A method for realizing optical vortex conversion from vector polarization to arbitrary-order longitudinal polarization

Abstract

A method for realizing the conversion of vector polarization to arbitrary-order longitudinal polarization optical vortex relates to the technical field of optical vortex focal field modulation. The method comprises the following steps: step 1, analyzing the polarization distribution of the incident light beam; step 2, establishing a tightly focused optical system; step 3, accurately calculating the electric field distribution of the incident light beam after focusing; step 4, determining the vector polarization state required to generate an arbitrary-order optical vortex; step 5, establishing the relationship between the vector polarization distribution and the position coordinates of the hybrid Poincare sphere; step 6, analyzing the tightly focused light field. In the method for realizing the conversion of vector polarization to arbitrary-order longitudinal polarization optical vortex, a tightly focused optical system is introduced, and an arbitrary-order longitudinal polarization optical vortex can be generated by customizing the specific polarization state of the vector field and adjusting the angular polarization index.

Description

Technical Field

[0001] The invention relates to the technical field of optical vortex focal field modulation, and in particular to a method for realizing optical vortex conversion from vector polarization to arbitrary-order longitudinal polarization. Background Art

[0002] An optical vortex is a unique light field. Its particularity is mainly manifested in the presence of a phase singularity at the center of the light beam, where the light intensity is zero and the light field is distributed in a ring shape. The orbital angular momentum carried by each photon in such a vortex beam can be transferred to the particle, driving the particle to rotate, thereby achieving the capture and translation of the particle. Due to the unique hollow ring-shaped light intensity distribution, the central dark spot will reduce the damage to living matter, and the particles can be bound in the center of the beam. Therefore, vortex beams have unique advantages in biomedicine and are widely used in particle manipulation fields such as capturing mitochondria, lysosomes, metal particles, inorganic and organic particles. Due to its unique photon orbital angular momentum characteristics, vortex beams have potential applications in quantum information processing, optical encryption and holography, optical metrology and optical imaging.

[0003] Polarization, as an important property of light, describes the relationship between the vibration direction of the electric vector of the light wave and the propagation direction, and is an important degree of freedom in light field control. In three-dimensional space, the non-uniform distribution of the polarization mode of the light beam leads to the formation of a complex vector light field structure. The vector light field expands the polarization state characteristics of the traditional plane wave. For example, a stronger longitudinal field component and a smaller focal spot size can be obtained when focusing with a high numerical aperture objective. Transverse spin angular momentum can be obtained through the longitudinal field, and it can also be further structured to produce longitudinal polarized light needles or longitudinal vortex lines. Therefore, vector polarization modulation can provide richer and more flexible polarization degrees of freedom, which provides opportunities for manipulating higher-order orbital angular momentum.

[0004] Although there are methods for generating orbital angular momentum beams, there are still many limitations. In the prior art, orbital angular momentum beams can be generated by a variety of methods such as spiral phase plates, spatial light modulators or sub-wavelength gratings. However, due to the wavelength dependence of various optical elements in the above methods, they can only match narrow-band light waves with specific wavelengths. When the light waves are in a wide band, this method cannot be used to generate orbital angular momentum beams of any order. Since then, researchers have proposed another method for generating orbital angular momentum beams. The light beam passes through a tight focusing system composed of a microscope objective with a high numerical aperture. Due to the spin-orbit coupling effect of light, the polarization freedom of the light wave itself is used to generate an orbital angular momentum beam, realizing the conversion from spin to orbital angular momentum. However, since the spin-orbit coupling effect process follows the law of conservation of angular momentum and is limited by the spin angular momentum in the traditional circular / elliptically polarized incident field, although it can be applied to broadband light waves, it can only generate orbital angular momentum beams carrying topological charges of ±1, which is relatively difficult to achieve for generating optical vortices with high-order topological charges. Summary of the invention

[0005] The technical problem to be solved by the present invention is: to overcome the shortcomings of the prior art and provide a method for converting vector polarization to any order of longitudinal polarization optical vortex by introducing a tight focusing optical system, customizing the specific polarization state of the vector field, and adjusting the angular polarization index, so as to generate any order of longitudinal polarization optical vortex.

[0006] The technical solution adopted by the present invention to solve the technical problem is: the method for realizing the conversion of vector polarization to arbitrary-order longitudinal polarization optical vortex is characterized by comprising the following steps:

[0007] Step 1, analyzing the polarization distribution of the incident light beam;

[0008] Step 2, establishing a tight focusing optical system;

[0009] Step 3, using Debye vector diffraction integral theory to analyze the tight focusing optical system established in step 2, and calculating the electric field distribution of the incident light beam after focusing;

[0010] Step 4, analyzing according to the integral theory in step 3 to determine the vector polarization state required to realize an optical vortex structure with any order;

[0011] Step 5, calculating the Stokes parameters corresponding to the required vector polarization state, constructing the corresponding hybrid Poincare sphere model, and establishing the relationship between the vector polarization distribution and the position coordinates of the hybrid Poincare sphere;

[0012] Step 6, analyzing the characteristics of the focal field through the relationship between the electric field distribution and the vector polarization distribution and the position coordinates of the hybrid Poincare sphere.

[0013] Preferably, in step 1, for a monochromatic paraxial beam, its polarization state is expressed in the form of a two-dimensional Jones vector:

[0014]

[0015] in,{ N m , S m} is a pair of orthogonal local linear polarization basis vectors, satisfying , Ψ N and Ψ S is the weight coefficient, which determines the relative intensity of the local linear polarization basis vector.

[0016] Preferably, the orthogonal local linear polarization basis vectors are expressed as:

[0017]

[0018] in,{ N m , S m} respectively describe the m and- m Orthogonal localized linearly polarized optical vortices with topological charges of order 1, and Represents the unit vectors along the x-axis and y-axis respectively, and the parameters γ Determines the orientation of local linear polarization.

[0019] Preferably, when the polarization state is a unit vector, the weight coefficient Ψ N and Ψ S Respectively expressed as:

[0020]

[0021] in, τ∈ [0, π / 2], decided Ψ N and Ψ S Relative strength, is the relative phase between the two basis vectors.

[0022] Preferably, in step 3, the focused electric field is expressed in a cylindrical coordinate system It is expressed as:

[0023]

[0024] in, f andk denote the focal length of the objective lens and the wave number in the focal field, respectively. θ and are the tangent angle relative to the z-axis and the azimuth angle relative to the x-axis respectively; α =arcsin(NA / n 1) The numerical aperture NA of the system and the image space refractive index n 1 Joint decision, β is the ratio of pupil radius to beam waist, V represents the intensity factor of the polarization state of the incident field in image space, i Represents the imaginary unit.

[0025] Preferably, the three mutually perpendicular components V of the intensity factor V of the polarization state of the incident field in the image space are x 、V y 、V z It is expressed as:

[0026] in, τ∈ [0, π / 2], decided Ψ N and Ψ S Relative strength, θ and are the tangent angle relative to the z-axis and the azimuth angle relative to the x-axis respectively; the parameters γ Determines the orientation of local linear polarization, m The topological charge of the vortex beam indicates the spiral change of the phase at the center of the beam. is the relative phase between the two basis vectors.

[0027] Preferably, the parameters γ = When , the longitudinal component of the electric field is expressed as:

[0028]

[0029] in, f and k denote the focal length of the objective lens and the wave number in the focal field, respectively. θ and are the tangent angle relative to the z-axis and the azimuth angle relative to the x-axis respectively; α =arcsin(NA / n 1) The numerical aperture NA of the system and the image space refractive index n 1 Joint decision, β is the ratio of pupil radius to beam waist, V represents the intensity factor of the polarization state of the incident field in image space, i represents the imaginary unit, mThe topological charge of the vortex beam indicates the spiral change of the phase at the center of the beam. J m The order is m The Bessel function of the first kind, ρ Represents the radius of any point in the image space in the cylindrical coordinate system.

[0030] Preferably, in step 5,

[0031] The normalized Stokes parameter corresponding to the polarization state of the longitudinal component vector of the electric field is expressed as:

[0032]

[0033] in, is the relative phase between two basis vectors, , , and Represents the polarization state of a beam, which is used to describe the intensity and phase relationship of different polarization modes in the beam. As the unit radius from the origin, , and For the Cartesian coordinate system of the sphere, the corresponding hybrid Poincare sphere model is constructed. The latitude and longitude (2Φ, 2Θ) and Stokes parameters of the hybrid Poincare sphere model satisfy:

[0034] .

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] In the method for realizing the conversion of vector polarization to arbitrary-order longitudinal polarization optical vortex, a tight focusing optical system is introduced, and arbitrary-order longitudinal polarization optical vortex can be generated by customizing the specific polarization state of the vector field and adjusting the angular polarization index.

[0037] In this method for realizing the conversion of vector polarization to arbitrary-order optical vortex, the polarization state of the incident light beam is analyzed, and tight focusing is achieved by using a high numerical aperture microscope objective lens. The electric field distribution of the incident light beam after focusing is accurately calculated to determine the vector polarization state required to realize an arbitrary-order optical vortex structure. The Stokes parameters of the corresponding polarization state are calculated, and the corresponding hybrid Poincare sphere model is constructed to establish the relationship between the vector polarization distribution and the position coordinates of the hybrid Poincare sphere. This method breaks the limitation that the original technology can only produce ±1-order optical vortices, and broadens the related fields of high-order optical vortices.

[0038] By realizing the method of converting vector polarization to arbitrary-order optical vortex, the arbitrary-order optical vortex conversion technology is suitable for a variety of light field control applications, including but not limited to optical communication, optical encryption and holography, optical metrology, optical imaging, optical manipulation and quantum information processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Flowchart of the method for realizing optical vortex conversion from vector polarization to arbitrary-order longitudinal polarization.

[0040] Figure 2 Schematic diagram of a tightly focusing optical system for realizing the method of optical vortex conversion from vector polarization to arbitrary order longitudinal polarization.

[0041] Figure 3 In order to realize the method of converting vector polarization to arbitrary order optical vortex m =1 first-order mixed Poincare sphere model diagram.

[0042] Figure 4 In order to realize the method of converting vector polarization to arbitrary order optical vortex m =-2 negative second-order mixed Poincare sphere model diagram.

[0043] Figure 5 In order to realize the method of converting vector polarization to arbitrary order optical vortex m =3.

[0044] Figures 6 to 11 In order to realize the method of converting vector polarization to arbitrary order optical vortex m =1 first-order mixed Poincare sphere model corresponding to the tight focusing field at points P1 and P2, the total electric field intensity, the electric field intensity of the longitudinal component and the corresponding phase distribution diagram.

[0045] Figures 12 to 17 In order to realize the method of converting vector polarization to arbitrary order optical vortex m = -2 of negative second order, m =3 corresponding to the third-order mixed Poincare sphere model at points P3 and P4 in the tight focusing field, the total electric field intensity, the electric field intensity of the longitudinal component and the corresponding phase distribution diagram. DETAILED DESCRIPTION

[0046] Figures 1 to 17 The best embodiment of the present invention is shown below in conjunction with the attached Figures 1 to 17 The present invention is further described.

[0047] like Figure 1 As shown, a method for realizing the conversion of vector polarization to arbitrary-order longitudinal polarization optical vortex comprises the following steps:

[0048] Step 1, analyzing the polarization distribution of the incident light beam;

[0049] The polarization distribution of the incident light beam is analyzed. In this method of realizing the conversion of vector polarization to arbitrary-order optical vortex, polarization, as an important property of light, describes the relationship between the vibration direction of the electric vector of the light wave and the propagation direction, and is an important degree of freedom in light field control. For a monochromatic paraxial light beam, its polarization state is expressed in the form of a two-dimensional Jones vector:

[0050]

[0051] in,{ N m , S m} is a pair of orthogonal local linear polarization basis vectors, satisfying , Ψ N and Ψ S is the weight coefficient, which determines the relative intensity of the local linear polarization basis vector.

[0052] The orthogonal local linear polarization basis vectors are expressed as:

[0053]

[0054] in,{ N m , S m} respectively describe the m and- m Orthogonal localized linearly polarized optical vortices with topological charges of order 1. and Represents the unit vectors along the x-axis and y-axis respectively, and the parameters γ Determines the orientation of local linear polarization.

[0055] If the polarization state is a unit vector, then the weight coefficient Ψ N and Ψ S Respectively expressed as:

[0056]

[0057] in, τ∈ [0, π / 2], decided Ψ N and Ψ S Relative strength, is the relative phase between the two basis vectors.

[0058] Step 2, establishing a tight focusing optical system;

[0059] A tight focusing optical system is established by a single high numerical aperture objective lens. In the method for realizing the conversion of vector polarization to arbitrary order optical vortex, the numerical aperture NA of the tight focusing optical system is 0.95. Figure 2 As shown in the figure, in order to accurately describe and analyze the propagation characteristics of the light beam in the tight focusing optical system, a reference rectangular coordinate system is established in the tight focusing optical system. The origin of the coordinate system is set at the focus of the objective lens, which is the reference center of the light beam propagation and transformation. The z-axis of the coordinate system coincides with the optical axis of the objective lens, representing the propagation direction of the light beam along the axis of the objective lens. The xy plane is defined as the focal plane of the tight focusing optical system, which is perpendicular to the z-axis and is the plane where the light beam forms the smallest spot after being focused by the objective lens.

[0060] Step 3, accurately calculate the electric field distribution of the incident light beam after focusing;

[0061] The Debye vector diffraction integral theory is used to analyze the tight focusing optical system established in step 2, and the electric field distribution of the incident light beam after focusing is accurately calculated.

[0062] The vortex beam is called orbital angular momentum beam because it has a spiral phase and carries orbital angular momentum. In the method of realizing the conversion of vector polarization to arbitrary-order optical vortex, the Laguerre-Gauss (LG) beam carrying rich orbital angular momentum is used. l,p ) beam as the incident beam, where l and p represents the number of interlaced spirals and additional concentric rings, when l =0, p = 0, according to Debye vector diffraction integral theory, the focused electric field is expressed in cylindrical coordinates. It is expressed as:

[0063]

[0064] in, f and k denote the focal length of the objective lens and the wave number in the focal field, respectively. θ and are the tangent angle relative to the z-axis and the azimuth angle relative to the x-axis respectively; α =arcsin(NA / n 1) The numerical aperture NA of the system and the image space refractive index n 1 Joint decision, β is the ratio of the pupil radius to the beam waist. V represents the intensity factor of the polarization state of the incident field in the image space, i Represents the imaginary unit.

[0065] Its three mutually perpendicular components V x 、V y 、Vz It is expressed as:

[0066] in, τ∈ [0, π / 2], decided Ψ N and Ψ S Relative strength, θ and are the tangent angle relative to the z-axis and the azimuth angle relative to the x-axis respectively; the parameters γ Determines the orientation of local linear polarization, m Represents the topological charge of a vortex beam, indicating the spiral variation of the phase at the center of the beam.

[0067] If the parameters in the equation γ = , then the longitudinal component of the electric field is expressed as:

[0068]

[0069] in, f and k denote the focal length of the objective lens and the wave number in the focal field, respectively. θ and are the tangent angle relative to the z-axis and the azimuth angle relative to the x-axis respectively; α =arcsin(NA / n 1) The numerical aperture NA of the system and the image space refractive index n 1 Joint decision, β is the ratio of the pupil radius to the beam waist. V represents the intensity factor of the polarization state of the incident field in the image space, i represents the imaginary unit, m The topological charge of the vortex beam indicates the spiral change of the phase at the center of the beam. J m express m Bessel functions of the first kind of order, ρ The radius of any point in image space in cylindrical coordinates.

[0070] Step 4, determining the vector polarization state required to generate an arbitrary order optical vortex;

[0071] According to the integral theory in step 3, the vector polarization state required to realize an optical vortex structure of arbitrary order is determined.

[0072] Angular polarization index m Determines the polarization state of the beam as it changes with azimuth The frequency of change, different mThe value of will lead to different polarization modes, thus affecting the propagation characteristics of the light beam. The longitudinal component of the electric field contains the factor , with a topological charge determined by m The phase vortex, The appearance of indicates that a topological charge number of m The longitudinally polarized optical vortex, m It can take any value, thus realizing the transformation of vector polarization into any-order longitudinal polarization optical vortex, breaking the limitation that the spin-orbit coupling effect can only produce positive or negative first-order longitudinal polarization optical vortex due to the restrictions of spin topological charge number and angular momentum conservation conditions, and only needs to utilize the inherent degree of freedom polarization of the light field, thus realizing the transformation of broadband arbitrary-order longitudinal polarization optical vortex at the same time.

[0073] when m = 0, the light field is a scalar. This traditional uniform polarization distribution mode is easily restricted by the spin angular momentum of the elliptical / circular polarization in the incident field during the spin-orbit coupling process, and it is difficult to generate an optical vortex with arbitrary topological charge. m When ≥1, the light field is a vector. The vector light field extends the characteristics of traditional uniform polarization. When focusing with a high numerical aperture objective lens, a stronger longitudinal field component and a smaller focal spot size can be obtained, thereby obtaining transverse spin angular momentum. By customizing the specific polarization state distribution of the vector light field, a more flexible and rich polarization degree of freedom can be generated, providing new possibilities for generating arbitrary-order optical vortices through vector polarization modulation. Therefore, a longitudinally polarized optical vortex capable of carrying arbitrary orbital angular momentum can be realized by modulating the optical intrinsic degree of freedom vector polarization state.

[0074] Step 5, establishing the relationship between the vector polarization distribution and the position coordinates of the hybrid Poincare sphere;

[0075] The Stokes parameters corresponding to the required vector polarization state are calculated, and the corresponding hybrid Poincare sphere model is constructed to establish the relationship between the vector polarization distribution and the position coordinates of the hybrid Poincare sphere.

[0076] Using reverse constructed parameters γ , the normalized Stokes parameter corresponding to the polarization state of the longitudinal component vector of the electric field proposed above is expressed as:

[0077]

[0078] in, , , and Represents the polarization state of a light beam, and is used to describe the intensity and phase relationship of different polarization modes in the light beam. As the unit radius from the origin, , and For the Cartesian coordinate system of the sphere, the corresponding hybrid Poincare sphere model is constructed. The latitude and longitude (2Φ, 2Θ) of the hybrid Poincare sphere model and the Stokes parameters satisfy the following relationship:

[0079]

[0080] From the above, it can be seen that the relationship between the vector polarization distribution and the position coordinates of the hybrid Poincare sphere is established. Figure 3 for m =1 first-order hybrid Poincare sphere model, the poles (2Φ, ±π / 2) represent orthogonal radial and angular polarized optical vortices with topological charges of 1 and -1 respectively. Other points correspond to complex angularly varying mixed polarization states, with linear polarization, elliptical polarization, and circular polarization existing simultaneously on the beam cross section; Figure 4 for m =-2 negative second-order mixed Poincare sphere model, the poles (2Φ, ±π / 2) represent orthogonal radial and angular polarized optical vortices with topological charges of -2 and 2, respectively, and other points correspond to complex angularly varying mixed polarization states; Figure 5 for m =3, the poles (2Φ, ±π / 2) represent orthogonal radial and angular polarized optical vortices with topological charges of 3 and -3 respectively, and the other points correspond to complex angularly varying mixed polarization states.

[0081] Step 6, analyzing the tightly focused light field;

[0082] Through the above formula of electric field distribution in the focal area and the established relationship between the vector polarization distribution and the position coordinates of the hybrid Poincare sphere, the characteristics of the focal field can be analyzed, including the focusing characteristics of the light beam, polarization distribution, phase distribution, and the shape and size of the focal spot.

[0083] The following example further verifies the above conversion method:

[0084] First consider m = 1, construct the corresponding first-order mixed Poincare sphere as Figure 3 As shown. According to the formula expression of the longitudinal component of the electric field in step 3, when τ=π / 2, the longitudinal component of the electric field is 0. Therefore, without loss of generality, two input polarization states located at points P1 and P2 on the first-order mixed Poincare sphere are selected as examples to analyze the corresponding focal field distribution. Figure 6~Figure 7 The total electric field intensity distribution corresponding to points P1 and P2 on the first-order mixed Poincare sphere shows the propagation characteristics of the light beam. Both are hotspot distributions on the optical axis, and the longitudinal spot sizes are almost the same, while in the transverse direction, the spot size at P2 is significantly larger than the spot size at P1; Figure 8 , Fig.11 is the electric field intensity of the longitudinal component at P1 and P2 and the corresponding phase distribution. Figure 8~Figure 9 It is clear that the longitudinal component of the electric field presents a circular intensity distribution of different sizes. The reason why the contour of P2 is larger than that of P1 is that the increase of 2θ will induce cos τ The growth of θ results in a stronger longitudinal component of the electric field. Unlike the spin-orbit coupling of the circularly polarized incident field, the size of the longitudinal component in this method can be adjusted by changing the value of 2θ, which helps to meet the needs of different applications. In addition, the longitudinal component is located outside the focal spot, so the stronger longitudinal component of the electric field will inevitably lead to an increase in the total transverse field size. This is Figure 6~Figure 7 The reason why the spot size at P2 is larger than that at P1 in the lateral direction. Fig.10 , Fig.11 The longitudinal components of the two electric fields are both distributed in a clockwise spiral phase, indicating that both input polarization states realize longitudinal polarization optical vortices with topological charge 1. is π / 2 smaller than P2, so Fig.10 compared to, Fig.11 The phase distribution is rotated counterclockwise by π / 2.

[0085] When | m When | increases, a longitudinally polarized optical vortex with a higher-order topological charge can be realized. Figures 4 and 5 as well as Figures 12 to 17 ,by m =-2 and m =3 as an example, that is, taking the vector polarization state of point P3 on the negative second-order hybrid Poincare sphere and point P4 on the third-order hybrid Poincare sphere as examples, the corresponding focal field distribution is studied. Due to the adjustment of the angular polarization index, although point P3 (P4) is at the same position as point P1 (P2) in the first-order hybrid Poincare sphere, its vector polarization state has changed greatly. Fig.12 , Fig.13 As shown, with | m | increases, the total electric field intensity is distributed in a hollow coaxial profile on the propagation plane, and the size of the optical channel also increases. Figure 14~Figure 15 In the process, the longitudinal component of the electric field always presents a circular intensity distribution, which is consistent with m = 1. However, the size of the ring changes with | m | increases, resulting in a gradual increase in the area of ​​the dark ring. The change in the longitudinal component of the electric field is manifested in Figure 16-17The phase distribution shown shows double clockwise and triple counterclockwise spiral phase distributions, respectively. This shows that the longitudinally polarized optical vortex with high-order topological charge is obtained by vector polarization modulation. According to the clear relationship established between the vector polarization of the input field and the high-order phase vortex distribution of the output field, the corresponding vector polarization state should be described on the surface of the high-order hybrid Poincare sphere. Based on this, it is revealed that the modulation of vector polarization can realize the longitudinally polarized optical vortex, which can have arbitrary order topological charge in the non-coaxial propagation of tightly focused Laguerre-Gaussian beams.

[0086] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A method for realizing optical vortex conversion from vector polarization to arbitrary-order longitudinal polarization, characterized in that: The steps include: Step 1, analyzing the polarization distribution of the incident light beam; Step 2, establishing a tight focusing optical system; Step 3, using Debye vector diffraction integral theory to analyze the tight focusing optical system established in step 2, and calculating the electric field distribution of the incident light beam after focusing; Step 4, analyzing according to the integral theory in step 3 to determine the vector polarization state required to realize an optical vortex structure with any order; Step 5, calculating the Stokes parameters corresponding to the required vector polarization state, constructing the corresponding hybrid Poincare sphere model, and establishing the relationship between the vector polarization distribution and the position coordinates of the hybrid Poincare sphere; Step 6, analyzing the characteristics of the focal field through the relationship between the electric field distribution and the vector polarization distribution and the position coordinates of the hybrid Poincare sphere; In step 3, the focused electric field is expressed in cylindrical coordinates It is expressed as: in, f and k denote the focal length of the objective lens and the wave number in the focal field, respectively. θ and are the tangent angle relative to the z-axis and the azimuth angle relative to the x-axis respectively; α =arcsin(NA / n 1) The numerical aperture NA of the system and the image space refractive index n 1 Joint decision, β is the ratio of pupil radius to beam waist, V represents the intensity factor of the polarization state of the incident field in image space, i represents the imaginary unit; The three mutually perpendicular components V of the intensity factor V of the polarization state of the incident field in the image space x 、V y 、V z It is expressed as: in, τ∈ [0, π / 2], decided Ψ N and Ψ S Relative strength, θ and are the tangent angle relative to the z-axis and the azimuth angle relative to the x-axis respectively; the parameters γ Determines the orientation of local linear polarization, m The topological charge of the vortex beam indicates the spiral change of the phase at the center of the beam. is the relative phase between the two basis vectors; parameter γ = When , the longitudinal component of the electric field is expressed as: in, f and k denote the focal length of the objective lens and the wave number in the focal field, respectively. θ and are the tangent angle relative to the z-axis and the azimuth angle relative to the x-axis respectively; α =arcsin(NA / n 1) The numerical aperture NA of the system and the image space refractive index n 1 Joint decision, β is the ratio of pupil radius to beam waist, V represents the intensity factor of the polarization state of the incident field in image space, i represents the imaginary unit, m The topological charge of the vortex beam indicates the spiral change of the phase at the center of the beam. J m The order is m The Bessel function of the first kind, ρ Represents the radius of any point in the image space in the cylindrical coordinate system.

2. The method for realizing optical vortex conversion from vector polarization to arbitrary-order longitudinal polarization according to claim 1, characterized in that: In step 1, for a monochromatic paraxial beam, its polarization state is expressed in the form of a two-dimensional Jones vector: in,{ N m , S m } is a pair of orthogonal local linear polarization basis vectors, satisfying , Ψ N and Ψ S is the weight coefficient, which determines the relative intensity of the local linear polarization basis vector.

3. The method for realizing optical vortex conversion from vector polarization to arbitrary-order longitudinal polarization according to claim 2, characterized in that: The orthogonal local linear polarization basis vectors are expressed as: in,{ N m , S m } respectively describe the m and- m Orthogonal localized linearly polarized optical vortices with topological charges of order 1, and Represents the unit vectors along the x-axis and y-axis respectively, and the parameters γ Determines the orientation of local linear polarization.

4. The method for realizing optical vortex conversion from vector polarization to arbitrary-order longitudinal polarization according to claim 2 or 3, characterized in that: When the polarization state is a unit vector, the weight coefficient Ψ N and Ψ S Respectively expressed as: in, τ∈ [0, π / 2], decided Ψ N and Ψ S Relative strength, is the relative phase between the two basis vectors.

5. The method for realizing optical vortex conversion from vector polarization to arbitrary-order longitudinal polarization according to claim 1, characterized in that: In step 5, The normalized Stokes parameter corresponding to the polarization state of the longitudinal component vector of the electric field is expressed as: in, is the relative phase between the two basis vectors, , , and Represents the polarization state of a beam, which is used to describe the intensity and phase relationship of different polarization modes in the beam. As the unit radius from the origin, , and For the Cartesian coordinate system of the sphere, the corresponding hybrid Poincare sphere model is constructed. The latitude and longitude (2Φ, 2Θ) and Stokes parameters of the hybrid Poincare sphere model satisfy: 。

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