Method for inducing generation of magnetic ring by highly localized light ring

Abstract

This invention relates to the field of optical focal field customization technology. It discloses a method for generating a magnetic ring induced by a highly localized optical ring, comprising the following steps: customizing an orthogonal dipole pair antenna model and solving for its radiation field; modulating a spiral phase factor with the same spatial orientation on the radiation field; obtaining the entrance pupil field distribution by inversely solving the radiation field after modulation by the spiral phase factor; calculating the highly localized optical focal field distribution characteristics of the entrance pupil field in the focal region of a 4π focusing system based on Richard Wolf vector diffraction integral theory; and applying the optical focal field to a magneto-optical material based on the focal field distribution, and combining the inverse Faraday effect to solve for the spatial distribution characteristics of the magnetization field induced in the magneto-optical material. The magnetic ring generated by the highly localized optical ring customized in this application has the characteristic of independently adjustable spatial orientation and hollow size, and has broad application prospects in optical capture and manipulation, spin wave modulation, and magnetic topology manipulation.

Description

Technical Field

[0001] This invention relates to the field of optical focal field customization technology, and in particular to a method for inducing the generation of magnetic rings by highly localized optical rings. Background Technology

[0002] Structured light fields with specific spatial distributions of amplitude, phase, or polarization states are one of the core research directions in the field of modern optical manipulation. Highly localized annular focal fields, as a type of structured light field with a unique hollow topological intensity distribution, have demonstrated significant application value in cutting-edge fields such as optical capture and manipulation, super-resolution microscopy, and light-matter interactions, and are currently one of the most important and widely studied forms of structured light fields.

[0003] In the field of optical capture and manipulation, a ring-shaped light field can confine particles to a ring-shaped high-intensity region and drive the particles to rotate along the ring orbit through the transfer of orbital angular momentum, providing a powerful means for the precise manipulation of micro- and nano-scale objects. In the field of super-resolution microscopy, the ring-shaped light field is the core light field component of stimulated emission depletion microscopy, and the focal field structure formed by its hollow intensity distribution determines the upper limit of the effective resolution of the imaging system. Regarding light field-induced magnetization structures, the inverse Faraday effect (IFE) provides the basic physical mechanism for optical focal field-induced magnetization structures: a light field with a non-zero photon spin angular momentum density can induce an equivalent static magnetization field in magneto-optical materials, the direction and intensity of which are determined by the curl of the light field and its spatial intensity distribution. Based on this mechanism, by precisely controlling the polarization state, phase, and amplitude of the incident beam, combined with high numerical aperture tight focusing techniques, local magnetization structures with specific geometric morphologies can be induced in the magneto-optical materials in the focal region. In the study of optically induced magnetization structures, existing work mainly focuses on structural morphologies such as longitudinal magnetization spots, longitudinal magnetization needles, and magnetic vortex cores. Jiang et al., using a tightly focused azimuth vortex beam, achieved for the first time a sub-diffraction-limited pure longitudinal magnetization spot in the entire focal plane, with a transverse full width at half maximum (FWHM) of 0.508λ (Opt. Lett. 38, 2957, 2013); Nie et al., through 4π tight focusing of a hollow Gaussian vortex beam, further generated a three-dimensional spherical, subwavelength (approximately 0.43λ) pure longitudinal magnetization spot near the focal point (Opt. Express 23, 690, 2015). Wang et al. used a ring-shaped vortex binary optical element to generate a purely longitudinally magnetized needle with a longitudinal extension of 7.48λ and a lateral width of 0.38λ, achieving an aspect ratio of 20 (Opt. Lett. 39, 5022, 2014). Ma et al. further increased the aspect ratio to 103, achieving a longitudinal extension of 28λ and a lateral width compressed to 0.27λ (Chin. Opt. Lett. 13, 052101, 2015). Liu et al. demonstrated the all-optical construction of scalable super-resolution magnetic vortex kernels by tightly focusing two phase-modulated, opposing, radially polarized ring-shaped Gaussian beams (Opt. Express. 30, 10354, 2022).

[0004] However, the magnetized structures produced by the above schemes are all limited to an axisymmetric solid distribution. The root cause lies in the limited tunable dimension of the highly localized optical focal field itself, which serves as the induction source. Therefore, a new method is urgently needed to break through the bottleneck of the tunable dimension of the existing highly localized optical field, starting from the customization of the optical focal field. This method would allow for independent control of both the spatial orientation and the hollow inner diameter of the focal area's optical ring, and further, by utilizing the inverse Faraday effect, transform it into a similarly flexibly tunable magnetic ring. This would meet the needs of precise customization of the optical field topology and the functional application of the magnetized structure. Summary of the Invention

[0005] The purpose of this invention is to provide a method for generating magnetic rings by inducing highly localized optical rings, so as to solve the problems mentioned in the background art.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for inducing the generation of a magnetic ring by a highly localized optical ring, comprising the following steps: Step (1): Customize the orthogonal dipole pair antenna model and solve its radiation field; Step (2): Modulate spiral phase factors with the same spatial orientation on the radiation field; Step (3): Based on the radiation field modulated by the spiral phase factor, the entrance pupil field distribution is obtained by inverse solution; Step (4): Based on Richard Wolf's vector diffraction integral theory, calculate the highly localized focal field distribution characteristics of the entrance pupil field in the focal region of the 4π focusing system; Step (5): Based on the optical focal field distribution, the optical focal field is applied to the magneto-optical material, and combined with the inverse Faraday effect, the spatial distribution characteristics of the photomagnetization field induced in the magneto-optical material are solved.

[0007] Preferably, the specific process of step (1) is as follows: First, establish a 4π optical focusing system consisting of two objective lenses with confocal regions; A pair of orthogonal dipole pairs is placed in a space with the center point of the 4π optical focusing system as the origin. The orthogonal dipole pairs are placed orthogonally in this space, and the feed currents of the orthogonal dipole pairs are out of phase by π / 2. The orthogonal dipole pair is rotated with the center point of the 4π optical focusing system as the fulcrum; Calculate the radiation field of the rotated orthogonal dipole pair.

[0008] Preferably, the 4π optical focusing system consists of two high numerical aperture objectives with identical external dimensions and optical parameters, and the optical axes of the two objectives are on the same straight line and are placed confocally. A global rectangular coordinate system is established in the 4π optical focusing system; wherein, the origin O of the global rectangular coordinate system is the common focal point of the two objectives; the direction of the optical axis is taken as the z-axis, and the z-axis is perpendicular to the focal plane, i.e., the xy plane.

[0009] Preferably, the specific arrangement of a pair of orthogonal dipoles is as follows: If two electric dipoles constituting orthogonal dipoles are placed on the x-axis and y-axis of a global rectangular coordinate system, respectively, and their feed currents are phased by π / 2, then the coherent superposition of their radiation fields in the xy-plane is circularly polarized: when the feed current of the y-axis electric dipole lags the x-axis by π / 2, the coherent superposition of their radiation fields in the xy-plane exhibits left-handed circular polarization, with its spin angular momentum along the +z-axis; conversely, when the y-axis leads the x-axis by π / 2, the superimposed radiation field exhibits right-handed circular polarization, with its spin angular momentum along the −z-axis. According to the inverse Faraday effect, the focal field of the circularly polarized state can induce a magnetization field in the magneto-optical material that is aligned with the direction of its spin angular momentum.

[0010] The preferred method for calculating the radiation field of the rotated orthogonal dipole pair is as follows: The origin O of the global rectangular coordinate system is the pivot point of rotation. z shaft edge Plane rotation in one step θ 0 degrees, forming a local rectangular coordinate system, at this time z The spatial orientation of the axis is , x shaft and y The shaft rotates synchronously as x 'and y 'axis,( x '-, y '-, z The three principal axes of the local rectangular coordinate system are formed by '-); originally located at x shaft and y The electric dipoles on the axis also rotate synchronously, and after rotation, they are located in the reference coordinate system. x 'and y 'axis, when y 'Axial electric dipole current phase lag x If the axis is π / 2, then the spin direction of the coherent superposition radiation field of the two electric dipoles after rotation is + z 'axis; According to electromagnetic radiation theory, the three principal axes of the global rectangular coordinate system ( x -, y -, z -) The analytical expression for the dipole radiation field is as follows: (1) in, These are complex coefficients that are independent of the direction of the radiation field. f Let ω be the focal length of the focusing system, and ω be the angular frequency. The permeability of free space, This represents the amplitude of the dipole current. The length of the dipole. k For free space wavenumber; If the local coordinate system is known x'axis, y 'axis and z The axes are respectively related to the global rectangular coordinate system. x , y and z The included angles of the axes are respectively ( α 1, β 1, γ 1) ( α 2, β 2, γ 2) and ( α 3, β 3, γ 3), then it lies on the three principal axes of the local rectangular coordinate system ( x '-, y '-, z The radiation field of an electric dipole is obtained through matrix operations: (2) in, for The direction cosine matrix pointing in space is expressed as follows: (3) When originally located in the global coordinate system x and y The orthogonal dipole pairs of the axes rotate together with the coordinate system to the local Cartesian coordinate system. x 'and y If the axis is ', then the combined radiation field after the coherent superposition of the two is: (4) In the formula, when the topological load number T n When it is a positive number, y The phase lags the electric dipole current by π / 2; conversely, when the topological charge is negative... y 'Axial electric dipole current phase leads by π / 2; charge number' T n is an independent control parameter of the spiral phase factor in step (2); j is the imaginary unit; e is the base of the natural logarithm; and These are the unit vectors in the spherical coordinates θ and φ of the radiation field, respectively.

[0011] Preferably, in step (2), a spiral phase factor with a specified topological charge number is used, which is modulated on the radiation field and aligned with the normal of the plane containing the orthogonal dipole pair. The specific calculation method of the spiral phase factor is as follows: The normal of an orthogonal dipole to its plane is... z 'axis, at this point the spiral phase factor is based on x '- yThe calculation is performed on a plane, and its expression is as follows: (5) in, for x '- y 'Plane Self x 'Azimuth angle measured counterclockwise from the axis; The transformation relationship between the coordinate variables of the global rectangular coordinate system and the rotated local rectangular coordinate system is as follows: (6) Thus, the analytical expression for the radiation field of orthogonal dipole pairs modulated with the same spatially oriented spiral phase factor is obtained as follows: (7).

[0012] Preferably, step (3) is to obtain the vector field of the entrance pupil surface by combining the spiral phase-modulated radiation field shown in equation (7) with the apodization function of the lens; the entrance pupil field is obtained in reverse by the modulated radiation field of equation (7), without the need for a complex iterative optimization design process.

[0013] Preferably, step (4) is the light field obtained from step (3) after being focused by a 4π focusing system, and is quantitatively evaluated using Richard Wolf vector diffraction integral theory: (8) in, The focal field in cylindrical coordinates. θ max This is the maximum convergence angle of the objective lens, which is related to the numerical aperture of the objective lens; Let be the approximate spherical wavefront of the entrance pupil field after refraction through the lens; the two double integrals on the right side of the equation represent the tightly focused fields of the two lenses, where the factor in the second integral is... This indicates that the instantaneous polarization directions of the two entrance pupil vector light fields are opposite, i.e., the phase difference is π. Furthermore, since the focal field converged by the two lenses from the entrance pupil fields on both sides is calculated by integration in a unified coordinate system and coherently superimposed, the polar angle range of the second integral calculation formula needs to be shifted by π angle relative to the first integral calculation formula.

[0014] Preferably, step (5) is based on the inverse Faraday effect, where a magneto-optical material is placed at the confocal region of the 4π optical focusing system. The highly localized optical focal field constructed in step (4) can induce a photomagnetized field on the magneto-optical material, the characteristics of which are calculated and characterized by the following formula: (9) In the formula and Let be the electric field vector of the optical focal field and its conjugate vector. The coupling coefficient is related to the magneto-optical material.

[0015] As can be seen from the above description of the structure of the present invention, compared with the prior art, the present invention has the following advantages: This invention is based on a novel method combining orthogonal electric dipole pair radiation field and spiral phase modulation. By precisely constructing a near-circularly polarized optical ring focal field in the transverse cross section, a magnetic ring is induced in the magneto-optical material using the inverse Faraday effect, and its spatial orientation and hollow size can be independently controlled. The magnetic ring customized by this method has the characteristic of independent adjustment of both spatial orientation and hollow size, and has broad application prospects in the fields of optical capture and manipulation, spin wave modulation, and magnetic topology manipulation. Attached Figure Description

[0016] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of the method for generating magnetic rings by inducing highly localized optical rings according to the present invention; Figure 2 This is a schematic diagram of the orthogonal dipole pair antenna model of the present invention; Figure 3 This is a contour diagram of the light ring intensity when the orthogonal dipole pairs are located in the xy plane in Embodiment 1 of the present invention; Figure 4 The intensity and polarization distribution of the principal plane of the optical annulus when the orthogonal dipole pairs are located in the xy plane in Embodiment 1 of the present invention; Figure 5 This is a contour diagram of the induced magnetic ring intensity when the orthogonal dipole pairs are located in the xy plane in Embodiment 1 of the present invention; Figure 6 The diagram shows the principal plane intensity and polarization distribution of the induced magnetic ring when the orthogonal dipole pairs are located in the xy plane in Embodiment 1 of the present invention. Figure 7 This is a contour diagram of the light ring intensity when the orthogonal dipole pairs are located in the yz plane in Embodiment 2 of the present invention; Figure 8 This is a yz plane view of the light ring intensity when the orthogonal dipole pairs are located in the yz plane in Embodiment 2 of the present invention; Figure 9 This is a contour diagram of the induced magnetic ring intensity when the orthogonal dipole pairs are located in the yz plane in Embodiment 2 of the present invention; Figure 10 This is a yz-plane view of the induced magnetic ring intensity when the orthogonal dipole pairs are located in the yz-plane in Embodiment 2 of the present invention; Figure 11This is the intensity profile of the optical ring when the orthogonal dipole pairs are located in the xz plane in Embodiment 3 of the present invention; Figure 12 This is an xz-plane view of the intensity of the optical ring when the orthogonal dipole pairs are located in the xz-plane in Embodiment 3 of the present invention; Figure 13 This is a contour diagram of the induced magnetic ring intensity when the orthogonal dipole pairs are located in the xz plane in Embodiment 3 of the present invention; Figure 14 This is an xz-plane view of the induced magnetic ring intensity when the orthogonal dipole pairs are located in the xz-plane in Embodiment 3 of the present invention; Figure 15 This is the intensity profile of the optical ring when the orthogonal dipole pairs are located in any non-principal plane in Embodiment 4 of the present invention; Figure 16 This is a profile of the induced magnetic ring intensity when the orthogonal dipole pairs are located in any non-principal plane in Embodiment 4 of the present invention. Detailed Implementation

[0017] To better understand the technical solution of the present invention, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] refer to Figure 1 and Figure 2 As shown, a method for inducing the generation of a magnetic ring by a highly localized optical ring includes the following steps: customizing an orthogonal dipole pair antenna model and solving its radiation field; modulating a spiral phase factor with the same spatial orientation on the radiation field; obtaining the entrance pupil field distribution by inversely solving the radiation field after modulation by the spiral phase factor; calculating the highly localized optical focal field distribution characteristics of the entrance pupil field in the focal region of the 4π focusing system based on the Richard Wolf vector diffraction integral theory; and applying the optical focal field to a magneto-optical material based on the optical focal field distribution, and combining the inverse Faraday effect to solve the spatial distribution characteristics of the photomagnetization field induced by the optical focal field in the magneto-optical material.

[0019] This invention is based on a novel method combining orthogonal electric dipole pair radiation field and spiral phase modulation. By precisely constructing a near-circularly polarized optical ring focal field in the transverse cross section, a magnetic ring is induced in the magneto-optical material using the inverse Faraday effect, and its spatial orientation and hollow size can be independently controlled. The magnetic ring customized by this method has the characteristic of independent adjustment of both spatial orientation and hollow size, and has broad application prospects in the fields of optical capture and manipulation, spin wave modulation, and magnetic topology manipulation.

[0020] The specific implementation steps of the method of the present invention will now be described in detail: (1) Customize the orthogonal dipole pair antenna model and solve its radiation field: The 4π optical focusing system consists of two high numerical aperture objectives with identical external dimensions and optical parameters. The optical axes of the two objectives are on the same straight line and are placed confocally. In a 4π optical focusing system, a global rectangular coordinate system is established; the origin O of the global rectangular coordinate system is the common focal point of the two objectives; the direction of the optical axis is taken as the z-axis, and the z-axis is perpendicular to the focal plane, i.e., the xy plane.

[0021] A pair of orthogonal dipole pairs is placed in a space with the center point of the 4π optical focusing system as the origin. The orthogonal dipole pairs are placed orthogonally in this space, and the feed currents of the orthogonal dipole pairs are out of phase by π / 2. If two electric dipoles constituting an orthogonal dipole pair are placed on the x-axis and y-axis of a global rectangular coordinate system, respectively, and their feed currents are phase-differentiated by π / 2, then the coherent superposition of their radiation fields in the xy plane is circularly polarized: when the feed current of the y-axis electric dipole lags the x-axis by π / 2, the coherent superposition of their radiation fields in the xy plane exhibits left-handed circular polarization, with its spin angular momentum along the +z-axis; conversely, when the y-axis leads the x-axis by π / 2, the superimposed radiation field exhibits right-handed circular polarization, with its spin angular momentum along the −z-axis. According to the inverse Faraday effect, the focal field of the circularly polarized state can induce a magnetization field in the magneto-optical material that is aligned with the direction of its spin angular momentum. The specific method for calculating the radiation field of rotated orthogonal dipole pairs is as follows: The origin O of the global rectangular coordinate system is the pivot point of rotation. z shaft edge Plane rotation in one step θ 0 degrees, forming a local rectangular coordinate system, at this time z The spatial orientation of the axis is , x shaft and y The shaft rotates synchronously as x 'and y 'axis,( x '-, y '-, z The three principal axes of the local rectangular coordinate system are formed by '-); originally located at x shaft and y The electric dipoles on the axis also rotate synchronously, and after rotation, they are located in the reference coordinate system. x 'and y 'axis, when y 'Axial electric dipole current phase lag x If the axis is π / 2, then the spin direction of the coherent superposition radiation field of the two electric dipoles after rotation is + z 'axis; According to electromagnetic radiation theory, the three principal axes of the global rectangular coordinate system ( x -, y -, z-) The analytical expression for the dipole radiation field is as follows: (1) in, These are complex coefficients that are independent of the direction of the radiation field. f Let ω be the focal length of the focusing system, and ω be the angular frequency. The permeability of free space, This represents the amplitude of the dipole current. The length of the dipole. k For free space wavenumber; If the local coordinate system is known x 'axis, y 'axis and z The axes are respectively related to the global rectangular coordinate system. x , y and z The included angles of the axes are respectively ( α 1, β 1, γ 1) ( α 2, β 2, γ 2) and ( α 3, β 3, γ 3), then it lies on the three principal axes of the local rectangular coordinate system ( x '-, y '-, z The radiation field of an electric dipole is obtained through matrix operations: (2) in, for The direction cosine matrix pointing in space is expressed as follows: (3) When originally located in the global coordinate system x and y The orthogonal dipole pairs of the axes rotate together with the coordinate system to the local Cartesian coordinate system. x 'and y If the axis is ', then the combined radiation field after the coherent superposition of the two is: (4) In the formula, when the topological load number T n When it is a positive number, y The phase lags the electric dipole current by π / 2; conversely, when the topological charge is negative... y 'Axial electric dipole current phase leads by π / 2; charge number' T nis an independent control parameter of the spiral phase factor in step (2); j is the imaginary unit; e is the base of the natural logarithm; and These are the unit vectors in the spherical coordinates θ and φ of the radiation field, respectively. In this application, the circular polarization chirality of the orthogonal dipole pair in the radiation field and the sign of Tn are configured in such a way that the tightly focused field can correctly induce the target magnetization field.

[0022] (2) The modulation spiral phase factor on the radiation field obtained in step (1): In step (1), the focal field simulated by the radiation field is a solid structure. In order to form a ring structure, a spiral phase factor with a specified topological charge number is used to modulate the normal of the plane containing the orthogonal dipole pair on the above radiation field.

[0023] The specific calculation method for the spiral phase factor is as follows; Figure 2 In the model, the normal to the plane containing the orthogonal dipole is... z 'axis; at this time, the spiral phase factor is based on x '- y The calculation is performed on a plane, and its expression is as follows: (5) in, for x '- y 'Plane Self x The azimuth angle measured counterclockwise from the axis.

[0024] The transformation relationship between the coordinate variables of the global rectangular coordinate system and the rotated local rectangular coordinate system is as follows: (6) Thus, the analytical expression for the radiation field of orthogonal dipole pairs modulated with the same spatially oriented spiral phase factor is obtained as follows: (7).

[0025] (3) Solve the entrance pupil field in reverse order based on the radiation field of the modulation spiral phase factor obtained in steps (1) and (2): The radiation field modulated by the spiral phase as shown in Equation (7), combined with the apodization function of the lens, can be used to obtain the vector field of the entrance pupil surface in reverse. Note that the entrance pupil field is obtained in reverse through the modulated radiation field of Equation (7), without the need for a complex iterative optimization design process.

[0026] (4) Quantitative evaluation of its 4π focused light field characteristics based on Richard Wolf vector diffraction integral theory: The light field obtained from step (3) after being focused by the 4π focusing system is quantitatively evaluated using Richard Wolf vector diffraction integral theory: (8) in, The focal field in cylindrical coordinates. θ max This is the maximum convergence angle of the objective lens, which is related to the numerical aperture of the objective lens; Let be the approximate spherical wavefront of the entrance pupil field after refraction through the lens; the two double integrals on the right side of the equation represent the tightly focused fields of the two lenses, where the factor in the second integral is... This indicates that the instantaneous polarization directions of the two entrance pupil vector light fields are opposite, i.e., the phase difference is π. Furthermore, since the focal field converged by the two lenses from the entrance pupil fields on both sides is calculated by integration in a unified coordinate system and coherently superimposed, the polar angle range of the second integral calculation formula needs to be shifted by π angle relative to the first integral calculation formula.

[0027] (5) Based on the optical focal field obtained in step (4) combined with the inverse Faraday effect, evaluate the characteristics of the photomagnetization field induced on the magneto-optical material: Based on the inverse Faraday effect, a magneto-optical material is placed in the focal region of the 4π focusing system. The highly localized optical focal field constructed in step (4) can induce a photomagnetized field on the magneto-optical material, the characteristics of which are calculated and characterized by the following formula: (9) In the formula and Let be the electric field vector of the optical focal field and its conjugate vector. The coupling coefficient is related to the magneto-optical material; the optical ring constructed in step (4) in this application can induce a coupling coefficient located at... x '- y 'A planar magnetic ring.'

[0028] The following specific embodiments demonstrate the effectiveness of the method proposed in this invention.

[0029] To simplify calculations, the parameters C and γ, which are independent of the shape and polarization of the optical focal field and the induced magnetization field, are normalized in the examples listed; and a high numerical aperture objective lens convergence angle is used to converge all the radiation fields of the orthogonal dipole pairs with superimposed spiral phase factors. .

[0030] Example 1: Setting orthogonal dipole pairs located at x - y Plane, topological load T n It is 5.

[0031] Using the methods described above, the numerical values ​​of the optical focal field and the magnetization field induced in the magneto-optical material are calculated using equations (8) and (9), and their intensity and polarization characteristics are visualized, such as... Figure 3 ,Figure 4 , Figure 5 and Figure 6 As shown, the intensity profiles of the optical ring and the induced magnetic ring are displayed in red and blue patterns, respectively.

[0032] Depend on Figure 3 , Figure 4 , Figure 5 and Figure 6 It can be seen that the focal region achieves a hollow annular optical field distribution and the magnetic rings it induces, both of which are located in... x - y The plane is consistent with the plane containing the orthogonal dipole pairs. Through Figure 4 The intensity distribution of the optical ring in the three principal planes of the Cartesian coordinate system can be used to further determine its ring structure, and the FWHM of the optical ring intensity can be measured to be 1.23λ, the magnitude of which is related to the topological charge. T n The size is related; at the same time, through Figure 4 It can be observed that the optical ring is located in its annular region. x - y The plane polarization distribution is near-circular polarization, which is why it can successfully induce magnetic rings in magneto-optical materials. When the topological charge... T n Invert the sign, focal field x - y The rotation direction of near-circular polarization in a plane will be reversed. Figure 5 From the magnetic ring strength and polarization distribution, we can obtain that the magnetization field has only a longitudinal component, and the FWHM of the hollow region of the magnetic ring is 1.86λ, the magnitude of which is also related to the topological charge. T n It is related to the size.

[0033] Example 2: Setting orthogonal dipole pairs located at y -z plane, topological charge number T n The value is 1.

[0034] Similarly, the numerical values ​​of the optical focal field and the magnetization field induced by it are calculated using equations (8) and (9), and their characteristics are visualized, such as... Figure 7 , Figure 8 , Figure 9 , Figure 10 As shown.

[0035] Depend on Figure 7 , Figure 8 , Figure 9 , Figure 10 It can be seen that in the focal area y The hollow annular optical field distribution and its induced magnetic ring were successfully constructed in the -z plane, and were arranged with orthogonal dipole pairs in... yThe -z plane is consistent, and it can be seen that the FWHM of both the optical ring and the magnetic ring intensities are less than those in Example 1. This is because the topological charge number of this embodiment is... T n Because it is smaller.

[0036] Example 3: Setting orthogonal dipole pairs located at x -z plane, topological charge number T n The value is 4.

[0037] Following the same operational steps, the numerical value of the optical focal field and its induced magnetization field are calculated, and their characteristics are visualized, such as... Figure 11 , Figure 12 , Figure 13 , Figure 14 As shown.

[0038] Depend on Figure 11 , Figure 12 , Figure 13 , Figure 14 It can be seen that in the focal area x The hollow annular optical field distribution and its induced magnetic ring were successfully constructed in the -z plane, and were arranged with orthogonal dipole pairs in... x The -z plane is consistent, and it can be seen that the FWHM of both the optical ring and the magnetic ring intensities are greater than those in Example 2. This is because the topological charge number of this example is... T n The reason is relatively large.

[0039] Example 4: Orthogonal dipole pairs are set in any non-principal plane, with topological charge number... T n for .

[0040] The optical rings and their induced magnetic rings constructed in Examples 1 to 3 all have their toroidal surfaces located in the principal plane of the global Cartesian coordinate system. Example 4 demonstrates that the method proposed in this invention can construct reconfigurable optically induced magnetic rings in any plane of the focal region; without loss of generality, [the following is taken...] , For example, the obtained stereoscopic characterization results are as follows: Figure 15 and Figure 16 As shown.

[0041] Depend on Figure 15 and Figure 16 It can be seen that corresponding optical rings and optically induced magnetic rings were constructed on the specified plane. Further measurements show that their characteristics are consistent with the rules of the previous examples.

[0042] The above embodiments demonstrate the effectiveness of the method proposed in this application. Based on a novel method combining orthogonal electric dipole pair radiation field and spiral phase modulation, a near-circularly polarized optical ring focal field with a transverse cross-section is precisely constructed. This induces a magnetic ring in magneto-optical materials using the inverse Faraday effect, enabling independent control over its spatial orientation and hollow size. The highly localized optical ring and induced magnetic ring customized in this application, possessing dual degrees of freedom for adjustable spatial orientation and hollow size, have broad application prospects in fields such as optical capture and manipulation, and magnetic topology control.

[0043] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for inducing the generation of a magnetic ring using a highly localized optical ring, characterized in that, Includes the following steps: Step (1): Customize the orthogonal dipole pair antenna model and solve its radiation field; Step (2): Modulate spiral phase factors with the same spatial orientation on the radiation field; Step (3): Based on the radiation field modulated by the spiral phase factor, the entrance pupil field distribution is obtained by inverse solution; Step (4): Based on Richard Wolf's vector diffraction integral theory, calculate the highly localized focal field distribution characteristics of the entrance pupil field in the focal region of the 4π focusing system; Step (5): Based on the optical focal field distribution, the optical focal field is applied to the magneto-optical material, and combined with the inverse Faraday effect, the spatial distribution characteristics of the magnetization field induced in the magneto-optical material are solved.

2. The method for inducing the generation of a magnetic ring using a highly localized optical ring according to claim 1, characterized in that, The specific process of step (1) is as follows: First, establish a 4π optical focusing system consisting of two objective lenses with confocal regions; A pair of orthogonal dipole pairs is placed in a space with the center point of the 4π optical focusing system as the origin. The orthogonal dipole pairs are placed orthogonally in this space, and the feed currents of the orthogonal dipole pairs are out of phase by π / 2. The orthogonal dipole pair is rotated with the center point of the 4π optical focusing system as the fulcrum; Calculate the radiation field of the rotated orthogonal dipole pair.

3. The method for inducing the generation of a magnetic ring using a highly localized optical ring according to claim 2, characterized in that: The 4π optical focusing system consists of two high numerical aperture objectives with identical external dimensions and optical parameters. The optical axes of the two objectives are on the same straight line and are placed confocally. A global rectangular coordinate system is established in the 4π optical focusing system; wherein, the origin O of the global rectangular coordinate system is the common focal point of the two objectives; the direction of the optical axis is taken as the z-axis, and the z-axis is perpendicular to the focal plane, i.e., the xy plane.

4. The method for inducing the generation of a magnetic ring using a highly localized optical ring according to claim 2, characterized in that, The specific configuration of a pair of orthogonal dipoles is as follows: If two electric dipoles constituting orthogonal dipoles are placed on the x-axis and y-axis of a global rectangular coordinate system, respectively, and their feed currents are phased by π / 2, then the coherent superposition of their radiation fields in the xy-plane is circularly polarized: when the feed current of the y-axis electric dipole lags the x-axis by π / 2, the coherent superposition of their radiation fields in the xy-plane exhibits left-handed circular polarization, with its spin angular momentum along the +z-axis; conversely, when the y-axis leads the x-axis by π / 2, the superimposed radiation field exhibits right-handed circular polarization, with its spin angular momentum along the −z-axis. According to the inverse Faraday effect, the focal field of the circularly polarized state can induce a magnetization field in the magneto-optical material that is aligned with the direction of its spin angular momentum.

5. The method for inducing the generation of a magnetic ring using a highly localized optical ring according to claim 2, characterized in that, The specific method for calculating the radiation field of rotated orthogonal dipole pairs is as follows: The origin O of the global rectangular coordinate system is the pivot point of rotation. z shaft edge Plane rotation in one step θ 0 degrees, forming a local rectangular coordinate system, at this time z The spatial orientation of the axis is , x shaft and y The shaft rotates synchronously as x 'and y 'axis,( x '-, y '-, z The three principal axes of the local rectangular coordinate system are formed by '-); originally located at x shaft and y The electric dipoles on the axis also rotate synchronously, and after rotation, they are located in the reference coordinate system. x 'and y 'axis, when y 'Axial electric dipole current phase lag x If the axis is π / 2, then the spin direction of the coherent superposition radiation field of the two electric dipoles after rotation is + z 'axis; According to electromagnetic radiation theory, the three principal axes of the global rectangular coordinate system ( x -, y -, z -) The analytical expression for the dipole radiation field is as follows: (1) in, These are complex coefficients that are independent of the direction of the radiation field. f Let ω be the focal length of the focusing system, and ω be the angular frequency. The permeability of free space, This represents the amplitude of the dipole current. The length of the dipole. k For free space wavenumber; If the local coordinate system is known x 'axis, y 'axis and z The axes are respectively related to the global rectangular coordinate system. x , y and z The included angles of the axes are respectively ( α 1, β 1, γ 1) ( α 2, β 2, γ 2) and ( α 3, β 3, γ 3), then it lies on the three principal axes of the local rectangular coordinate system ( x '-, y '-, z The radiation field of an electric dipole is obtained through matrix operations: (2) in, for The direction cosine matrix pointing in space is expressed as follows: (3) When originally located in the global coordinate system x and y The orthogonal dipole pairs of the axes rotate together with the coordinate system to the local Cartesian coordinate system. x 'and y If the axis is ', then the combined radiation field after the coherent superposition of the two is: (4) In the formula, when the topological load number T n When it is a positive number, y The phase lags the electric dipole current by π / 2; conversely, when the topological charge is negative... y 'Axial electric dipole current phase leads by π / 2; charge number' T n is an independent control parameter of the spiral phase factor in step (2); j is the imaginary unit; e is the base of the natural logarithm; and These are the unit vectors in the spherical coordinates θ and φ of the radiation field, respectively.

6. The method for inducing the generation of a magnetic ring using a highly localized optical ring according to claim 1, characterized in that, In step (2), a spiral phase factor with a specified topological charge number is used to modulate the radiation field and align it with the normal of the plane containing the orthogonal dipole pair. The specific calculation method of the spiral phase factor is as follows: The normal of an orthogonal dipole to its plane is... z 'axis, at this point the spiral phase factor is based on x '- y The calculation is performed on a plane, and its expression is as follows: (5) in, for x '- y 'Plane Self x 'Azimuth angle measured counterclockwise from the axis; The transformation relationship between the coordinate variables of the global rectangular coordinate system and the rotated local rectangular coordinate system is as follows: (6) Thus, the analytical expression for the radiation field of orthogonal dipole pairs modulated with the same spatially oriented spiral phase factor is obtained as follows: (7)。 7. The method for inducing the generation of a magnetic ring using a highly localized optical ring according to claim 1, characterized in that: The step (3) is to obtain the vector field of the entrance pupil surface by combining the spiral phase-modulated radiation field shown in equation (7) with the apodization function of the lens; the entrance pupil field is obtained by inversely using the modulated radiation field of equation (7), without the need for a complex iterative optimization design process.

8. The method for inducing the generation of a magnetic ring using a highly localized optical ring according to claim 1, characterized in that: Step (4) is the light field obtained from step (3) after being focused by the 4π focusing system, and is quantitatively evaluated using Richard Wolf vector diffraction integral theory: (8) in, The focal field in cylindrical coordinates. θ max This is the maximum convergence angle of the objective lens, which is related to the numerical aperture of the objective lens; Let be the approximate spherical wavefront of the entrance pupil field after refraction through the lens; the two double integrals on the right side of the equation represent the tightly focused fields of the two lenses, where the factor in the second integral is... This indicates that the instantaneous polarization directions of the two entrance pupil vector light fields are opposite, i.e., the phase difference is π. Furthermore, since the focal field converged by the two lenses from the entrance pupil fields on both sides is calculated by integration in a unified coordinate system and coherently superimposed, the polar angle range of the second integral calculation formula needs to be shifted by π angle relative to the first integral calculation formula.

9. The method for inducing the generation of a magnetic ring using a highly localized optical ring according to claim 1, characterized in that: Step (5) is based on the inverse Faraday effect. A magneto-optical material is placed at the confocal region of the 4π optical focusing system. The highly localized optical focal field constructed in step (4) can induce a magnetization field on the magneto-optical material. Its characteristics are calculated and characterized by the following formula: (9) In the formula and Let be the electric field vector of the optical focal field and its conjugate vector. The coupling coefficient is related to the magneto-optical material.

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