A method for generating a power-exponential phase accelerated ring optical soliton lattice

Abstract

A method for generating power-exponential phase accelerated ring optical skyrmion textures, two perfect vortex modes are selected as spatial modes to be coherently superimposed, and their technical parameters are determined respectively. The traditional linear azimuthal phase is replaced by a power-exponential azimuthal phase to obtain two perfect vortex beams modulated by the power-exponential azimuthal phase, and adjusted to right and left circularly polarized modes. According to the relative phase γ, the two beams are coherently superimposed. By setting the power-exponential phase order, the azimuthal evolution of the ring optical skyrmion texture is changed from a uniform linear process to a nonlinear accelerated process. The normalized Stokes vector field is used, and the generated ring optical skyrmion texture is characterized according to the skyrmion number and the azimuthal polarization gradient. This method uses power-exponential phase, and coherently superimposes two perfect vortex beams modulated by the power-exponential azimuthal phase after giving them orthogonal circular polarization, thereby generating ring optical skyrmions with power-exponential accelerated azimuthal polarization texture evolution while keeping the ring intensity distribution unchanged.

Description

Technical Field

[0001] This invention belongs to the field of structured light field, polarization topology and optical manipulation technology, specifically a method for generating ring optical skyrmion textures using power-law phase modulation. Background Technology

[0002] Optical skyrmions are a class of topologically structured optical fields composed of spatially varying polarization states. Their polarization texture is typically described using a normalized Stokes vector field, and their topological properties are characterized by skyrmion numbers. Due to their stable topological structure, tunable polarization distribution, and rich vector optical field degrees of freedom, optical skyrmions exhibit significant application value in vector imaging, precision sensing, optical micromanipulation, and topological photonics. Ring-shaped optical skyrmions further confine the polarization topology to a ring-shaped intensity distribution region, providing clear boundaries for the optical field's interaction region and facilitating the generation of optical skyrmion textures with higher topological numbers.

[0003] In recent years, researchers have conducted extensive research on the generation and manipulation of optical skyrmions. Du et al. [Nat. Phys. 15, 650-654 (2019)] reported deep subwavelength features of photonic skyrmions carrying orbital angular momentum in confined electromagnetic fields, but this work mainly focused on local topological structures in confined electromagnetic fields, not on the intensity-invariant manipulation of free-space ring optical skyrmion textures; Shen et al. [ACS Photonics 9, 296-303 (2022)] proposed tunable Néel-type, Bloch-type, and Anti-type optical skyrmion texture generation methods, but their polarization textures mainly evolve uniformly along the azimuth direction, failing to achieve non-uniform enhancement of local polarization gradients; Wang et al. [Appl. Phys. Lett. 126, 201103 (2025)] realized ring optical skyrmions with high topological numbers, and Zeng et al. [Laser Photonics Rev. 19, e00732]

[2025] Further achieved the manipulation of ultra-high-order optical skyrmions, but the above methods mainly focus on topology number enhancement and ring structure construction, failing to independently control the azimuth texture evolution rate while maintaining the ring intensity geometry. Shen et al. [Opt. Express 27, 24642 ​​(2019)] proposed a method for generating and propagating power-law phase vortex beams, and Yuan et al. [Optica 12, 853-859 (2025)] proved that polarization gradient light fields can be used to construct three-dimensional optical manipulation force distributions. However, these techniques have not yet been combined with the polarization topology construction of ring optical skyrmions. The above optical skyrmion generation techniques are limited by the single azimuth evolution mode, the basically fixed local polarization gradient distribution, and the coupling of intensity geometry and polarization texture control, and cannot construct ring optical skyrmion textures with power-law accelerated evolution in the azimuth direction while keeping the ring intensity distribution unchanged.

[0004] In summary, there is currently a lack of a method for generating annular optical skyrmion textures that can produce exponentially accelerated evolution of the annular optical skyrmion texture along the azimuth direction while maintaining the annular intensity distribution unchanged, and simultaneously generate spatially non-uniformly enhanced azimuth polarization gradients. Summary of the Invention

[0005] The purpose of this invention is to provide a method for generating ring optical skyrmions with power-law phase acceleration. This method replaces the traditional linear azimuth phase with a power-law phase, and coherently superimposes two perfectly vortex beams modulated by power-law phases with orthogonal circular polarization, thereby generating ring optical skyrmions with power-law accelerated evolution of azimuth polarization texture while maintaining the ring intensity distribution unchanged.

[0006] The technical solution adopted in this invention is: a method for generating ring optical skyrmion textures with power-law phase acceleration, the steps of which are as follows: S1. First, select two perfect vortex modes as spatial modes to be coherently superimposed, and determine the amplitude A0, ring radius R, ring thickness T, topological charge l, power exponent phase order n, and relative phase γ between the two modes respectively. S2. Then, the traditional linear azimuth phase is replaced with a power-law azimuth phase to obtain the first power-law phase modulated perfect vortex beam and the second power-law phase modulated perfect vortex beam (PEPPV), respectively, whose expressions are: (1) In the formula, r and θ are the radial coordinate and azimuth angle in polar coordinates, respectively, A0 is the beam amplitude, R is the ring radius, T is the ring thickness, l is the topological charge, n is the power-law phase order, and rem(lθ,2π) is the remainder function used to limit the azimuth phase to the range of 0 to 2π. When n=1, the above formula degenerates into a conventional linear spiral phase; when n>1, the azimuth phase changes exponentially with θ. S3. Convert the first power-law phase-modulated perfect vortex beam into a right circular polarization mode, and convert the second power-law phase-modulated perfect vortex beam into a left circular polarization mode. Then, coherently superimpose them according to their relative phase γ to obtain the target annular optical skyrmion texture light field, the expression of which is: (2) In the formula, and These represent the right circular polarization mode and the left circular polarization mode, respectively. PEPPV1 and PEPPV2 represent the first and second power-law phase-modulated perfect vortex beams, respectively. γ is the adjustable relative phase between the two modes. The topological charge difference Δl = l2 - l1 between the two modes is used to adjust the skyrmion number, the relative phase γ is used to adjust the skyrmion texture type, and the power-law phase order n is used to adjust the evolution rate of the texture along the azimuth direction. S4. By setting the power-law phase order n, the orientation evolution of the ring optical skyrmion texture is changed from a uniform linear process to a nonlinear accelerated process, and its orientation function can be expressed as: (3) In the formula, Used to characterize the azimuth distribution of the transverse field component. When n > 1, As θ increases exponentially, the polarization texture completes rotation more quickly in certain azimuth ranges, forming an exponentially accelerated ring-shaped optical skyrmion texture. S5. The normalized Stokes vector field is calculated using Stokes parameters, and the generated annular optical skyrmion texture is characterized based on the skyrmion number and azimuth polarization gradient, where the skyrmion number can be expressed as: (4) In the formula, N sk Describe the Sgarming subnumber, Let σ be the normalized Stokes vector field, and σ be the integration region.

[0007] In this scheme, the azimuth polarization gradient mentioned in step S5 can be characterized by the optical field amplitude, ellipticity, and polarization ellipse orientation angle, and its expression is: (5) In the formula, The polarization gradient is represented by u, the amplitude of the optical field is represented by χ, and the ellipticity is represented by χ. Indicates the orientation angle of the polarization ellipse. express The partial derivative with respect to the azimuth angle θ. Power-law accelerated textures can create spatially non-uniform and enhanced azimuth polarization gradients.

[0008] In this scheme, the principle of computational holography is adopted. By dividing the spatial light modulator into two independent display areas, a first digital hologram and a second digital hologram are generated respectively, which are used to generate a first beam and a second beam of power-law phase modulation perfect vortex beams.

[0009] In this scheme, the first digital hologram and the second digital hologram are loaded onto two independent regions of the spatial light modulator. The first and second power-phase modulated perfect vortex beams are reproduced by first-order diffraction, and then the target annular optical skyrmion texture light field is generated by orthogonal circular polarization coherent superposition.

[0010] In this scheme, the power-law phase-accelerated annular optical skyrmion texture is any one of Néel type, Bloch type or Anti type, and the switching of the three texture types is achieved by adjusting the relative phase γ between the two beam modes.

[0011] Technical effects of the present invention: This invention proposes a method for controlling ring-shaped optical skyrmion textures using power-law phase modulation. Compared to traditional linear azimuth phase-modulated ring-shaped skyrmion textures, this invention independently adjusts the evolution rate of the azimuth polarization texture by controlling the power-law phase order n, enabling the texture to undergo power-law accelerated evolution while maintaining the ring intensity distribution. The skyrmion number is adjusted by the topological charge difference Δl, and the Néel-type, Bloch-type, and Anti-type power-law accelerated texture types are adjusted by the relative phase γ, achieving multi-parameter programmable control of the ring-shaped optical skyrmion texture. This method can further generate spatially non-uniformly enhanced azimuth polarization gradients, providing a tunable structured optical field for vector optical tweezers and topological photonic coding. Attached Figure Description

[0012] Figure 1 This presents the vector calculation results of three types of power-exponentially accelerated annular optical skyrmion textures generated under the condition of power-exponential phase order n=2. Among them, (a) to (c) are the three-dimensional normalized Stokes vector distributions of Néel-type, Bloch-type, and Anti-type power-exponentially accelerated textures, respectively, and (d) to (f) are the corresponding two-dimensional plane normalized light intensity distribution and in-plane Stokes vector projection distribution, respectively; the calculation parameters are T1=T2=0.4mm, R1=1.6mm, and R2=0.65R1.

[0013] Figure 2 This is an experimental polarization analysis result of the n=2 power-law accelerated ring optical skyrmion texture in an embodiment of the present invention. Among them, (a) is the total experimental light intensity distribution collected under no polarization condition, and (b) to (e) are the experimental intensity distributions obtained when the transmission direction of the polarizer is 0°, 45°, 90° and 135°, respectively; the gray bars on the right represent the normalized light intensity.

[0014] Figure 3 This invention relates to a dual-region digital hologram for generating two power-law phase-modulated perfect vortex beams. The left and right display areas are used to encode the complex amplitude information of the first and second power-law phase-modulated perfect vortex beams, respectively. After the digital hologram is loaded onto a spatial light modulator, the corresponding spatial mode is reproduced by first-order diffraction, and the target annular optical skyrmion texture light field is generated by orthogonal circular polarization coherent superposition. Detailed Implementation

[0015] This invention utilizes the principles of computational holography and polarization coherent superposition to obtain a digital hologram of two perfectly vortex beams with power-law phase modulation through computer encoding. The two beams are then converted into orthogonal circularly polarized states and coherently superimposed to obtain a ring-shaped optical skyrmion texture light field with an unchanged ring intensity distribution and exponentially accelerated evolution of polarization texture along the azimuth direction.

[0016] The following is in conjunction with the appendix Figures 1 to 3 The present invention is further illustrated by the embodiments: A method for generating ring-shaped optical skyrmion textures using power-law phase acceleration is proposed, comprising the following steps: First, two perfectly vortex beams with power-law phase modulation are constructed. The radial amplitude term of each beam depends only on r, therefore, the light intensity in the initial plane is I(r,θ)=|A(r)|. 2 It is independent of the power-law phase. Therefore, the power-law phase mainly changes the azimuth evolution of the polarization texture without altering the annular intensity distribution. Then, a perfect vortex beam modulated by the first power-law phase is assigned to the right circular polarization state, and a perfect vortex beam modulated by the second power-law phase is assigned to the left circular polarization state, and these are coherently superimposed. By adjusting the difference Δl between l1 and l2, annular optical skyrmion textures with different skyrmion numbers can be obtained; by adjusting γ, different texture types can be obtained; and by adjusting n, continuous control from conventional linear evolution to power-law accelerated evolution can be achieved.

[0017] To facilitate the generation of the two beams mentioned above using a spatial light modulator, the spatial light modulator is divided into two independent display areas, and a first digital hologram and a second digital hologram are generated respectively. For the j-th beam, j=1,2, the target complex amplitude E is first obtained according to formula (1). j (x,y)=A j (x,y)exp[iΦ j [x,y)], where A j (x,y) represents the annular amplitude term, Φ j (x,y)=2π[rem(l j θ,2π) / (2π)] n The power-law azimuth phase term is then used; the target complex amplitude and the blazed grating phase P are then combined. j (x,y)=2π(xcosβ j +ysinβ j Encode using ) / d, where β j Let H represent the direction angle of the j-th blazed grating, and d represent the blazed grating period, to obtain a digital hologram for display in a spatial light modulator. For a phase-type spatial light modulator, H can be taken as... j (x,y)=mod[Φ j (x,y)+P j [x,y),2π] and map it to a grayscale image; for cases where both amplitude and phase need to be encoded simultaneously, a complex amplitude encoding method can be used to encode A. j (x,y) and Φ j (x,y) are written together into H j(x,y). The loaded digital hologram reproduces the corresponding power-law phase-modulated perfect vortex beam in first-order diffraction, and then the orthogonal circularly polarized coherent superposition is performed by formula (2) to obtain the target annular optical skyrmion texture light field.

[0018] When measuring the Stokes parameters of the obtained optical field, a combination of a quarter-wave plate and a linear polarizer can be used to measure S0, S1, S2, and S3. The Stokes vector field can be obtained by normalizing S1, S2, and S3.

[0019] Example In this embodiment, a continuous-wave solid-state laser with a wavelength of 532nm and adjustable power from 0 to 1.5W is selected. The laser light is filtered through a pinhole, expanded, collimated, and polarized by a linear polarizer to form horizontally linearly polarized parallel light, which is then incident on a reflective spatial light modulator. The spatial light modulator can be a reflective spatial light modulator with a resolution of 4096×2160 and a pixel size of 3.8μm×3.8μm. Digital holograms encoding two perfectly vortex beams with exponential phase modulation are input into two independent regions of the spatial light modulator via a computer.

[0020] In this embodiment, the parameters of the perfect vortex beam with power-law phase modulation can be set as T1=T2=0.4mm, R1=1.6mm, R2=0.65R1, and n=2. Setting l1=0, l2=1, and γ=0 generates a Néel-type power-law accelerated annular optical skyrmion texture; maintaining l1=0, l2=1, and setting γ=π / 2 generates a Bloch-type power-law accelerated annular optical skyrmion texture; setting l1=1, l2=0, and γ=0 generates an Anti-type power-law accelerated annular optical skyrmion texture. Compared to the conventional annular optical skyrmion texture with n=1, the texture corresponding to n=2 exhibits faster azimuth polarization evolution within the same observation window, and the annular intensity distribution remains stable.

[0021] like Figure 1 As shown, under the condition of n=2, the Néel-type, Bloch-type, and Anti-type power-exponentially accelerated textures all exhibit non-uniform orientation evolution within the annular region; their three-dimensional normalized Stokes vector distribution corresponds to the two-dimensional plane Stokes vector projection, indicating that power-exponential phase modulation can change the local orientation gradient of the polarization texture while maintaining the annular intensity structure.

[0022] like Figure 2 As shown, when performing unanalyzed and 0°, 45°, 90°, and 135° polarization measurements on the n=2 texture, an annular experimental intensity distribution that varies with the polarization angle can be obtained, thereby verifying the spatial polarization texture formed by the coherent superposition of orthogonal circular polarization.

[0023] Figure 3 The image shown is a dual-region digital hologram used in this embodiment to generate two power-law phase-modulated perfect vortex beams. This digital hologram includes two independent coded regions, corresponding to the first and second power-law phase-modulated perfect vortex beams, respectively; each coded region is holographically encoded according to the annular amplitude term, power-law azimuth phase term, and blazed grating phase of the target complex amplitude. Figure 3 After the digital hologram shown is loaded into the spatial light modulator, two spatial modes to be coherently superimposed can be obtained by selecting first-order diffraction light. Then, the two spatial modes are converted into orthogonal circular polarization states and coherently superimposed by the polarization conversion and coherent superposition module, thereby forming the target annular optical skyrmion texture light field.

[0024] In summary, this invention proposes a power-law phase-accelerated method for generating ring-shaped optical skyrmion textures. Taking Néel-type, Bloch-type, and Anti-type power-law accelerated ring-shaped skyrmion textures under n=2 conditions as examples, the Stokes vector calculation results, experimental polarization analysis results, and specific holographic implementation routes are presented. This method controls the azimuth texture evolution rate by adjusting the power-law phase order, the skyrmion number by adjusting the topological charge difference, and the texture type by adjusting the relative phase, thus achieving accelerated control of optical skyrmion textures under the condition of constant ring intensity distribution.

[0025] The above-described method for generating ring optical skyrmion textures using power-law phase acceleration is merely one specific embodiment of the present invention and should not be construed as limiting the scope of protection of the present invention. It should be noted that those skilled in the art can make various modifications and improvements to the specific implementation details proposed in this patent without departing from the basic idea of ​​the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for generating ring-shaped optical skyrmion textures using power-law phase acceleration, characterized in that, Includes the following steps: S1. Select two perfect vortex modes as the spatial modes to be coherently superimposed, and determine the beam amplitudes of the first and second modes respectively. A 0. Ring radius R Ring thickness T Topological load l power exponent phase order n and the relative phase between the two beam modes γ ; S2. Replacing the traditional linear azimuth phase with a power-law azimuth phase yields the first and second perfect vortex beams modulated by the power-law phase, respectively. Their expressions are as follows: In the formula, r and θ These represent the radial coordinate and azimuth angle in polar coordinates, respectively, rem( lθ (2π) is the remainder function; S3. Convert the first power-law phase-modulated perfect vortex beam into a right circular polarization mode, and convert the second power-law phase-modulated perfect vortex beam into a left circular polarization mode, according to their relative phases. γ Coherent superposition yields the target annular optical skyrmion texture light field, expressed as: In the formula, and These represent the right circular polarization mode and the left circular polarization mode, respectively. PEPPV1 and PEPPV2 represent the first and second power-law phase-modulated perfect vortex beams, respectively. γ The adjustable relative phase between the two beam modes; S4. By setting the phase order of the power exponent n This transforms the orientation evolution of the ring-shaped optical skyrmion texture from a uniform linear process to a nonlinear accelerated process, and its orientation function is expressed as: In the formula, Used to characterize the azimuth distribution of the transverse field component, when n When >1, Follow θ It exhibits power-law growth, forming a power-law accelerated ring-shaped optical skyrmion texture; S5. The normalized Stokes vector field is calculated using Stokes parameters, and the generated annular optical skyrmion texture is characterized based on the skyrmion number and azimuth polarization gradient, where the skyrmion number can be expressed as: In the formula, N sk Describe the Sgarming subnumber, For the normalized Stokes vector field, σ This is the integration region.

2. The method for generating ring optical skyrmion textures with power-law phase acceleration according to claim 1, characterized in that, In step S2, when the power exponent phase order n When = 1, the power-law azimuth phase degenerates into a regular linear spiral phase; when the power-law phase order... n When >1, the azimuth phase varies with the azimuth angle. θ It exhibits a power-law variation.

3. The method for generating ring optical skyrmion textures with power-law phase acceleration according to claim 1, characterized in that, In step S3, the topological load difference Δ between the two beam modes l = l 2- l 1 is used to adjust the skyrmion number and relative phase. γ Used to adjust the skymintz texture type, power-law phase order. n Used to adjust the rate of texture evolution along the orientation direction.

4. The method for generating ring optical skyrmion textures with power-law phase acceleration according to claim 1, characterized in that, In step S5, the azimuth polarization gradient can be characterized by the optical field amplitude, ellipticity, and polarization ellipse orientation angle, and its expression is: In the formula, Indicates the azimuth polarization gradient. u Indicates the amplitude of the light field. χ Indicates the elliptic declination angle. Indicates the orientation angle of the polarization ellipse. express opposite angle θ The partial derivatives of .

5. The method for generating ring optical skyrmion textures with power-law phase acceleration according to claim 1, characterized in that, Using the principle of computational holography, the spatial light modulator is divided into two independent display areas to generate a first digital hologram and a second digital hologram, which are used to generate a first and a second power-law phase modulated perfect vortex beam.

6. The method for generating ring optical skyrmion textures with power-law phase acceleration according to claim 1, characterized in that, The first and second digital holograms are loaded into two independent regions of the spatial light modulator. The first and second power-phase modulated perfect vortex beams are reproduced by first-order diffraction, and then the target annular optical skyrmion texture light field is generated by orthogonal circular polarization coherent superposition.

7. The method for generating ring optical skyrmion textures with power-law phase acceleration according to claim 1, characterized in that, The power-law phase-accelerated annular optical skyrmion texture is any one of Néel, Bloch, or Anti type, and is achieved by adjusting the relative phase between the two beam modes. γ Implement switching between three texture types.

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