A method for overcoming beam breaking to generate skyrmion topology

Abstract

The present invention discloses a method for overcoming beam breakage to generate skyrmion topology, comprising: S1, coherently superposing left-handed Gaussian light with high-order right-handed Laguerre Gaussian light to generate a skyrmion beam with a specific topological structure; S2, constructing shielding templates of different shapes, wherein the shielding templates are used to shield the skyrmion beam, thereby introducing breakage of different shapes during the beam propagation; S3, focusing the skyrmion beam after the breakage through an objective lens, analyzing the focal field, observing its intensity and topological state distribution, evaluating the robustness of the skyrmion beam under different breakage conditions, and the reconstruction effect of focusing on the broken skyrmion beam. According to the present invention, by constructing shielding masks of different shapes and focusing the broken beam, the robustness of the skyrmion beam under different breakage conditions can be comprehensively evaluated, which is used to solve the problem of skyrmion beams being destroyed during propagation in free space.

Description

Technical Field

[0001] The present invention relates to the field of vector light field control, and in particular to a method for overcoming light beam breaking to generate skyrmion topology. Background Art

[0002] Skyrmions were first proposed by British physicist Tony Skyrme in 1962 to describe the stability of hadrons in high-energy physics. Skyrmions possess an integer topological invariant, known as the skyrmion number. The skyrmion number measures the degree of field distortion and possesses topologically protected properties, which make skyrmions a stable field. The concept of skyrmions has been widely generalized and applied to a variety of physical systems, such as condensed matter physics, spintronics, magnetism, acoustics, and optics. In 2018, S. Tsesses et al. used circularly polarized light to excite surface plasmons in a hexagonal grating structure on a gold film. They then manipulated the surface plasmons to interfere, forming standing waves on the gold film's surface, generating a stable optical skyrmion lattice composed of an electric field. This was the first time that optical skyrmions were generated. Subsequently, S. Gao et al. constructed a skyrmion beam by coherently superposing two Laguerre-Gaussian modes with orthogonal polarization states and different topological charges. Using their Stokes parameters as skyrmion vectors, they were able to construct a skyrmion topology. Building on this, Y. Shen further proposed that the coherent superposition of two Laguerre-Gaussian beams with non-orthogonal polarizations but orthogonal spatial modes could be used to generate a vector beam carrying bimeron topology. Controlling the relative phase difference between the two superposed modes could be used to manipulate the topological state of the bimeron. D. Marco et al. constructed an optical Meron lattice that is propagation-invariant in space based on the Stokes parameters of the beam, and the lattice shape is adjustable. J. Ma et al. constructed Y-shaped and L-shaped optical skyrmion arrays based on the Stokes parameters in a strongly focused light field. In addition, some researchers have also conducted integrated generation of Stokes skyrmions. W.Lin et al. fabricated a silicon ring resonator on a silicon-on-insulator substrate, and designed two angular diffraction gratings consisting of half-etched holes on the ring of the resonator to diffract different polarization states and orbital angular momentum orders. This integrated device can generate Stokes skyrmions with specific topological invariants. T.He et al. designed some metasurface structures on optical fibers to generate high-quality Stokes skyrmions, demonstrating the topological switchability and topological stability of skyrmion beams. A.Wang et al. studied the robustness of Stokes skyrmion beams in complex media and demonstrated that the topological stability of optical skyrmions comes from their boundary structures.

[0003] The formation of Stokes parameter skyrmion beams is based on a special polarization modulation. Different polarization states of the light field correspond to different Stokes parameters. By mapping the Stokes parameters onto the Poincare sphere, a vector arrow can be synthesized from the three parameters. This arrow clearly represents the spatial state of the light's polarization. By customizing the polarization distribution at different locations in the vector field, a unique structure consistent with the skyrmion topology can be derived from the vector field. Beam breaking refers to the disruption of the integrity and symmetry of the beam, resulting in a change in the distribution of the light field. Although researchers have conducted extensive research on optical skyrmions, research on skyrmion beam breaking is still scarce, and there is a lack of in-depth and systematic exploration methods. This paper proposes a method to overcome beam breaking to generate skyrmion topology, illustrating an innovative solution that injects new vitality and depth into research in this field. It has important implications and impetus, and also provides new avenues for the study and application of skyrmions, providing ideas and references for subsequent scientific research. Summary of the Invention

[0004] In response to the shortcomings of the prior art, the present invention aims to provide a method for overcoming beam breakage to generate skyrmion topology. By constructing a mask with different breakage shapes and sizes and focusing the broken beam, the robustness of the skyrmion beam under different breakage conditions can be comprehensively evaluated, thereby solving the problem of skyrmion beams being destroyed during propagation in free space. To achieve the above-mentioned purpose and other advantages of the present invention, a method for overcoming beam breakage to generate skyrmion topology is provided, comprising:

[0005] S1. Coherently superpose left-handed Gaussian light and high-order right-handed Laguerre-Gaussian light to generate a skyrmion beam with a specific topological structure; the Laguerre-Gaussian beam expression is

[0006]

[0007] The fundamental mode expression of Laguerre-Gaussian beam is:

[0008]

[0009] is a Laguerre polynomial, Describes the change of beam radius with propagation distance z, w0 is the beam waist radius, is the Rayleigh distance, p is the radial index, R(z)=z[1+(z R / z) 2 ] is the wavefront curvature radius, l is the orbital angular momentum topological charge, k = 2π / λ is the wave number, λ is the wavelength of the incident light, ψ(z) = tan -1 (z / z R) is a Gouy aspect;

[0010] S2. Constructing shielding masks of different shapes to shield the skyrmion beam, thereby introducing different shapes of breaks during beam propagation; wherein the shapes of the shielding masks include but are not limited to fan-shaped, rectangular, cross-shaped, and irregular shapes;

[0011] S3. Use an objective lens to focus the broken skyrmion beam, analyze the focal field, observe its intensity and topological state distribution, evaluate the robustness of the skyrmion beam under different breaking conditions, and the effect of focusing on the reconstruction of the broken skyrmion beam.

[0012] Preferably, in step S1, the superposition of left-handed Gaussian light and high-order right-handed Laguerre-Gaussian light is a key step in generating a skyrmion beam. Skyrmion beams of different orders can be generated by controlling the topological charge of the orbital angular momentum carried by the high-order Laguerre-Gaussian light.

[0013] Preferably, in step S2, when analyzing the skyrmion topological state of the light beam, the Stokes parameter is measured to characterize the polarization distribution of the light beam and to construct the skyrmion vector of the light beam, so as to observe the influence of the breaking on the skyrmion beam.

[0014] Preferably, in step S3, an objective lens is used to focus the broken skyrmion beam, focusing the beam onto a focal plane, obtaining the field distribution of the focal field through the Richard Wolf vector diffraction formula, calculating the Stokes parameter of the focal field, and regenerating the skyrmion topological state.

[0015] Preferably, in step S3, the simulation results are analyzed in depth, and multiple numerical simulations are performed by adjusting the shape of the breaking to evaluate the performance of the skyrmion beam under different conditions. The skyrmion beam reconstruction under various breaking conditions is relatively ideal, indicating that the focusing process can effectively overcome the adverse effects of the breaking on the skyrmion beam and regenerate the skyrmion topology in the focal field.

[0016] Compared with the prior art, the present invention has the following beneficial effects:

[0017] 1. By comparing the changes in light field intensity, polarization distribution, and topological states under different obstruction conditions, this paper allows for an in-depth study of the effects of beam breaking on the generation of skyrmions in the focal field. This approach, which is not addressed or explored in depth by prior art, helps fill a gap in the study of skyrmion topology generated under beam breaking, providing insights and references for subsequent scientific research.

[0018] 2. The present invention offers powerful performance. By focusing a broken skyrmion beam, a skyrmion topology can be reconstructed within the focal field. This topological structure is complete, ensuring its stable existence within the physical system. The method provided by this invention can regenerate skyrmion topology in a variety of broken skyrmion scenarios, demonstrating a degree of universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the principle of the method for overcoming beam breakage and generating skyrmion topology in the present invention, wherein the shape of the mask used to block the skyrmion beam includes but is not limited to fan-shaped, rectangular, and cross-shaped, etc. By focusing the broken skyrmion beam, the skyrmion topology can be regenerated in the focal field;

[0020] Figure 2 The intensity and polarization distribution of the incident light beam under the cross-shaped mask in the present invention (a), and the topological distribution constructed from its Stokes vector (b); the figure also shows the intensity and polarization distribution of the corresponding focal field (c), and the topological distribution constructed from the Stokes vector of the focal field (d);

[0021] Figure 3 The intensity and polarization distribution of the incident light beam under the rectangular mask in the present invention (a), and the topological distribution constructed from its Stokes vector (b); the figure also shows the intensity and polarization distribution of the corresponding focal field (c), and the topological distribution constructed from the Stokes vector of the focal field (d);

[0022] Figure 4 The intensity and polarization distribution of the incident light beam under the 60° sector mask in the invention (a), and the topological distribution constructed by its Stokes vector (b); the figure also shows the intensity and polarization distribution of the corresponding focal field (c), and the topological distribution constructed by the Stokes vector of the focal field (d). DETAILED DESCRIPTION

[0023] 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.

[0024] Reference Figure 1 A method for overcoming beam breaking to generate skyrmion topology comprises the following steps:

[0025] S1. Coherently superpose left-handed Gaussian light and high-order right-handed Laguerre-Gaussian light to generate a skyrmion beam with a specific topological structure; the Laguerre-Gaussian beam expression is

[0026]

[0027] The fundamental mode expression of Laguerre-Gaussian beam is:

[0028]

[0029] is a Laguerre polynomial, Describes the change of beam radius with propagation distance z, w0 is the beam waist radius, is the Rayleigh distance, p is the radial index, R(z)=z[1+(z R / z) 2 ] is the wavefront curvature radius, l is the orbital angular momentum topological charge, k = 2π / λ is the wave number, λ is the wavelength of the incident light, ψ(z) = tan -1 (z / z R ) is a Gouy aspect;

[0030] S2. Constructing shielding masks of different shapes to shield the skyrmion beam, thereby introducing different shapes of breaks during beam propagation; wherein the shapes of the shielding masks include but are not limited to fan-shaped, rectangular, cross-shaped, and irregular shapes;

[0031] S3. Use an objective lens to focus the broken skyrmion beam, analyze the focal field, observe its intensity and topological state distribution, evaluate the robustness of the skyrmion beam under different breaking conditions, and the effect of focusing on the reconstruction of the broken skyrmion beam.

[0032] Furthermore, in step S1, the superposition of left-handed Gaussian light and high-order right-handed Laguerre-Gaussian light is a key step in generating a skyrmion beam. By controlling the topological charge of the orbital angular momentum carried by the high-order Laguerre-Gaussian light, skyrmion beams of different orders can be generated.

[0033] Furthermore, in step S2, when analyzing the skyrmion topological state of the light beam, the Stokes parameter is measured to characterize the polarization distribution of the light beam and to construct the skyrmion vector of the light beam, so as to observe the effect of the breaking on the skyrmion beam.

[0034] Furthermore, in step S3, an objective lens is used to focus the broken skyrmion beam, focusing the beam onto a focal plane. The field distribution of the focal field is obtained by the Richard Wolf vector diffraction formula, the Stokes parameter of the focal field is calculated, and the skyrmion topological state is regenerated.

[0035] Furthermore, in step S3, the simulation results were further analyzed. Multiple numerical simulations were performed by adjusting the shape of the breaking to evaluate the performance of the skyrmion beam under different conditions. The skyrmion beam was reconstructed ideally under various breaking conditions, demonstrating that the focusing process can effectively overcome the adverse effects of the breaking on the skyrmion beam and regenerate the skyrmion topology in the focal field.

[0036] like Figure 1 As shown, a customized incident light beam carrying a specific skyrmion topology can be blocked by constructed masks of different shapes (such as fan-shaped, cross-shaped, and rectangular) and then focused by an objective lens to regenerate a stable skyrmion topology in the focal field. The field distribution of the focused light field can be calculated using the Richard Wolf vector diffraction formula. Here, the constructed cross-shaped, rectangular, and fan-shaped masks are used as examples to illustrate the specific implementation of the technical solution, which includes the following steps:

[0037] Step 1: For the first-order skyrmion, we can determine p = 0, l = -1, and substitute into formula (1), ignoring the constant term, to obtain

[0038]

[0039] To simplify the expression of the incident beam, we can take z = 0, and then determine the incident field as

[0040]

[0041] Where L = [e x ie y ] T Represents left-handed circularly polarized light, R=[e x -ie y ] T Represents right-handed circularly polarized light.

[0042] Step 2: Construct rectangular, fan-shaped and cross-shaped masks. The expression of the cross-shaped mask is

[0043]

[0044] Wherein, d0 is half of the width of the light-blocking portion in the cross-shaped mask. In this embodiment, d0 is 0.3 mm.

[0045] The expression of the rectangular mask is

[0046]

[0047] Wherein, D0 is half of the width of the light-blocking portion of the rectangular mask. In this embodiment, D0 is 0.3 mm.

[0048] The expression of the sector mask is

[0049]

[0050] Wherein, φ0 is the central angle of the light-blocking portion of the sector mask. In this embodiment, φ0 is set to π / 3. These three masks are used to block the incident field to generate a broken vector beam E·mask ε (x, y), ε = cross, rect, sector.

[0051] Step 3: Use the objective lens to focus the broken vector beam. According to Richard Wolf's vector diffraction formula, the focal field can be obtained as

[0052]

[0053] Among them E Ω (θ, φ) is the refracted field at the rear surface of the objective lens, which is expressed as follows:

[0054]

[0055] represents the radial coordinate on the focal plane, represents the azimuth angle on the focal plane, is the apodization function of the objective lens. max =sin -1 (NA) is the angle between the focused light and the optical axis, and NA is the numerical aperture of the objective lens. In this embodiment, NA is 0.9 and the focal length of the objective lens is 2 mm.

[0056] Under the action of the cross-shaped mask, the intensity and polarization distribution of the incident light beam are as follows: Figure 2 As shown in (a), a cross-shaped break appears in the incident field, making the incident beam incomplete. The topological structure constructed based on the Stokes parameters of the broken incident beam is as follows: Figure 2 As shown in (b), the topological structure of the incident beam is no longer complete, and its skyrmion number is only -0.28, indicating that the incident beam no longer has skyrmion topology. The incident field is focused by the objective lens, and the intensity and polarization distribution of the focal field are shown as follows: Figure 2 As shown in (c), the focal field is restored to a complete light spot, and its polarization distribution is non-uniform. The topological structure constructed based on the Stokes parameters of the focal field is as follows: Figure 2 As shown in (d), it can be seen that the focal field has a complete topological structure and its skyrmion number is -1.00, indicating that there is skyrmion topology in the focal field.

[0057] Under the action of the rectangular mask, the intensity and polarization distribution of the incident light beam are as follows: Figure 3 As shown in (a), a rectangular break appears in the incident field. The topological structure constructed based on the Stokes parameters of the incident beam after the break is as follows: Figure 3 As shown in (b), the topological structure of the incident beam is no longer complete, and its skyrmion number is only -0.39, indicating that the incident beam no longer has skyrmion topology. The incident field is focused by the objective lens, and the intensity and polarization distribution of the focal field are shown as follows: Figure 3 As shown in (c), the focal field is restored to a complete light spot, and its polarization distribution is non-uniform. The topological structure constructed based on the Stokes parameters of the focal field is as follows: Figure 3 As shown in (d), it can be seen that the focal field has a complete topological structure, and its skyrmion number is -0.96, indicating that there is skyrmion topology in the focal field.

[0058] Under the action of the 60° sector mask, the intensity and polarization distribution of the incident beam are as follows: Figure 4 As shown in (a), a fan-shaped break appears in the incident field. The topological structure constructed based on the Stokes parameters of the incident beam after the break is as follows: Figure 4 As shown in (b), the topological structure of the incident beam is no longer complete, and its skyrmion number is only -0.74, indicating that the incident beam no longer has skyrmion topology. The incident field is focused by the objective lens, and the intensity and polarization distribution of the focal field are shown as follows: Figure 4 As shown in (c), the focal field is restored to a complete light spot, and its polarization distribution is non-uniform. The topological structure constructed based on the Stokes parameters of the focal field is as follows: Figure 4 As shown in (d), it can be seen that the focal field has a complete topological structure, and its skyrmion number is -0.95, indicating that there is skyrmion topology in the focal field.

[0059] In summary, for skyrmion beams with cross-shaped, rectangular, and fan-shaped breaks, the skyrmion topology can be regenerated in the focal field after being focused by the objective lens, demonstrating the effectiveness of the method proposed in the present invention to overcome beam breakage and generate skyrmion topology.

[0060] The number of devices and processing scales described herein are intended to simplify the description of the present invention, and applications, modifications, and variations of the present invention will be apparent to those skilled in the art.

[0061] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and implementation methods. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for overcoming beam breaking to generate skyrmion topology, characterized in that: include: S1. The left-handed Gaussian light is coherently superimposed with the high-order right-handed Laguerre-Gaussian light to generate a skyrmion beam with a specific topological structure; the Laguerre-Gaussian beam expression is The fundamental mode expression of Laguerre-Gaussian beam is: is a Laguerre polynomial, Describes the change of beam radius with propagation distance z, w0 is the beam waist radius, is the Rayleigh distance, p is the radial index, R(z)=z[1+(z R / z) 2 ] is the wavefront curvature radius, l is the orbital angular momentum topological charge, k = 2π / λ is the wave number, λ is the wavelength of the incident light, ψ(z) = tan -1 (z / z R ) is a Gouy aspect; S2. Constructing shielding masks of different shapes to shield the skyrmion beam, thereby introducing different shapes of breaks during beam propagation; wherein the shapes of the shielding masks include but are not limited to fan-shaped, rectangular, cross-shaped, and irregular shapes; S3. Use an objective lens to focus the broken skyrmion beam, analyze the focal field, observe its intensity and topological state distribution, evaluate the robustness of the skyrmion beam under different breaking conditions, and the effect of focusing on the reconstruction of the broken skyrmion beam.

2. A method for overcoming beam breaking and generating skyrmion topology according to claim 1, characterized in that: In step S1, the superposition of left-handed Gaussian light and high-order right-handed Laguerre-Gaussian light is the key step in generating a skyrmion beam. By controlling the topological charge of the orbital angular momentum carried by the high-order Laguerre-Gaussian light, skyrmion beams of different orders are generated.

3. A method for generating skyrmion topology by overcoming beam breaking according to claim 1, characterized in that: In step S2, when analyzing the skyrmion topological state of the light beam, the Stokes parameter is measured to characterize the polarization distribution of the light beam and to construct the skyrmion vector of the light beam to observe the effect of the breaking on the skyrmion beam.

4. A method for generating skyrmion topology by overcoming beam breaking according to claim 1, characterized in that: In step S3, the broken skyrmion beam is focused using an objective lens to focus the beam onto the focal plane. The field distribution of the focal field is obtained using the Richard Wolf vector diffraction formula, the Stokes parameters of the focal field are calculated, and the skyrmion topological state is regenerated.

5. A method for generating skyrmion topology by overcoming beam breaking according to claim 1, characterized in that: In step S3, an in-depth analysis of the simulation results is conducted. Multiple numerical simulations are performed by adjusting the shape of the breaking to evaluate the performance of the skyrmion beam under different conditions. The reconstruction of the skyrmion beam under various breaking conditions is relatively ideal, indicating that the focusing process can effectively overcome the adverse effects of the breaking on the skyrmion beam and regenerate the skyrmion topology in the focal field.

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