one and a super-surface two;the two super-surfaces each comprise a SiO2 substrate and a micro-nano structure array;the micro-nano structure array is composed of a plurality of cylindrical monocrystalline silicon with different diameters, the period of adjacent cylindrical monocrystalline silicon is a subwavelength size, and the layout of the plurality of cylindrical monocrystalline silicon with different diameters is formed by a phase formula.The two super-surfaces can change the relative rotation angle, thereby providing additional vortex phases with different orders for a light beam, and a perfect vortex beam with continuous variable order can be generated by using only two super-surfaces; and the application has simple structure and can increase the stability of the light beam to a certain extent.

Description

Technical Field

[0001] This invention relates to the field of micro-nano optics technology, and in particular to a metasurface-based continuously variable perfect vortex beam generator. Background Technology

[0002] Compared to ordinary Gaussian beams, vortex beams possess the characteristic of carrying orbital angular momentum, and their wavefront phase surface exhibits helical branching. Due to their unique properties, such beam structures have attracted considerable attention in several fields in recent years, such as quantum information processing, particle manipulation, and fiber optic communication. However, because the annular radius profile of the vortex intensity distribution strongly depends on the topological charge, they are not ideal for applications requiring the spatial superposition of vortex beams with different topological charges. Against this backdrop, the concept of a perfect vortex beam was proposed, which possesses a constant annular intensity distribution and a diameter independent of the topological charge.

[0003] Traditional methods for generating such beams include axial pyramids, spiral phase plates, and spatial light modulators. Axiopy generation is not conducive to the miniaturization and integration of optical platforms. While spiral phase plates offer the advantage of small size, like axial pyramids, they can only generate beams of a single order. Spatial light modulators, although capable of convenient control of multiple orders, suffer from the characteristics of liquid crystal materials, resulting in a low damage threshold and susceptibility to high-power damage. Furthermore, as active devices, they increase the size of integrated components and require additional polarizers for coordination, further compressing the usable space. All of these factors inevitably increase the complexity of the system and hinder the integration of perfect vortex beams in related fields.

[0004] A metasurface is a two-dimensional planar metamaterial composed of numerous micro- and nanostructures, with a thickness much smaller than the wavelength. The unique feature of metasurfaces is their ability to precisely manipulate the wavefront of incident light, enabling arbitrary phase transformations and optical field control. Therefore, they offer significant advantages in replacing traditional lenses.

[0005] Chinese patent publication number "CN117434720A" is titled "A Perfect Vortex Beam Multiplexing Generation Device and Its Design Method." This method proposes a non-superposition perfect vortex beam multiplexing generation device based on a geometrical phase metasurface. It can generate a perfect vortex beam with successively varying topological charges at a designed location under incident light of either left-handed or right-handed circularly polarized light at the operating wavelength. However, when faced with changes in beam order, this method still requires additional phase devices to achieve the order change, and this order change is singular, failing to meet the application requirements of perfect vortex beams in scenarios with continuously varying order. Summary of the Invention

[0006] To address the problems of discontinuous multi-order beam transformation and complex transformation methods in existing technologies, this invention provides a metasurface-based perfect vortex beam generator with continuous order transformation. This device can achieve continuous order transformation of a perfect vortex beam simply by mechanically changing the relative rotation angle between two metasurfaces. This simple design method can increase beam stability to a certain extent and also helps to realize a compact and user-friendly light source structure, which is beneficial to the further integration of micro-nano optical platforms.

[0007] The technical solution of this invention to solve the technical problem is as follows:

[0008] A continuously variable perfect vortex beam generator based on metasurfaces, comprising metasurface one and metasurface two placed in the same orientation.

[0009] Both metasurfaces comprise a SiO2 substrate and a micro / nano structure array.

[0010] The micro / nano structure array is composed of multiple cylindrical elemental silicon atoms of different diameters, and the period of adjacent cylindrical elemental silicon atoms is a subwavelength dimension.

[0011] The arrangement of the plurality of cylindrical elemental silicon atoms of different diameters is formed by the phase formula;

[0012] The phase corresponding to the metasurface satisfies formula (1):

[0013]

[0014] Where a is a positive integer. The azimuth angle is the angle corresponding to the center position of the metasurface. (x1, y1) represents the spatial coordinates of the metasurface with its center as the origin.

[0015] The parameter a is taken from the value of formula (2).

[0016]

[0017] Where n is the order of the corresponding perfect vortex beam, and θ is the relative rotation angle between the two metasurfaces.

[0018] Wherein, the phase corresponding to the second metasurface satisfies formula (3):

[0019]

[0020] in The term represents the phase of the axial cone mirror. The term represents the phase of the Fresnel focusing lens, (x2, y2) represents the spatial coordinates of the metasurface with the center as the origin, d is a preset constant, λ is the incident wavelength, and f is the position where the perfect vortex beam is generated.

[0021] In the formula, d satisfies formula (4):

[0022]

[0023] Where ρ is the ring radius of a continuously variable perfect vortex beam generated based on a metasurface.

[0024] The phase of the multiple cylindrical elemental silicon with different diameters is controlled by changing the diameter of the cylinders, and then a metasurface-micro-nano structure array is established according to the phase formula (1); a metasurface-micro-nano structure array is established according to the phase formula (3).

[0025] The two metasurfaces can provide additional vortex phases of different orders to the beam by changing the relative rotation angle (θ), thus producing a perfectly vortex beam with continuously variable order.

[0026] The continuously variable perfect vortex beam is generated at position f. The position of the generated perfect vortex beam is controlled by changing the value of f. The ring radius of the perfect vortex beam is controlled by parameter d in formula (4). The maximum continuously variable order of the perfect vortex beam can be controlled by parameter a in formula (2).

[0027] Compared with the prior art, the beneficial effects of the present invention are:

[0028] 1. Compared to using metasurfaces to generate a single-order perfect vortex beam, the two metasurfaces of this invention can provide additional vortex phases of different orders for the beam by changing the relative rotation angle, and a continuously variable perfect vortex beam can be generated using only two metasurfaces.

[0029] 2. Compared with other methods for generating perfect vortex beams with variable order, this invention only requires mechanically changing the relative rotation angle of the two metasurfaces to achieve a perfect vortex beam with continuously variable order. This structure is simple and can increase the stability of the beam to a certain extent. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of a continuously variable perfect vortex beam generator based on a metasurface according to the present invention.

[0031] Figure 2 This is a schematic diagram of the micro / nano structure and the corresponding periodic substrate structure described in the embodiments of the present invention;

[0032] Figure 3 It uses FDTD simulation to show the phase change and transmittance curves of cylindrical elemental silicon with different diameters.

[0033] Figure 4This is a schematic diagram illustrating the principle of phase superposition of different orders generated by metasurface one and metasurface two in an embodiment of the present invention.

[0034] Figure 5 (a) is the XOY plane light intensity distribution diagram of the 0th order perfect vortex beam generated at a propagation distance of 150μm when metasurface one and metasurface two are placed in the forward orientation (without relative rotation angle) in an embodiment of the present invention. Figure 5 (b) is Figure 5 (a) shows the corresponding Y-axis light intensity cross-section. Figure 5 (c) is Figure 5 The phase distribution diagram corresponding to (a);

[0035] Figure 6 The XOY plane light intensity distribution diagrams and corresponding phase distribution diagrams of the 1st, 3rd, and 6th order perfect vortex beams generated at a propagation distance of 150μm by changing the relative rotation angle of the metasurface to 4°, 12°, and 24° respectively. Detailed Implementation

[0036] The present invention will now be described in further detail with reference to the accompanying drawings.

[0037] like Figure 1 As shown, a continuously variable perfect vortex beam generator based on metasurfaces includes metasurface 1 and metasurface 2 placed in the same orientation.

[0038] Both metasurfaces include a SiO2 substrate and a micro / nano structure array, that is, they are composed of periodic micro / nano structures and corresponding periodic substrates.

[0039] The micro / nano structure array is composed of multiple cylindrical elemental silicon atoms of different diameters (D), with the period of adjacent cylindrical elemental silicon atoms being a subwavelength dimension; each micro / nano structure is a cylindrical elemental silicon atom.

[0040] The arrangement of the plurality of cylindrical elemental silicon atoms of different diameters is formed by the phase formula;

[0041] The phase corresponding to metasurface 1 satisfies formula (1):

[0042]

[0043] Where a is a positive integer. The azimuth angle is the angle corresponding to the center position of the metasurface. (x1, y1) are the spatial coordinates of the metasurface 1 with its center as the origin.

[0044] The parameter a is taken from the value of formula (2).

[0045]

[0046] Where n is the order of the corresponding perfect vortex beam, and θ is the relative rotation angle between the two metasurfaces.

[0047] Wherein, the phase corresponding to the metasurface 2 satisfies formula (3):

[0048]

[0049] in The term represents the phase of the axial cone mirror. The term represents the phase of the Fresnel focusing lens, (x2, y2) represents the spatial coordinates of the metasurface 2 with the center as the origin, d is a preset constant, λ is the incident wavelength, and f is the position where the perfect vortex beam is generated.

[0050] In the formula, d satisfies formula (4):

[0051]

[0052] Where ρ is the ring radius of a continuously variable perfect vortex beam generated based on a metasurface.

[0053] The phase of the multiple cylindrical elemental silicon with different diameters is controlled by changing the diameter of the cylinders, and then a metasurface-1 micro-nano structure array is established according to the phase formula (1); a metasurface-2 micro-nano structure array is established according to the phase formula (3).

[0054] The two metasurfaces, by changing their relative rotation angle θ, provide the beam with additional vortex phases of different orders, producing a perfect vortex beam with continuously variable order.

[0055] The continuously variable perfect vortex beam is generated at position f. The position of the generated perfect vortex beam is controlled by changing the value of f. The ring radius of the perfect vortex beam is controlled by parameter d in formula (4). The maximum continuously variable order of the perfect vortex beam is controlled by parameter a in formula (2).

[0056] Example:

[0057] like Figure 2 The diagram shows the micro / nano structure of the metasurface of this invention and its corresponding substrate, which consists of a SiO2 cube substrate and Si cylinders. The side length of each SiO2 cube, which is also the period of the micro / nano structure, is P = 0.8 μm, and the height of the Si cylinder is H = 0.9 μm.

[0058] like Figure 3As shown, the micro-nano structures that make up the metasurface are simulated using the finite-difference time-domain (FDTD) software. Each micro-nano structure has a height of H = 0.9 μm. The simulation shows the phase change and transmittance curves when light with a wavelength of 1550 nm passes through a SiO2 substrate and a Si pillar, and the diameter of a single micro-nano structure changes from 0.2 μm to 0.52 μm. During the simulation, periodic boundary conditions are set in the X and Y directions, and the propagation direction Z is set as a perfectly matched layer. Figure 3 The horizontal axis represents the diameter (μm) of the Si cylinder, the left Y-axis represents the phase change, and the right Y-axis represents the transmittance.

[0059] Figure 4 Phase diagrams of perfect vortex beams of different orders are given when there is a certain rotation angle between metasurface 1 and metasurface 2. Figure 4 The paper demonstrates the 0th, 3rd, and 6th order perfect vortex beam phase diagrams obtained when the relative rotation angles of metasurface 1 and metasurface 2 are 0, 12, and 24 degrees.

[0060] Preferably, the diameter of the continuously variable perfect vortex beam generator is 90 μm, the design parameter f is 150 μm, the wavelength λ is 1550 nm, the parameter a is 45, the parameter d is 20 μm, and the simulation boundary conditions in the X, Y, and Z directions are all set as perfectly matched layers.

[0061] like Figure 5 As shown, when the incident beam passes sequentially through a metasurface placed upright with no relative rotation angle, a perfect vortex beam of order 0 is generated. Figure 5 (a) shows the light intensity distribution of the XOY plane at a preset propagation distance f = 150 μm. Its intensity distribution conforms to the characteristics of a perfect vortex beam of order 0, that is, the beam is concentrated at the center and at the preset diameter ring. Figure 5 (b) is a cross-sectional view of the light intensity along the Y-axis at 150 μm, which can further verify the beam concentration position and the perfect ring feature, and the ring radius meets the preset. Figure 5 (c) is the phase diagram corresponding to the intensity distribution of a 0th-order perfect vortex beam in the XOY plane at 150 μm, which is related to... Figure 4 The corresponding theoretical phase diagram is consistent with that in the original text.

[0062] Figure 6 The XOY plane intensity distribution and corresponding phase diagrams of the 1st, 3rd, and 6th order perfect vortex beams generated at 150 μm by changing the rotation angles of metasurface 2 to 4, 12, and 24 degrees, respectively, are shown. These results were obtained from FDTD simulations. Figure 6As shown in the XOY plane, the vast majority of the energy of the perfect vortex beam is concentrated in a ring, and the diameter of the ring hardly changes, further verifying the "perfect" characteristic during the order change process. Figure 6 The order characteristics can be verified by examining the phase diagrams corresponding to each order, specifically manifested in the appearance of spiral branches corresponding to the order. Figure 6 The diagram shows the spiral branches of order 3 and order 6, as indicated by the arrows in the diagram.

[0063] The design method proposed in this invention can be used to design a corresponding metasurface-based continuously variable perfect vortex beam generator according to actual needs (perfect vortex beam order, halo diameter, generation distance, and size of metasurface devices).

Claims

1. A continuously variable-order perfect vortex beam generator based on metasurfaces, characterized in that, It includes metasurface one and metasurface two placed in the same orientation; Both metasurfaces comprise a SiO2 substrate and a micro / nano structure array. The micro / nano structure array is composed of multiple cylindrical elemental silicon atoms of different diameters, and the period of adjacent cylindrical elemental silicon atoms is a subwavelength dimension. The arrangement of the plurality of cylindrical elemental silicon atoms of different diameters is formed by the phase formula; The phase corresponding to the metasurface satisfies formula (1): Where a is a positive integer. The azimuth angle is the angle corresponding to the center position of the metasurface. (x1, y1) are the spatial coordinates of the metasurface with its center as the origin. The parameter a is taken from the value of formula (2); Where n is the order of the corresponding perfect vortex beam, and θ is the relative rotation angle between the two metasurfaces; Wherein, the phase corresponding to the second metasurface satisfies formula (3): in The term represents the phase of the axial cone mirror. The term is the phase of the Fresnel focusing lens, (x2, y2) is the spatial position coordinate of the metasurface II with the center as the origin, d is a preset constant, λ is the incident wavelength, and f is the position where the perfect vortex beam is generated. In the formula, d satisfies formula (4): Where ρ is the ring radius of a continuously variable perfect vortex beam generated based on a metasurface.

2. The continuously variable-order perfect vortex beam generator based on metasurfaces according to claim 1, characterized in that, The phase of the multiple cylindrical elemental silicon with different diameters is controlled by changing the diameter of the cylinders, and then a metasurface-micro-nano structure array is established according to the phase formula (1); a metasurface-micro-nano structure array is established according to the phase formula (3).

3. The continuously variable-order perfect vortex beam generator based on metasurfaces according to claim 1, characterized in that, The two metasurfaces, by changing their relative rotation angle θ, provide the beam with additional vortex phases of different orders, producing a perfect vortex beam with continuously variable order.

4. A continuously variable-order perfect vortex beam generator based on a metasurface according to claim 1, characterized in that, The continuously variable perfect vortex beam is generated at f. The position of the generated perfect vortex beam is controlled by changing the size of f. The ring radius of the perfect vortex beam is controlled by the parameter d in formula (4). The maximum order of the continuously variable perfect vortex beam is controlled by the parameter a in formula (2).

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