Mask plate design method of quasi-periodic high-order optical vortex lattice

Abstract

A method for designing a mask plate of a quasi-periodic high-order optical vortex lattice comprises the following steps: firstly, acquiring an electric field expression of an optical vortex lattice with a high-order topological charge, and obtaining a complex transmittance function of the mask plate of the quasi-periodic high-order optical vortex lattice in combination with the amplitude and phase of the quasi-periodic high-order optical vortex lattice and a blazed grating; the mask plate described based on the function is the mask plate of the quasi-periodic high-order optical vortex lattice. The mask plate designed by the invention can generate a quasi-periodic high-order optical vortex lattice. Different initial additional phases can be applied to waves participating in interference by adjusting the parameter p, so that quasi-periodic optical vortex lattices with different structures can be obtained, quasi-periodic optical vortex lattices with different topological charge orders can be obtained by changing the topological charge m in the field, and the limitation that the topological charge value of sub-vortexes is very equal to + / -1 is effectively broken through. Therefore, the method has a very important application prospect in the fields of multi-particle manipulation and high-capacity optical communication.

Description

Technical Field

[0001] The present invention relates to the technical fields of particle manipulation and quantum information encoding, and specifically to a method for designing a mask template with a quasi-periodic structure of higher-order optical vortex lattices. Background Art

[0002] Quasicrystals have a unique circular symmetric structure and do not possess the periodic structure and translational symmetry of crystals. Different from crystals, quasicrystals can possess discrete rotational symmetries of any order, such as five-fold, seven-fold or higher-order symmetries, etc. So far, quasicrystal structures have been successively observed and successfully prepared in alloys, ultracold atomic gases, and optoelectronic and photonic systems [Phys. Rev. Lett. 122, 110404 (2019)]. In the optical field, quasicrystal structures exhibit a variety of novel physical properties, such as disorder-enhanced wave transport [Science 332, 1541 (2011)], light localization and delocalization [Nature 577, 42 (2020)], and optical solitons [Nat. Photonics 14, 663 (2020)].

[0003] On the other hand, when there are optical vortices carrying orbital angular momentum in a photonic quasicrystal structure, it is called a quasi-periodic optical vortex lattice. Due to its unique quasi-periodic spatial structure distribution and the provision of additional degrees of freedom, it has been widely studied and applied in many frontier fields such as optical communication [Appl. Phys. Lett. 123, 091105 (2023)], particle manipulation [Opt. Lett. 48, 3535 (2023)], information encryption and storage [Adv. Photonics Nexus 2, 036013 (2023)], etc. The propagation and evolution laws of quasi-crystalline light beams generated based on multi-wave interference [Opt. Lett. 46, 102 (2021)] and the relationship between light localization and the order of discrete rotational symmetry in quasicrystals [Nat. Photonics 18, 224 (2024)] have been successively explored. However, the regulation of sub-vortices in existing quasi-periodic vortex lattices is complex, and the topological charge value is always equal to ±1, which greatly limits its further application.

[0004] In summary, there is currently a lack of a quasi-periodic higher-order optical vortex lattice laser mode that can be applied to the fields of multi-particle manipulation and high-capacity optical communication. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for designing a mask template of a quasi-periodic higher-order optical vortex lattice, and use this mask template to generate a quasi-periodic higher-order optical vortex lattice.

[0006] The technical solution adopted by the present invention to solve the above technical problems is as follows: A method for designing a mask of a quasi-periodic high-order optical vortex lattice, the steps are as follows: S1. Obtain the electric field expression of the optical vortex lattice, and its electric field expression is: where A is the amplitude, j is an indicator variable, n is the number of wave vectors, (x, y) are rectangular coordinates, k x,j and k y,j are the components of the wave vector along the x-axis and y-axis, θ j represents the initial additional phase of the wave,; S2. Obtain the electric field expression of the optical vortex lattice with high-order topological charges, and its electric field expression is: where m is an integer parameter representing the topological charge; by adjusting m, the free adjustment of the topological charge of the entire quasi-periodic optical vortex lattice can be realized, thereby generating a high-order optical vortex lattice with quasi-periodic characteristics; S3. Based on the above content, combining the amplitude, phase of the quasi-periodic high-order optical vortex lattice and a blazed grating, obtain the complex transmittance function of the mask of the quasi-periodic high-order optical vortex lattice, and its expression is: t = |A(η, ξ)|exp[j(angle(E(x, y)) + P0)] where angle() is the phase-taking function, and the mask described by this complex transmittance function is the mask of the quasi-periodic high-order optical vortex lattice. As a preferred solution, in the formula of step S1, θ j = p(2π / n)(j - 1), where p is a non-negative integer starting from 0, and it combines 2π / n to control the phase difference between adjacent waves. As a preferred solution, by adjusting the number of wave vectors n and the additional phase-related parameter p, quasi-periodic optical vortex lattices with different structures can be obtained. As a preferred solution, in step S3, the phase expression of the blazed grating is P0 = 2πx / d, where d is the period of the blazed grating. This solution also includes a method for generating a quasi-periodic high-order optical vortex lattice using the mask prepared by the above design method. The parallel beam generated by a continuous-wave solid-state laser is irradiated on a spatial light modulator loaded with the mask of the quasi-periodic high-order optical vortex lattice, and at the same time, the number of wave vectors n and the additional phase-related parameter p are adjusted, and quasi-periodic optical vortex lattices with different structures can be obtained. The technical effects of the present invention:

[0007] The mask designed by the present invention can generate a quasi-periodic high-order optical vortex lattice. By adjusting the parameter p, different initial additional phases can be applied to the waves participating in the interference, so as to obtain quasi-periodic optical vortex lattices with different structures. By changing the topological charge m in the field, quasi-periodic optical vortex lattices with different topological charge orders can be obtained, thus effectively breaking the limitation that the topological charge value of the sub-vortices is equal to ±1. Therefore, it has very important application prospects in the fields of multi-particle manipulation and high-capacity optical communication. Brief Description of the Drawings

[0008] Figure 1 are masks obtained when the modulation parameter n of the quasi-periodic high-order optical vortex lattice is 5, when m = 1, p = 0 and m = 3, p = 0, 1, 2 respectively.

[0009] Figure 2 is Figure 1 the quasi-periodic high-order optical vortex lattice generated by the shown mask. Detailed Embodiment

[0010] By combining the additional phase modulation technology of spatially structured beams and the phase doubling technology, the present invention modulates the phase function of the quasi-periodic optical vortex lattice, so as to generate a quasi-periodic high-order optical vortex lattice with a rich spatial structure distribution and free topological charge regulation.

[0011] Figure 1 is the mask of the quasi-periodic high-order optical vortex lattice generated by the present invention. The detailed embodiment is as follows: First, the electric field expression of the optical vortex lattice is: In the formula, θ j = p(2π / n)(j - 1), where A is the amplitude, j is the indicator variable (the value range is 1 - n), n is the number of wave vectors, (x, y) are rectangular coordinates, k x,j and k y,j are the components of the wave vector along the x-axis and y-axis, θ j represents the initial additional phase of the wave, and p is a non-negative integer starting from 0, which combines 2π / n to control the phase difference between adjacent waves. When the number of wave vectors n = 2, 3, 4, 6, the generated light field reveals the periodic mosaic of the two-dimensional plane, while when n = 5, 7, 8,......, the generated lattice structure shows a rotational symmetry with quasi-periodic characteristics of 2π / n. By regulating the number of wave vectors n and the additional phase-related parameter p, quasi-periodic optical vortex lattices with different structures can be obtained. The electric field expression of the optical vortex lattice with high-order topological charge is: Where m is an integer parameter representing the topological charge. By regulating m, free regulation of the topological charge of the entire quasi-periodic optical vortex lattice can be achieved, thereby generating a high-order optical vortex lattice with quasi-periodic characteristics. A design method for a mask of a quasi-periodic high-order optical vortex lattice, characterized by combining the amplitude, phase of the quasi-periodic high-order optical vortex lattice and a blazed grating to obtain the complex transmittance function of the mask of the quasi-periodic high-order optical vortex lattice, and its expression is: t = |A(η, ξ)| exp[j(angle(E(x, y)) + P0)] Where angle() is the phase extraction function, P0 = 2πx / d is the phase expression of the blazed grating, and d is the period of the blazed grating. Its function is to separate the above-mentioned quasi-periodic optical vortex lattice from the diffraction order in the experiment. The mask described by this complex transmittance function is the mask of the quasi-periodic high-order optical vortex lattice of the present invention.

[0012] In the experiment, the number of wave vectors n = 5 is selected. Based on the additional phase modulation technology and the phase doubling technology, when the topological charge value m = 1, the additional phase parameter p = 0 and m = 3, p = 0, 1, 2, a quasi-periodic optical vortex lattice with high-order topological charge is obtained. Figure 1 They are the masks of the quasi-periodic high-order optical vortex lattice obtained under the corresponding parameters respectively.

[0013] The present invention utilizes the principle of computer-generated hologram to obtain an amplitude-modulated phase mask of a high-order quasi-periodic optical vortex lattice through computer coding, which can generate a quasi-periodic high-order optical vortex lattice with rich structures, effectively breaking the limitation that the topological charge value of the sub-vortex is equal to ±1, and improving the regulation freedom of the quasi-periodic optical vortex lattice. Therefore, it has important application value in the fields of multi-particle manipulation and high-capacity optical communication. Embodiment

[0014] Taking a mask with a size of 1024×1024 as an example, a mask of a quasi-periodic high-order optical vortex lattice is given for a laser with a wavelength of 532 nm. The number of wave vectors of this mask n = 5. Taking the topological charge value m = 1, the additional phase parameter p = 0 and m = 3, p = 0, 1, 2 as examples, the mask of the quasi-periodic high-order optical vortex lattice is finally obtained according to the mask transmittance function in the specific implementation manner. Figure 1This is the quasi-periodic high-order optical vortex lattice mask obtained under different parameters used in the embodiments. This mask of the quasi-periodic high-order optical vortex lattice can be realized by a spatial light modulator. Taking the PLUTO-VIS-061 type phase spatial light modulator of Holoeye Company in Germany as an example, its pixel size is 8μm, the fill factor is 93%, and the resolution is 1920pixel×1080pixel. A continuous wave solid laser with a wavelength of 532nm and a power of 50mW is used in the experiment.

[0015] Figure 2 As shown, this is the quasi-periodic high-order optical vortex lattice generated in the embodiments. It can be seen from the figure that we have obtained the quasi-periodic high-order optical vortex lattice, and the different quasi-periodic spatial structure distributions in the experiment are clearly distinguishable, and the change of the lattice sub-vortex dark core with the increase of the topological charge is clearly distinguishable.

[0016] To sum up, the present invention proposes a specific design scheme and implementation scheme for the mask of the quasi-periodic high-order optical vortex lattice. Taking the number of wave vectors n = 5, the topological charge value m = 1, the additional phase parameter p = 0 and m = 3, p = 0, 1, 2 as examples, a technical implementation route for the mask of the quasi-periodic high-order optical vortex lattice is proposed for a laser with a working wavelength of 532nm.

[0017] The parts not described in detail in this embodiment are prior art.

[0018] The mask for generating the quasi-periodic high-order optical vortex lattice described above only represents a specific implementation manner of the present invention, and should not be construed as a limitation on the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the basic idea of the present invention, several deformations and improvements can be made to the specific implementation details proposed in this patent, and these all belong to the protection scope of the present invention.

Claims

1. A design method for a mask of a quasi-periodic high-order optical vortex lattice, characterized in that: The steps are as follows: S1. Obtain the electric field expression of the optical vortex lattice: where A is the amplitude, j is the indicator variable, n is the number of wave vectors, (x, y) are the rectangular coordinates, k x,j and k y,j are the components of the wave vector along the x-axis and y-axis, and θ j represents the initial additional phase of the wave; S2. Obtain the electric field expression of the optical vortex lattice with high-order topological charges: where m is an integer parameter representing the topological charge; S3. Based on the above, combining the amplitude, phase of the quasi-periodic high-order optical vortex lattice and a blazed grating, obtain the complex transmittance function of the mask of the quasi-periodic high-order optical vortex lattice, and its expression is: t = |A(η, ξ)| exp[j(angle(E(x, y)) + P0)] where angle() is the phase extraction function, and the mask described by this complex transmittance function is the mask of the quasi-periodic high-order optical vortex lattice.

2. A method for designing a mask of a quasi-periodic high-order optical vortex lattice according to claim 1, characterized in that: In step S1, θ j = p(2π / n)(j - 1), where p is a non - negative integer starting from 0, which controls the phase difference between adjacent waves in combination with 2π / n.

3. A method for designing a mask for a quasi-periodic high-order optical vortex lattice according to claim 2, characterized in that: By adjusting the number of wave vectors n and the additional phase-related parameter p, quasi-periodic optical vortex lattices with different structures are obtained.

4. A method for designing a mask of a quasi-periodic high-order optical vortex lattice according to claim 1, characterized in that: In step S3, the phase expression of the blazed grating is P0 = 2πx / d, where d is the period of the blazed grating.

5. A method for generating a quasi-periodic high-order optical vortex lattice using a mask plate prepared by the design method according to any one of claims 1-4, characterized in that: By irradiating a parallel beam generated by a continuous-wave solid-state laser on a spatial light modulator loaded with a mask of a quasi-periodic high-order optical vortex lattice, and simultaneously adjusting the number of wave vectors n and the additional phase-related parameter p, quasi-periodic optical vortex lattices with different structures can be obtained.

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