CN116736526A - Method for generating three-dimensional polarization crystal lattice in non-paraxial system - Google Patents
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Abstract
The invention relates to a method for generating a three-dimensional unpolarized lattice in a non-paraxial system, which comprises the following steps: determining that the incident light field is a coherence matrix of the partially coherent Xie Ermo light beam; calculating the three-dimensional polarization dimension and the three-dimensional polarization degree of the partially coherent Xie Ermo light beam in a tightly focused focal field according to the coherence matrix; and (3) adjusting the coherence length of the partially coherent Xie Ermo light beam according to the three-dimensional polarization dimension and the three-dimensional polarization degree, and returning to the step (2) until the three-dimensional polarization degree is 0 or the three-dimensional polarization dimension is 3, so as to obtain a three-dimensional unpolarized field; and adjusting the coherent structure distribution of the partially coherent Xie Ermo light beam based on the three-dimensional unpolarized field to obtain a three-dimensional unpolarized lattice. The invention can generate three-dimensional unpolarized crystal lattice in a non-paraxial system, and has the advantages of high speed of generating crystal lattice, high image precision and stable unpolarized characteristic of the generated crystal lattice at two sides of a focal plane.
Description
Technical Field
The invention relates to the technical field of optical lattices, in particular to a method for generating a three-dimensional unpolarized lattice in a non-paraxial system.
Background
Polarization is an intrinsic property of light, and mainly describes the vibration of a light beam in a section perpendicular to the propagation direction of light. Traditionally, research into light polarization has been limited to planar wave fields. However, for evanescent optical near-fields as well as tightly focused fields, three-dimensional analysis of the field is required to fully characterize its polarization state due to the three orthogonal components, and therefore three-dimensional polarization levels are introduced to describe the average correlation between the three field components. When the three orthogonal electric field component values are equal and have no correlation with each other, a three-dimensional unpolarized field is represented, such as in blackbody radiation, the polarization degree of light emitted from a small blackbody opening is 0 at a point in the far zone. The three-dimensional unpolarized field has important application in nano photonics and near field optics, and the main method for generating the polarized field in the prior research is to obtain the near three-dimensional unpolarized field by utilizing a multi-laser device through superposition of incident light or total reflection of the incident light at an interface, however, the methods have strict requirements on the incident angle, the operation difficulty coefficient is higher, and how to quickly and efficiently obtain the highly unpolarized three-dimensional field is still a problem to be solved.
On the other hand, optical lattices are a long-standing research hotspot. An optical lattice is a periodic potential energy structure formed by a laser beam or other form of optical field. This structure is similar to an array of atoms in a crystal, but it is based on photons rather than atoms. The periodic arrangement of various lattices such as light intensity, polarization, phase distribution and coherence has wide application in the fields of laser cooling, lattice light sheet microscopy, microscopic particle sorting, photonic crystal engineering and the like, and has important significance in generating Bessel vortex and high-order polarization vortex. In recent years, research on various three-dimensional lattices provides a new view angle for application of artificial micro-nano structures. Array lattice beams, such as Gaussian vortex and Airy arrays, facilitate fabrication of composite lattice and Ta l bot effect arrays. However, these studies are based on beam paraxial transport, and whether there is a lattice in the non-paraxial system is not investigated for a while.
The tightly focused field is typically a non-paraxial system in which a lens with a large numerical aperture is present, through which the beam is deflected to create a new longitudinal component, and a three-dimensional polarizing structure is developed in the focal field. Studies have shown that a fully coherent light field has only one or two-dimensional polarized fields, and that a true three-dimensional field exists in a partially coherent or partially polarized evanescent wave field or in a tightly focused field. In tight focusing systems, how to generate a three-dimensional unpolarized field, and further to generate a three-dimensional unpolarized lattice, is what requires major research.
In the prior art, the generation of the unpolarized field generally adopts the following two schemes:
1. using a multi-laser device, regarding the incident light as a superposition of a plurality of light beams, wherein the ratio of s polarization to p polarization of each light beam is equal, and the incident light beams have the same incident angle and different azimuth angles; when the incident angle and the ratio of refractive indexes at two sides of an incident light interface are known, the sum of transmission fields of a plurality of light beams behind the interface is a three-dimensional unpolarized field by controlling the s-polarized intensity and the p-polarized intensity; when the multi-laser device is used, the incident light angles are controlled to be equal, azimuth angles are uniformly distributed, meanwhile, the s-polarization intensity and the p-polarization intensity are required to meet specific requirements, the requirements on the accuracy and the accuracy adjustment of the incident light are high, and meanwhile, a plurality of light beams are controlled to cause a plurality of error sources;
2. calculating the total electric field obtained by total reflection of two beams with mutually orthogonal incidence surfaces by utilizing total reflection at an interface to obtain a polarization matrix related to an incidence angle and a transmission coefficient, and changing each parameter according to a three-dimensional polarization degree expression to obtain a three-dimensional unpolarized field; when total reflection is used, the incident angle also needs to be controlled, and the calculation of obtaining the three-dimensional unpolarized field by total reflection is complex.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a method for generating a three-dimensional unpolarized lattice in a non-paraxial system, which can generate the three-dimensional unpolarized lattice in the non-paraxial system, has high generating lattice speed, realizes the diversity of lattice structures, and ensures that the generated lattice maintains stable unpolarized characteristics at two sides of a focal plane.
According to the technical scheme provided by the invention, the method for generating the three-dimensional unpolarized crystal lattice in the non-paraxial system comprises the following steps:
step 1, determining that an incident light field is a coherent matrix of a partially coherent Xie Ermo light beam;
step 2, calculating the three-dimensional polarization dimension and the three-dimensional polarization degree of the partially coherent Xie Ermo light beam in a tightly focused focal field according to the coherence matrix;
step 3, the coherence length of the partially coherent Xie Ermo light beam is adjusted according to the three-dimensional polarization dimension and the three-dimensional polarization degree, and the step 2 is returned until the three-dimensional polarization degree is 0 or the three-dimensional polarization dimension is 3, so that a three-dimensional unpolarized field is obtained;
and 4, adjusting the coherent structure distribution of the partially coherent Xie Ermo light beam based on the three-dimensional unpolarized field to obtain a three-dimensional unpolarized lattice.
In one embodiment of the present invention, in step 4, adjusting the coherent structural distribution of the partially coherent Xie Ermo beam includes: multiplying the coherence matrix by a corresponding off-axis phase;
wherein ,μαβ Represents the coherent structure matrix μ (ρ 1 -ρ 2 ) Element delta in (a) 0 Representing coherence length, V 0n ＝(V 0xn ,V 0yn ) Representing off-axis displacement, V 0xn Representing displacement in the x-direction, V 0yn Representing the displacement in the y-direction,representing the off-axis phase.
In one embodiment of the invention, in adjusting the coherent structural distribution of the partially coherent Xie Ermo beam, the off-axis phase is written in the form of:
V 0n ＝(l*m,l*n)
wherein l, m and n all represent natural numbers.
In one embodiment of the present invention, the coherence matrix is:
wherein, superscriptRepresenting complex conjugation; brackets'<>"means ensemble averaging; ρ=ρ (cos Φ, sin Φ) represents the coordinates of any point on the incident plane; ρ represents the distance of the incident point from the optical axis of the lens, φ ε (0, 2π)]Indicating the azimuth angle of the incident point relative to the optical axis; e (E) 0 (ρ) represents the electric field of the incident light.
In one embodiment of the present invention, calculating the three-dimensional polarization dimension and the three-dimensional polarization degree of the partially coherent Xie Ermo light beam in the tightly focused focal field according to the coherence matrix in step 2 includes:
step 2.1, calculating an electric field which is closely attached to the rear surface of the lens according to the coordinate transformation relation between the Cartesian coordinates and the polar coordinates based on the coherence matrix;
step 2.2, calculating and obtaining an electric field at a tightly focused focal field according to a vector diffraction principle based on the electric field tightly attached to the rear surface of the lens;
step 2.3, performing ensemble averaging on the electric field at the tightly focused focal field to obtain a cross spectral density matrix of the partially coherent Xie Ermo light beam at the focal field;
step 2.4, according to positive definite conditions, introducing a new coordinate expression and Fourier transformation, writing each matrix element of the cross spectral density matrix at the focal field into a form of the sum of four convolutions, and solving each matrix element to obtain a tightly focused polarization matrix;
and 2.5, rotating the tight focusing polarization matrix to the intrinsic surface of the tight focusing polarization matrix, and calculating to obtain the three-dimensional polarization dimension and the three-dimensional polarization degree of the partially coherent Xie Ermo light beam in the tight focusing focal field.
In one embodiment of the present invention, the electric field closely attached to the rear surface of the lens is:
E t (ρ)＝P(θ)E 0 (ρ)N(ρ)
wherein ,represents the apodization function at the diaphragm, θ ε [0 ], α]The angle between the optical axis and the line connecting the incident point and the focus is represented, and N (ρ) represents the coordinate transformation matrix.
In one embodiment of the invention, the electric field at the tightly focused focal field is:
where r= (x, y) represents the cross-sectional coordinates of the observation point near the focal point; d (ρ) represents a truncated function, and D (ρ) =1 when ρ is less than or equal to R; otherwise, 0, Z represents the longitudinal distance from the observation point to the focal point, λ represents the wavelength of incident light, k x ＝-kcosφsinθ,k y ＝-ksinφsinθ,k z ＝kcosθ,K represents the wave vector.
In one embodiment of the present invention, the matrix elements of the tightly focused polarization matrix are:
wherein ,Aai and ABj Representing the elements in matrix a, representing the conjugate, representing the fourier transform, f representing the focal length.
In one embodiment of the invention, step 2.5 comprises:
and rotating the tight focusing polarization matrix to the intrinsic plane by using a three-dimensional rotation matrix to obtain the real part and the imaginary part of the tight focusing polarization matrix, solving the eigenvalue of the real part, and calculating to obtain the three-dimensional polarization dimension of the partially coherent Xie Ermo light beam in the tight focusing focal field.
In one embodiment of the present invention, the three-dimensional polarization degree is:
where tr denotes the eigenvalue of the matrix, P 3D (r) represents the three-dimensional degree of polarization, and Φ (r) represents the tightly focused polarization matrix.
Compared with the prior art, the technical scheme of the invention has the following advantages:
according to the invention, the three-dimensional polarization degree and polarization dimension are rapidly calculated by using a convolution algorithm, the calculation time is greatly reduced, the accuracy of the result is also improved, a three-dimensional unpolarized field is obtained by selecting the coherent length of incident light, and a three-dimensional unpolarized lattice is generated in a non-paraxial system by regulating and controlling the coherent structure of the incident light, wherein the structure of the lattice is determined by the spatial distribution of an initial coherent structure matrix; through the regulation and control of the incident light coherent structure, three-dimensional unpolarized lattices with different spatial distributions can be obtained in a focal field, so that the diversity of lattice structures is realized; compared with the traditional method, the method of the invention has high lattice speed, can realize diversity of lattice structures, has almost three-dimensional unpolarized result, and can keep the unpolarized characteristic of the lattice well at both sides of a focal plane.
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In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments thereof that are illustrated in the appended drawings.
FIG. 1 is a flow chart of a method for generating a three-dimensional unpolarized lattice in a non-paraxial system in accordance with the present invention;
FIG. 2 is a flow chart of one embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to be limiting, so that those skilled in the art will better understand the invention and practice it.
Referring to fig. 1, the three-dimensional unpolarized crystal lattice can be rapidly generated in a non-paraxial system, and the generated crystal lattice can maintain stable unpolarized characteristics at both sides of a focal plane, and the present invention includes:
step 1, determining that an incident light field is a coherent matrix of a partially coherent Xie Ermo light beam;
specifically, the incident light is a radial polarized partially coherent Xie Ermo light beam, and according to the unified theory of coherence and polarization, for a vector partially coherent light field transmitted along the z-axis direction, a 2×2 cross spectral density matrix, namely a coherence matrix, can be used for representing the second-order statistical characteristics of the vector partially coherent light field in a space-frequency domain:
wherein, superscriptAnd angle brackets'<>"represents complex conjugate and ensemble average, ρ, respectively i (i=1, 2) represents the coordinates of an arbitrary point on the incidence plane, and when a light beam is incident on a high numerical aperture, ρ=ρ (cos Φ, sin Φ), ρ represents the distance of the incidence point from the optical axis of the lens, Φ∈ (0, 2 pi)]For the azimuth angle of the incident point relative to the optical axis, E 0 (ρ) represents the electric field of the incident light, and each element of the cross spectral density matrix can be expressed as:
τ 01 and τ02 The amplitudes in the x and y directions of the incident field, respectively. Mu (mu) αβ Is a coherent structure matrix μ (ρ) 1 -ρ 2 ) The coherent structure matrix is:
step 2, calculating the three-dimensional polarization dimension and the three-dimensional polarization degree of the partially coherent Xie Ermo light beam in a tightly focused focal field according to the coherence matrix;
specifically, the method utilizes positive definite conditions, replacement coordinates, fourier transformation, convolution operation and the like to calculate, simplifies the partial coherent Xie Ermo light beam tight focusing polarization matrix into a convolution form which can be rapidly processed by software Mat l ab, thereby efficiently solving the three-dimensional polarization dimension of the partial coherent Xie Ermo light beam, greatly reducing time consumption, rapidly calculating the three-dimensional polarization degree and the polarization dimension by using a convolution algorithm, greatly reducing calculation time and improving the precision of results, and comprises the following steps:
step 2.1, calculating an electric field which is closely attached to the rear surface of the lens according to the coordinate transformation relation between the Cartesian coordinates and the polar coordinates based on the coherence matrix;
specifically, for any one electric field of vector incident light, it can be split into a superposition of radial and angular components:
wherein , and />Amplitude of radial and angular components, respectively, +.> and />The unit vectors in radial direction and angular direction are respectively represented, and the following conversion relation exists between the unit vectors and the x and y directions in a Cartesian coordinate system:
wherein , and />The unit vectors in the x and y directions in the Cartesian coordinate system, respectively, are derived from the radial component of the incident light, which is refracted by the lens after passing through the tight focusing system, to a strong longitudinal component while the angular component remains unchanged. The unit vectors in radial and angular directions evolve as:
wherein θ ε [0 ], α]Indicating the angle between the point of incidence and the focal point and the optical axis, represents the maximum convergence angle of the lens, NA represents the numerical aperture of the lens, R represents the maximum radius of the lens, f represents the focal length of the lens, n t Representing the refractive index of the surrounding medium.
The electric field behind the lens can be expressed as two components:
wherein ,tr and tφ The transmission coefficients of radial polarization and angular polarization are respectively expressed, and are known from the energy conservation and sine conditionsThe electric field behind the lens can be further:
order the
The electric field behind the lens can be written as:
E t (ρ)＝P(θ)E 0 (ρ)N(ρ)
wherein ,representing the apodization function at the diaphragm, N (p) represents the coordinate transformation matrix.
Step 2.2, calculating and obtaining an electric field at a tightly focused focal field according to a vector diffraction principle based on the electric field tightly attached to the rear surface of the lens;
specifically, the electric field at the tightly focused focal field can be given in terms of Ri chards-Wo l f vector diffraction integral:
where r= (x, y) represents the cross-sectional coordinates of the observation point near the focal point; d (ρ) represents a truncated function, and D (ρ) =1 when ρ is equal to or less than R, which is determined by the parameters of the lens; otherwise, 0.z is the longitudinal distance from the point of view to the focal point and λ is the wavelength of the incident light. The component of wave vector k is expressed as:
k x ＝-kcosφsinθ,k y ＝-ksinφsinθ,k z ＝kcosθ,
step 2.3, performing ensemble averaging on the electric field at the tightly focused focal field to obtain a cross spectral density matrix of the partially coherent Xie Ermo light beam at the tightly focused focal field;
the 3 x 3 cross spectral density matrix of the partial coherence vector at the tightly focused focal field is:
substituting the electric field at the tight focus focal field into the calculation to obtain a cross spectral density matrix at the tight focus focal field:
step 2.4, according to positive definite conditions, introducing a new coordinate expression and Fourier transformation, writing each matrix element of the cross spectral density matrix at the tight focusing focal field into a form of the sum of four convolutions, and solving each matrix element to obtain a tight focusing polarization matrix;
specifically, the matrix elements of the incident light cross spectral density matrix are known to satisfy a positive definite condition:
wherein H1 and H2 As an arbitrary function, here in the form of a fourier transform:
wherein ,pαβ (v) And (3) the matrix elements which are equal to or more than 0 are weight matrixes:
τ 01 and τ02 Representing the amplitude in the x and y directions of the incident field, respectively, for a radially polarized gaussian schel-mode beam:
introducing a new matrix a:
the cross spectral density matrix at the focal field can be factorized as:
wherein A1i ，A 1j ，A 2i ，A 2j Is an element in matrix a.
Introducing a new coordinate expression:
ρ d ＝ρ 1 -ρ 2
r d ＝r 1 -r 2
then formula (18) may be further rewritten as:
wherein "-" represents fourier transform, "x" represents conjugate, "u 1 "introduced during Fourier transform, let r 1 ＝r 2 ＝r：
r d ＝r 1 -r 2 ＝0,
The cross spectral density matrix elements can be rewritten as tightly focused polarization matrix elements:
wherein ,representing a convolution operation. Each element of the tightly focused polarization matrix may be written in the form of a sum of four convolutions. After each matrix element of the tight focusing polarization matrix is obtained, the tight focusing polarization matrix can be obtained.
And 2.5, rotating the tight focusing polarization matrix to the intrinsic surface of the tight focusing polarization matrix, and calculating to obtain the three-dimensional polarization dimension and the three-dimensional polarization degree of the partially coherent Xie Ermo light beam in the tight focusing focal field.
Specifically, from the polarization matrix, the average correlation between three orthogonal component fields is described by means of three-dimensional polarization degrees:
wherein tr represents a characteristic value of the matrix, the three-dimensional polarization degree is independent of the orientation of the coordinate system, and is between 0 and 1, 0 represents an unpolarized field, 1 represents a three-dimensional polarized field, and Φ (r) represents a tightly focused polarization matrix.
At the same time, the polarization characteristic of the field can be characterized by the polarization dimension, and the three-dimensional rotation matrix Q is needed to be utilized first 0 Rotating the polarization matrix onto its eigenplane, the tightly focused polarization matrix on the eigenplane being:
wherein i is an imaginary number, and real parts and imaginary parts are respectively:
real part phi' 0 (r) is a diagonal matrix with three eigenvalues a 1 ≥a 2 ≥a 3 Element n= (n) of imaginary part 1 ,n 2 ,n 3 ) Representing an angular momentum vector. By means of the eigenvalues of the real part, the polarization dimension can be expressed as:
wherein ,a1 ≥a 2 ≥a 3 0 is the eigenvalue of the real part of the polarization matrix phi (r, z)
Step 3, the coherence length of the partially coherent Xie Ermo light beam is adjusted according to the three-dimensional polarization dimension and the three-dimensional polarization degree, and the step 2 is returned until the three-dimensional polarization degree is 0 or the three-dimensional polarization dimension is 3, so that a three-dimensional unpolarized field is obtained;
specifically, to obtain a three-dimensional unpolarized field, the coherence length of the incident light needs to be controlled, and it is found through calculation that if the coherence length is close to the beam waist width of the light beam, delta is obtained in the invention 0 =1.27 mm, a three-dimensional unpolarized field was generated at the tightly focused focal field.
And 4, adjusting the coherent structure distribution of the partially coherent Xie Ermo light beam based on the three-dimensional unpolarized field to obtain a three-dimensional unpolarized lattice.
In order to further obtain a three-dimensional unpolarized lattice, the coherent structure of the light beam needs to be further modulated. In the invention, the coherent structure is considered to be regulated into a corresponding lattice form, and the original coherent structure is required to be multiplied by a corresponding off-axis phase:
wherein ,V0n ＝(V 0xn ,V 0yn ) Representing off-axisThe displacement, during the operation, the off-axis displacement is written as follows:
V 0n ＝(l*m,l*n)
the values of l, m and n can set the interval between each point and the number of the points, and can be selected according to actual conditions. As with size selection, l=15000, m, n= -1:1:1, a coherence profile of 9 points is described, each point being separated by an equal distance. Still taking delta at the initial coherence length 0 In the case of =1.27 mm, the initial electric field remains unchanged, and the three-dimensional polarization degree and polarization dimension of the focal field are recovered after the same tight focusing calculation as described above. Calculations have shown that in this case a three-dimensional unpolarized lattice can be produced in the focal field and that this lattice has proved to maintain good unpolarized properties on both sides of the focal plane. It has also been shown to produce a lattice of different structure at the focal plane when the off-axis displacement is continually varied to cause the initial coherence matrix to exhibit a different spatial distribution.
As shown in fig. 2, which is a flowchart of the algorithm described above, a specific algorithm is as follows:
1. partially coherent radially polarized gaussian schel-mode beam: an incident light field;
2. and (3) decomposition: acting on a partially coherent radially polarized gaussian schorl mode beam;
3. amplitude, coherent structure matrix: decomposing an incident light field to obtain amplitudes in x and y directions of the incident field and initial coherent structure distribution;
4. initial light field decomposition, coordinate transformation: acting on an incident electric field;
5. lens rear surface electric field: obtaining an electric field closely attached to the rear surface of the lens according to the transformation relation between the incident electric field and the electric field of the rear surface of the lens;
6. Richards-Wolf vector diffraction theory: an electric field acting against the rear surface of the lens;
7. electric field at focal field: an electric field in the vicinity of the focal region after the incident light is tightly focused;
8. ensemble averaging: the statistical property of the partial coherent light beam in the focal field is represented by the ensemble average of the product of the electric field and the conjugate thereof;
9. matrix operation: the physical quantities such as the electric field of the incident light, a coherent structure, a focal region electric field, a transformation relation between coordinates and the like are expressed in a matrix form, and correlation operation is carried out;
10. cross spectral density matrix at focal field: the method comprises the steps of obtaining incident light and parameters of a tight focusing system through matrix operation;
11. positive definite condition: each matrix element in the cross spectral density matrix is required to meet a positive definite condition;
12. coordinate transformation: introducing a new sum and difference coordinate expression;
13. fourier transform: rewriting the integral term into a fourier transform form;
14. and (3) convolution calculation: writing each term of the cross spectral density matrix as the sum of four convolutions;
15. tightly focused polarization matrix: let r 1 ＝r 2 When r, a tightly focused polarization matrix is obtained from the cross spectral density matrix;
16. calculating three-dimensional polarization degree and polarization dimension: obtaining the three-dimensional polarization degree and polarization dimension of the focal field by the polarization matrix and the corresponding calculation formula;
17. adjusting the coherence length of incident light: adjusting the coherence length of incident light so that P 3D ＝0,D＝3；
18. Three-dimensional unpolarized field: a field exhibiting a three-dimensional polarization degree of 0 or a polarization dimension of 3;
19. adjusting the coherent structure of the incident light: at this coherence length, the incident light coherence structure is tuned to the form of a lattice;
20. three-dimensional unpolarized lattice: the required three-dimensional unpolarized crystal lattice is obtained in the focal field through the regulation and control of the incident light coherent structure.
According to the method, the convolution result is calculated rapidly by means of matlab software, the three-dimensional unpolarized result of the focal field can be obtained in a short time, and the calculation speed is improved rapidly; through the regulation and control of the incident light coherent structure, three-dimensional unpolarized lattices with different spatial distributions can be obtained in a focal field, so that the diversity of lattice structures is realized, and the practical application value is improved.
It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations and modifications of the present invention will be apparent to those of ordinary skill in the art in light of the foregoing description. It is not necessary here nor is it exhaustive of all embodiments. And obvious variations or modifications thereof are contemplated as falling within the scope of the present invention.
Claims (10)
1. A method of generating a three-dimensional unpolarized lattice in a non-paraxial system, comprising:
step 1, determining that an incident light field is a coherent matrix of a partially coherent Xie Ermo light beam;
step 2, calculating the three-dimensional polarization dimension and the three-dimensional polarization degree of the partially coherent Xie Ermo light beam in a tightly focused focal field according to the coherence matrix;
step 3, the coherence length of the partially coherent Xie Ermo light beam is adjusted according to the three-dimensional polarization dimension and the three-dimensional polarization degree, and the step 2 is returned until the three-dimensional polarization degree is 0 or the three-dimensional polarization dimension is 3, so that a three-dimensional unpolarized field is obtained;
and 4, adjusting the coherent structure distribution of the partially coherent Xie Ermo light beam based on the three-dimensional unpolarized field to obtain a three-dimensional unpolarized lattice.
2. The method of claim 1, wherein in step 4, adjusting the coherent structural distribution of the partially coherent Xie Ermo beam comprises: multiplying the coherence matrix by a corresponding off-axis phase;
wherein ,μαβ Represents the coherent structure matrix μ (ρ 1 -ρ 2 ) Element delta in (a) 0 The coherence length is indicated as such,
V 0n ＝(V 0xn ,V 0yn ) Representing off-axis displacement, V 0xn Representation ofDisplacement in x direction, V 0yn Representing the displacement in the y-direction,representing the off-axis phase.
3. The method of claim 2, wherein in adjusting the coherent structural distribution of the partially coherent Xie Ermo beam, the off-axis phase is written in the form of:
V 0n ＝(l*m,l*n)
wherein l, m and n all represent natural numbers.
4. The method for generating a three-dimensional unpolarized lattice in a non-paraxial system according to claim 1, wherein the coherence matrix is:
wherein, superscriptRepresenting complex conjugation; brackets'<>"means ensemble averaging; ρ=ρ (cos Φ, sin Φ) represents the coordinates of any point on the incident plane; ρ represents the distance of the incident point from the optical axis of the lens, φ ε (0, 2π)]Indicating the azimuth angle of the incident point relative to the optical axis; e (E) 0 (ρ) represents the electric field of the incident light.
5. The method of claim 1, wherein calculating the three-dimensional polarization dimension and the three-dimensional polarization degree of the partially coherent Xie Ermo beam in the tightly focused focal field according to the coherence matrix in step 2 comprises:
step 2.1, calculating an electric field which is closely attached to the rear surface of the lens according to the coordinate transformation relation between the Cartesian coordinates and the polar coordinates based on the coherence matrix;
step 2.2, calculating and obtaining an electric field at a tightly focused focal field according to a vector diffraction principle based on the electric field tightly attached to the rear surface of the lens;
step 2.3, performing ensemble averaging on the electric field at the tightly focused focal field to obtain a cross spectral density matrix of the partially coherent Xie Ermo light beam at the focal field;
step 2.4, according to positive definite conditions, introducing a new coordinate expression and Fourier transformation, writing each matrix element of the cross spectral density matrix at the focal field into a form of the sum of four convolutions, and solving each matrix element to obtain a tightly focused polarization matrix;
and 2.5, rotating the tight focusing polarization matrix to the intrinsic surface of the tight focusing polarization matrix, and calculating to obtain the three-dimensional polarization dimension and the three-dimensional polarization degree of the partially coherent Xie Ermo light beam in the tight focusing focal field.
6. The method of generating a three-dimensional non-polarizing lattice in a non-paraxial system according to claim 5, wherein the electric field closely contacting the rear surface of the lens is:
E t (ρ)＝P(θ)E 0 (ρ)N(ρ)
wherein ,represents the apodization function at the diaphragm, θ ε [0 ], α]The angle between the optical axis and the line connecting the incident point and the focus is represented, and N (ρ) represents the coordinate transformation matrix.
7. The method of generating a three-dimensional unpolarized lattice in a non-paraxial system of claim 5, wherein the electric field at the tightly focused focal field is:
where r= (x, y) represents the cross-sectional coordinates of the observation point near the focal point; d (ρ) represents a truncated function, and D (ρ) =1 when ρ is less than or equal to R; otherwise, 0, Z represents the longitudinal direction from the viewpoint to the focusThe distance, λ, represents the wavelength of the incident light, k x ＝-kcosφsinθ,k y ＝-ksinφsinθ,k z ＝kcosθ,K represents the wave vector.
8. The method for generating a three-dimensional unpolarized lattice in a non-paraxial system as claimed in claim 5, wherein the matrix elements of the tightly focused polarization matrix are:
wherein ,Aai and ABj Representing the elements in matrix a, representing the conjugate, representing the fourier transform, f representing the focal length.
9. The method of generating a three-dimensional unpolarized lattice in a non-paraxial system as claimed in claim 5, wherein step 2.5 comprises:
and rotating the tight focusing polarization matrix to the intrinsic plane by using a three-dimensional rotation matrix to obtain the real part and the imaginary part of the tight focusing polarization matrix, solving the eigenvalue of the real part, and calculating to obtain the three-dimensional polarization dimension of the partially coherent Xie Ermo light beam in the tight focusing focal field.
10. The method of generating a three-dimensional unpolarized lattice in a non-paraxial system of claim 5, wherein the three-dimensional degree of polarization is:
where tr denotes the eigenvalue of the matrix, P 3D (r) represents the three-dimensional degree of polarization, and Φ (r) represents the tightly focused polarization matrix.
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