A method for generating a radially polarized high-order twisted nonuniformly correlated beam

Abstract

The application discloses a method for generating a radially polarized high-order twisted non-uniform correlation light beam, and the method comprises the following steps: step 1, setting a weight matrix and a kernel function; step 2, obtaining a light beam cross-spectral density matrix element by integrating the weight matrix element and the kernel function; step 3, determining a restriction condition of a twist factor; step 4, setting a restriction condition of a light beam polarization state satisfying radial polarization; and step 5, determining a cross-spectral density matrix element of the radially polarized high-order twisted non-uniform correlation light beam according to the restriction conditions of the light beam twist factor and the polarization state satisfying radial polarization. The application enriches the partial coherent vector beam regulation method and provides a novel light field model with application value for the fields of optical micro-manipulation and anti-depolarization optical communication.

Description

Technical Field

[0001] This invention belongs to the field of optical field manipulation technology, and in particular relates to a method for generating radially polarized high-order twisted non-uniform correlated beams. Background Technology

[0002] In recent years, partially coherent non-uniformly correlated beams have broken through the limitations of spatial translation invariance, exhibiting novel physical properties such as self-focusing, trajectory self-misalignment, and multimodal evolution, thus attracting considerable attention in the field of structured optical field manipulation. However, the theoretical construction of existing partially coherent higher-order non-uniformly correlated beams still faces bottlenecks. If it is possible to simultaneously introduce higher-order correlation structures and complex cross-coupling phases (such as twisted phases) into a non-uniform correlation framework, the traditional method of directly nesting orthogonal polynomials or power-law phase terms in the cross-spectral density function cannot guarantee the physical realizability of the optical field. Based on this, some studies have proposed cleverly introducing higher-order terms into the non-negative weighting function of partially coherent twisted Gaussian Sherman mode beams, thereby generating higher-order twisted non-uniformly correlated beams that meet the requirements of physical realizability.

[0003] For scalar light fields, the focus is on the spatial distribution of light intensity and coherence, while neglecting another core degree of freedom—polarization. Polarization, as an essential physical property of light fields, plays an irreplaceable role in optical micromanipulation, high-resolution imaging, and free-space optical communication. In recent years, vector beams with spatially non-uniform polarization distributions, especially radially polarized beams, have become a research hotspot in modern optics due to their unique tight-focusing characteristics and excellent resistance to atmospheric turbulence.

[0004] However, there are still many gaps in the understanding of combining radial polarization with complex non-uniform correlation structures. Summary of the Invention

[0005] The purpose of this invention is to solve the problems mentioned in the background art and to propose a method for generating radially polarized high-order twisted non-uniform correlated beams.

[0006] This application combines high-order correlation structures, distorted phases, and radial polarization to generate a partially coherent beam with unique physical properties such as self-focusing, self-splitting, and rotation.

[0007] Step 1: Set the weight matrix and kernel function;

[0008] The expressions for the beam weight matrix and kernel function are as follows, with higher-order terms introduced in the weight function:

[0009] ;

[0010] ;

[0011] It is a weight matrix. It is a kernel function; where, It is any position vector in space. It is a unitless vector that is not limited by dimensions. It is an antisymmetric matrix; They are The amplitudes of the two orthogonal components in the two directions, and ; It is the multiple correlation coefficient. It is a beam of light direction and The multiple correlation coefficient in the direction, It is a beam of light direction and The multiple correlation coefficient in the direction, therefore ; Represents a beam of light direction and The multiple correlation coefficient in direction; The order of the beam represents the number of beams and affects the beam. Light intensity distribution in the direction; It also represents the order of the beam, affecting the beam's properties. Light intensity distribution in the direction; All values ​​are zero or any positive integer; It is a positive parameter. It refers to beam width and wavenumber. , It is the wavelength of the light beam. It is a distortion factor.

[0012] Step 2: Obtain the beam cross-spectral density matrix elements through the weight matrix elements and kernel function integration. The forms of the weight matrix elements and kernel function integration, as well as the expression for the cross-spectral density matrix elements of a radially polarized higher-order twisted non-uniform correlated beam, are as follows: ; ;

[0013] These are the elements of the cross spectral density matrix of the beam. It is a weight matrix. It is a kernel function; and Represents any two position vectors in space. , It is the beam coherence width;

[0014] Step 3: Determine the constraints that satisfy the distortion factor.

[0015] In a partially coherent beam containing a distortion factor, the following distortion factor constraint must be satisfied: ;because The constraints are automatically met.

[0016] Step 4: Set the beam polarization state to meet the radial polarization constraint.

[0017] The polarization state of a radially polarized higher-order twisted non-uniform correlated beam must satisfy the radial polarization condition, i.e., the minor axis of the polarization ellipse is 0, and the azimuth angle points to the central origin, which is expressed as follows:

[0018] ;

[0019] ;

[0020] The derivation is .

[0021] Step 5: Determine the cross spectral density matrix elements of the radially polarized higher-order twisted non-uniform correlated beam based on the beam distortion factor and the constraint condition that the polarization state satisfies radial polarization.

[0022] The cross spectral density matrix elements of a radially polarized higher-order twisted non-uniform correlated beam are expressed as:

[0023] .

[0024] Compared with existing technologies, the significant advancement of this invention lies in the simultaneous introduction of a twisted phase and a higher-order non-uniform correlation structure while maintaining the radial polarization state. This profoundly reveals the multidimensional manipulation of the polarization state and degree of polarization of the vector light field by the twisted phase and the higher-order non-uniform correlation structure. The beam simultaneously retains the rotational characteristics brought by the twisted phase and the splitting characteristics brought by the higher-order non-uniform correlation structure, and the polarization characteristics of the light field are also modulated during free-space propagation. The proposed beam enriches the theory of partially coherent vector beam manipulation and provides a novel light field model with certain application value for fields such as optical micromanipulation and anti-depolarization communication.

[0025] To more clearly illustrate the functional characteristics and structural parameters of the present invention, further explanation is provided below in conjunction with the accompanying drawings and specific embodiments. Attached Figure Description

[0026] Figure 1 This is a distribution diagram of light intensity and polarization state of a radially polarized high-order twisted non-uniform correlated beam at different transmission distances; Figure 1 In the middle, (a1-a4): (b1-b4): (c1-c4): ;

[0027] Figure 2 This is a distribution diagram of light intensity and polarization state of a radially polarized high-order twisted non-uniform correlated beam at different transmission distances; Figure 2 In the middle, (a1-a4): (b1-b4): (c1-c4): ;

[0028] Figure 3 This is a diagram of an experimental setup for radially polarized higher-order twisted non-uniform correlated beams.

[0029] The corresponding numbers in the attached figures are:

[0030] 1 Solid-state laser; 2 Horizontal linear polarizer; 3 Beam expander; 4 Mirror; 5 Digital micromirror device (DMD); 6 Lens; 7 Aperture; 8 Lens; 9 Horizontal linear polarizer; 10 First-order vortex half-wave plate; 11 Lens; 12 Analyzer; 13 Charge-coupled device (CCD). Detailed Implementation

[0031] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] When non-uniform correlations or other phase structures are introduced into the cross-spectral density matrix of a partially coherent radially polarized beam, coherence and polarization properties are deeply coupled, enabling multi-parameter optical field manipulation. Based on this, exploring the combination of higher-order non-uniform correlation structures, distorted phases, Hermitian polynomials, and radial polarization will generate more novel optical field evolution phenomena, further expanding the application scenarios of partially coherent vector beams.

[0033] This invention relates to the theoretical control and experimental synthesis of radially polarized high-order twisted non-uniform correlated beams. The aim is to combine high-order non-uniform correlated structures, twisted phases, and radial polarization characteristics to successfully control multiple parameters and explore the evolution of light intensity and polarization characteristics during free-space propagation.

[0034] This invention proposes a method for generating radially polarized higher-order twisted non-uniform correlated beams. In generating such partially coherent beams, a higher-order term is first introduced into the weighting function and extended to the vector domain to generate the radially polarized higher-order twisted non-uniform correlated beam. Experimentally, a scalar optical field is first generated, and then the polarization state of the scalar optical field is converted to radial polarization using a polarization conversion element, thereby obtaining the radially polarized higher-order twisted non-uniform correlated beam.

[0035] The feasibility of this application will be further illustrated by specific experiments below.

[0036] In this invention, the values ​​of each parameter are respectively wavelength. Beam width ,parameter Distortion factor And the coherence width can be calculated. order Pick Six sets of values ​​were used to investigate the evolution of light intensity and polarization state of radially polarized high-order twisted non-uniform correlated beams at different transmission distances, with different order values.

[0037] The experimental optical path is as follows: First, a fundamental Gaussian beam with a wavelength of 532.8 nm is emitted by a laser. Then, it passes through a horizontal polarizer LP1 to form horizontally linearly polarized light. The beam is then collimated and amplified by a beam expander before being incident on the surface of a DMD through a mirror. The DMD cyclically loads a pre-loaded beam hologram to dynamically modulate the incident light field at high speed. The modulated beam enters a 4f filter system consisting of lens1, aperture PH, and lens2, resulting in first-order diffracted light carrying beam phase information. The distance between the DMD and lens1 is 150 mm, and the focal lengths of lenses1 and 2 are also 150 mm. The filtered beam then passes through a horizontal linear polarizer LP2 to ensure horizontal polarization, and then through a first-order vortex half-wave plate to ensure the horizontal polarization is converted to radial polarization. The radially polarized HTGSM beam is thus generated, with a distance of 150 mm between lens2 and VHWP. The light beam first travels 100mm in free space, then passes through lens 3 and continues in free space before being captured and its cross-sectional intensity information is recorded by a CCD camera placed on the output plane. Before CCD recording, the rotating analyzer LP3 can detect the polarization component of the generated beam to verify the polarization characteristics of the vector light field.

[0038] The experiment employs a synthesis scheme that first modulates the coherent structure of the scalar optical field and then transforms it into a vector polarization state. The core idea is to break down the originally complex vector optical field generation process into two independent operational steps: coherent statistical superposition in the time dimension and geometric mapping of the polarization state in the spatial dimension. The basic architecture is based on the experiment with a scalar beam, with a polarization conversion element added at the end of the optical path to achieve the conversion of the scalar optical field into a radially polarized vector optical field.

[0039] In the experimental synthesis of this beam, a pseudo-mode superposition approach was employed. A two-dimensional comb sampling function was used to discretize the continuous weighting function, transforming the integral expression of the cross-spectral density function into a linear superposition of these finite number of discrete pseudo-modes. The sampling range of the beam was determined through MATLAB simulation. The number of modes is 29 × 29 = 841. During the hologram generation process, based on the sampling range and number of samples, and the previously set parameter values, code was written to generate holograms of high-order non-uniformly correlated beams. The DMD was imported before the experiment began.

[0040] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for generating radially polarized higher-order twisted non-uniform correlated beams, characterized in that, The method is used to generate radially polarized higher-order twisted non-uniform correlated beams, and the method includes: Step 1: Set the weight matrix and kernel function; Step 2: Obtain the beam cross spectral density matrix elements by integrating the weight matrix elements and the kernel function; Step 3: Determine the constraints that satisfy the distortion factor; Step 4: Set the beam polarization state to satisfy the radial polarization constraint. Step 5: Determine the cross spectral density matrix elements of the radially polarized higher-order twisted non-uniform correlated beam based on the beam distortion factor and the constraint condition that the polarization state satisfies radial polarization.

2. The method according to claim 1, characterized in that, Step 1, set the weight matrix and kernel function, including: The expressions for the beam weight matrix and kernel function are as follows, with higher-order terms introduced in the weight function: ； ； It is a weight matrix. It is a kernel function; where, It is any position vector in space. It is a unitless vector that is not limited by dimensions. It is an antisymmetric matrix; They are The amplitudes of the two orthogonal components in the two directions, and ; It is the multiple correlation coefficient. It is a beam of light direction and The multiple correlation coefficient in the direction, It is a beam of light direction and The multiple correlation coefficient in the direction, therefore ; Represents a beam of light direction and The multiple correlation coefficient in direction; The order of the beam represents the number of beams and affects the beam. Light intensity distribution in the direction; It also represents the order of the beam, affecting the beam's properties. Light intensity distribution in the direction; All values ​​are zero or any positive integer; It is a positive parameter. It refers to beam width and wavenumber. , It is the wavelength of the light beam. It is a distortion factor.

3. The method according to claim 2, characterized in that, Step 2: Obtain the beam cross-spectral density matrix elements through integration of the weight matrix elements and the kernel function, including: The forms of the weight matrix elements and kernel function integrals, and the expressions for the cross spectral density matrix elements of radially polarized higher-order twisted non-uniform correlated beams are as follows: ; ; These are the elements of the cross spectral density matrix of the beam. It is a weight matrix. It is a kernel function; and Represents any two position vectors in space. , It is the beam coherence width.

4. The method according to claim 3, characterized in that, Step 3, determine the constraints that satisfy the distortion factor, including: In a partially coherent beam containing a distortion factor, the following distortion factor constraint must be satisfied: ;because The constraints are automatically met.

5. The method according to claim 4, characterized in that, Step 4, set the beam polarization state to satisfy the radial polarization constraint, including: The polarization state of a radially polarized higher-order twisted non-uniform correlated beam must satisfy the radial polarization condition, i.e., the minor axis of the polarization ellipse is 0, and the azimuth angle points to the central origin, which is expressed as follows: ； ； The derivation is .

6. The method according to claim 5, characterized in that, Step 5: Based on the constraint that the torsion factor and polarization state satisfy radial polarization, determine the cross spectral density matrix elements of the radially polarized higher-order torsion non-uniform correlated beam; including: The cross spectral density matrix elements of a radially polarized higher-order twisted non-uniform correlated beam are expressed as: 。

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