A method for realizing a non-diffracting self-focusing light beam based on vortex-anti-vortex interaction mechanism

Abstract

The present application relates to the technical field of light field regulation, and is a method for realizing a non-diffracting self-focusing light beam based on a vortex-anti-vortex interaction mechanism, comprising the following steps: amplifying and collimating a laser beam; constructing a vortex-anti-vortex circular array structure light field, deriving an analytical expression of a target light field based on a paraxial wave equation and a Fourier domain, encoding the amplitude and phase of the target light field to generate a hologram; loading a phase diagram on a spatial light modulator to modulate the laser beam and generate the target light field; sequentially passing the target light field through a beam splitter, a mirror, a lens, and then using an aperture to screen a vortex diffraction light beam; placing a camera at a focal length of the lens, moving the position of the camera multiple times and at equal intervals, and recording the evolution of the circular array structure at different positions. The non-diffracting self-focusing light beam of the present application can keep the spot size substantially unchanged within two Rayleigh distances, without the need for a complex preparation process.

Description

Technical Field

[0001] This invention relates to the field of light field manipulation technology, and more specifically to a method for achieving a diffraction-free self-focusing beam based on a vortex-antivortex interaction mechanism. Background Technology

[0002] Structured light, due to its unique properties, has been extensively studied. Diffraction-free self-focusing beams, with their advantages of maintaining beam shape over long distances and highly focused energy, have been applied in high-end manufacturing, precision medicine, and optical communication since their discovery. Traditional optical methods for generating diffraction-free beams mainly rely on precise optical components such as axial pyramids or annular slits and lenses. However, these methods suffer from fixed beam size, inflexible adjustment, and low energy utilization efficiency, severely limiting their application scenarios. Therefore, finding simpler and more efficient generation methods has become an urgent need for scientific research and industrial production.

[0003] In recent years, methods for generating diffraction-free self-focusing beams have become increasingly diverse, including spatial light modulators to generate computational holograms, diffractive optical elements with micro / nano structures such as metasurfaces, or digital lasers. Different generation methods are adopted for different application scenarios, which is of great significance for the generation and application of special structured light.

[0004] The fundamental principle of generating a diffraction-free self-focusing beam lies in the precise control of the phase of the light wave, enabling it to resist diffraction and focus energy during propagation. Its control methods are divided into passive and active control. Passive control involves modifying a regular laser using external devices (such as a spatial light modulator), while active control generates the beam directly from within the laser. Both methods suffer from problems such as complex design of specific functions and high manufacturing costs.

[0005] Ordinary light beams (such as Gaussian beams) propagating in free space or a medium will undergo diffraction and diffusion. That is, as the propagation distance increases, the lateral size of the beam continuously expands, leading to a decrease in energy density and degradation of spatial structure. This diffraction has a significant adverse effect on long-distance laser transmission, precision laser processing, and high-resolution optical imaging. How to achieve a stable light field distribution with a spatial structure over long distances has always been one of the important problems in modern optics. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a method for generating a diffraction-free self-focusing beam based on a vortex-antivortex interaction mechanism. The method utilizes the vortex-antivortex interaction mechanism to generate a diffraction-free self-focusing beam, which can maintain a basically unchanged spot size within two Rayleigh distances without requiring complex fabrication processes.

[0007] On one hand, this invention provides a method for achieving a diffraction-free self-focusing beam based on a vortex-antivortex interaction mechanism, comprising the following steps:

[0008] The laser beam is amplified and collimated so that it completely covers the liquid crystal surface of the spatial light modulator.

[0009] A vortex-antivortex circular array structured light field is constructed, and the analytical expression of the target light field is derived based on the paraxial wave equation and the Fourier domain. The amplitude and phase information of the target light field are encoded by phase modulation technology to generate the required hologram.

[0010] A phase diagram is loaded onto the spatial light modulator to modulate the laser beam and generate the target light field. The target light field is then passed through a beam splitter, a mirror, and a lens in sequence. The lens performs a Fourier transform on the target light field, and an aperture is used to filter the vortex diffraction beam to block other diffraction order beams.

[0011] The camera is positioned at one focal length of the lens, and its position is moved multiple times at equal intervals to record the evolution of the vortex-antivortex circular array structure at different positions, thereby measuring the evolution of the vortex-antivortex circular array.

[0012] On the other hand, embodiments of the present invention also provide a system for generating a diffraction-free self-focusing beam based on a vortex-antivortex interaction mechanism, implemented according to the above-described method for generating a diffraction-free self-focusing beam. The system includes a helium-neon laser, a beam expander, a beam splitter, a mirror, a lens, an aperture, a camera, and a spatial light modulator connected in sequence on the optical path, as well as the beam splitter.

[0013] Compared with the prior art, the technical effects achieved by the present invention include:

[0014] 1. This invention differs from previous methods for generating diffraction-free self-focusing beams. It utilizes the interaction mechanism between vortices and antivortices in a structured light field to induce the generation of diffraction-free self-focusing beams. Specifically, by designing an initial light field, namely a centrally symmetric circular array of vortices, the vortices and antivortices undergo orbit-orbit interactions due to their different topological charge values ​​as they propagate in free space. This causes them to attract and annihilate each other, and the beam type changes, ultimately generating a diffraction-free self-focusing beam in the central region of the light field. This is a completely new generation method.

[0015] 2. The diffraction-free self-focusing beam generated by this invention can maintain a basically unchanged spot size within two Rayleigh distances.

[0016] 3. Compared with existing technologies such as axial pyramids, lens combinations, metasurfaces, and resonant cavities, this invention is relatively simple and does not require complex fabrication processes. The generated beam has good non-diffraction properties and has great application value and significance in fields such as biomedical microscopy systems, optical micromanipulation, and adaptive optics. Attached Figure Description

[0017] To more clearly illustrate the embodiments or technical solutions of the present invention, the accompanying drawings used in the embodiments or technical solutions will be briefly described below. Obviously, the drawings described below are only some embodiments of the present invention, and not all embodiments. Those skilled in the art can obtain other technical solutions and drawings based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the system structure for achieving a diffraction-free self-focusing beam based on the vortex-antivortex interaction mechanism in an embodiment of the present invention;

[0019] Figure 2 This is a schematic diagram of the initial structure of the vortex-antivortex circular array in an embodiment of the present invention, wherein (a) the circular array of the sub-figure has a radius of 250 μm and has 3 pairs of vortex dipoles; (b) the circular array of the sub-figure has a radius of 280 μm and has 5 pairs of vortex dipoles; and (c) the circular array of the sub-figure has a radius of 400 μm and has 8 pairs of vortex dipoles.

[0020] Figure 3 These are spot images of the non-diffraction self-focusing beam at different transmission distances in embodiments of the present invention, wherein (a)~(c) represent spot images of 3 pairs of vortex dipoles at z = 100, 500, and 800 mm, respectively; (d)~(f) represent spot images of 5 pairs of vortex dipoles at z = 100, 500, and 800 mm, respectively; and (g)~(i) represent spot images of 8 pairs of vortex dipoles at z = 100, 500, and 800 mm, respectively.

[0021] Figure 4 This is a schematic diagram of the yz cross-sectional distribution of the light intensity of the non-diffraction self-focusing beam during transmission, the normalized light intensity along the central axis (y=0), and the corresponding change in the spot size in the non-diffraction interval, in an embodiment of the present invention. (a)~(c) correspond to the yz cross-sectional distribution of the beam intensity when n = 3, 5, and 8, respectively; (d)~(f) correspond to the normalized light intensity along the central axis (y = 0) in (a)~(c), respectively, and the insets of each represent the changing trend of the central spot size in the non-diffraction interval. Detailed Implementation

[0022] Vortex light, as an important branch of structured light field research in recent years, is characterized by a spiral phase structure in its light field, which is usually expressed as a phase factor. ,in For topological load number, The azimuth angle is given. Unlike traditional circularly polarized light that only carries spin angular momentum, vortex light carries orbital angular momentum (OAM), providing new optical degrees of freedom and important means for optical field manipulation and information encoding. Vortex light carrying different orbital angular momentum (OAM) interacts during free space propagation, resulting in many interesting phenomena or effects, including mutual attraction and annihilation between vortices, the OAM Hall effect, and stable propagation of vortex arrays. This invention, through the study of structured optical fields such as optical vortex arrays, has discovered an interesting new effect during their free space propagation: the generation of diffraction-free self-focusing beams can be induced under the vortex-antivortex interaction mechanism.

[0023] In this invention, a Gaussian beam emitted from a helium-neon laser is modulated by specific devices, such as a pure phase spatial modulator (SLM) or a digital micromirror array (DMD), to generate a structured beam with Gaussian light as the background and embedded vortex-antivortex elements. Due to the different topological charge values ​​of the vortices and antivortices, the vortex singularities interact during free-space propagation, attracting and annihilating each other, subsequently regenerating a nearly circular light spot in the central region. During free-space propagation, this spot maintains a relatively constant size over a certain distance while exhibiting a maximum intensity variation; that is, the circular light spot generated in the central region possesses the characteristic of non-diffraction self-focusing. This invention, based on the interaction mechanism between vortices (topological charge of +1) and antivortices (topological charge of -1), cleverly designs the initial structure of the vortex array, spontaneously generating a non-diffraction self-focusing beam during the propagation stage of the vortex beam. This is a novel effect under vortex orbit-orbit interaction and a new mechanism for generating non-diffraction self-focusing beams.

[0024] To enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be described in detail below with reference to the embodiments and accompanying drawings, but the implementation of the present invention is not limited thereto.

[0025] Example

[0026] This embodiment proposes a system for generating a diffraction-free self-focusing beam based on a vortex-antivortex interaction mechanism. (See also...) Figure 1 It includes a helium-neon laser (Laser), beam expander (BE), beam splitter (BS), mirror (Mirror), lens (500 mm focal length), aperture (Iris), camera (CCD), and spatial light modulator (SLM) connected in sequence along the optical path.

[0027] This embodiment also proposes a method for generating a diffraction-free self-focusing beam based on a vortex-antivortex interaction mechanism, including the following steps:

[0028] The laser output from the helium-neon laser is amplified and collimated by a beam expander so that the output laser completely covers the liquid crystal surface of the spatial light modulator. At this time, the incident beam is approximately a plane wave.

[0029] A vortex-antivortex circular array structured light field was constructed, and the analytical expression of the target light field was derived based on the paraxial wave equation and the Fourier domain. The amplitude and phase information of the target light field were encoded into the computer through phase modulation technology to generate the required hologram.

[0030] A phase diagram is loaded onto the spatial light modulator to modulate the laser beam and generate the target light field. The target light field is then passed through a beam splitter, a mirror, and a lens in sequence. The lens performs a Fourier transform on the target light field, and an aperture is used to filter the required +1 order diffraction beam, i.e., the vortex diffraction beam, to block other diffraction order beams.

[0031] Position the camera's CCD at one focal length of the lens; this position is considered... The position of the camera CCD is moved multiple times at equal intervals to record the evolution of the vortex-antivortex circular array structure at different positions, thereby measuring the evolution of the vortex-antivortex circular array and characterizing its diffraction-free and self-focusing properties.

[0032] In this embodiment, the target light field is a structured light field with a Gaussian envelope as the background and embedded with several interacting vortices and antivortices. The vortices can be represented by complex polynomials. This means that antivortices can be expressed using conjugate complex polynomials. This means that the structured light field can be expressed as the product of its Gaussian envelope, i.e.:

[0033] ;

[0034] in, , representing the embedding in the structured light field A vortex; , representing the embedding in the structured light field An anti-vortex.

[0035] Structured light field Substituting into the paraxial Schrödinger wave equation: ;

[0036] The analytical solution of the structured light field was obtained. ;

[0037] in The envelope is Gaussian. Related to transmission distance, Represents Rayleigh distance; Let the radius of the Gaussian envelope waist be . Let be the radius of the circular array. λ is the wavelength.

[0038] ,and , It is an uncoupled term, representing the independent motion of the vortex in the light field;

[0039] ,and , All are polynomials related to z. It is a coupling term, representing the interaction between vortices and antivortices, which manifests as mutual attraction, annihilation, regeneration, and other behaviors.

[0040] In this embodiment, according to the polynomial and The root determines the position coordinates of the vortex and antivortex in the target light field. By pre-arranging the positions of the vortex and antivortex, a vortex array light field of arbitrary array structure can be realized. For the setting of a vortex-antivortex circular array, the general expression for the vortex coordinates is: The expression for the anti-vortex coordinates is: ,in Let be the radius of the circular array. , It is the logarithm of the dipole, meaning the target light field exists. A vortex and An anti-vortex.

[0041] The vortex-antivortex circular array optical field constructed in this embodiment has an equal number of vortices and antivortices with opposite polarities. The vortices and antivortices are arranged alternately and at equal intervals and angles on a circle centered at the origin. Figure 2 As shown. In Figure 2 In the diagram (a), the circular array has a radius of 250 μm, with three pairs of vortex dipoles (three positive and three negative, for a total of six vortices) arranged alternately at equal angles on the circumference, and the vortices and anti-vortices are spaced apart. Subgraph (b) has a circular array radius of 280 μm, with 5 pairs of vortex dipoles (5 positive and 5 negative, a total of 10 vortices) alternating at equal angles on the circumference, and vortices and antivortices spaced apart. The circular array in sub-figure (c) has a radius of 400 μm, with 8 pairs of vortex dipoles (8 positive and 8 negative, a total of 16 vortices) alternating at equal angles on the circumference, and vortices and anti-vortices spaced apart. .

[0042] Furthermore, this embodiment, through a holographic encoding method, can generate arbitrary vortex array structures, including the target light field. The process of encoding the target light field to generate the desired hologram in this embodiment includes:

[0043] First, the structured light field Rewrite the Fourier spectrum: ,in Represents the rewritten Fourier spectrum The amplitude, Represents the rewritten Fourier spectrum The phase.

[0044] Then, the rewritten Fourier spectrum The total phase and amplitude are encoded into the phase hologram:

[0045] ;

[0046] in, , ; Modulo operation is represented. , Indicates that the grating is in Periodicity in direction, in this embodiment Finally, the generated hologram is loaded to produce the target light field.

[0047] The partial spot pattern of the non-diffraction self-focusing beam generated in this embodiment is as follows: Figure 3 As shown, (a)~(c) represent the spot patterns of 3 pairs of vortex dipoles (n = 3) at z = 100, 500, and 800 mm, respectively; (d)~(f) represent the spot patterns of 5 pairs of vortex dipoles (n = 5) at z = 100, 500, and 800 mm, respectively; and (g)~(i) represent the spot patterns of 8 pairs of vortex dipoles (n = 8) at z = 100, 500, and 800 mm, respectively. The diffraction-free self-focusing effect induced by the optical vortex-antivortex interaction is as follows: Figure 4 As shown.

[0048] In summary, this invention proposes a method and system for generating a diffraction-free self-focusing beam based on a vortex-antivortex interaction mechanism. Utilizing the interaction between optical vortices and antivortices, the vortices and antivortices in the optical field approach and annihilate each other. Due to the conservation of overall angular momentum and its algebraic value of zero, the beam spot further evolves with increasing transmission distance, gradually inducing the formation of a diffraction-free self-focusing beam in the central region. This novel mechanism generates a diffraction-free self-focusing beam without the need for high-power lasers, nonlinear crystals, or other complex precision optical components. It relies solely on the interaction mechanism between vortices and antivortices within the structured optical field to induce its generation, and maintains a substantially unchanged central beam spot size at twice the Rayleigh distance. This method has significant practical value and is expected to be widely applied.

[0049] Obviously, the above-described embodiments are only some embodiments of the present invention, and not all embodiments. The present invention is not limited to the details of the above embodiments. Any appropriate changes or modifications made by those skilled in the art are considered to be within the scope of protection of the present invention.

Claims

1. A method for achieving diffraction-free self-focusing beams based on vortex-antivortex interaction mechanism, characterized in that, Includes the following steps: The laser beam is amplified and collimated so that it completely covers the liquid crystal surface of the spatial light modulator. A vortex-antivortex circular array structured optical field was constructed, and the analytical expression of the target optical field was derived based on the paraxial wave equation and the Fourier domain. Phase modulation technology is used to encode the amplitude and phase information of the target light field in order to generate the required hologram; A phase diagram is loaded onto the spatial light modulator to modulate the laser beam and generate the target light field. The target light field is then passed through a beam splitter, a mirror, and a lens in sequence. The lens performs a Fourier transform on the target light field, and an aperture is used to filter the vortex diffraction beam to block other diffraction order beams. The camera is positioned at one focal length of the lens, and its position is moved multiple times at equal intervals to record the evolution of the vortex-antivortex circular array structure at different positions, thereby measuring the evolution of the vortex-antivortex circular array.

2. The method for a non-diffraction self-focusing beam according to claim 1, characterized in that, The constructed vortex-antivortex circular array structured light field has an equal number of vortices and antivortices with opposite polarities. The vortices and antivortices are arranged alternately and at equal intervals and angles on a circle centered on the origin.

3. The method for a non-diffraction self-focusing beam according to claim 1, characterized in that, The target light field is a structured light field with a Gaussian envelope as the background, containing several interacting vortices and antivortices; the vortices are represented by complex polynomials. This indicates that the antivortex is represented by a conjugate complex polynomial. The structured light field is expressed as the product of its Gaussian envelope, i.e.: ； in, , representing the embedding in the structured light field A vortex; , representing the embedding in the structured light field An anti-vortex.

4. The method for a diffraction-free self-focusing beam according to claim 3, characterized in that, The analytical solution for the structured light field is: ; in The envelope is Gaussian. Related to transmission distance, Represents Rayleigh distance; Let the radius of the Gaussian envelope waist be . Let be the radius of the circular array. Wavelength; ,and , It is an uncoupled term, representing the independent motion of the vortex in the light field; ,and , All are polynomials related to z. It is a coupling term, representing the interaction between vortices and antivortices.

5. The method for a non-diffraction self-focusing beam according to claim 4, characterized in that, According to polynomials and The root determines the position coordinates of the vortex and antivortex in the target light field, and the positions of the vortex and antivortex are pre-arranged to realize the vortex array light field of arbitrary array structure.

6. The method for a diffraction-free self-focusing beam according to claim 5, characterized in that, For the setup of a vortex-antivortex circular array, the expression for the vortex coordinates is: The expression for anti-vortex coordinates is: , , It is the logarithm of the dipole.

7. The method for a diffraction-free self-focusing beam according to claim 3, characterized in that, The amplitude and phase information of the target light field are encoded to generate the desired hologram, including: Structured light field Rewrite the Fourier spectrum: ,in Represents the rewritten Fourier spectrum The amplitude, Represents the rewritten Fourier spectrum The phase; The rewritten Fourier spectrum The total phase and amplitude are encoded into the phase hologram: ； in, , ; Modulo operation is represented. , Indicates that the grating is in The periodicity in direction; finally, the generated hologram is loaded to produce the target light field.

8. A system for generating a diffraction-free self-focusing beam based on a vortex-antivortex interaction mechanism, implemented according to the method for generating a diffraction-free self-focusing beam according to any one of claims 1-7, characterized in that, The system includes a helium-neon laser, a beam expander, a beam splitter, a reflector, a lens, an aperture, a camera, and a spatial light modulator connected in sequence along the optical path, as well as the beam splitter.

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