Method for generating elliptical Airy beam carrying off-axis vortex and detecting topological charge

Abstract

The invention discloses a method for generating an elliptic Airy beam carrying an off-axis vortex and detecting topological charge, which comprises the following steps of: firstly, generating a linear polarization Gaussian beam by a laser, and sequentially passing through a polarization beam splitter, a beam expanding system consisting of two lenses, a half-wave plate and a reflective pure phase spatial light modulator coded with a specific hologram, and then through a 4f system consisting of a lens group, a reflector and a diaphragm, an expected elliptic Airy beam carrying the off-axis vortex can be obtained at a rear focal plane of a rear lens of the 4f system. A camera can be used for measuring and recording in the transmission direction of the generated light beam; compared with a circular Airy beam, the intensity of a focusing plane carrying the off-axis vortex elliptical Airy beam is no longer in solid distribution, and a secondary self-focusing phenomenon can occur; and inclined stripes related to the topological charges appear on a focusing plane of the optical vortex, and the size and the symbol of the topological charges of the optical vortex can be accurately obtained by directly measuring the orientation and the number of the stripes.

Description

Technical Field

[0001] The present invention relates to the field of light field regulation, and in particular to a method for generating an off-axis vortex-carrying elliptical Airy beam and detecting a topological charge. Background Art

[0002] Airy beams have attracted extensive attention and in-depth research in the academic community due to their unique properties such as non-diffraction, self-healing and self-bending [GA Siviloglou, J. Broky, A. Dogariu, and DN Christodoulides, "Observation of accelerating Airy beams", Physical Review Letters 99(21), 213901(2007)]. These properties make Airy beams very useful in optical micromanipulation [J.Baumgartl, M.Mazilu, and K.Dholakia, “Optically mediated particle clearing using Airy wavepackets”, Nature Photonics 2(11), 675(2008)], optical communications [J.Hu, Z.Guo, J.Shi, X.Jiang, Q.Chen, H.Chen, Z.He, Q.Song, S.Xiao, S.Yu, N.Chi and C.Shen, “A metasurface-based full-color circular auto-focusing Airy beam transmitter for stable high-speedunderwater wireless optical communications”, Nature Communications 15(1), 2944(2024)] and laser medical therapy [P.Polynkin, M.Kolesik, J.V.Money, G.A.Siviloglou, and D.N.Christodoulides, “Curved plasma channel generation using ultraintense Airybeams”, Science 324(5924),229(2009)] and other fields. When the Airy beam expands from radial symmetry to circular Airy beam, a new phenomenon occurs, the so-called "abruptly autofocusing" [NK Efremidisand DN Christodoulides, "Abruptly autofocusing waves", Optics Letters 35(23),4045(2010)]. This phenomenon describes that the beam maintains a low intensity mode during propagation until it approaches the focus, and then the intensity increases rapidly by several orders of magnitude.This sudden self-focusing property enables circular Airy beams to achieve higher energy densities when focused.

[0003] Screw dislocation is a prominent feature of the phase structure of a vortex beam, which is manifested as zero amplitude at the center of the beam, forming a dark core. One of the most prominent features of a vortex beam is that it carries orbital angular momentum [L. Allen, MW Beijersbergen, RJC Spreeuw, and JP Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes", Physical Review A 45 (11), 8185 (1992)], the size and direction of which depend on the topological charge of the vortex. The larger the topological charge, the faster the phase rotation of the beam, thus carrying more orbital angular momentum. Vortex beams have a wide range of applications in optical tweezers, optical communications, and quantum information. In optical tweezers, vortex beams can capture and manipulate tiny objects without damage, and the orbital angular momentum they carry can achieve rotational control of the captured object. In optical communications, the orbital angular momentum of a vortex beam can be used as an extra dimension of information, significantly improving communication capacity and transmission efficiency. In the field of quantum information, vortex beams can be used to achieve tasks such as quantum entanglement and quantum computing. Among the various factors that affect the transmission of vortex beams, intensity gradient and phase gradient are one of the main considerations.

[0004] The sudden self-focusing effect has broad application prospects in biomedical treatment, optical radar, photon bullets and multi-photopolymerization. Circular Airy beams are one of the typical representatives of this type of sudden self-focusing beams. However, circular Airy beams only have the ability to self-focus once, and the intensity distribution of their focal plane is solid, which limits their use in applications that require precise control of the intensity distribution. Recently, we introduced off-axis vortices into elliptical Airy beams and found that while retaining the self-focusing ability and carrying orbital angular momentum, this beam also exhibits secondary self-focusing characteristics different from circular Airy beams. Interestingly, tilted fringes appear in the intensity pattern of the off-axis vortex elliptical Airy beam during secondary focusing. By observing the orientation of these tilted fringes, the positive and negative topological charge can be distinguished; and by reading the number of fringes, the size of the topological charge of the vortex beam can be measured intuitively and easily. Summary of the invention

[0005] Purpose of the invention: The present invention aims to provide a method for generating an elliptical Airy beam carrying an off-axis vortex and detecting a topological charge. The method uses a laser to generate a linearly polarized Gaussian beam, which is first expanded, then passes through a specifically coded spatial light modulator, and then passes through a 4f system composed of a lens group. An elliptical Airy beam carrying an off-axis vortex can be obtained on the rear focal plane of the rear lens of the 4f system. By using a detector to record in the direction of beam transmission, the intensity distribution at different propagation distances can be measured.

[0006] The technical solution adopted by the present invention is: a method for generating an off-axis vortex elliptical Airy beam and detecting a topological charge, comprising the following steps:

[0007] Step 1: A linearly polarized Gaussian beam is generated by a laser. After passing through a polarization beam splitter, the beam is expanded by a lens group, then passes through a half-wave plate, and finally incident on a reflective pure phase spatial light modulator. In order to generate an elliptical Airy beam carrying an off-axis vortex, the information needs to be encoded into a pure phase computer-generated hologram and loaded into the above-mentioned pure phase spatial light modulator.

[0008] Step 2: After the modulated light beam reflected from the pure phase spatial light modulator passes through the 4f system composed of a lens group, a reflector and an aperture, an elliptical Airy beam carrying an off-axis vortex can be obtained at the rear focal plane of the rear lens of the 4f system; the reflector is used to adjust the direction of the light beam, and the aperture is used to filter out unnecessary stray light;

[0009] Step 3: Place a detector in the transmission direction of the off-axis vortex elliptical Airy beam to record the intensity profile distribution of the beam at different propagation distances;

[0010] Step 4: The generated elliptical Airy beam carrying off-axis vortices has inclined stripes on its focusing plane while retaining its self-focusing capability. The inclination direction of the stripes is related to the sign of the topological charge, and the number of stripes is related to the size of the topological charge, thereby realizing the detection of the size and sign of the topological charge of the beam.

[0011] Furthermore, the field distribution of the off-axis vortex elliptical Airy beam on the source plane in step 1 can be expressed by the following formula:

[0012]

[0013] Where x, y, z are spatial coordinates, a is the exponential decay factor, r0 is the radius of the main ring, t is the ellipse parameter (here the ellipse parameter is less than 1), and w0 is the scale factor. represents the azimuth, is the position of the optical vortex, l is the topological charge, and Ai(·) is the Airy function.

[0014] By adjusting the positions of different optical vortices, the off-axis vortex elliptical Airy beams at different transmission distances can be obtained using the Fresnel diffraction formula:

[0015]

[0016] Where x, y, z are spatial coordinates, k is the wave number, and λ is the wavelength.

[0017] Furthermore, in step 3, the detector is a camera or a beam analyzer.

[0018] The present invention combines an optical vortex with an elliptical Airy beam to form an off-axis vortex elliptical Airy beam. A specific phase hologram is generated using computational holography technology and loaded onto a pure phase spatial light modulator. Subsequently, a linearly polarized Gaussian beam that has undergone beam expansion is irradiated onto a pure phase spatial light modulator, and after phase modulation, a specific off-axis vortex elliptical Airy beam is generated. The linearly polarized Gaussian beam generated by a laser passes through a polarization beam splitter, a beam expansion system, a reflector, a specifically encoded reflective pure phase spatial light modulator, and then passes through a 4f system. The source field distribution of the off-axis vortex elliptical Airy beam can be obtained on the rear focal plane of the rear lens of the 4f system. In the transmission direction of the elliptical Airy beam carrying the off-axis vortex, a detector is moved to measure the intensity distribution at different propagation distances.

[0019] The beneficial effects of the present invention are as follows: the present invention proposes an elliptical Airy beam carrying an off-axis vortex, which combines the characteristics of an elliptical Airy beam and an optical vortex to achieve tunability. By adjusting the off-axis parameters of the optical vortex, different propagation behaviors of the off-axis vortex elliptical Airy beam can be observed. Using a relatively simple optical device, an elliptical Airy beam carrying an off-axis vortex was successfully generated, and the intensity profile of the beam can be conveniently measured. The elliptical Airy beam embedded with an off-axis vortex not only increases the degree of freedom of regulation, allowing it to exhibit a variety of intensity patterns, but also exhibits a secondary self-focusing phenomenon while retaining the self-focusing ability and carrying orbital angular momentum. The size and sign of the vortex topological charge can be accurately measured by the number and tilt direction of the first focusing intensity distribution and the second focusing intensity distribution of the off-axis vortex elliptical Airy beam. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic diagram of a device for generating an off-axis vortex elliptical Airy beam provided in an embodiment of the present invention.

[0021] Figure 2 To generate a pure phase CGH carrying an off-axis vortex elliptical Airy beam; where l = 2, r k =0.5,

[0022] Figure 3 is the two-dimensional intensity distribution diagram of the off-axis vortex elliptical Airy beam at different observation planes; where l = 2, r k =0, (a) z = 0, (b) z = 0.2m, (c) z = 0.388m, (d) z = 0.5m, (e) z = 0.612m, (f) z = 0.8m; (a1) - (f1) are theoretical simulation diagrams, and (a2) - (f2) are experimental result diagrams.

[0023] Figure 4 is the two-dimensional intensity distribution diagram of the off-axis vortex elliptical Airy beam at different observation planes; where l = 2, r k =0.5, (a) z = 0, (b) z = 0.2m, (c) z = 0.388m, (d) z = 0.5m, (e) z = 0.588m, (f) z = 0.8m; (a1) - (f1) are theoretical simulation diagrams, and (a2) - (f2) are experimental result diagrams.

[0024] Figure 5 is the two-dimensional intensity distribution diagram of the off-axis vortex elliptical Airy beam at different observation planes; where l = 2, r k =0.5, (a) z = 0, (b) z = 0.2m, (c) z = 0.382m, (d) z = 0.5m, (e) z = 0.604m, (f) z = 0.8m; (a1)-(f1) are theoretical simulation diagrams, and (a2)-(f2) are experimental result diagrams.

[0025] Figure 6 The experimental results of the measured two-dimensional intensity distribution of off-axis vortex elliptical Airy beams carrying different topological charges in the secondary focusing plane; where r k =0.25mm, When r is , (a1)-(a4) are the first focusing intensity distribution diagrams when the topological charge is 2, 3, 4, -4, and (b1)-(b4) are the second focusing intensity distribution diagrams when the topological charge is 2, 3, 4, -4. k =0.5mm, When , (c1)-(c4) are the first focusing intensity distribution diagrams when the topological charge is 2, 3, 4, -4, and (d1)-(d4) are the second focusing intensity distribution diagrams when the topological charge is 2, 3, 4, -4. DETAILED DESCRIPTION

[0026] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments of the present invention.

[0027] like Figure 1As shown, a laser with a wavelength of 1064nm generates a linearly polarized Gaussian beam. The linearly polarized Gaussian beam first passes through a polarization beam splitter, and then is expanded by a beam expansion system composed of lens L1 and lens L2 (f1=5cm, f2=15cm). The expanded beam passes through a half-wave plate and enters a reflective pure phase spatial light modulator SLM (model: HoloeyePluto-2, liquid crystal unit size: 8um×8um). Figure 2 To generate a pure phase-type computer-generated hologram carrying an off-axis vortex elliptical Airy beam, where l = 2, r k =0.5, This information is encoded on the above-mentioned spatial light modulator SLM. The expanded light is modulated by the spatial light modulator and then reflected, and passes through a 4f system composed of lens L3 (f3 = 20cm), reflector RM, aperture CA, reflector RM, and lens L4 (f4 = 20cm) in sequence. The aperture is used to block unnecessary background light and filter out the required light. The expected off-axis vortex elliptical Airy beam can be obtained at the rear focal plane of lens L4. A detector is placed in the transmission direction of the light beam, and the position of the detector is moved to record the intensity distribution diagram at different transmission distances.

[0028] The light field distribution of the off-axis vortex elliptical Airy beam generated in this embodiment on the source plane can be described by the following formula:

[0029]

[0030] Where x, y, z are spatial coordinates, a is the exponential decay factor, r0 is the radius of the main ring, t is the ellipse parameter (here the ellipse parameter is less than 1), and w0 is the scale factor. represents the azimuth, is the position of the optical vortex, l is the topological charge, and Ai(·) is the Airy function.

[0031] The transmission process of the off-axis vortex elliptical Airy beam can be expressed as follows:

[0032]

[0033] Where x, y, z are spatial coordinates, k is the wave number, and λ is the wavelength.

[0034] Figure 3 The theoretical simulation diagram and experimental result diagram of the intensity distribution of the off-axis vortex elliptical Airy beam on different observation planes are given respectively. k =0, Figure 3 In (a)-(f), z=0, 0.2m, 0.388m, 0.5m, 0.612m, and 0.8m respectively. Figure 3(a1)-(f1) correspond to the theoretical simulation diagrams of the intensity distribution on different observation planes. Figure 3 (a2)-(f2) in the figure correspond to the experimental results of the intensity distribution on different observation planes. The evolution process of the light beam during transmission can be clearly seen. On the initial plane, the main lobe of the light beam presents an intensity distribution surrounded by a series of elliptical rings. Within a short transmission distance, the elliptical distribution is maintained. When the light beam is further transmitted along the z direction, the minor axis of the ellipse will decrease. After being transmitted to a certain distance, the light beam presents a nearly vertical distribution, and two bright spots will appear. Between the bright spots, a stripe tilted to the right will appear. This is the first focusing plane (z f1 =0.388m) Figure 3 As shown in (c1). After the first focusing plane, the beam begins to compress, as shown by two bright spots moving toward the minor axis of the original ellipse. As the beam continues to transmit, its profile rotates, and eventually the major axis of the intensity ellipse is 90 degrees to the position of the first focusing plane. This is the second focusing plane (z f2 =0.612m) Figure 3 After the second focusing plane, the beam will continue to be stretched in the horizontal direction and the intensity of the beam will decrease.

[0035] Figure 4 The theoretical simulation diagram and experimental result diagram of the intensity distribution of the off-axis vortex elliptical Airy beam on different observation planes are given respectively. k =0.5mm, Figure 4 In (a)-(f), z=0, 0.2m, 0.392m, 0.5m, 0.6m, and 0.8m respectively. Figure 4 (a1)-(f1) correspond to the theoretical simulation diagrams of the intensity distribution on different observation planes. Figure 4 (a2)-(f2) in the middle correspond to the experimental results of the intensity distribution on different observation planes. It can be seen from the figure that the central symmetry of the beam intensity is broken, and the intensity is strong on the left and weak on the right. The beam still presents an elliptical distribution. As the beam is transmitted, the minor axis of the ellipse decreases first. When the beam is transmitted to 0.392m (i.e., the first focusing plane), the beam appears to be nearly vertically distributed and two bright spots appear. A stripe tilted to the right appears between the bright spots. The beam no longer presents a symmetrical distribution and the energy on the right is transferred to the left. After the first focusing plane, the two bright spots of the beam move toward the direction of the minor axis of the ellipse. At this time, it can be found that the beam presents a squid shape, and the intensity on the right is significantly greater than that on the left. This also shows that the energy on the left has moved to the right during the transmission process. The beam continues to transmit, and its contour rotates, eventually making the major axis of the intensity ellipse 90 degrees to the position of the first focusing plane. The two bright spots merge into one and reach the second focusing plane (z=0.6m). Figure 4After passing through the second focusing plane, the beam profile will be elongated in the horizontal direction and the intensity of the beam will also decrease.

[0036] Figure 5 The theoretical simulation diagram and experimental result diagram of the intensity distribution of the off-axis vortex elliptical Airy beam on different observation planes are given respectively. k =0.5mm, Figure 5 In (a)-(f), z=0, 0.2m, 0.388m, 0.5m, 0.588m, and 0.8m respectively. Figure 5 (a1)-(f1) correspond to the theoretical simulation diagrams of the intensity distribution on different observation planes. Figure 5 (a2)-(f2) in the middle correspond to the experimental results of the intensity distribution on different observation planes. The optical vortex on the initial plane is no longer on the right side of the minor axis of the ellipse, and is rotated 90° clockwise with the direction of the minor axis of the ellipse, and is on the lower side of the major axis of the elliptical beam. The central symmetry of the beam intensity is also broken, and the beam still presents an elliptical distribution, with a phenomenon of strong on the upper side and weak on the lower side, indicating that the optical vortex has rotated 90° clockwise. As the beam is transmitted, the minor axis of the ellipse also decreases first. When the beam is transmitted to 0.388m (i.e., the first focusing plane), the beam presents a tadpole shape, with a nearly vertical distribution and only one bright spot. Below the bright spot, there are still stripes tilted to the right. After passing the first focusing plane, a bright spot of the beam moves in the direction of the minor axis of the ellipse. The beam continues to transmit, and its contour rotates, eventually making the major axis of the intensity ellipse 90 degrees to the position of the first focusing plane, reaching the second focusing plane (z=0.588m). Figure 4 The difference between (e1) and (e2) is that the energy on the upper side of the beam is greater than the energy on the lower side. After passing through the second focusing plane, the profile of the beam will be elongated in the horizontal direction and the intensity of the beam will also decrease.

[0037] Figure 6 Figure 2 shows the focusing intensity of off-axis vortex elliptical Airy beams carrying different topological charges. Figure 6 It can be seen that both the topological charge and the radial position will cause changes in the beam self-focusing pattern. A larger topological charge will make the pattern larger, while changes in the radial position will destroy the symmetry of the beam self-focusing pattern. Figure 6 (a1)-(d1) represents the radial position r k =0.25mm, the first focusing intensity distribution diagram of the elliptical Airy beam with topological charge l=2, 3, 4, -4 respectively. It can be found that when the topological charge is positive, the stripes in the pattern tilt to the left; when the topological charge is negative, the stripes in the pattern tilt to the right. Figure 6 (a2)-(d2) represents the radial position r k=0.25mm, the second focusing intensity distribution diagram of the elliptical Airy beam with topological charge l=2, 3, 4, and -4. It can be seen that the radial position has a greater impact on the symmetry of the second focusing pattern, and the intensity on one side will be stronger. k When =0.5mm, the topological charges are l=2, 3, 4, -4 respectively. As the topological charge increases, the first self-focusing pattern shows a phenomenon of extremely high intensity on one side. As the topological charge increases, the second self-focusing pattern gradually becomes weaker on one side, and only one end is the brightest. It is unstable for high-order vortices, and after asymmetric focusing during propagation, it will split into multiple first-order vortices. The positive and negative and size of the topological charge can be directly derived from the inclination direction of the first self-focusing pattern and the number of stripes sandwiched by the bright spots at the two ends. The size of the topological charge can still be obtained through the second self-focusing pattern, but the direction is more difficult to judge. Therefore, the off-axis vortex elliptical Airy beam can realize the detection of topological charge.

[0038] The generated off-axis vortex-carrying elliptical Airy beam has a secondary self-focusing capability and carries orbital angular momentum while retaining the self-focusing capability. Therefore, the off-axis vortex-carrying elliptical Airy beam has good application prospects. Due to its secondary self-focusing capability, it can provide high-resolution optical imaging, which is helpful for cell observation and tissue analysis in the biomedical field. Due to the existence of orbital angular momentum, it has a variety of potential applications in the fields of optics and laser technology, which helps to improve the performance of optical systems and expand the functions of optical devices.

[0039] The above is a detailed description of the embodiments of the present invention in conjunction with the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, deformations or substitutions made within the essential scope of the present invention still belong to the protection scope of the present invention.

Claims

1. A method for generating an off-axis vortex elliptical Airy beam and detecting topological charge, characterized in that: The steps include: Step 1: A linearly polarized Gaussian beam is generated by a laser. After passing through a polarization beam splitter, the beam is expanded by a lens group, then passes through a half-wave plate, and finally incident on a reflective pure phase spatial light modulator. In order to generate an elliptical Airy beam carrying an off-axis vortex, the information needs to be encoded into a pure phase computer-generated hologram and loaded into the above-mentioned pure phase spatial light modulator. Step 2: After the modulated light beam reflected from the pure phase spatial light modulator passes through the 4f system composed of a lens group, a reflector and an aperture, an elliptical Airy beam carrying an off-axis vortex can be obtained at the rear focal plane of the rear lens of the 4f system; the reflector is used to adjust the direction of the light beam, and the aperture is used to filter out unnecessary stray light; Step 3: Place a detector in the transmission direction of the off-axis vortex elliptical Airy beam to record the intensity profile distribution of the beam at different propagation distances; Step 4: The generated elliptical Airy beam carrying off-axis vortices has inclined stripes on its focusing plane while retaining its self-focusing capability. The inclination direction of the stripes is related to the sign of the topological charge, and the number of stripes is related to the size of the topological charge, thereby realizing the detection of the size and sign of the topological charge of the beam.

2. The method for generating an off-axis vortex elliptical Airy beam and detecting a topological charge according to claim 1, characterized in that: The field distribution of the off-axis vortex elliptical Airy beam on the source plane in step 1 is expressed by the following formula: Where x, y, z are spatial coordinates, a is the exponential decay factor, r0 is the radius of the main ring, t is the ellipse parameter, and w0 is the scale factor. represents the azimuth, is the position of the optical vortex, l is the topological charge, Ai(·) is the Airy function; By adjusting the positions of different optical vortices, the Fresnel diffraction formula is used to obtain the off-axis vortex elliptical Airy beams at different transmission distances: Where x, y, z are spatial coordinates, k is the wave number, and λ is the wavelength.

3. The method for generating an off-axis vortex elliptical Airy beam and detecting a topological charge according to claim 2, characterized in that: In step 3, the detector is a camera or a beam analyzer.

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