A method for simultaneously generating skyrmions and mobius ring topological states

Abstract

The application discloses a method for simultaneously generating a skyrmion and a Mobius ring topological state, comprising the following steps: using left-handed circularly polarized light and right-handed circularly polarized light as an orthogonal basis to construct a Stokes parameter skyrmion beam of an arbitrary order, and the order of the skyrmion beam depends on the difference between the topological charges of the orbital angular momentum carried by the left-handed component and the right-handed component; and performing tight focusing on the skyrmion beam to generate a three-dimensional polarization ellipse in a focal field; and based on any axis of the three-dimensional polarization ellipse, a Mobius ring can be constructed around the C point of the focal field; meanwhile, based on the Stokes parameter of the focal field, a skyrmion topological state with the same order as the incident field can also be constructed; and the twist number of the Mobius ring in the focal field can be controlled by changing the order of the skyrmion beam. According to the application, a focal field with both a skyrmion and a Mobius ring topological state is generated, and the generation, annihilation and twist number of the Mobius ring in the focal field can be controlled.

Description

Technical Field

[0001] This invention relates to the field of vector light field manipulation technology, and in particular to a method for simultaneously generating skyrmions and Möbius strip topological states. Background Technology

[0002] Skyrmions originated from a topologically protected theoretical model proposed by British physicist Skyrme in 1962. This model was initially used to describe the stability of hadrons in high-energy physics, but researchers later named vector field structures with the same topological configuration skyrmions. Now, skyrmions are widely used in condensed matter magnetic materials. Their spins are arranged in vortex or ring patterns, exhibiting nontrivial topological properties and topological robustness, making them considered information carriers for next-generation magnetic storage and logic devices. The stability and low energy consumption of skyrmions have attracted considerable attention; they have become a spin structure at the micro- and nanoscale and are widely considered an ideal information storage unit in non-transferable spin storage devices. In recent years, skyrmions have attracted significant research attention, and this special topological state has been realized in various systems, including Bose-Einstein condensates, quantum Hall systems, twisted graphene, ferroelectric nanocomposites, and polarized exciton superfluids. These nontrivial topologies have recently been extended to the field of optics, leading to rapid progress in the research of emerging optical skyrmions. In 2018, S. Tsesses et al. generated skyrmion lattices by controlling the interference of surface plasmons on metal surfaces. In 2019, Du Luping et al. constructed skyrmions with subwavelength scale characteristics based on the spin angular momentum of evanescent vortex fields. In 2020, Sijia Gao et al. constructed skyrmions based on the Stokes parameters of vector beams propagating in free space, with their skyrmion number simply related to the topological properties of the beam. In 2022, Changxu Liu et al. first observed disorder-induced topological state transitions in the skyrmion family and discovered the robustness of the topological structure of optical skyrmions to scattering by continuously varying random media. The development of optical skyrmions has significant application potential in communication, light-matter interaction, high-resolution imaging, and quantum technology.

[0003] A Möbius strip is a special three-dimensional topological structure with only one surface and one edge, making its surface unorientable. Möbius topology plays an important role in multiple disciplines. In 2003, Sergej O. Demokritov et al. discovered a symmetry-breaking Möbius soliton in the mode spectrum of a spin-wave soliton in a nonlinear active ring composed of magnetic ferrite thin films; it requires two rotations around the ring to satisfy the initial phase condition. In 2005, Claire Castro et al. realized aromatic cycloalkenes with a Möbius structure in aromatic compounds, forming a unique aromatic mode. In 2015, Bauer et al. experimentally observed an optical Möbius strip. They tightly focused a Poincaré beam and traced a polarization ellipse around point C on the focal plane. Due to the strong longitudinal component of the electric field generated by focusing, the major axis of the polarization ellipse underwent a distortion deviating from the focal plane in three-dimensional space, forming a Möbius strip. In 2023, Jiawei Wang and colleagues successfully observed and controlled the Berry phase in an optical Möbius strip microcavity, providing new possibilities for applications such as all-optical data processing, quantum mechanics and its simulation, sensing, and computing. Skyrmions and Möbius strips are two topological structures with unique properties in the field of optics. Currently, only the two topological states are studied separately, and there are no reports of the simultaneous existence of the two topological states. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a method for simultaneously generating skyrmions and Möbius strip topological states, thereby achieving the generation of a focal field possessing both skyrmions and Möbius strip topological states, and allowing control over the generation, annihilation, and torsion number of the Möbius strip within the focal field. To achieve the above-mentioned objectives and other advantages of the present invention, a method for simultaneously generating skyrmions and Möbius strip topological states is provided, comprising:

[0005] S1. Using left-handed and right-handed circularly polarized light carrying orbital angular momentum as orthogonal basis, construct the incident field according to the desired skyrmion order;

[0006] S2. Focus the incident field of the structure using a high numerical aperture objective lens and calculate the field distribution on the focal plane.

[0007] S3. Determine the existence of a Möbius strip based on the number of twists of the focal field polarization elliptical strip corresponding to the difference in the topological charge of the orbital angular momentum generated by the left-hand and right-hand circular polarization components in the focal field z-component.

[0008] Simultaneously, based on the Stokes parameter in the focal field, a skyrmion topological state is constructed, and a Möbius strip is constructed using the arbitrary axis of the three-dimensional polarization ellipse in the focal field, thus obtaining that the skyrmion and the Möbius strip coexist in the focal field.

[0009] Preferably, the formula for constructing the incident field based on the desired skyrmion order in step S1 is as follows:

[0010] E = ψ TL L+ψ TR R (1)

[0011] in:

[0012]

[0013] Where R = [e] x -ie y ] T Represents right-handed circularly polarized light, L = [e x ie y ] T This indicates left-handed circularly polarized light. (T) L and T R T represents the topological charge number of the orbital angular momentum carried by the left-handed and right-handed components in the incident field, respectively. L -T R Let x be the skyrmion number, and let x and y be the abscissa and ordinate of the Cartesian coordinate system in the incident field, respectively. The radial distance in the incident field. denoted as azimuth in the incident field, and w represents the beam waist radius.

[0014] Preferably, the difference in topological charge T between the orbital angular momentum carried by the left-handed and right-handed circularly polarized components in step S1 is... L -T R The order of the skyrmion topology also affects the number of twists in the focal field Möbius strip. By changing the order T of the skyrmion... L -T R It can control the number of times the Möbius strip twists in the focal field.

[0015] Preferably, step S3 specifically comprises the following steps:

[0016] S31. The major and minor axes of the three-dimensional polarization ellipse in the focal field can be calculated as follows:

[0017]

[0018]

[0019] Where α represents the major axis of the ellipse, β is the minor axis of the ellipse, Re(.) represents taking the real part of the part inside the parentheses, and Im(.) represents taking the imaginary part of the part inside the parentheses. Indicates focal field E f .

[0020] S32. Draw a circle with point C as the center in the focal field and select a suitable radius. Draw the major axes of all polarization ellipses on this circumference to obtain a polarization ellipse annulus;

[0021] S33. Calculate the Stokes parameters of the focal field based on the x and y components of the focal field, and then select a suitable spot radius in the focal field. Draw the skyrmion topology based on the Stokes vector in this area;

[0022] S34. Affected by the spin-orbit coupling effect during the focusing process, circularly polarized light will change the topological charge of the orbital angular momentum carried by the z component in the focal field. The left-handed circularly polarized component will generate a topological charge of +1, and the right-handed circularly polarized component will generate a topological charge of -1. Coupled with the orbital angular momentum they carry, new topological charge numbers are obtained. The difference in the topological charge numbers of the left-handed and right-handed circularly polarized components in the z component of the focal field is the twist number of the Möbius ring in the focal field, which can be expressed as the twist number T a =|T L +2 - T R |.

[0023] S35. Change the skyrmion order T L -T R , and observe the changes in the skyrmion order of the focal field and the twist number of the polarization ellipse annulus;

[0024] When T L -T [[ID=​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​

[0028] (1) The method of simultaneously generating skyrmion and Möbius strip topological states has significant application prospects in a range of fields involving optical topology. Compared with traditional vector light fields carrying topological structures, this method realizes the simultaneous generation of skyrmion and Möbius strip structures in vector light fields, and finds the law of topological structure change, clarifying the method of customizing skyrmion and Möbius strip topologies. This provides a new degree of freedom for highly localized light fields and has great application potential in fields such as skyrmion devices, light-matter interaction, optical information processing, data storage, information encryption, and quantum technology.

[0029] (2) This invention has powerful performance. This invention can effectively control the number of twists of the Möbius strip and the order of the skyrmion. The generation and annihilation of the Möbius strip can be controlled by the order of the skyrmion. The same number of twists of the Möbius strip can correspond to skyrmions of different orders. Furthermore, the Möbius strip and the skyrmion can be localized simultaneously within the sub-diffraction limit scale. Attached Figure Description

[0030] Figure 1 A schematic diagram of the method for simultaneously generating skyrmions and Möbius strip topological states according to the present invention;

[0031] Figure 2 The intensity distribution of the incident field of a Néel-type skyrmion and the skyrmion topological state (b) are shown in Figure (b) for the method of simultaneously generating skyrmions and Möbius ring topological states according to the present invention. The color of the arrows in Figure (b) is indicated by the magnitude of the z-component.

[0032] Figure 3 Figure (a) shows the intensity distribution of the focal field obtained after focusing a Néel-type skyrmion field, a Bloch-type skyrmion topological state (b), and a Möbius ring formed by the major axis of a polarization ellipse, according to the method of simultaneously generating skyrmion and Möbius ring topological states according to the present invention. The small circle at the center of the light spot in Figure (a) marks point C in the light spot.

[0033] Figure 4 For the method of simultaneously generating skyrmions and Möbius strip topological states according to the present invention, with respect to T in the incident field R The number of twists of the Möbius strip, T a The relationship is given, and the three-dimensional structure of the Möbius strip and the two-dimensional structure projected onto the xOy plane (a)-(d) are also given, along with its corresponding skyrmion topological state (e)-(h). Figure 4 The arrows in (a)-4(d) indicate the direction of the Möbius strip's twist;

[0034] Figure 5To construct a Möbius ring using any axis αcost + βsint (-π ≤ t ≤ π) of the polarization ellipse according to the method of simultaneously generating skyrmions and Möbius ring topological states according to the present invention, Figure (a) uses the major axis at t = 0, Figure (c) uses the minor axis at t = π / 2, while Figures (b) and (d) use axes at t = 3π / 10 and t = 7π / 10 respectively to construct the Möbius ring. Detailed Implementation

[0035] 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.

[0036] Reference Figure 1 A method for simultaneously generating skyrmions and Möbius strip topological states includes the following steps:

[0037] S1. Using left-handed and right-handed circularly polarized light carrying orbital angular momentum as orthogonal basis, construct the incident field according to the desired skyrmion order. The skyrmion order is equal to the difference in topological charge of the orbital angular momentum carried by the left-handed and right-handed circularly polarized light. The skyrmion order of the focal field is consistent with the skyrmion order of the incident field.

[0038] S2. Focusing the incident field of the structure using a high numerical aperture objective lens will generate a strong z-component in the focal field, thus transforming the polarization ellipse in the focal field from two-dimensional to three-dimensional, making the formation of a Möbius strip possible. The field distribution E on the focal plane is calculated using Richard Wolf's vector diffraction integral formula. f ;

[0039] S3. During the focusing process, the spin-orbit coupling effect causes the circularly polarized light carrying spin angular momentum to generate a new orbital angular momentum in the z-component of the focal field. The existence of a Möbius strip is determined by the number of twists of the focal field polarization ellipse strip corresponding to the difference in topological charge of the orbital angular momentum generated by the left-hand and right-hand circularly polarized components in the z-component of the focal field. Based on the Stokes parameter in the focal field, a skyrmion topological state is constructed. A Möbius strip is constructed using an arbitrary axis of the three-dimensional polarization ellipse in the focal field, revealing that both the skyrmion and the Möbius strip exist simultaneously in the focal field.

[0040] Furthermore, the formula for constructing the incident field based on the desired skyrmion order in step S1 is as follows:

[0041] E = ψ TL L+ψ TR R (1)

[0042] in:

[0043]

[0044]

[0045] Where R = [e] x -ie y ] T Represents right-handed circularly polarized light, L = [e x ie y ] T This indicates left-handed circularly polarized light. (T) L and T R T represents the topological charge number of the orbital angular momentum carried by the left-handed and right-handed components in the incident field, respectively. L -T R Let x be the skyrmion number, and let x and y be the abscissa and ordinate of the Cartesian coordinate system in the incident field, respectively. The radial distance in the incident field. denoted as azimuth in the incident field, and w represents the beam waist radius.

[0046] Furthermore, the difference in topological charge T between the orbital angular momentum carried by the left-handed and right-handed circularly polarized components in step S1... L -T R The order of the skyrmion topology also affects the number of twists in the focal field Möbius strip. By changing the order T of the skyrmion... L -T R It can control the number of times the Möbius strip twists in the focal field.

[0047] Furthermore, step S3 also includes the following steps:

[0048] S31. The major and minor axes of the three-dimensional polarization ellipse in the focal field can be calculated as follows:

[0049]

[0050] Where α represents the major axis of the ellipse, β is the minor axis of the ellipse, Re(.) represents taking the real part of the part inside the parentheses, and Im(.) represents taking the imaginary part of the part inside the parentheses. Indicates focal field E f .

[0051] S32. In the focal field, take point C as the center and draw a circle with a suitable radius. Draw the major axes of all polarization ellipses on this circle to obtain a polarization ellipse ring.

[0052] S33. Calculate the Stokes parameters of the focal field based on the x and y components of the focal field, and then select an appropriate spot radius in the focal field. Draw the skyrmion topology based on the Stokes vector in this region.

[0053] S34. Affected by the spin-orbit coupling effect during the focusing process, circularly polarized light will change the topological charge of the orbital angular momentum carried by the z component in the focal field. The left-handed circularly polarized component will generate a topological charge of +1, and the right-handed circularly polarized component will generate a topological charge of -1. Coupled with the orbital angular momentum they carry, new topological charge numbers are obtained. The difference in the topological charge numbers generated by the left-handed and right-handed circularly polarized components in the z component of the focal field is the twisting number of the Möbius ring in the focal field, which can be expressed as the twisting number T a =|T L +2-T R |.

[0054] S35. Change the skyrmion order T L -T R , and observe the changes in the skyrmion order and the twisting number of the polarization ellipse annulus in the focal field. When T L -T R is odd, the polarization ellipse annulus forms a Möbius ring. At this time, there are skyrmions with order T L -T R and a Möbius ring with a twisting number of T a =|T L +2-T R | in the focal field. When T L -T R is even, the polarization ellipse annulus with an even number of twists has two surfaces and two edges, that is, the Möbius ring disappears. However, there are still skyrmions with order T L -T R in the focal field.

[0055] Further, in step S3, when T L -T R is odd, select any axis of the polarization ellipse αcost + βsint (-π ≤ t ≤ π), and the Möbius ring still exists. Therefore, the Möbius ring can be flexibly constructed.

[0056] As Figure 1 shown, the customized incident field carrying a specific skyrmion number is focused by an objective lens with a high numerical aperture, and skyrmions and Möbius rings with the expected topology can be obtained in the focal field. The intensity and phase of the focused light field can be calculated using the Richards-Wolf vector diffraction integral formula. Here, taking the generation of a Möbius ring with a skyrmion number of -1 and a twisting number of 1 in the focal field as an example, the specific implementation manner of the technical solution is described, including the following steps:

[0057] Step 1: For a first-order skyrmion and a Möbius strip with a twist number of 1, first determine T. a =1, according to T a =|T L +2-T R |, then T L -T R = -1 or -3; and since the skymin number is -1, we can obtain T L -T R =-1, so let T be here. L =0,T R =1.

[0058] Step 2: Based on the obtained T L and T R Combining formula (1), the incident field can be determined:

[0059]

[0060] The intensity and polarization distribution of the obtained Stokes parametric skyrmion beam are as follows: Figure 2 As shown in (a). Figure 2 (b) gives the topological state of skyrmions based on Stokes parameters, with a skyrmion number of -0.93.

[0061] Step 3: Perform coordinate transformation on the incident field to obtain the expression for the light field behind the lens.

[0062]

[0063] Substituting Richard Wolf's vector integral diffraction formula, we obtain the focal field expression:

[0064]

[0065] Among them, z f =0 is the result of the focal plane. The obtained first-order Bloch-type Stokes parametric skyrmion and the Möbius strip with a torsion order of 1 are as follows: Figure 3 As shown in (a)-3(c), here Figure 3 (a) shows the intensity and polarization distribution of the light field on the focal plane. Figure 3 (b) is the topological state of a skyrmion with a skyrmion number of -0.93. Figure 3 (c) is a Möbius strip formed by the major axis of the polarization ellipse. Without loss of generality, the Stokes parameter has been normalized here.

[0066] from Figure 3 As can be seen in (a), the effective intensity diameter of the focused spot is approximately 1.17λ, indicating that the focused spot is a near-diffraction-limited spot. From Figure 3As can be seen in (b), the topological state of the skyrmion undergoes spatial orientation evolution at a scale smaller than the diffraction limit. Figure 3 (c) simultaneously presents the three-dimensional structure of the Möbius strip and its two-dimensional structure projected onto the xOy plane. The color changes on the Möbius strip represent the changes in the angle between the torus and the focal plane. The number of times the color changes from dark to light indicates the number of twists in the Möbius strip. Here, point C is selected as the reference point. Figure 3 (a) A Möbius strip is formed by the major axes of all polarization ellipses on a circle with a radius of 0.3λ centered at the central circle. In summary, after the incident field carrying a first-order skyrmion is focused by an objective lens with a high numerical aperture, both skyrmion and Möbius strip topological states can be generated in the focal field.

[0067] After generating a focal field containing both a first-order skyrmion and a Möbius strip with a torsion order of 1, more diverse results can be generated using the same method to verify the incident field (T). L ,T R The effect of ) on the order of the skyrmion, and the relationship between the order of the skyrmion and the number of twists of the Möbius strip. Construct (T) L ,T R The incident fields of (0,-2), (0,-3), (0,3) and (-1,-2) are expressed as: E = ψ0L + ψ -2 R, E = ψ0L + ψ -3 R, E=ψ0L+ψ3R and E=ψ -1 L+ψ -2 R. The incident beam waist radius is w = 1. After focusing, a circle with radius 0.3λ centered at point C is selected in the focal field. A ring is formed by the major axes of all polarization ellipses on this circle, and the corresponding skyrmion topological states are plotted. The results are as follows: Figure 4 As shown in (a)-4(h), Figure 4 (a)-4(d) are respectively (T) L ,T R The polarization elliptical bands of the focal field corresponding to (0,-2), (0,-3), (0,3) and (-1,-2) Figure 4 (e)-4(h) are respectively Figure 4 (a)-4(d) corresponds to the skymin topological state. According to T a =|T L +2-T R The number of twists of the polarization elliptical band can be obtained as T. a =4, 5, 1 and 3, and Figure 4The results (a)-4(c) are consistent; their corresponding skyrmion numbers are 1.99, 2.99, -2.96 and 0.99, respectively. Considering that the finite spot size will introduce a certain skyrmion number error, this result corresponds to the difference T between the topological charge of the orbital angular momentum carried by the left-hand and right-hand circularly polarized components of the incident field. L -T R It should be noted that when the number of twists is even, the Möbius strip disappears, and the ring formed by its major axis of polarization ellipse (or other axes) has two faces and two edges, lacking the topological properties of a Möbius strip. However, when the number of twists is odd, the ring can be started from any axis and moved in any direction, with its endpoint connected to the starting point in the opposite direction. This ring has only one face and one edge, and the Möbius strip exists. Therefore, the order T of the skyrmion can be changed. L -T R Controlling the generation and annihilation of Möbius strips. (Comparison) Figure 4 In (b) and 4(c), when the skyrmion numbers in their incident fields are opposite, the twisting directions of the focal field Möbius strip are also opposite. This demonstrates the high flexibility of this method, allowing for customization of the topological order of the skyrmions and the number of twists in the Möbius strip.

[0068] Figure 5 This section presents four examples of constructing a Möbius strip by selecting different axes within the polarization ellipse. The axis of the polarization ellipse is denoted by αcost + βsint (-π ≤ t ≤ π), where t represents the angle between the selected axis and the major axis of the polarization ellipse. The incident field is expressed as E = ψ0L + ψ1R, with a beam waist radius w = 1. All polarization ellipses within a circle centered at point C with a radius of 0.3λ are selected. The upper right corner shows a schematic diagram of the selected polarization ellipse axes; the straight lines within the ellipse represent the selected axes. Figure 5 (a) is a Möbius strip formed by selecting the major axis α of the polarization ellipse (at which point t=0), and rotating the major axis clockwise around the center of the ellipse, resulting in... Figure 5 (b) shows that the axis at t = 3π / 10 can still form a Möbius strip. When t = π / 2, the minor axis β of the ellipse can be obtained, which is orthogonal to the major axis. A Möbius strip constructed using the minor axis is shown below. Figure 5 (c) Because the minor axis is shorter, the width of its ring is also greatly reduced. Continuing to rotate clockwise yields... Figure 5 (d) At this point, t = 7π / 10, a Möbius strip can still be formed. Then, rotating clockwise returns to the starting position. Figure 5 (a). It can be seen that the Möbius strip is constructed from multiple angles, and any axis of the polarization ellipse can form a Möbius strip.

[0069] 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.

[0070] 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 method for simultaneously generating skyrmions and Möbius strip topological states, characterized in that, include: S1. Using left-handed and right-handed circularly polarized light carrying orbital angular momentum as orthogonal basis, construct the incident field according to the desired skyrmion order; S2. Focus the incident field of the structure using a high numerical aperture objective lens and calculate the field distribution on the focal plane. S3. Determine the existence of a Möbius strip based on the number of twists of the focal field polarization elliptical strip corresponding to the difference in the topological charge of the orbital angular momentum generated by the left-hand and right-hand circularly polarized components in the focal field z-component; the difference in the topological charge of the orbital angular momentum carried by the left-hand and right-hand circularly polarized components. The order of the skyrmion topology also affects the number of twists in the focal field Möbius strip. By changing the order of the skyrmion... It can control the number of times the Möbius strip twists in the focal field; Simultaneously, based on the Stokes parameter in the focal field, a skyrmion topological state is constructed, and a Möbius strip is constructed using the arbitrary axis of the three-dimensional polarization ellipse in the focal field, thus obtaining that the skyrmion and the Möbius strip coexist in the focal field.

2. The method for simultaneously generating skyrmions and Möbius strip topological states as described in claim 1, characterized in that, The formula for constructing the incident field based on the desired skymin order in step S1 is as follows: (1) in: (2) (3) in This indicates right-handed circularly polarized light. Indicates left-handed circularly polarized light; and Let represent the topological charge numbers of the orbital angular momentum carried by the left-handed and right-handed components in the incident field, respectively. Let x be the skyrmion number, and let x and y be the abscissa and ordinate of the Cartesian coordinate system in the incident field, respectively. The radial distance in the incident field. The azimuth angle in the incident field. The waist radius represents the beam length.

3. The method for simultaneously generating skyrmions and Möbius strip topological states as described in claim 1, characterized in that, The specific steps of step S3 are as follows: S31. The major and minor axes of the three-dimensional polarization ellipse in the focal field can be calculated as follows: (4) (5) in, Represents the major axis of the ellipse. Let be the minor axis of the ellipse. This indicates taking the real part of the text within the parentheses. This indicates taking the imaginary part within the parentheses; Indicates focal field The complex conjugate; S32. In the focal field, take point C as the center and draw a circle with a suitable radius. Draw the major axes of all polarization ellipses on this circle to obtain a polarization ellipse ring. S33. Calculate the Stokes parameters of the focal field based on the x and y components of the focal field, and then select an appropriate spot radius in the focal field to draw the skymin topology based on the Stokes vector in this region. S34. Circularly polarized light, affected by spin-orbit coupling during focusing, alters the topological charge of the orbital angular momentum carried by the z-component in the focal field. The left-hand circularly polarized component generates a +1 topological charge, while the right-hand circularly polarized component generates a -1 topological charge. Coupled with their own orbital angular momentum, a new topological charge number is obtained. The difference in topological charge numbers between the left-hand and right-hand circularly polarized components in the z-component of the focal field is the number of twists of the Möbius strip in the focal field, which can be expressed as the number of twists. ; S35. Changing the order of the skyrmions in the incident field. Observe the changes in the skyrmion order of the focal field and the number of twists in the polarization ellipse ring; when When the order is odd, the polarization elliptical rings form a Möbius strip, and at this time, the focal field simultaneously contains elements of order 1. The number of skemins and torsions is The Möbius strip; When is an even number, the polarization elliptical annulus with an even number of twists has two surfaces and two edges, that is, the Möbius ring disappears, but at this time, skyrmions with an order of still exist in the focal field.

4. The method for simultaneously generating skyrmions and Möbius strip topological states as described in claim 1, characterized in that, In step S3, when When the number is odd, choose any axis of the polarization ellipse. ( The Möbius strip still exists and can be flexibly constructed.

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