Method for simultaneously generating Skyrmion and Mobius ring topological states

Abstract

The invention discloses a method for simultaneously generating Skyrmion and Mobius ring topological states, which comprises the following steps of: constructing a Stokes parameter Skyrmion beam of any order by using left-hand circularly polarized light and right-hand circularly polarized light as orthogonal substrates; the order of the Skyrmion beam depends on the difference value of topological charges of orbital angular momentums carried by the left-handed component and the right-handed component. The Skyrmion beam is tightly focused, and a three-dimensional polarization ellipse can be generated in a focal field. Based on any axis of a three-dimensional polarization ellipse, a Mobius ring can be constructed around a point C of a focal field. Meanwhile, the Skyrmion topology state with the same order as the incident field can be constructed based on the Stokes parameter of the focal field. The torsion times of the Mobius ring in the focal field can be controlled by changing the order of the Skyrmion light beam. According to the invention, the generation of the focal field with the Skyrmion topology state and the Mobius ring topology state is realized, and the generation, annihilation and torsion times of the Mobius ring in the focal field can be controlled.

Description

Technical Field

[0001] The present invention relates to the technical field of vector light field control, and in particular to a method for simultaneously generating skyrmions and Möbius ring topological states. Background Art

[0002] Skyrmions originated from a theoretical model of topological protection proposed by British physicist Skyrme in 1962. This theoretical model was originally used to describe the stability of hadrons in high-energy physics, but later researchers named vector field structures with the same topological configuration skyrmions. Now, skyrmions are widely used in condensed magnetic materials. Its spins are arranged in a vortex or ring shape, and the whole has non-trivial topological properties and topological robustness. It is considered to be an information carrier of the new generation of magnetic storage and logic devices. The stability and low energy consumption of skyrmions have attracted much attention. It has become a spin structure at the micro-nano scale and is widely regarded as an ideal information storage unit in non-transient spin memory devices. Skyrmions have attracted the attention of a large number of researchers in recent years, and this special topological state has been realized in various systems, including Bose-Einstein condensates, quantum Hall systems, twisted graphene, ferroelectric nanocomposites and polariton superfluids. These non-trivial topologies have recently been extended to the field of optics, making the research of emerging optical skyrmions progress rapidly. In 2018, S. Tsesses et al. generated a skyrmion lattice by controlling the interference of surface plasmons on the metal surface. In 2019, Du Luping et al. constructed skyrmions with subwavelength-scale characteristics based on the spin angular momentum of the evanescent light vortex field. In 2020, Sijia Gao et al. constructed skyrmions based on the Stokes parameters of a vector light beam propagating in free space, and the number of skyrmions was simply related to the topological properties of the light beam. In 2022, Changxu Liu et al. observed for the first time the disorder-induced topological state transition in the skyrmion family, and discovered the robustness of the topological structure of optical skyrmions to the scattering of continuously changing random media. The development of optical skyrmions has important application potential in communications, light-matter interactions, high-resolution imaging, quantum technology, and other fields.

[0003] The Möbius strip is a special three-dimensional topological structure with only one surface and only one edge, so its surface cannot be oriented. The Möbius topological structure plays an important role in many disciplines. In 2003, Sergej O. Demokritov et al. discovered a "Möbius" soliton with symmetry breaking in the mode spectrum of spin wave solitons in a nonlinear active ring composed of magnetic ferrite films. It needs to go around the ring twice to meet the initial phase condition. In 2005, Claire Castro et al. realized aromatic cycloolefins with Möbius structures in aromatic compounds, forming a unique aromatic mode. In 2015, Bauer et al. observed an optical Möbius strip in an experiment. They tightly focused the Poincare beam and tracked the polarization ellipse around point C in the focal plane. Because the focusing produces a strong longitudinal component of the electric field, the long axis of the polarization ellipse undergoes a distortion away from the focal plane in three-dimensional space, forming a Möbius strip. In 2023, Jiawei Wang and others successfully observed and controlled the Berry phase in an optical Möbius strip microcavity, providing new possibilities for all-optical data processing, quantum mechanics and its simulation, sensing and computing. Skyrmions and Möbius strips are two topological structures with their own unique properties in the field of optics. Currently, only the two topological states have been studied separately, and there has been no report of the simultaneous existence of the two topological states. Summary of the invention

[0004] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a method for simultaneously generating skyrmions and Möbius strip topological states, so as to achieve the generation of a focal field having both skyrmions and Möbius strip topological states, and to control the generation, annihilation and torsion times of the Möbius strip in the focal field. In order to achieve the above-mentioned purpose and other advantages according to the present invention, a method for simultaneously generating skyrmions and Möbius strip topological states is provided, comprising:

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

[0006] S2, focusing the incident field of the structure through a high numerical aperture objective lens, and calculating the field distribution on the focal plane;

[0007] S3, judging whether a Möbius ring exists according to the number of twists of the focal field polarization elliptical strip corresponding to the topological charge difference of the orbital angular momentum generated by the left-handed and right-handed circular polarization components in the focal field z component;

[0008] At the same time, the skyrmion topological state is constructed based on the Stokes parameters in the focal field, and the Möbius strip is constructed using any axis of the three-dimensional polarization ellipse in the focal field, resulting in the simultaneous existence of skyrmions and Möbius strips in the focal field.

[0009] Preferably, the formula for constructing the incident field according to the desired skyrmion order in step S1 is:

[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 Indicates left-handed circularly polarized light. L and T R denote the topological charge of the orbital angular momentum carried by the left-handed and right-handed components in the incident field, T L -T R is the skyrmion number, x and y are the abscissa and ordinate axes of the Cartesian coordinate system in the incident field, respectively. is the radial distance in the incident field, is the azimuth angle in the incident field, and w represents the waist radius of the light beam.

[0014] Preferably, the topological charge difference T of the orbital angular momentum carried by the left-handed and right-handed circularly polarized components in step S1 is L -T R It is not only the order of the skyrmion topology, but also affects the number of twists of the focal field Möbius strip. By changing the order of the skyrmion T L -T R The number of twists of the Möbius strip in the focal field can be controlled.

[0015] Preferably, the specific steps of step S3 are:

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

[0017]

[0018]

[0019] Among them, α represents the major axis of the ellipse, β represents the minor axis of the ellipse, Re(.) means taking the real part in the brackets, and Im(.) means taking the imaginary part in the brackets. Indicates focal field E f The complex conjugate of .

[0020] S32, in the focal field, taking point C as the center, selecting a suitable radius to draw a circle, and drawing the major axes of all polarization ellipses on the circumference, to obtain a polarization ellipse ring;

[0021] S33, calculating the Stokes parameter of the focal field based on the x-component and the y-component of the focal field, and then selecting a suitable spot radius in the focal field, and drawing a skyrmion topology based on the Stokes vector in this area;

[0022] S34. Circularly polarized light is affected by the spin-orbit coupling in the focusing process, which will change the topological charge of the orbital angular momentum carried by the z component in the focal field. The left-handed circular polarization component will produce a topological charge of +1, and the right-handed circular polarization component will produce a topological charge of -1. They couple with the orbital angular momentum they carry to obtain a new topological charge. The difference in the topological charge of the left-handed and right-handed circular polarization components in the z component of the focal field is the twisting number of the Möbius strip in the focal field, which can be expressed as the twisting number T a =|T L +2-T R |.

[0023] S35. Change the Skyrmion order T of the incident field L -T R , observe the changes in the skyrmion order of the focal field and the number of twists of the polarization elliptical ring;

[0024] When T L -T R When it is an odd number, the polarization elliptical ring forms a Möbius ring. At this time, there are also orders of T in the focal field. L -T R The skyrmion and the twisting number is T a =|T L +2-T R |The Möbius strip;

[0025] When T L -T R When it is an even number, the polarization elliptical ring with an even number of twists has two faces and two edges, that is, the Möbius ring disappears, but at this time there is still a polarization elliptical ring with an order of T in the focal field. L -T R The Sigeminzi.

[0026] Preferably, in step S3, when T L -T R When it is an odd number, by selecting any axis αcost+βsint(-π≤t≤π) of the polarization ellipse, the Möbius loop still exists and the Möbius loop can be constructed flexibly.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1The method of simultaneously generating skyrmions and Möbius strip topological states has great application prospects in a series of fields involving optical topology. Compared with the traditional vector light field carrying topological structure, this method can simultaneously generate skyrmion structure and Möbius strip structure in the vector light field, find the law of topological structure change, clarify the method of customizing the topology of skyrmions and Möbius strips, and provide a new degree of freedom for highly localized light fields. It has great application potential in the fields of skyrmion devices, light-matter interaction, optical information processing, data storage, information encryption, quantum technology, etc.

[0029] (2 The present invention has powerful performance. The present invention can effectively control the number of twists of the Möbius strip and the order of the skyrmion, and can control the generation and annihilation of the Möbius strip by the order of the skyrmion. The Möbius strip with the same number of twists can correspond to skyrmions of different orders, and the Möbius strip and the skyrmion can be localized simultaneously within the sub-diffraction limit scale. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 A schematic diagram of the structure 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 (a) and the skyrmion topological state (b) according to the method for simultaneously generating a skyrmion and a Möbius strip topological state of the present invention, wherein the color of the arrow in (b) is marked by the size of the z component;

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

[0033] Figure 4 The method for simultaneously generating skyrmions and Möbius strip topological states according to the present invention is related to the incident field T R Twist times T with the Möbius strip a The relationship between the three-dimensional structure of the Möbius strip and the two-dimensional structure when projected onto the xOy plane (a)-(d), and the corresponding skyrmion topological states (e)-(h) are given. Figure 4 The arrows in (a)-4(d) indicate the twisting direction of the Möbius strip;

[0034] Figure 5In order to simultaneously generate skyrmions and Möbius strip topological states according to the method of the present invention, any axis αcost+βsint (-π≤t≤π) of the polarization ellipse is selected to form a Möbius strip. In Figure (a), the major axis at t=0 is selected, in Figure (c), the minor axis at t=π / 2 is selected, and in Figures (b) and (d), the axes at t=3π / 10 and t=7π / 10 are selected respectively to form the Möbius strip. DETAILED DESCRIPTION

[0035] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work 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, comprising 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 of which is equal to the difference of the topological charge of the orbital angular momentum carried by the left-handed and right-handed circularly polarized light, and the focal field skyrmion order is consistent with the incident field skyrmion order;

[0038] S2. Focusing the incident field with a high numerical aperture objective lens will produce a strong z component in the focal field, thus changing the polarization ellipse in the focal field from two-dimensional to three-dimensional, making it possible to form a Möbius ring. Using the Richard Wolf vector diffraction integral formula, calculate the field distribution E on the focal plane. f ;

[0039] S3. The spin-orbit coupling in the focusing process will cause the circularly polarized light carrying the spin angular momentum to generate a new orbital angular momentum in the z component of the focal field. The existence of the Möbius strip is determined by the number of twists of the polarization ellipse strip in the focal field corresponding to the topological charge difference of the orbital angular momentum generated by the left-handed and right-handed circularly polarized components in the z component of the focal field. The skyrmion topological state is constructed based on the Stokes parameters in the focal field, and the Möbius strip is constructed using any axis of the three-dimensional polarization ellipse in the focal field, and the skyrmion and the Möbius strip are obtained to exist in the focal field at the same time.

[0040] Furthermore, the formula for constructing the incident field according to the desired skyrmion order in step S1 is:

[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 Indicates left-handed circularly polarized light. L and T R denote the topological charge of the orbital angular momentum carried by the left-handed and right-handed components in the incident field, T L -T R is the skyrmion number, x and y are the abscissa and ordinate axes of the Cartesian coordinate system in the incident field, respectively. is the radial distance in the incident field, is the azimuth angle in the incident field, and w represents the waist radius of the light beam.

[0046] Furthermore, the topological charge difference T of the orbital angular momentum carried by the left-handed and right-handed circularly polarized components in step S1 is L -T R It is not only the order of the skyrmion topology, but also affects the number of twists of the focal field Möbius strip. By changing the order of the skyrmion T L -T R The number of twists of the Möbius strip in the focal field can be controlled.

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

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

[0049]

[0050] Among them, α represents the major axis of the ellipse, β represents the minor axis of the ellipse, Re(.) means taking the real part in the brackets, and Im(.) means taking the imaginary part in the brackets. Indicates focal field E f The complex conjugate of .

[0051] S32, in the focal field, taking point C as the center, selecting a suitable radius to draw a circle, and drawing the major axes of all polarization ellipses on the circumference, to obtain a polarization ellipse ring;

[0052] S33, calculating the Stokes parameter of the focal field based on the x-component and the y-component of the focal field, and then selecting a suitable spot radius in the focal field, and drawing a skyrmion topology based on the Stokes vector in this area;

[0053] S34. Circularly polarized light is affected by the spin-orbit coupling effect during the focusing process, which will change the topological charge of the orbital angular momentum carried by the z component in the focal field. The left-handed circular polarization component will produce a topological charge of +1, and the right-handed circular polarization component will produce a topological charge of -1. They couple with the orbital angular momentum they carry to obtain a new topological charge. The difference in the topological charge numbers generated by the left-handed and right-handed circular polarization 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 twist number T a =|T L +2-T R |.

[0054] S35. Change the Skyrmion order T of the incident field L -T R , observe the changes in the skyrmion order of the focal field and the number of twists of the polarization elliptical ring. L -T R When it is an odd number, the polarization elliptical ring forms a Möbius ring. At this time, there are also orders of T in the focal field. L -T R The skyrmion and the twisting number is T a =|T L +2-T R |Mobius strip. When T L -T R When it is an even number, the polarization elliptical ring with an even number of twists has two faces and two edges, that is, the Möbius ring disappears, but at this time there is still a polarization elliptical ring with an order of T in the focal field. L -T R The Sigeminzi.

[0055] Furthermore, in step S3, when T L -T R When it is an odd number, by selecting any axis αcost+βsint(-π≤t≤π) of the polarization ellipse, the Möbius strip still exists, so the Möbius strip can be constructed flexibly.

[0056] like Figure 1 As shown, after the customized incident field carrying a specific number of skyrmions is focused by a high numerical aperture objective lens, 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 Richard Wolf vector diffraction integral formula. Here, the specific implementation of the technical solution is illustrated by taking the generation of a Möbius ring with a focal field skyrmion number of -1 and a twisting number of 1 as an example, which includes the following steps:

[0057] Step 1: For a first-order skyrmion and a Möbius strip with a twist order of 1, first determine T a =1, according to T a =|T L +2-T R |, then T L -T R = -1 or -3; at the same time, because the skyrmion number is -1, we can get T L -T R =-1, so here we set T L =0, T R =1.

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

[0059]

[0060] The intensity and polarization distribution of the Stokes parameter skyrmion beam are obtained as Figure 2 (a) shown. Figure 2 (b) shows the topological state of the skyrmion based on the Stokes parameter, whose skyrmion number is -0.93.

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

[0062]

[0063] Substituting into Richard Wolf's vector integral diffraction formula, the focal field expression can be obtained:

[0064]

[0065] Among them, z f = 0 is the result of the focal plane. The first-order Bloch-type Stokes parameter skyrmion and the Möbius ring with a twisting order of 1 are obtained as follows Figure 3 (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 the skyrmion, and its skyrmion number is -0.93. Figure 3 (c) is the Möbius strip formed by the major axis of the polarization ellipse. Without loss of generality, the Stokes parameters are normalized here.

[0066] from Figure 3 As can be seen in (a), the effective light intensity diameter of the focused light spot is about 1.17λ, indicating that the focused light spot is close to the diffraction limit. Figure 3As can be seen in (b), the topological state of the skyrmion evolves in a spatially directed manner on a scale smaller than the diffraction limit. Figure 3 In (c), the three-dimensional structure of the Möbius strip and the two-dimensional structure projected onto the xOy plane are given at the same time. The change in color on the Möbius strip represents the change in the angle between the strip and the focal plane. The number of times the color changes from dark to light can show the number of twists of the Möbius strip. Here, we select the point C ( Figure 3 (a) The center circle) is the center of the circle, and the major axis of all polarization ellipses on the circumference with a radius of 0.3λ constitutes a Möbius strip. In summary, after the incident field carrying the first-order skyrmion is focused by a high numerical aperture objective lens, skyrmions and Möbius strip topological states can be generated simultaneously in the focal field.

[0067] After generating the focal field with both first-order skyrmions and a Möbius strip with a twist order of 1, the same method can be used to generate more diverse results to verify the incident field (T L ,T R ) on the skyrmion order, and the relationship between the skyrmion order and the number of twists of the Möbius strip. L ,T R )=(0,-2), (0,-3), (0,3) and (-1,-2), the incident field expressions are: E=ψ0L+ψ -2 R,E=ψ0L+ψ -3 R, E = ψ0L + ψ3R and E = ψ -1 L+ψ -2 R. The incident field waist radius is w = 1. After focusing, a circle with a radius of 0.3λ and a center of point C is selected in the focal field. The long axes of all polarization ellipses on the circle form a ring, and the corresponding skyrmion topological state is drawn. The result is as follows Figure 4 (a)-4(h), where Figure 4 (a)-4(d) are (T L ,T R )=(0,-2), (0,-3), (0,3) and (-1,-2) corresponding to the polarization ellipse of the focal field, Figure 4 (e)-4(h) are Figure 4 (a)-4(d) corresponds to the skyrmion topological state. According to T a =|T L +2-T R |The twisting times of polarization ellipse bands are T a =4, 5, 1 and 3, and Figure 4The results of (a)-4(c) are consistent; at the same time, the corresponding skyrmion numbers are 1.99, 2.99, -2.96 and 0.99 respectively. Considering that the finite spot size will bring a certain error in the skyrmion number, this result corresponds to the difference in topological charge T between the orbital angular momentum carried by the left-handed and right-handed circularly polarized components of the incident field. L -T R It should be pointed out that when the number of twists is an even number, the Möbius strip disappears, and the ring formed by the major axis of the polarization ellipse (other axes can also be selected) has two faces and two edges, and does not have the topological properties of the Möbius strip. When the number of twists is an odd number, the ring can select any axis as the starting point and move in any direction. Its end point is connected to the starting point in the opposite direction. The ring has only one face and one edge, and the Möbius strip exists. Therefore, it can be changed by changing the order of the skyrmion T L -T R Controls the creation and destruction of a Möbius strip. Figure 4 (b) and 4(c), when the number of skyrmions in the incident field is opposite, the twisting direction of the Möbius strip in the focal field is also opposite. It can be seen that this method has high flexibility and can customize the topological order of skyrmions and the number of twists of the Möbius strip.

[0068] Figure 5 These are four examples of selecting different axes in the polarization ellipse to form a Möbius strip. The axis of the polarization ellipse is represented by αcost+βsint(-π≤t≤π), and t represents the angle between the selected axis and the major axis of the polarization ellipse. The incident field expression is set to E=ψ0L+ψ1R, the beam waist radius w=1, and all polarization ellipses on the circle with a radius of 0.3λ and a center at point C in the focal field are selected. The upper right corner is a schematic diagram of the selected polarization ellipse axis, and the straight line in the ellipse is the selected axis. Among them Figure 5 (a) is a Möbius loop formed by selecting the major axis α of the polarization ellipse (at t = 0), and rotating the major axis clockwise around the center of the ellipse to obtain Figure 5 (b) The axis with t = 3π / 10 can still form a Möbius loop. When t = π / 2, the minor axis β of the ellipse can be obtained, which is orthogonal to the major axis. The Möbius loop formed by the minor axis is shown in Figure 5 (c) Because the minor axis is shorter, the width of the annulus is also reduced. Continue to rotate clockwise to obtain Figure 5 (d), at this time t = 7π / 10, it can still form a Möbius strip, and then rotate clockwise to return to Figure 5 (a). It can be seen that the formation of the Möbius strip is multi-angle, and any axis of the polarization ellipse can form a Möbius strip.

[0069] The number of devices and processing scales described here are used to simplify the description of the present invention, and the application, modification and variation of the present invention will be obvious to those skilled in the art.

[0070] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and implementation modes. 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 the illustrations shown and described herein.

Claims

1. A method for simultaneously generating skyrmions and Möbius strip topological states, characterized in that: include: S1, constructing the incident field according to the desired skyrmion order by using left-handed and right-handed circularly polarized light carrying orbital angular momentum as orthogonal basis; S2, focusing the incident field of the structure through a high numerical aperture objective lens, and calculating the field distribution on the focal plane; S3, judging whether a Möbius ring exists according to the number of twists of the focal field polarization elliptical strip corresponding to the topological charge difference of the orbital angular momentum generated by the left-handed and right-handed circular polarization components in the focal field z component; At the same time, the skyrmion topological state is constructed based on the Stokes parameters in the focal field, and the Möbius strip is constructed using any axis of the three-dimensional polarization ellipse in the focal field, resulting in the simultaneous existence of skyrmions and Möbius strips in the focal field.

2. A method for simultaneously generating skyrmions and Möbius strip topological states according to claim 1, characterized in that: The formula for constructing the incident field according to the desired skyrmion order in step S1 is: in: Where R = [e x -ie y ] T represents right-handed circularly polarized light, L = [e x ie y ] T Indicates left-handed circularly polarized light. L and T R denote the topological charge of the orbital angular momentum carried by the left-handed and right-handed components in the incident field, T L -T R is the skyrmion number, x and y are the abscissa and ordinate axes of the Cartesian coordinate system in the incident field, respectively. is the radial distance in the incident field, is the azimuth angle in the incident field, and w represents the waist radius of the light beam.

3. A method for simultaneously generating skyrmions and Möbius strip topological states as claimed in claim 2, characterized in that: The topological charge difference T of the orbital angular momentum carried by the left-handed and right-handed circularly polarized components in step S1 L -T R It is not only the order of the skyrmion topology, but also affects the number of twists of the focal field Möbius strip. By changing the order of the skyrmion T L -T R The number of twists of the Möbius strip in the focal field can be controlled.

4. The method for simultaneously generating skyrmions and Möbius strip topological states according to claim 1, characterized in that: The specific steps of step S3 are: S31. The major axis and minor axis of the three-dimensional polarization ellipse in the focal field can be calculated as: Among them, α represents the major axis of the ellipse, β represents the minor axis of the ellipse, Re(.) means taking the real part in the brackets, and Im(.) means taking the imaginary part in the brackets; Indicates focal field E f The complex conjugate of S32, in the focal field, taking point C as the center, selecting a suitable radius to draw a circle, and drawing the major axes of all polarization ellipses on the circumference, to obtain a polarization ellipse ring; S33, calculating the Stokes parameter of the focal field based on the x-component and the y-component of the focal field, and then selecting a suitable spot radius in the focal field, and drawing a skyrmion topology based on the Stokes vector in this area; S34. Circularly polarized light is affected by the spin-orbit coupling in the focusing process, which will change the topological charge of the orbital angular momentum carried by the z component in the focal field. The left-handed circular polarization component will produce a topological charge of +1, and the right-handed circular polarization component will produce a topological charge of -1. They couple with the orbital angular momentum they carry to obtain a new topological charge. The difference in the topological charge of the left-handed and right-handed circular polarization components in the z component of the focal field is the twisting number of the Möbius strip in the focal field, which can be expressed as the twisting number T a =|T L +2-T R |; S35. Change the Skyrmion order T of the incident field L -T R , observe the changes in the skyrmion order of the focal field and the number of twists of the polarization ellipse ring; When T L -T R When it is an odd number, the polarization elliptical ring forms a Möbius ring. At this time, there are also orders of T in the focal field. L -T R The skyrmion and the twisting number is T a =|T L +2-T R |The Möbius strip; When T L -T R When it is an even number, the polarization elliptical ring with an even number of twists has two faces and two edges, that is, the Möbius ring disappears, but at this time there is still a polarization elliptical ring with an order of T in the focal field. L -T R The Sigeminzi.

5. The method for simultaneously generating skyrmions and Möbius strip topological states according to claim 1, characterized in that: In step S3, when T L -T R When it is an odd number, by selecting any axis αcost+βsint (-π≤t≤π) of the polarization ellipse, the Möbius loop still exists and the Möbius loop can be constructed flexibly.

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