A lattice optimization method for orthogonal polarization

Abstract

The present invention discloses a dot matrix optimization method for orthogonal polarization, belonging to the field of optical technology. The specific steps are as follows: Step S1: Determine the initial phase and target amplitude; Step S2: Based on angular spectrum theory, perform light field propagation to forward and reverse propagate the initial phase to obtain forward complex amplitude and reverse complex amplitude; Step S3: Modulate the forward complex amplitude and reverse complex amplitude; Step S4: Perform inverse reconstruction based on the modulated forward complex amplitude and reverse complex amplitude to obtain an updated phase; Step S5: Repeat Steps S2 and S4 using the updated phase as the initial phase until convergence conditions are met, and output the optimized phase. Using the above-mentioned dot matrix optimization method for orthogonal polarization, each optical point in the dot matrix maintains an orthogonal polarization state with its adjacent points, effectively increasing the upper limit of the dot matrix density. Using an improved Günlü-Saxton algorithm, the convergence speed of phase iteration is improved.

Description

Technical Field

[0001] The present invention relates to the field of optical technology, and in particular to a lattice optimization method for orthogonal polarization. Background Art

[0002] Optical lattice generation technology serves as a core technology supporting modern photonics, quantum control, and precision measurement. Its performance optimization has always been a key area of ​​research in optical engineering. With the continued growth in demand for high-density lattices in cutting-edge fields such as quantum computing and super-resolution microscopy, the dual bottlenecks of traditional lattice generation methods at the physical principle and algorithm levels are becoming increasingly prominent. In particular, in applications such as micro-nano optics and optical tweezers manipulation that require subwavelength lattice spacing, the lattice overlap problem caused by the diffraction effect of light has become a key factor restricting system performance improvements. The industry's current pursuit of lattice density requires not only breaking through the physical limitations of the optical diffraction limit, but also urgently requires breakthroughs in phase control algorithms.

[0003] Current dot matrix generation technologies mainly include the following methods: utilizing optical diffraction of pinhole arrays, regulation based on diffractive optical elements, phase control of spatial light modulators, and focusing effects of microlens arrays. Traditional solutions have essential limitations: First, in single-polarization working mode, the diffracted light fields of adjacent dot matrix units will produce strong coherent superposition due to the consistent polarization state, resulting in the dot spacing being limited by the physical limit of the Rayleigh criterion. Even through algorithm optimization, it is difficult to break through the technical bottleneck of sub-wavelength dot matrix density; second, the Gutchberg-Saxton algorithm uses fixed weight parameters in the iterative process. When dealing with complex phase distributions of high-density dot matrices, the convergence speed often drops sharply or even diverges because the iterative path falls into a local optimal solution. Although some improved algorithms have attempted to introduce static weighting factors or regularization constraints, these methods lack dynamic feedback capabilities. Summary of the Invention

[0004] The purpose of the present invention is to provide a lattice optimization method for orthogonal polarization to solve the above technical problems.

[0005] To achieve the above objectives, the present invention provides a method for optimizing orthogonal polarization lattices, the specific steps of which are as follows:

[0006] Step S1: Determine the initial phase and target amplitude;

[0007] Step S2: Based on the angular spectrum theory, the light field is propagated and the initial phase is propagated forward and backward to obtain the forward complex amplitude and the reverse complex amplitude;

[0008] Step S3: modulating the forward complex amplitude and the reverse complex amplitude;

[0009] Step S4: performing inverse reconstruction according to the modulated forward complex amplitude and reverse complex amplitude to obtain an updated phase;

[0010] Step S5: Repeat steps S2 to S4 with the updated phase as the initial phase until the convergence condition is met and output the optimized phase.

[0011] Preferably, in step S1, a random phase distribution or a pre-optimized phase obtained by reverse angular spectrum propagation of the target lattice is used as the initial phase .

[0012] Preferably, in step S2, the light field propagation transfer function based on angular spectrum theory is as follows:

[0013] ;

[0014] in, is the transfer function, is the exponential function of e, is the imaginary unit, is the propagation distance, is the wavelength of light, and They are and The spatial frequency components in the direction;

[0015] The forward complex amplitude and reverse complex amplitude are and , and are the amplitude components of the forward complex amplitude and the reverse complex amplitude, and are the phases of the forward complex amplitude and the reverse complex amplitude, respectively.

[0016] Preferably, in step S3, the modulation process is: the target amplitude includes a positive target amplitude component and the reverse target amplitude component ; Replace the amplitude components in the forward complex amplitude and reverse complex amplitude with the forward target amplitude components respectively and the reverse target amplitude component , and get the modulated positive complex amplitude and the modulated inverse complex amplitude .

[0017] Preferably, in step S4, the reverse reconstruction process is as follows:

[0018] The modulated positive complex amplitude and the modulated inverse complex amplitude Perform reverse propagation and forward propagation respectively, perform vector superposition on the phase components of the two, and obtain the updated phase ,in, To update the phase, is the phase function, and are the forward complex amplitude after modulation The reconstructed amplitude component and reconstructed phase after back propagation, and are the forward complex amplitude after modulation Reconstructed amplitude component and reconstructed phase after forward propagation.

[0019] Preferably, in step S5, an improved Gutchberg-Saxton algorithm is used to perform iterative optimization of phase recovery, and the iterative equation of the improved Gutchberg-Saxton algorithm is as follows:

[0020] ;

[0021] in, For the The phase after iterations, is the Fourier transform operator, For the The complex amplitude distribution of the iterations, is the adaptive weight function, and the expression of the adaptive weight function is as follows:

[0022] and ;

[0023] Among them, among them, Expressed as The positive complex amplitude of the reconstructed image.

[0024] Therefore, the present invention adopts the above-mentioned orthogonal polarization lattice optimization method, which has the following beneficial effects:

[0025] (1) Orthogonal polarization phase modulation technology is introduced. Based on the angular spectrum theory, the initial phase is propagated forward and reversely to obtain the forward complex amplitude and reverse complex amplitude respectively; the forward complex amplitude and reverse complex amplitude are modulated; and the updated phase is obtained by reverse reconstruction based on the modulated forward complex amplitude and reverse complex amplitude, so that each optical point in the lattice maintains an orthogonal polarization state with its adjacent points, effectively improving the upper limit of the lattice density.

[0026] (2) The improved Gutchberg-Saxton algorithm is adopted to replace the original feedback factor with an adaptive weight function, which significantly improves the convergence speed of the phase iteration and solves the iterative divergence problem caused by unstable numerical calculation.

[0027] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a flow chart of a method for optimizing orthogonal polarization lattice according to the present invention;

[0029] Figure 2 It is a non-polarized light image;

[0030] Figure 3 is the electric field intensity distribution curve of non-polarized light along the y=0 line;

[0031] Figure 4 It is a polarized light image;

[0032] Figure 5 is the electric field intensity distribution curve of polarized light along the y=0 line;

[0033] Figure 6 It is a simulated dot matrix. DETAILED DESCRIPTION

[0034] In the description of the present invention, it should be noted that the terms "upper", "lower", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, or the orientations or positional relationships in which the inventive product is usually placed when in use. These are only for the convenience of describing the present invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, they cannot be understood as limitations on the present invention. In the description of the present invention, it should also be noted that, unless otherwise expressly specified and limited, the terms "setting", "installation" and "connection" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be a communication between the internal parts of two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0035] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0036] The polarization states of two beams of light are antipodal to each other on the Poincare sphere (e.g., horizontal / vertical linear polarization, left-handed / right-handed circular polarization), and their Jones vectors satisfy the inner product of zero. Liquid crystal is a substance between a liquid and a crystal, with its molecules arranged in a directional pattern. This arrangement results in anisotropy in the optical properties of liquid crystals, meaning that light from different directions experiences different refractive indices. When linearly polarized light enters a liquid crystal, it decomposes into two beams of orthogonal polarization, as follows:

[0037] 1) Ordinary light (o light): The polarization direction is perpendicular to the long axis of the liquid crystal molecules (optical axis);

[0038] 2) Extraordinary light (e-light): The polarization direction is parallel to the long axis of the liquid crystal molecules.

[0039] This embodiment uses a diffraction optical element made of liquid crystal, which can modulate the light wavefront. According to the characteristics of liquid crystal, a dot matrix with orthogonal polarization can be generated. Assume that two adjacent points in the dot matrix are adjacent points. and , and their electric fields are and ,but Point and Composite electric field at a point as follows:

[0040] ;

[0041] The detector detects light intensity. and electric field strength is proportional to the square of ;

[0042] The total light intensity as follows:

[0043] ;

[0044] in, for The conjugate transpose of , when the two points are orthogonal in polarization, their inner product is 0, that is, .therefore, , the orthogonal polarization causes the interference term to disappear, and the total light intensity is , to achieve crosstalk-free superposition. Figure 2-Figure 5 As shown, Figure 3 and Figure 5 In the figure, the horizontal axis is the pixel position, and the electric field intensity is the normalized electric field intensity, dimensionless unit. There is a clear difference between non-polarized light and polarized light. Polarized light has no crosstalk superposition, so Point and Composite electric field at a point There is a more pronounced trough in the middle.

[0045] like Figure 1 As shown in FIG, a lattice optimization method for orthogonal polarization is shown, and the specific steps are as follows:

[0046] Step S1: Determine the initial phase and target amplitude. Use a random phase distribution or a pre-optimized phase obtained by reverse angular spectrum propagation of the target lattice as the initial phase. .

[0047] Step S2: Perform light field propagation based on angular spectrum theory. Perform forward propagation and reverse propagation on the initial phase to obtain forward complex amplitude and reverse complex amplitude. The light field propagation transfer function based on angular spectrum theory is as follows:

[0048] ;

[0049] in, is the transfer function, is the exponential function of e, is the imaginary unit, is the propagation distance, is the wavelength of light, and They are and The spatial frequency components in the direction;

[0050] The forward complex amplitude and reverse complex amplitude are and , and are the amplitude components of the forward complex amplitude and the reverse complex amplitude, and are the phases of the forward complex amplitude and the reverse complex amplitude, respectively.

[0051] Step S3: modulate the forward complex amplitude and the reverse complex amplitude; the modulation process is: the target amplitude includes the forward target amplitude component and the reverse target amplitude component ; Replace the amplitude components in the forward complex amplitude and reverse complex amplitude with the forward target amplitude components respectively and the reverse target amplitude component , and get the modulated positive complex amplitude and the modulated inverse complex amplitude .

[0052] Step S4: Perform reverse reconstruction based on the modulated forward complex amplitude and reverse complex amplitude to obtain the updated phase. The reverse reconstruction process is as follows:

[0053] The modulated positive complex amplitude and the modulated inverse complex amplitude Perform reverse propagation and forward propagation respectively, perform vector superposition on the phase components of the two, and obtain the updated phase ,in, To update the phase, is the phase function, and are the forward complex amplitude after modulation The reconstructed amplitude component and reconstructed phase after back propagation, and are the forward complex amplitude after modulation Reconstructed amplitude component and reconstructed phase after forward propagation.

[0054] Step S5: Repeat steps S2 to S4 with the updated phase as the initial phase until the convergence condition is met and the optimized phase is output. In step S5, the improved Gütschberg-Saxton algorithm is used to iteratively optimize the phase recovery. The iterative equation of the improved Gütschberg-Saxton algorithm (GS algorithm) is as follows:

[0055] ;

[0056] in, For the The phase after iterations, is the Fourier transform operator, For the The complex amplitude distribution of the iterations, is the adaptive weight function, and the expression of the adaptive weight function is as follows:

[0057] and ;

[0058] in, Expressed as The positive complex amplitude of the reconstructed image.

[0059] The original feedback factor of the Gutchberg-Saxton algorithm is ,in, is a dynamic adjustment factor, when When , the local weights diverge, i.e. , which makes the value unstable during the iteration process. This embodiment adopts an adaptive weight function. When , the weight value is approximately equal to 1, which meets the weighting requirements. , the weight increases exponentially, but is limited by The value of ensures the boundedness of the weight, and the value of the weight is limited to Therefore, the iterative divergence problem caused by the instability of numerical calculation in the traditional weighted GS algorithm is solved.

[0060] In order to verify the effectiveness of this embodiment, a simulation experiment was carried out. Figure 6 As shown, after the dot matrix 1 and the dot matrix 2 are superimposed, the density increases and there is no crosstalk superposition.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for optimizing orthogonal polarization lattice, characterized in that: The specific steps are as follows: the diffractive optical device used is made of liquid crystal, and the light wavefront is adjusted to generate a dot matrix of orthogonal polarizations according to the characteristics of the liquid crystal; Step S1: Determine the initial phase and target amplitude; Step S2: Based on the angular spectrum theory, the light field is propagated and the initial phase is propagated forward and backward to obtain the forward complex amplitude and the reverse complex amplitude; Step S3: modulating the forward complex amplitude and the reverse complex amplitude; Step S4: performing inverse reconstruction according to the modulated forward complex amplitude and reverse complex amplitude to obtain an updated phase; Step S5: Repeat steps S2 to S4 with the updated phase as the initial phase until the convergence condition is met and output the optimized phase.

2. The orthogonal polarization lattice optimization method according to claim 1, characterized in that: In step S1, a random phase distribution or a pre-optimized phase obtained by reverse angular spectrum propagation of the target lattice is used as the initial phase .

3. The orthogonal polarization lattice optimization method according to claim 2, characterized in that: In step S2, the light field propagation transfer function based on angular spectrum theory is as follows: ； in, is the transfer function, is the e exponential function, is the imaginary unit, is the propagation distance, is the wavelength of light, and They are and The spatial frequency components in the direction; The forward complex amplitude and reverse complex amplitude are and , and are the amplitude components of the forward complex amplitude and the reverse complex amplitude, and are the phases of the forward complex amplitude and the reverse complex amplitude, respectively.

4. The orthogonal polarization lattice optimization method according to claim 3, characterized in that: In step S3, the modulation process is: the target amplitude includes a positive target amplitude component and the reverse target amplitude component ; Replace the amplitude components in the forward complex amplitude and reverse complex amplitude with the forward target amplitude components respectively and the reverse target amplitude component , and get the modulated positive complex amplitude and the modulated inverse complex amplitude .

5. The orthogonal polarization lattice optimization method according to claim 3, characterized in that: In step S4, the reverse reconstruction process is as follows: The modulated positive complex amplitude and the modulated inverse complex amplitude Perform reverse propagation and forward propagation respectively, perform vector superposition on the phase components of the two, and obtain the updated phase ,in, To update the phase, is the phase function, and are the forward complex amplitude after modulation The reconstructed amplitude component and reconstructed phase after back propagation, and are the forward complex amplitude after modulation Reconstructed amplitude component and reconstructed phase after forward propagation.

6. The orthogonal polarization lattice optimization method according to claim 5, characterized in that: In step S5, an improved Gutchberg-Saxton algorithm is used to perform iterative optimization of phase recovery. The iterative equation of the improved Gutchberg-Saxton algorithm is as follows: in, For the The phase after iterations, is the Fourier transform operator, For the The complex amplitude distribution of the iterations, is the adaptive weight function, and the expression of the adaptive weight function is as follows: and ; in, Expressed as The positive complex amplitude of the reconstructed image.

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