Method for generating Skyrmion tube and Skyrmion tube array through tight focusing

Abstract

The invention discloses a method for generating a Skyrmion tube and an array thereof through tight focusing. The method comprises the following steps: constructing the Skyrmion tube or the Skyrmion tube array in a focal field in advance; the method comprises the following steps: slicing a pre-constructed focal field along an optical axis direction, and obtaining incident field distribution on an objective lens aperture surface corresponding to a slice through a tight focusing inverse operation process; coherently superposing the incident fields corresponding to all the slices to obtain total incident field distribution; and carrying out tight focusing on the total incident field by using an objective lens to obtain complex amplitude of a focal field, observing intensity and topological state distribution of the focal field in a three-dimensional space of a focusing area, and optimizing intervals between slices to obtain a tight focusing field with the skyrmion tubes or the skyrmion tube array. According to the method, the Skyrmion tube or the Skyrmion tube array is constructed in the focal field in advance, the focal field with the preset topological characteristic is obtained, and the method provided by the invention has certain universality.

Description

Technical Field

[0001] The present invention relates to the technical field of vector light field control, and in particular to a method for generating a skyrmion tube and an array thereof through tight focusing. Background Art

[0002] Skyrmion topology was first proposed by Tony Skyrme in 1962 as a stable particle-like solution to nonlinear field equations in nuclear physics. These quasiparticles are characterized by the continuous and smooth winding of their spin or polarization vectors, which makes them robust to small perturbations. They are characterized by a topological invariant called the skyrmion number, which quantifies the topological charge of the skyrmion configuration. Skyrmion topology has been widely demonstrated in magnetic materials, liquid crystals, Bose-Einstein condensates, and even water waves.

[0003] In recent years, with the advancement of optical research, the concept of skyrmions has been extended to the field of optics. This topological structure can be realized by vector fields composed of certain physical quantities of the optical field, opening up new research directions. In 2018, S. Tsesses' research team discovered Néel-type electric-field vector-optical skyrmions by using surface plasmon interferometry excited in a hexagonal grating structure on a metal surface. That same year, X. Yuan's research team also observed spin-vector-optical skyrmions by using surface plasmon interferometry excited on a metal surface. These discoveries demonstrate that the topological structure of skyrmions is not limited to traditional states of matter but can also be realized by vector fields composed of certain physical quantities of the optical field. Subsequently, research in this field rapidly expanded to encompass various applications of three-dimensional optical vector fields. For example, S. Gao et al., leveraging the property that the Stokes parameters representing the polarization state of light can be described as three-dimensional vectors on the Poincare sphere, generated skyrmion structures composed of Stokes vectors in a paraxial beam with a spatially varying polarization structure. For example, in 2024, S. Wang et al. theoretically proved the existence of Poynting vector skyrmions, further revealing the topological characteristics of light energy flow and emphasizing the importance and diversity of skyrmions in the field of optics.

[0004] During tight focusing, high-numerical-aperture objectives focus the light beam to a subwavelength scale. These lenses allow for a wide angle of incidence, resulting in significantly different lightwave paths near the focal point. These path differences can cause longitudinal interference and diffraction, generating a significant longitudinal electric field component. The tight focusing process causes the electric field to exhibit a three-dimensional vector distribution at the focal point, making it possible to construct skyrmion topological structures within the electric field. Although relevant research has been conducted on generating skyrmions via tight focusing methods, research on how to generate skyrmion tubes and their arrays in free space is still scarce, and there is a lack of in-depth and systematic exploration methods. The present invention proposes a method for generating electric field vector skyrmion tubes and their arrays via tight focusing, which solves the problem of rapid calculation and optimization of incident field vector holograms, opens up a new path for exploring skyrmion properties based on vector holography, and has important guiding significance for promoting the engineering application of skyrmion topology in optical communications, information storage, quantum computing and other fields. Summary of the Invention

[0005] In response to the shortcomings of the prior art, the present invention aims to provide a method for generating skyrmions and their arrays through tight focusing. The method pre-constructs a skyrmion or skyrmion array in the focal field, slices the focal field along the optical axis, obtains the complex amplitude distribution of the incident field corresponding to these slices based on the inverse operation process of tight focusing, and coherently superimposes all the incident fields to obtain a vector hologram of the total incident field. This solves the problem of generating electric field vector skyrmions and their arrays in free space, bringing new possibilities for information processing, data storage, and transmission, and providing strong support for the future development of optical computing and quantum information technology. In order to achieve the above-mentioned purpose and other advantages of the present invention, a method for generating skyrmions and their arrays through tight focusing is provided, comprising:

[0006] S1. Pre-constructing a skyrmion tube or a skyrmion tube array in the focal field, wherein the electric field vector distribution on the cross section of each skyrmion tube constitutes a skyrmion topology, and the light field intensity of each skyrmion tube along the optical axis is columnarly distributed;

[0007] S2. Slicing the focal field along the optical axis in the pre-constructed focal field, and obtaining the incident field distribution on the objective lens aperture plane corresponding to the slice through the inverse operation process of tight focusing; and coherently superimposing the incident fields corresponding to all the slices to obtain the total incident field distribution;

[0008] S3. Use an objective lens to tightly focus the total incident field to obtain the complex amplitude of the focal field, observe the intensity and topological state distribution of the focal field in the three-dimensional space of the focal region, and obtain a tightly focused field with a skyrmion tube or skyrmion tube array by optimizing the intervals between each slice.

[0009] Preferably, the skyrmion tube and its array generated by the present application are very ideal, and the skyrmion topological structure is complete and clear in the cross section of the focal field along the optical axis. It can be seen that this method can generate a highly localized vector light field with a skyrmion tube and its array.

[0010] Compared with existing technologies, this invention offers the following advantages: by pre-constructing a skyrmion or skyrmion array within the focal field and slicing the focal field along the optical axis, a vector hologram of the total incident field on the objective lens aperture plane is generated based on Fourier transform, thereby obtaining a focal field with pre-defined topological properties. This approach addresses a research area not addressed or explored in depth by existing technologies, and this method helps fill a research gap in generating vector light fields with skyrmions or skyrmion arrays, providing insights and references for subsequent scientific research.

[0011] The present invention has powerful performance. The method provided by the present invention can be extended to generate Stokes vector or spin vector skyrmion tubes and arrays thereof under tight focusing conditions, and has certain universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 This is a schematic diagram of the principle of the method for generating a skyrmion tube and its array by tight focusing according to the present invention. The dashed box shows a schematic diagram of the skyrmion tube array. In each skyrmion tube, slices at different positions along the optical axis all have skyrmion topology.

[0013] Figure 2 Figure 1 is a diagram illustrating the process of slicing a focal field along the optical axis in a pre-constructed focal field, obtaining incident fields corresponding to all slices through an inverse operation of tight focusing, and then coherently superimposing the slices according to the method for generating a skyrmion tube and an array thereof by tight focusing according to the present invention. (a) shows the slice positions used for the inverse operation in the pre-constructed focal field, (b) shows the intensity distribution of the x-polarization component in the total incident field after coherent superposition, (c) shows the phase distribution of the x-polarization component, (d) shows the intensity distribution of the y-polarization component in the total incident field, and (e) shows the phase distribution of the y-polarization component.

[0014] Figure 3 The intensity distribution of the x-polarization component (a), the intensity distribution of the y-polarization component (b), the intensity distribution of the z-polarization component (c), and the distribution of the total intensity of the focal field (d) in a skyrmion according to the method for generating a skyrmion and its array by tight focusing of the present invention are shown; the figure also shows the real part distributions of the x-, y-, and z-polarization components in the focal field (e)-(g), and the topological structure formed by the electric field vector at a cross section along the optical axis (h);

[0015] Figure 4The relationship between the number of skyrmions and the slice position of the topological structure formed by the electric field vectors at each cross section of the skyrmion tube along the optical axis in the method for generating a skyrmion tube and an array thereof by tight focusing according to the present invention;

[0016] Figure 5 Intensity distribution of a pre-constructed 3×3 skyrmion array according to the method for generating skyrmions and skyrmion arrays by tight focusing according to the present invention (a), intensity distribution of the x-polarization component in the total incident field (b), phase distribution of the x-polarization component (c), intensity distribution of the y-polarization component in the total incident field (d), and phase distribution of the y-polarization component (e);

[0017] Figure 6 The 3×3 skyrmion array generated by the method for generating skyrmion tubes and skyrmion arrays by tight focusing according to the present invention is at z f =-1.25λ,z f =0 and z f =1.25λ, and the topological structures of the electric field vectors in these three slices (b), (d), and (f). DETAILED DESCRIPTION

[0018] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0019] Reference Figure 1 A method for generating a skyrmion tube and an array thereof by tight focusing comprises the following steps:

[0020] S1. Pre-constructing a skyrmion tube or a skyrmion tube array in the focal field, wherein the electric field vector distribution on the cross section of each skyrmion tube constitutes a skyrmion topology, and the light field intensity of each skyrmion tube along the optical axis exhibits a columnar distribution; in step S1, the skyrmion topology within the focal field is constructed based on the electric field vector of the focal field, and the topological states at different longitudinal positions in the skyrmion tube are the same.

[0021] Furthermore, the complex amplitudes of the three polarization components of the pre-constructed skyrmion tube or skyrmion tube array can be expressed as:

[0022]

[0023] in and are the amplitudes of the x, y, and z polarization components in any cross section of the preset focal field, M and N are the number of rows and columns of the skyrmion array, respectively. f is the polar diameter of each skyrmion in the polar coordinate within the cross section, w f is the beam waist radius of the light spot in the focal field cross section. mn is the angle between the electric field vector of each skyrmion in the cross section and the plane normal, η mn =(p+1)π / 2-pπr f,mn / R s , when p = 1, the vector in the middle of the skyrmion topology is perpendicular to the plane of the topology and downward, while the outermost vector is perpendicular to the plane of the topology and upward; when p = -1, the opposite is true, R s is the radius of the skyrmion. is the azimuth of the polar coordinate of each skyrmion in the cross section, v is the vorticity and ψ0 represents the helicity. m and d n are the horizontal and vertical coordinates of the central axis of each skyrmion tube in the focal field, respectively.

[0024] S2. Slice the pre-constructed focal field along the optical axis and obtain the incident field distribution on the objective lens aperture corresponding to the slice through the inverse process of tight focusing. The incident fields corresponding to all slices are coherently superimposed to obtain the total incident field distribution. The complex amplitude distribution of the incident field on the objective lens aperture corresponding to each slice of the focal field can be obtained through fast Fourier transform, significantly improving computational efficiency. Multiple focusing simulations are required on the vector hologram of the total incident field to evaluate the error between the obtained focal field and the pre-constructed focal field. These errors are reduced by optimizing the spacing between slices, so that the total incident field vector hologram can more accurately generate a skyrmion or skyrmion array.

[0025] Furthermore, according to the Fourier transform form of Richard Wolf's vector diffraction formula, the focal field slice The incident field on the aperture plane of the objective lens The relationship between

[0026]

[0027] Where k = 2π / λ, λ is the wavelength of the incident light, z f is the position of the focal field slice in the focusing space; P(ρ) is the aperture function, when ρ≤R, P(ρ)=1, and when ρ>R, P(ρ)=0, R is the radius of the aperture surface of the objective lens, A(θ) is the apodization function of the objective lens. For a sinusoidal objective lens, M is the polarization transformation matrix, which realizes the transformation of the incident field The polarization distribution is transformed to the rear surface of the objective lens, and the matrix expression is as follows

[0028]

[0029] φ is the azimuth angle in the aperture plane of the objective lens, φ = tan -1 (y / x), θ is the angle between the light and the z-axis during the focusing process. According to the inverse operation, we can get The corresponding incident field distribution It should be pointed out that directly performing the inverse operation according to formula (2) will result in an incident field with a z-polarization component, and the z-polarization component in the incident field needs to be excluded. It can be expressed as:

[0030]

[0031] The origin of the focusing space is at the focal position, and the propagation direction of the light beam is along the positive direction of the z axis. According to formula (4), we can get f The focal field distribution at The incident field Therefore, the focal field at z can be calculated by slicing the pre-constructed focal field along the optical axis. f =z h Slices at (h=1,2,…,H) The corresponding incident field All incident fields are coherently superimposed to obtain the vector hologram of the total incident field H is the number of slices in the focal field. It's important to note that when focusing the total incident field, crosstalk occurs between the slices in the focal field, causing a deviation between the actual focused field and the preset focal field. Based on this deviation, the spacing between slices in the preset focal field needs to be optimized to reduce crosstalk between slices and ensure that the actual focal field approximates the preset focal field. Figure 2 Schematic diagram of the optimized slice position when a single skyrmion tube is preset in the focal field, and the intensity and phase distribution of the x and y polarization components in the total incident field on the corresponding objective aperture plane.

[0032] In step S3, the total incident field is tightly focused using an objective lens to obtain the complex amplitude of the focal field. The intensity and topological state distribution of the focal field in the three-dimensional space of the focal region are observed. By optimizing the spacing between each slice, a tightly focused field with a skyrmion or skyrmion array is obtained. The vector hologram of the total incident field in step S2 is focused using an objective lens. Based on the Richard Wolf vector diffraction formula, the complex amplitude distribution of the x-, y-, and z-polarization components of the focal field is obtained. The intensity distribution of the focal field in the three-dimensional space of the focal region and the skyrmion topological state are analyzed to confirm that the focal field has a skyrmion or skyrmion array.

[0033] Further, such as Figure 1 and Figure 2 As shown, the incident field obtained by this method can be focused by an objective lens to obtain a skyrmion tube or a skyrmion tube array. Here, the construction of a single skyrmion tube and a 3×3 skyrmion tube array is used as an example to illustrate the specific implementation of the technical solution, including the following steps:

[0034] Step 1: Pre-construct a single skyrmion tube in the focal field (e.g. Figure 2 (a)) or a 3×3 skyrmion array (as Figure 5 (a), the complex amplitude distribution of a pre-constructed single skyrmion tube is

[0035]

[0036] In this case, M=N=1 in formula (1), so the subscript indicating the element number is omitted in formula (5). Vorticity v=1, helicity ψ0=0, and waist radius w f The value is 0.25 μm. The horizontal and vertical coordinates of the central axis of the skyrmion tube d m =d n =0, then If p is -1, then η=πr f / R s , R s Take 1μm, azimuth

[0037] The pre-constructed 3×3 skyrmion array can be expressed as:

[0038]

[0039] Where M = N = 3, vorticity v = 1, helicity ψ0 = 0, and waist radius w f The coordinate of the central axis of each skyrmion tube in the array (d m ,d n ) are respectively (-7.4114λ,-7.4114λ), (0,-7.4114λ), (7.4114λ,-7.4114λ), (-7.4114λ,0) , (0,0), (7.4114λ,0), (-7.4114λ,7.4114λ), (0,7.4114λ), (7.4114λ,7.4114λ), p is taken as -1, then η mn =πr f,mn / R s , R s Taken as 2.33μm, azimuth

[0040] Step 2: Slice along the optical axis in the pre-constructed focal field, perform inverse calculations using formula (4) to obtain the incident field distribution on the objective lens aperture plane corresponding to each slice, optimize the interval between slices, and obtain the slice position z according to the crosstalk degree. f =0, ±1.25λ, ±2.5λ, ±3.75λ, ±5λ, the number of slices H is 9, such as Figure 2 (a) As shown. The incident fields corresponding to all slices The total incident field is obtained after coherent superposition, and the intensity distribution and phase distribution of each polarization component of the total incident field of a single skyrmion tube are generated as follows: Figure 2 As shown in (b)-2(e), the intensity distribution and phase distribution of each polarization component of the incident field generating the skyrmion tube array are as follows Figure 5 (b)-5(e) shows.

[0041] Step 3: Use the objective lens to tightly focus the total incident field. According to formula (2), the complex amplitude distribution of the focal field can be obtained. In this embodiment, the wavelength of the incident light is 632.8nm, the objective lens is a sinusoidal objective lens, the numerical aperture of the objective lens is 0.9, the focal length of the objective lens is 2mm, and the aperture radius of the objective lens is 1.8mm. The relevant results of the single skyrmion tube generated by focusing are as follows: Figure 3 (a)-3(h) shows the generation result of the skyrmion array. Figure 6 shown.

[0042] In the generated single skyrmion tube, the intensity distribution of each polarization component of the focal field is as follows: Figure 3 (a)-3(c) shows that the total intensity distribution of the focal field is as follows Figure 3 As shown in (d), it can be seen that the total intensity distribution of the focal field formed by adding the intensities of the three polarization components is cylindrical along the optical axis. The distribution of the real parts of the three polarization components is as follows Figure 3 As shown in (e)-3(g), the real part of each polarization component changes periodically. To analyze the topological structure composed of the real part of each polarization component, without loss of generality, we take z f = 0.23λ to characterize the topological structure of the electric field vector distribution. The results are as follows Figure 3 As shown in (h), the arrows of the electric field vectors show a Néel-type topological distribution, and the skyrmion number is -0.9987, indicating that the electric field vector distribution within the slice constitutes a Néel-type skyrmion topology. Furthermore, the generated focal field is sliced ​​continuously along the optical axis, and the skyrmion number of the topological structure formed by the electric field vectors of each slice is calculated. The relationship between the skyrmion number and the slice position is obtained as follows: Figure 4As shown, the absolute value of the skyrmion number is greater than 0.9 at most locations, with a skyrmion number jump occurring only every 0.25λ, causing the absolute value of the skyrmion number to fall below 0.9. This is due to the periodic variation in the real parts of the three polarization components. It should be noted that these slices with skyrmion numbers less than 0.9 do not lack skyrmion topology. The real parts of some polarization components within these slices degenerate to 0 due to periodic variations. In this case, their imaginary parts can be used to construct the topological structure, and skyrmion topology can still be formed. Therefore, any slice along the optical axis in the focal field possesses skyrmion topology, indicating that this method can generate a single skyrmion tube in the focal field.

[0043] In the generated skyrmion array, the intensity distribution of the focal field is as follows: Figure 6 As shown, the morphology of each skyrmion tube is clearly visible. Without loss of generality, let z f =0 and z f = ±1.25λ for topological structure analysis. Figure 6 As can be seen in Figures 6(b), 6(d), and 6(f), all three slices contain a 3×3 array, and the absolute value of the skyrmion number in each topological structure in the array is greater than 0.9. The arrows all follow a Néel-like evolution pattern, indicating the presence of skyrmion arrays in all three slices. This shows that this method can generate skyrmion tube arrays in the focal field.

[0044] In summary, by slicing a single skyrmion or a 3×3 skyrmion array, optimizing the slicing interval and obtaining the total incident field based on the inverse operation of the focusing process, and then focusing the total incident field through an objective lens, the desired skyrmion or skyrmion array can be generated in the focal field. This demonstrates the effectiveness of the method proposed in the present invention for generating skyrmions and skyrmion arrays through tight focusing.

[0045] The number of devices and processing scales described herein are intended to simplify the description of the present invention, and the application, modification, and variation of the present invention will be apparent to those skilled in the art. Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiment. They can be applied to various fields suitable for the present invention. For those skilled in the art, additional modifications can be easily implemented. Therefore, the present invention is not limited to the specific details and illustrations shown and described herein without departing from the general concept defined by the claims and their equivalents.

Claims

1. A method for generating skyrmions and skyrmions arrays by tight focusing, characterized in that: The following steps are involved: S1. Pre-constructing a skyrmion tube or a skyrmion tube array in the focal field, wherein the electric field vector distribution on the cross section of each skyrmion tube constitutes a skyrmion topology, and the light field intensity of each skyrmion tube along the optical axis is columnarly distributed; S2. Slicing the focal field along the optical axis in the pre-constructed focal field, and obtaining the incident field distribution on the objective lens aperture plane corresponding to the slice through the inverse operation process of tight focusing; and coherently superimposing the incident fields corresponding to all the slices to obtain the total incident field distribution; S3. Use an objective lens to tightly focus the total incident field to obtain the complex amplitude of the focal field, observe the intensity and topological state distribution of the focal field in the three-dimensional space of the focal region, and obtain a tightly focused field with a skyrmion tube or skyrmion tube array by optimizing the intervals between each slice.

2. The method for generating a skyrmion tube and an array thereof by tight focusing according to claim 1, wherein: In step S1 , the skyrmion topology in the focal field is constructed based on the electric field vector of the focal field, and the topological states at different longitudinal positions in the skyrmion tube are the same.

3. The method for generating a skyrmion tube and an array thereof by tight focusing according to claim 1, wherein: In step S2, the complex amplitude distribution of the incident field on the objective lens aperture plane corresponding to each slice of the focal field is obtained by fast Fourier transform, which significantly improves the calculation efficiency.

4. The method for generating a skyrmion tube and an array thereof by tight focusing according to claim 1, wherein: In step S2, the incident fields corresponding to the slices are coherently superimposed to obtain a vector hologram of the total incident field.

5. The method for generating a skyrmion tube and an array thereof by tight focusing according to claim 4, wherein: In step S2, it is necessary to perform multiple focusing simulations on the vector hologram of the total incident field, and evaluate the error between the obtained focal field and the pre-constructed focal field. The error is reduced by optimizing the interval between slices.

6. The method for generating a skyrmion tube and an array thereof by tight focusing according to claim 5, characterized in that: In step S3, the total incident field vector hologram in S2 is focused by an objective lens, and the complex amplitude distributions of the x-, y-, and z-polarization components of the focal field are obtained based on the Richard Wolf vector diffraction formula. The intensity distribution and skyrmion topological state of the focal field in the three-dimensional space of the focal region are analyzed to determine whether the focal field has a skyrmion tube or a skyrmion tube array.

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