A method for generating skyrmions robust to random perturbations

Abstract

The application discloses a kind of robustness of random disturbance to Sagnac generation method, comprising: S1, generating incident beam;S2, construct random noise;S3, the incident beam is randomly disturbed by the random noise, and the disturbed light beam is obtained, and the disturbance degree of light beam is controlled by adjusting the mean or standard deviation of random noise;S4, the disturbed light beam is focused by objective lens, the field distribution on focal plane is calculated and the Sagnac topological state of focal field is observed.According to the application, the light beam after random disturbance is focused by objective lens, it is found that the focusing process can effectively eliminate the interference of random noise, so that the light field on focal plane has regular Sagnac topological state again.

Description

Technical Field

[0001] This invention relates to the technical field of vector light field manipulation, and in particular to a skyrmion generation method that is robust to random perturbations. Background Technology

[0002] Skyrmions are topologically protected particle-like stable field structures, first proposed in high-energy physics. In 1962, British physicist Skyrme, while theoretically solving nonlinear sigma noise, derived a nontrivial classical solution—the skyrmion; this discovery laid the theoretical foundation for subsequent skyrmion research. In 2009, Mühlbauer et al. successfully observed neutron diffraction points formed by magnetic skyrmions in reciprocal space on MnSi single crystals using neutron scattering techniques, experimentally confirming the existence of magnetic skyrmions for the first time. Subsequently, a series of studies found that magnetic skyrmions are widely present in non-centrosymmetric B20-type magnetic materials (such as MnSi, FeGe, FeCoSi, etc.) or in magnetic thin film interfaces with broken spatial inversion symmetry. In recent years, researchers have extended skyrmions to the field of optics, and optical skyrmions have attracted widespread attention due to their broad application potential in information storage, transmission, and quantum computing. In 2018, S. Tsesses et al. constructed an optical skyrmion lattice based on the electric field vectors of surface plasmons excited in a hexagonal grating structure. Subsequently, TJ Davis et al. used time-resolved vector microscopy to study the dynamic characteristics of the electric field vectors in these surface plasmon skyrmions, achieving sub-femtosecond temporal resolution and 10-nanometer spatial resolution. J. Yang et al. constructed electromagnetic Boschgrmions in a planar microwave resonant cavity using the electric field vectors of pseudo-local surface plasmons. J. Chen et al. created skyrmions and meron topologies by carefully designing the electric field vectors in a tightly focused field, and the topologies could be established on any plane within the focal region.

[0003] Optical skyrmions can also be realized using other physical quantities. For example, Professor Yuan's research team at Shenzhen University constructed optical skyrmions based on spin-orbit coupling in evanescent light vortices, utilizing their spin vectors. Subsequently, A. Ghosh et al. excited a square slit coupling structure with circularly polarized light, and the spin vector of the resulting surface plasmon wave could be used to construct a meron lattice. The Stokes vector of a vector beam can also be used to construct optical skyrmions. S. Gao et al. coherently superimposed a fundamental mode Gaussian beam with orthogonal polarization and a first-order Laguerre Gaussian beam, and the Stokes parameter of the constructed vector beam could form a skyrmion topology; such a vector beam is called a skyrmion beam. Y. Shen et al. demonstrated a generalized skyrmion beam based on a spatial light modulator, possessing tunable Stokes vector skyrmions that can switch between Néel, Bloch, and anti-skyrmion types. A. Forbes et al. constructed a nonlocal quantum skyrmion using the Stokes parameter of a two-photon entangled state. J. Chen et al. demonstrated, both theoretically and experimentally, the topological transformation between the incident skyrmion beam and the corresponding focused beam caused by the Gouy phase.

[0004] Although researchers have conducted a series of studies on optical skyrmion topologies, research on generating optical skyrmions under noisy conditions is still relatively limited. C. Liu et al. investigated the robustness of electric field vector optical skyrmions in highly localized optical fields using vector holography. However, studies on reconstructing Stokes vector skyrmion topologies from noisy skyrmion beams have not yet been reported. Studying the robustness of skyrmion beams and overcoming the influence of noise on skyrmion beams is of great significance for their application in complex environments and for promoting the development of related optical technologies. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a skyrmion generation method robust to random perturbations. This method enables the reconstruction of regular skyrmion topological states in the focal field when the topological state of a skyrmion beam is distorted or even destroyed, enriching the means of skyrmion beam generation and allowing for wide application in various fields such as light-matter interaction and high-density data storage. To achieve the above-mentioned objectives and other advantages of this invention, a skyrmion generation method robust to random perturbations is provided, comprising:

[0006] S1. Generate an incident beam, wherein the incident beam is generated by coherently superimposing a left-handed Gaussian beam with a right-handed Laguerre Gaussian beam carrying an orbital angular momentum of 1 topological charge, thereby generating a Stokes vector skyrmion beam.

[0007] S2. Construct random noise;

[0008] S3. Randomly disturb the incident beam with the random noise to obtain the disturbed beam, and control the degree of disturbance to the beam by adjusting the mean or standard deviation of the random noise.

[0009] S4. Focus the disturbed beam through the objective lens, calculate the field distribution on the focal plane, and observe the skyrmion topological state of the focal field.

[0010] Preferably, the specific steps for observing the skyrmion topological state of the focal field in step S4 are as follows:

[0011] S41. Calculate the field distribution after the Stokes vector skyrmion beam is focused following random perturbation;

[0012] S42. Calculate the Stokes vector of the focal field based on the horizontal and vertical polarization components of the focal field, and then select an appropriate spot radius in the focal field.

[0013] S43. Draw a topological structure based on Stokes vectors within the radius of the light spot, and calculate the skyrmion number of the topological structure to confirm that a regular skyrmion topological state has been regenerated in the focal field.

[0014] Preferably, the formula for constructing the incident field based on the desired Stokes vector skyrmion is:

[0015]

[0016] in:

[0017]

[0018] Where R = [e] x -ie y ] T Represents right-handed circularly polarized light, L = [e x ie y ] T This represents left-handed circularly polarized light. x and y are the abscissa and ordinate axes of the Cartesian coordinate system in the incident field, respectively. φ = arctan(y / x) is the azimuth angle in the incident field, w represents the beam waist radius, and Φ0 is the additional phase difference between the two polarization components.

[0019] Preferably, in step S2, the random noise N R It is a two-dimensional matrix, and its dimension is determined by the number of sampling points in the incident field. Random noise N R Each element in the matrix follows a Gaussian distribution, i.e.

[0020] N R (m,n)=σ·f(χ)+μ (4)

[0021] in:

[0022]

[0023] Where σ is the standard deviation of the random noise, μ is the mean of the random noise; f(χ) is a normal distribution function with a mean of 0 and a standard deviation of 1, and χ is the independent variable in the normal distribution function. m=1,2,…,U,n=1,2,…,V,U and V are the number of sampling points in the incident field in the x and y directions, respectively.

[0024] Preferably, in step S3, the horizontal and vertical polarization components of the incident field can be expressed as follows:

[0025]

[0026] For E x and E y With random noise added, it can be expressed as:

[0027] E x-noise =E x +N R (8)

[0028] E y-noise =E y +N R (9)

[0029] Where, N R Can simultaneously and independently target E x and E y By introducing interference and changing the mean and standard deviation of random noise, the robustness of the proposed method to noise can be comprehensively studied.

[0030] Compared with the prior art, the beneficial effects of this invention are:

[0031] 1. This invention provides an optical skyrmion generation method that is robust to random perturbations. By focusing a randomly perturbed light beam with an objective lens, it is found that the focusing process can effectively eliminate the interference of random noise and stably generate Stokes vector skyrmions. This enables the skyrmions generated by this method to have lower loss when transmitting and processing information, and has great application potential in fields such as high-density data storage, light-matter interaction, and optical communication.

[0032] 2. This invention boasts powerful performance. The method provided by this invention can not only effectively overcome the interference of Gaussian random noise, but can also be used to generate optical skyrmions under other noise backgrounds, including uniform noise, Rayleigh noise, etc. Furthermore, this invention can also be used to generate higher-order optical skyrmions under noisy backgrounds. Attached Figure Description

[0033] Figure 1 The above is a schematic diagram of the skyrmion generation method that is robust to random disturbances according to the present invention. After the skyrmion beam is subjected to random noise interference and then refocused, skyrmions can be reconstructed in the focal field.

[0034] Figure 2 For the skymin generation method of the present invention, which is robust to random perturbations, the standard deviation of the random noise is 0, and the mean is 0.000, 0.006, 0.030, and 0.054. The intensity and polarization distribution of the incident field are shown in (a)-(d), and the corresponding topological states formed by the Stokes vectors are shown in (e)-(h).

[0035] Figure 3 For the skymin generation method of the present invention, which is robust to random perturbations, the standard deviation of random noise is 0, and the mean is 0.000, 0.006, 0.030, and 0.054. The intensity and polarization distribution of the focal field are shown in (a)-(d), and the corresponding topological states formed by the Stokes vectors are shown in (e)-(h).

[0036] Figure 4 For the skymin generator method of the present invention, which is robust to random perturbations, when the mean of the random noise is 0 and the standard deviation is 0.008, 0.024, 0.056, and 0.072, the intensity and polarization distribution of the incident field are shown in (a)-(d), and the corresponding topological states formed by the Stokes vectors are shown in (e)-(h).

[0037] Figure 5 For the skymin generator method of the present invention, which is robust to random perturbations, when the mean of random noise is 0 and the standard deviation is 0.008, 0.024, 0.056, and 0.072, the intensity and polarization distribution of the focal field are shown in (a)-(d), and the corresponding topological states formed by the Stokes vectors are shown in (e)-(h).

[0038] Figure 6 The graphs (a) and (b) show the skyrmion number in the incident field and the skyrmion number in the focal field when the standard deviation of the fixed random noise is 0 and the mean is changed, for the skyrmion generation method of the present invention, which is robust to random disturbances. The graphs (c) and (d) show the skyrmion number in the incident field and the skyrmion number in the focal field when the standard deviation of the fixed random noise is 0. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] Reference Figure 1 A method for generating skyminets robust to random perturbations includes the following steps:

[0041] S1. A left-handed Gaussian beam is coherently superimposed with a right-handed Laguerre Gaussian beam carrying a topological charge of 1 orbital angular momentum to generate a Stokes vector skyrmion beam; the formula for constructing the incident field based on the desired Stokes vector skyrmion is as follows:

[0042]

[0043] in:

[0044]

[0045] Where R = [e] x -ie y ] T Represents right-handed circularly polarized light, L = [e x ie y ] T This represents left-handed circularly polarized light. x and y are the abscissa and ordinate axes of the Cartesian coordinate system in the incident field, respectively. φ = arctan(y / x) is the azimuth angle in the incident field, w represents the beam waist radius, and Φ0 is the additional phase difference between the two polarization components.

[0046] S2. Construct random noise, N. R It is a two-dimensional matrix, and its dimension is determined by the number of sampling points in the incident field. Random noise N R Each element in the matrix follows a Gaussian distribution, i.e.

[0047] N R (m,n)=σ·f(χ)+μ (4)

[0048] in:

[0049]

[0050] Where σ is the standard deviation of the random noise, μ is the mean of the random noise; f(χ) is a normal distribution function with a mean of 0 and a standard deviation of 1, and χ is the independent variable in the normal distribution function. m=1,2,…,U,n=1,2,…,V,U and V are the number of sampling points in the incident field in the x and y directions, respectively.

[0051] S3. Randomly perturb the Stokes vector skyrmion beam with the random noise, and control the degree of perturbation of the beam by adjusting the mean or standard deviation of the random noise, so as to study the robustness of the skyrmion beam under random perturbation.

[0052] The horizontal and vertical polarization components of the incident field can be expressed as:

[0053]

[0054] For E x and E y With random noise added, it can be expressed as:

[0055] E x-noise =E x +N R (8)

[0056] E y-noise =E y +N R (9)

[0057] Where, N R Can simultaneously and independently target E x and E y By introducing interference and changing the mean and standard deviation of random noise, the robustness of the proposed method to noise can be comprehensively studied.

[0058] S4. Focus the randomly perturbed beam using an objective lens, calculate the field distribution on the focal plane, and observe the skyrmion topological state of the focal field. The specific steps for observing the skyrmion topological state of the focal field are as follows:

[0059] S41. Calculate the field distribution after the Stokes vector skyrmion beam is focused following random perturbation;

[0060] S42. Calculate the Stokes vector of the focal field based on the horizontal and vertical polarization components of the focal field, and then select an appropriate spot radius in the focal field.

[0061] S43. Draw a topological structure based on Stokes vectors within the radius of the light spot, and calculate the skyrmion number of the topological structure to confirm that a regular skyrmion topological state has been regenerated in the focal field.

[0062] like Figure 1 As shown, after focusing a randomly perturbed light beam, the objective lens can re-observe the regular skyrmion topology in the focal field. The intensity and phase of the focused light field can be calculated using the Richard Wolf vector diffraction integral formula. The specific implementation of the technical solution is described in detail below, including the following steps:

[0063] Step 1: Combining formulas (1)-(3), and taking Φ0=0, the incident field can be determined as follows:

[0064]

[0065] In this embodiment, the beam waist radius is taken as w = 0.7 mm, and the intensity and polarization distribution of the resulting Stokes vector skyrmion beam are as follows: Figure 2 As shown in (a). Figure 2 (e) gives the skyrmion topology constructed based on the Stokes vector in the incident beam at this time, with a skyrmion number of -0.93. It can be seen that the incident field determined by formula (10) carries the first-order Stokes vector skyrmion topology.

[0066] Step 2: Sample 101 data points in both the x and y directions of the incident field, i.e., U = 101 and V = 101. Set the mean and standard deviation of the random noise, and generate a random noise matrix N with a size of 101 × 101 according to equations (4) and (5). R .

[0067] Step 3: Combine equations (6) and (7) with the random noise N. R Substituting into equations (8) and (9), we can obtain E after noise interference. x-noise and E y-noise All are 101×101 matrices. Adjust the random noise N. R The mean μ or standard deviation σ can control the degree of perturbation to the incident beam. The mean controls the average interference level of random noise, and the standard deviation controls the dispersion of random noise. By controlling one variable at a time to change the average interference level or dispersion of the noise, the beam is perturbed, thus allowing the study of the robustness of the skyrmion beam under random perturbation. It should be noted that when perturbing E and E' respectively, the random noise matrix needs to be regenerated to maintain the stability of the random noise matrix as xy...

[0068] The independence of machine noise.

[0069] Step 4: Focus the disturbed beam using a sinusoidal objective lens. The apodization function of the sinusoidal objective lens is... Let θ be the angle between the refracted ray and the optical axis. Then the refracted field on the back surface of the objective lens is:

[0070]

[0071] Substituting into Richard Wolf's vector diffraction formula, the field distribution on the focal plane can be calculated as follows:

[0072]

[0073] Where λ is the wavelength of the incident light, R is the radius of the entrance pupil of the objective lens (in this embodiment, R = 1.8 mm), NA is the numerical aperture of the objective lens (in this embodiment, NA = 0.9), and k = 2π / λ is the wavenumber. It is the polar radius of the cd-th point on the focal plane. It is the azimuth angle of the cd-th point on the focal plane. f,cd and y f,cd θ represents the x-axis coordinates and y-axis coordinates of the cd-th point on the focal plane, respectively. In this embodiment, the number of sampling points along both the x-axis and y-axis of the focused field on the focal plane is 101, i.e., c = 1, 2, ..., 101, d = 1, 2, ..., 101. mn It is the θ value corresponding to the mn-th sampling point in the incident light, and 0 ≤ θ mn ≤θ max θ max =sin -1 (NA). Based on the calculated field distribution of the focal field, the Stokes parameters of the focal field can be further obtained. The Stokes parameters can be used to construct the Stokes vector of the focal field, and then the topological structure of the focal field can be drawn to analyze whether it is a skymin topology.

[0074] When observing the effect of random noise on the Stokes vector skyrmion beam, the standard deviation of the random noise was first fixed at 0. The mean values ​​were 0.000, 0.006, 0.030, and 0.054. The intensity and polarization distribution of the incident field were as follows: Figure 2 As shown in (a)-2(d), the corresponding topological states formed by the Stokes vectors are as follows: Figure 2 As shown in (e)-2(h), the skyrmion numbers are -0.92, -0.34, -0.07, and -0.05, respectively. It is evident that changes in the mean of random noise significantly affect the topology of the incident beam. Generally, when the absolute value of the skyrmion number is greater than or equal to 0.9 and less than or equal to 1, the beam can be considered to have a good skyrmion topology; otherwise, the skyrmion topology of the beam is destroyed. When the mean is 0 (i.e., no noise is added), the incident field has a good skyrmion topology. However, as the mean increases, the absolute value of the skyrmion number in the incident field becomes less than 0.9, and the skyrmion topology no longer exists in the incident beam. Under the latter three mean values, the topology of the incident beam is basically destroyed, and the skyrmion topology no longer exists in the incident beam. The intensity and polarization distribution of the focusing field corresponding to the above four incident beams are shown in the figures below. Figure 3 As shown in (a)-3(d), the topological states constructed based on the Stokes vector of the focal field are respectively as follows: Figure 3As shown in (e)-3(h), the skyrmion numbers are -0.92, -0.94, -0.92, and -0.90, respectively. It can be seen that the strong focusing process can effectively overcome the adverse effects of random noise and regenerate a good skyrmion topology in the focal field. Therefore, the strong focusing process has strong robustness to changes in the mean of random noise, and can regenerate the skyrmion topology in the focal field even when the skyrmion number in the incident field drops sharply.

[0075] Then, with the mean of the random noise fixed at 0 and the standard deviations set to 0.008, 0.024, 0.056, and 0.072, the intensity and polarization distribution of the incident field are as follows: Figure 4 As shown in (a)-4(d), the corresponding topological states formed by the Stokes vectors are as follows: Figure 4 As shown in (e)-4(h), their skyrmion numbers are -0.94, -1.23, -0.64, and -0.65, respectively. It is evident that variations in the standard deviation of random noise cause significant fluctuations in the skyrmion number of the incident beam. Therefore, with the addition of random noise, the skyrmion number of the incident field fluctuates drastically, and the evolution of the Stokes vector in the spatial direction of the incident beam gradually becomes uncontrolled and chaotic, indicating that the skyrmion topology of the incident beam has been destroyed. The intensity and polarization distribution of the focused field corresponding to the above four incident beams are shown in the figures below. Figure 5 As shown in (a)-5(d), the topological states constructed based on the Stokes vector of the focal field are respectively as follows: Figure 5 As shown in (e)-5(h), the skyrmion numbers are -0.92, -0.92, -0.94, and -0.90, respectively, and the evolution of the Stokes vector in the focal field all exhibits a regular and ordered state. Therefore, even with varying standard deviations, the strong focusing process can still overcome the adverse effects of random noise, and can regenerate the skyrmion topology in the focal field even when the skyrmion number in the incident field fluctuates drastically.

[0076] To more comprehensively study the effect of random noise on Stokes vector skyrmion beams, the standard deviation of the random noise was fixed at 0, and its mean was varied between 0.000 and 0.060 with a step size of 0.006. The skyrmion number curves for the incident field and focal field were obtained as follows: Figure 6 As shown in (a) and 6(b). From Figure 6 (a) and Figure 6As shown in (b), random noise has a significant impact on the skyrmion topology of the incident beam. A mean random noise greater than 0 results in an absolute skyrmion number of less than 0.9, indicating that the skyrmion topology in the incident beam has been destroyed. However, the skyrmion number in the focal field remains stable between -0.90 and -0.94, indicating that the strong focusing process can effectively overcome the interference of random noise, and even under strong noise interference, the skyrmion topology can be regenerated in the focal field. With the mean of the random noise fixed at 0, its standard deviation varied between 0.000 and 0.080 in a step size of 0.008, resulting in skyrmion number curves for the incident field and focal field, as shown below. Figure 6 As shown in (c) and 6(d), it can be seen that when the standard deviation of random noise changes, the skyrmion number of the incident field fluctuates greatly between -1.3 and -0.5, indicating that the incident field is significantly affected by random noise, and its skyrmion topology is basically destroyed. The skyrmion number of the focal field, on the other hand, is stable between -0.90 and -0.95, indicating that a good skyrmion topology always exists in the focal field. Therefore, the strong focusing process is also highly robust to fluctuations in random noise.

[0077] In summary, variations in the mean and standard deviation of random noise can significantly perturb or even destroy the skyrmion topology of the incident field. However, strong focusing of the incident beam can effectively overcome the adverse effects of these variations, allowing the skyrmion topology to be regenerated in the focal field. Therefore, by strongly focusing a noise-interfered skyrmion beam, the adverse effects of noise can be eliminated, and the skyrmion topology can be robustly regenerated in the focal field.

[0078] The number of devices and processing scale described herein are for the purpose of simplifying the description of the invention, and applications, modifications and variations thereof will be apparent to those skilled in the art.

[0079] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A skymin generation method robust to random perturbations, characterized in that, The method comprises the following steps: S1, generating an incident light beam, and the incident light beam is a Stokes vector skyrmion beam generated by coherently superimposing a left-handed Gaussian light and a right-handed Laguerre Gaussian light carrying orbital angular momentum with a topological charge of 1; the formula for constructing the incident field according to the desired Stokes vector skyrmion is: (1) Wherein: (2) (3) wherein represents right-handed circularly polarized light, represents left-handed circularly polarized light; x and y are the transverse and longitudinal coordinate axes, respectively, of a Cartesian coordinate system in the incident field, is the azimuthal angle in the incident field, represents the beam waist radius of the light beam, is the additional phase difference between the two polarization components; S2, construct random noise, the random noise is a two-dimensional matrix, and each element in the random noise obeys a Gaussian distribution; S3, randomly disturbing the incident light beam by the random noise to obtain a disturbed light beam, and adjusting the mean value or standard deviation of the random noise to control the disturbance degree of the light beam; S4, focusing the disturbed light beam by an objective lens, calculating the field distribution on the focal plane and observing the skyrmion topological state of the focal field; the specific steps for observing the skyrmion topological state of the focal field in the step S4 are: S41, calculating the field distribution after focusing of the Stokes vector skyrmion beam after random disturbance based on the Richard-Wolf vector diffraction formula; S42, calculating the Stokes vector of the focal field based on the horizontal polarization component and the vertical polarization component of the focal field; S43, selecting a suitable spot radius in the focal field, drawing a topological structure based on the Stokes vector within the spot radius, calculating the skyrmion number of the topological structure, and confirming that a regular skyrmion topological state is regenerated in the focal field.

2. The method of claim 1, wherein the method is robust to random perturbations. In the step S2, adjusting the mean value or standard deviation of the random noise can control the disturbance degree of the incident light beam, wherein the mean value controls the average disturbance degree of the random noise, the standard deviation controls the dispersion degree of the random noise, and the average disturbance degree or dispersion degree of the noise is changed by controlling one of the variables each time to disturb the light beam, thereby studying the robustness of the skyrmion beam under random disturbance.

3. A method for generating a skyrmion robust against random perturbation according to claim 2, wherein, The matrix dimension of the random noise is determined by the sampling point number of the incident field, that is (4) Wherein: (5) wherein, is the standard deviation of the random noise, is the mean of the random noise; is a normal distribution function with mean 0 and standard deviation 1, is the argument in the normal distribution function; , , and are the number of sampling points in the x- and y-directions, respectively, of the incident field.

4. The method of claim 1, wherein the method is robust to random perturbations. In the step S3, the horizontal and vertical polarization components of the incident field can be represented as: (6) (7) To and With random noise, it can be expressed as: (8) (9) wherein, The Sagnac effect can be simultaneously and independently interfered with and The mean and standard deviation of the random noise are changed, and the robustness of the Sagnac beam under random disturbance is studied.

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