Method and device for generating vortex light based on equidistant spiral rotational symmetry structure

Abstract

The application provides a vortex light generation method and device based on an equidistant spiral rotation symmetry structure, which can generate vortex light with a long distance and a non-diffraction characteristic, and the topological charge and non-diffraction distance of the generated vortex light can be regulated through structural parameters. The equidistant spiral rotation symmetry structure based on the application belongs to an amplitude type, and a channel is relatively flexible, which can be loaded and projected through material processing etching or a phase or amplitude type spatial light modulator. The rotation symmetry structure generates vortex light with a non-diffraction characteristic by inputting the rotation symmetry structure into an amplitude type spatial light modulator (SLM), and the transmittance function can be assumed as an amplitude binary function. Based on the technical scheme of the application, the effect of the non-diffraction vortex can be conveniently adjusted, a new method for generating vortex light with a non-diffraction characteristic is provided for a free space optical communication and a micro-particle control field, and has great application value.

Description

Technical Field

[0001] The present invention relates to the field of light field control technology, and in particular to a method and device for generating vortex light based on an equidistant spiral rotationally symmetrical structure. Background Art

[0002] Research on light field orbital angular momentum has largely focused on the generation and application of vortex light. Its quantized orbital angular momentum has been applied in numerous fields, such as particle manipulation, optical communications, optical imaging, and optical information storage. Its broad application potential has made it a major research hotspot in the field of light field manipulation.

[0003] Since Durnin [Phys. Rev. Lett. 58, 1499–1501 (1987)] first experimentally realized Bessel beams, a wealth of research results on non-diffracting beams has emerged. Essentially, the mechanism behind non-diffracting beams is a series of functions with non-diffracting properties, such as Bessel functions and Airy functions, special solutions of the paraxial Helmholtz equation. Non-diffracting beams can maintain their properties, such as intensity and phase, over long distances, and have enormous potential for application in the field of particle manipulation. Vortex light, due to its quantized orbital angular momentum, has become a core topic in optical orbital angular momentum research. However, methods for generating vortex light with non-diffracting properties are still relatively rare, and existing methods are characterized by high processing difficulty [Adv. Photonics 3, 045002 (2021)] or complex operation [Opt. Express 16, 18770–18775 (2008)].

[0004] In summary, there is currently a lack of a convenient, new method for generating vortex light with non-diffraction characteristics, which has the strong stability of the non-diffraction light beam to maintain its own stability, and also has the communication potential of quantized vortex light, to meet the demand for the non-diffraction vortex characteristic in the fields of optical communications and particle manipulation. Summary of the Invention

[0005] In response to the above-mentioned problems in the prior art, the present application proposes a method and device for generating vortex light based on an equidistant spiral rotationally symmetric structure. The generated vortex light with non-diffraction characteristics has both the orbital angular momentum (OAM) of quantized vortex light and the non-diffraction characteristics, and has important application value in the fields of free-space optical communication and particle manipulation.

[0006] This invention utilizes the principle of Fresnel diffraction and, through the design of a rotationally symmetric structure based on equidistant helices under specific parameters, produces vortex light with non-diffraction characteristics in the far field. This vortex light achieves stable beam intensity and phase over long distances, and has important applications in free-space optical communications and particle manipulation.

[0007] A method for generating vortex light based on a rotationally symmetric structure of equidistant spirals is used to generate vortex light with non-diffraction characteristics. Multiple, multi-turn equidistant spiral structures are used to add a conical phase to the incident light beam and change the intensity distribution of the incident light, thereby generating vortex light with non-diffraction characteristics in the far-field diffraction range. The equidistant spiral structure can be represented by a binary transmittance function:

[0008]

[0009] in is an amplitude function, which is used to load a conical phase to the incident light beam and change the intensity distribution of the transmitted light beam, thereby generating a vortex light with non-diffraction characteristics; represents the polar coordinates on the equidistant spiral structure; r0 is the initial radius of the spiral; dr0 is half the gap width; a is the parameter that controls the equidistant rotation of the spiral, and each rotation is equal to an increase of 2πa in the radial distance; r0 is the initial radius of the spiral; n is the number of turns of the spiral;

[0010] Substituting the designed equidistant spiral structure expression into the cylindrical coordinate Fresnel diffraction integral formula, the integral expression of the vortex light with non-diffraction characteristics can be obtained:

[0011]

[0012] (r,θ) is the polar coordinate of the receiving screen, E0 is the amplitude of the incident light field, λ is the wavelength of the incident light, W is the waist radius of the incident Gaussian beam, k is the wave vector, It is the surface element of the plane integral of the equidistant spiral structure.

[0013] In one embodiment, the initial radius r0∈[0.5mm, 1.1mm].

[0014] In one embodiment, dr0∈[10 μm, 40 μm].

[0015] In one embodiment, a∈[0.16 mm, 0.2 mm].

[0016] In one embodiment, the number of turns of the spiral is greater than or equal to 2.

[0017] In one embodiment, the integral expression of the vortex light with non-diffraction characteristics generated by the equidistant spiral rotational symmetric structure is firstly used to calculate the integral expression of the vortex light with non-diffraction characteristics. Simplify the integral, where N is the number of terms in the Bessel function integral expansion:

[0018]

[0019] Then the stable phase method is used to obtain the analytical results. The stable point here is ρ p =-Nz / (ak), the derivative of the phase function φ′(ρ)=ρ / z+N / (ak) is 0, and ρ=ρ p Substitute the formula and solve it:

[0020]

[0021] The electric field distribution has a vortex phase exp(iNθ) and has a Bessel term Therefore, the designed rotationally symmetric structure based on equidistant spirals can produce vortex light with non-diffraction characteristics.

[0022] The present application also relates to a vortex light generating device based on an equidistant spiral rotationally symmetrical structure, comprising a continuous helium-neon laser, a beam expansion 4f system consisting of two lenses, a polarization beam splitting cube, a reflective amplitude-type spatial light modulator, a polarizer after reflection, and a light field camera CMOS for detection; the light beam after passing through the beam expansion 4f system is approximately a plane wave, which is uniformly irradiated on the spatial light modulator based on the equidistant spiral rotationally symmetrical structure, and then the reflected light beam after passing through the beam splitting cube is detected by the light field camera after the stray light is filtered out by the polarizer, thereby finally obtaining vortex light with non-diffraction characteristics.

[0023] The present invention controls the topological charge, phase rotational direction, and beam quality of vortex light with non-diffraction characteristics by adjusting the structural parameters of the equidistant spirals and the number of spirals in the rotationally symmetric structure. The equidistant spiral structure can be expressed by the transmittance function as follows:

[0024]

[0025] in is an amplitude function, which is used to load a conical phase to the incident light beam and change the intensity distribution of the transmitted light beam, thereby generating a vortex light with non-diffraction characteristics; Represents the polar coordinates on the equidistant spiral structure; r0 is the initial radius of the spiral; dr0 is half the gap width; a is the parameter that controls the equidistant rotation of the spiral, for example, each rotation is equal to an increase of 2πa in the radial distance; r0 is the initial radius of the spiral; n is the number of turns of the spiral.

[0026] The equidistant spiral structure is generated by superimposing the transmittance function after rotating it at equal angles according to equal-angle rotational symmetry. This structure cleverly utilizes the number of spirals with helical symmetry to reflect the absolute value of the topological charge designed to generate vortex light.

[0027] The vortex light generating method and device based on the equidistance helix rotationally symmetrical structure can produce vortex light with non-diffraction characteristics in a long distance of a far field.

[0028] The light field camera is placed on an optical guide rail, and the light field distribution at different distances can be measured by moving the camera, so that the longitudinal propagation profile of the vortex light can be obtained.

[0029] The above technical features can be combined in various suitable ways or replaced by equivalent technical features, as long as the purpose of the application can be achieved.

[0030] The vortex light generating method and device based on the equidistance helix rotationally symmetrical structure can produce vortex light with non-diffraction characteristics in a long distance of a far field.

[0031] The rotationally symmetrical structure can produce vortex light with non-diffraction characteristics in a long distance of a far field; the number of helixes and the rotation direction are selected to control the topological charge of the generated vortex light; the number of helixes is selected to optimize the effect of generating vortex light; and the parameters of the structure are adjusted to adjust the starting distance of the non-diffraction phenomenon and the length of the non-diffraction distance.

[0032] Compared with a single-helix structure, the multi-helix structure has the following advantages:

[0033] 1. The multi-helix structure means that the light beams passing through the center of the structure will be more uniform, and the circular symmetry characteristics of the generated non-diffraction vortex light beam will be closer to the ideal vortex light beam intensity distribution.

[0034] 2. The multi-helix structure makes the diffraction focusing effect of the structure stronger, and the energy of the light beam can be more concentrated, which is beneficial to increase the non-diffraction characteristics of the generated vortex light beam.

[0035] 3. Since the structure parameters and the pixel size of the projected spatial light modulator in the present application are in the same size order, the multi-helix structure can as much as possible cope with the errors generated by the spatial light modulator projection, such as generating light intensity effect at the position of the second circle to compensate for the vortex light intensity defects generated by the first circle. Therefore, the multi-helix structure is more stable and practical in actual use.

[0036] 4. Multi-turn spiral structure improves the utilization of light beam energy, which can improve the transmission of light beam energy and maximize the conversion of input light intensity energy into output energy of non-diffractive vortex light beam.

[0037] In summary, the multi-turn spiral structure has obvious advantages over the single-turn structure in generating non-diffractive vortex light beam. BRIEF DESCRIPTION OF DRAWINGS

[0038] Hereinafter, the present application will be described in more detail based on the embodiments and with reference to the accompanying drawings. Among them:

[0039] Figure 1 (a1) shows the rotational symmetry structure designed by the present application; (a2)-(a4) are the light intensity distribution, phase distribution and longitudinal beam propagation diagram of the generated vortex light, respectively;

[0040] Figure 2 is the experimental beam diagram for generating vortex light with non-diffractive characteristics using the designed rotational symmetry structure, and measuring the effect of generating vortex light; In the figure, the upper left corner of the insert subgraph is the physical representation of the structure and the corresponding structure parameters designed by us, Laser is the output light beam of the approximate plane wave after our shaping, L1 and L2 constitute a 2-fold expanded beam system, PBS is a polarization beam splitting cube, SLM is a spatial light modulator for projecting our designed structure, P is a stray light beam filtered by the polarization direction of the spatial light modulator, and COMS is a light field camera for detecting the effect of generating vortex light;

[0041] Figure 3 The left column (a1), (b1) and (c1) are structures that can generate vortex light with different topological charges, and the right three columns are the light intensity distributions of vortex light at different distances under the action of the structure;

[0042] Figure 4 Indicates the longitudinal propagation effect of vortex light with different topological charges and non-diffractive characteristics. DETAILED DESCRIPTION

[0043] The present application will be further described below with reference to the accompanying drawings.

[0044] The present application provides a vortex light generation method and device based on equidistant spiral rotational symmetry structure, which adjusts the structure parameters of equidistant spiral and the number of spirals in the rotational symmetry structure arrangement to control the topological charge, phase rotation direction and beam quality of vortex light with non-diffractive characteristics; The equidistant spiral structure can be represented by a transmittance function as follows:

[0045]

[0046] Among them is an amplitude function, which is used to load a conical phase to the incident light beam and change the intensity distribution of the transmitted light beam, thereby generating a vortex light with non-diffraction characteristics; Represents the polar coordinates on the equidistant spiral structure; r0 is the initial radius of the spiral; dr0 is half the gap width; a is the parameter that controls the equidistant rotation of the spiral, for example, each rotation is equal to an increase of 2πa in the radial distance; r0 is the initial radius of the spiral; n is the number of turns of the spiral.

[0047] Figure 1 Each spiral in the central structure has two turns, and the spirals rotate clockwise, generating a vortex light topological charge of -5. The selected structural parameters are spiral equidistant parameter δ = 0.88 mm, initial radius r0 = 1 mm, and spiral width w0 = 73 μm. The rotationally symmetric structure based on equidistant spirals is generated by superimposing the transmittance function with equiangular rotations and equiangular rotational symmetry. This structure cleverly utilizes the number of spirals to reflect the absolute value of the topological charge generated by the design.

[0048] The structure designed in this invention incorporates a spatial light modulator (SLM), generating vortex light with non-diffraction characteristics over long distances in the far field. The specific optical path system includes: a continuous helium-neon laser, a 4f beam expansion system, a polarization beam splitter (PBS), a spatial light modulator (SLM), and a COMS light field camera, arranged sequentially along the incident light path. The beam, after passing through the 4f beam expansion system, is approximately a plane wave. After passing through the PBS, it is converted into horizontally linearly polarized light that can be modulated by the SLM. The light is then reflected by the SLM, passed through the PBS, and detected by the light field camera.

[0049] use Figure 2 The optical system shown generates vortex light with non-diffraction characteristics. The specific steps are as follows:

[0050] Step 1: Turn on the power of the Laser continuous helium-neon laser. The beam emitted by the Laser continuous helium-neon laser is amplified into a nearly planar beam by the 2x beam expansion system composed of L1 and L2. After passing through the PBS polarization beam splitter cube, only the horizontally polarized beam that can be modulated by the SLM spatial light modulator is retained.

[0051] Step 2: The light beam is modulated by the SLM reflective spatial light modulator having the rotationally symmetric structure designed by the present invention and then passes through the polarization beam splitter cube and the P polarizer again, and finally the intensity distribution of the generated vortex light is detected at the CMOS light field camera.

[0052] Step 3: Adjust the design parameters based on the vortex light effect generated by the CMOS light field camera feedback.

[0053] Figure 3The left columns (a1), (b1), and (c1) are structures that can generate vortex light with different topological charges, and the three columns on the right are the intensity distributions of vortex light at different distances under the action of the structures. Figure 4 It represents the longitudinal propagation effect of vortex light with non-diffraction characteristics under different topological charges.

[0054] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments.

Claims

1. A method for generating vortex light based on an equidistant helical rotationally symmetric structure, for generating vortex light with non-diffraction characteristics, characterized by: Through multiple multi-turn equidistant spiral structures, a conical phase is added to the incident light beam, and the incident light intensity distribution is changed, generating vortex light with non-diffraction characteristics in the far-field diffraction range; the equidistant spiral structure can be expressed by a binary transmittance function: in is an amplitude function, which is used to load a conical phase to the incident light beam and change the intensity distribution of the transmitted light beam, thereby generating a vortex light with non-diffraction characteristics; represents the polar coordinates on the equidistant spiral structure; r0 is the initial radius of the spiral; dr0 is half the gap width; a is the parameter that controls the equidistant rotation of the spiral, and each rotation is equivalent to an increase of 2πa in the radial distance; Substituting the binary transmittance function of the equidistant spiral structure into the Fresnel diffraction integral formula in cylindrical coordinates, the vortex light integral expression with non-diffraction characteristics is obtained: (r,θ) are the polar coordinates of the receiving screen, z is the propagation distance of the light beam from the moment the incident light beam contacts the equidistant spiral rotationally symmetric structure, E0 is the amplitude of the incident light field, λ is the wavelength of the incident light, W is the waist radius of the incident Gaussian beam, k is the wave vector, is the surface element of the plane integral of equidistant spirals.

2. The method for generating vortex light based on an equidistant spiral rotationally symmetrical structure according to claim 1, characterized in that: Initial radius r0∈[0.5mm,1.1mm].

3. The method for generating vortex light based on an equidistant spiral rotationally symmetrical structure according to claim 1, characterized in that: dr0∈[10μm,40μm].

4. The method for generating vortex light based on an equidistant spiral rotationally symmetrical structure according to claim 1, characterized in that: a∈[0.16mm,0.2mm].

5. The method for generating vortex light based on an equidistant spiral rotationally symmetric structure according to claim 1, characterized in that: Based on the integral expression of the vortex light with non-diffraction characteristics generated by the equidistant spiral rotational symmetric structure, the Bessel integral expression is first used. Simplify the integral, where N is the number of terms in the Bessel function integral expansion: Then the analytical result is obtained by using the stable phase method, where the stable point is ρ p =-Nz / (ak), the derivative of the phase function φ′(ρ)=ρ / z+N / (ak) is 0, and ρ=ρ p Substitute the formula and solve it: The electric field distribution has a vortex phase exp(iNθ) and has a Bessel term 6. A vortex light generating device based on an equidistant helical rotationally symmetrical structure, characterized by: The method for generating vortex light based on an equidistant spiral rotationally symmetric structure according to claim 1 comprises a continuous helium-neon laser, a beam expansion 4f system consisting of two lenses, a polarization beam splitting cube, a reflective amplitude-type spatial light modulator, a polarizer after reflection, and a light field camera CMOS for detection; the light beam after passing through the beam expansion 4f system is approximately a plane wave, uniformly irradiated on the spatial light modulator, and then the reflected light beam after passing through the beam splitting cube is filtered out of stray light by the polarizer and detected by the light field camera, ultimately obtaining vortex light with non-diffraction characteristics.

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