Circularly symmetrical Airy beam wavefront phase modulation method based on multi-focal-length lens

Abstract

The invention provides a circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal-length lens. The method comprises the following steps: determining beam parameters of a CAB; calculating the self-focusing focal length d of the CAB; shielding all other light rings except the nth light ring, and solving the diffraction integral of the single light ring so as to obtain a focal length dn; the modulation focal length fn is reasonably estimated according to the difference value between the self-focusing focal length d and the single halo focal length dn, and the modulation focal length fn of each stage of halo is finely adjusted based on the obtained modulation focal length fn of each stage of halo, so that the optimal modulation effect is realized. On the premise that CAB initial light intensity distribution is not changed, higher energy concentration and better focusing characteristics are achieved, and the focusing precision of light beams is improved.

Description

Technical Field

[0001] The invention relates to the technical field of wavefront phase modulation of multi-focal length lenses, and in particular to a circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens. Background Art

[0002] A circular Airy beam (CAB) is a self-focusing beam that does not require a lens to focus. Its characteristic is that when propagating in free space, the beam maintains the self-acceleration characteristics of the Airy beam, and the light field energy converges at the focus along the parabola, thereby maintaining an extreme light intensity distribution in front of the focus. When reaching the vicinity of the focus, the light intensity will suddenly increase by dozens or even hundreds of times, so it is also called an abruptly autofocusing beam (AAB).

[0003] As shown in the attached figure of the instruction manual Figure 1 As shown in the figure, compared with Gaussian focused beams, CAB has incomparable natural advantages in the fields of photodynamic therapy, nonlinear optics, laser 3D micromachining and optical tweezers manipulation. However, most of the energy of CAB will be dispersed in space during propagation, and the energy gathered at the focus only accounts for about 8% of the initial light field energy, which seriously hinders the application of beams. Therefore, how to maximize the self-focusing ability of CAB has become one of the core issues that researchers are concerned about.

[0004] In order to improve the self-focusing performance of CAB, researchers proposed a spectral high-pass filtering method, which effectively enhanced the focusing ability of the light beam. Furthermore, a spectral amplitude envelope modulation method was developed, which optimized the focusing characteristics of the light beam by flexibly controlling the spectrum width and energy ratio. However, the problem is that the focal spot size obtained by this spectral modulation method is smaller, and the total energy of the focal spot is only about 30% of the initial light field, which is less than 39% of the wavefront phase modulation method, resulting in the existing technology still having limitations in improving the energy of the focal spot. Summary of the invention

[0005] In view of the shortcomings of the prior art, the object of the present invention is to provide a circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens to solve the problems raised in the above background technology.

[0006] In order to achieve the above object, the present invention is implemented by the following technical scheme: a circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens, comprising the steps of:

[0007] Determine the beam parameters of the CAB; calculate the self-focusing focal length d of the CAB according to the preset error tolerance;

[0008] The nth order light ring is selected as the research object among multiple light rings of CAB. In the numerical simulation, all other light rings except the nth order light ring are blocked to perform numerical calculation on the selected nth order light ring, and the diffraction integral of the single light ring is solved. At the same time, in the calculation process of the diffraction integral, the focal position of the nth order single light ring is determined by searching the extreme point of the light intensity distribution, so as to obtain the focal length d n ; According to the self-focus focal length d and the single halo focal length d n The difference between n , so that the focal length of the single light ring of the nth light ring plus the phase modulation of the lens changes from d n becomes d; based on the obtained levels of light ring modulation focal length f n , by calculating the modulation effect of the overall beam on the modulation focal length f of each level of light ring n Make subtle adjustments for optimal modulation.

[0009] Compared with the prior art, the present invention has the following beneficial effects:

[0010] The wavefront phase modulation method proposed in the present invention is used to significantly improve the self-focusing ability of a circular Airy beam (CAB). By accurately calculating and adjusting the focal lengths of each light ring in the CAB, the method ensures that different light rings can converge at the same focus during propagation, thereby greatly enhancing the energy of the focal spot. At the same time, experimental results show that the light intensity of the modulated light beam at the focus is significantly increased, and the focal spot energy reaches 39% of the initial light intensity, which is nearly 5 times the 8% of the CAB focal spot energy before modulation. Compared with the existing spectrum modulation method, the present invention achieves higher energy concentration and better focusing characteristics without changing the initial light intensity distribution of the CAB, which not only improves the focusing accuracy of the light beam, but also provides new possibilities for performance optimization of CAB in various application fields such as photodynamic therapy, nonlinear optics, laser 3D micromachining and optical tweezers manipulation due to its easy implementation and efficient use of light source energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The disclosure of the present invention is described with reference to the accompanying drawings. It should be understood that the drawings are only for illustrative purposes and are not intended to limit the scope of protection of the present invention. In the drawings, the same reference numerals are used to refer to the same components. Among them:

[0012] Figure 1 A schematic diagram of the sudden self-focusing characteristics of CAB in the prior art;

[0013] Figure 2a A schematic diagram of an unmodulated strong CAB spectrum proposed in an embodiment of the present invention;

[0014] Figure 2bA schematic diagram of a spectrum after being modulated by envelopes of different parameters proposed in an embodiment of the present invention;

[0015] Figure 3a Schematic diagram of the initial surface light field distribution of the unmodulated strong CAB proposed in one embodiment of the present invention;

[0016] Figure 3b Schematic diagram of the initial surface light field distribution after spectrum envelope modulation proposed in one embodiment of the present invention;

[0017] Figure 4 A schematic diagram of phase distribution of a modulation function proposed in an embodiment of the present invention;

[0018] Figure 5 : is a comparison of the axial light intensity distribution of the light beam before modulation (A line) and after modulation (B line) proposed in one embodiment of the present invention, where I max (0) is a schematic diagram of the maximum value of the light beam on the initial surface;

[0019] Figure 6 Schematic diagram of comparison of the focal spot intensity distribution of the light beam before modulation (A line) and after modulation (B line) proposed in one embodiment of the present invention;

[0020] Figure 7 A schematic diagram of an experimental optical path constructed when evaluating the effectiveness of a wavefront phase modulation method proposed in an embodiment of the present invention;

[0021] Figure 8 A schematic diagram of the cross-sectional light intensity of a modulated light beam at different propagation distances proposed in one embodiment of the present invention;

[0022] Fig. 9 It is a schematic flow chart of a wavefront phase modulation method proposed in one embodiment of the present invention. DETAILED DESCRIPTION

[0023] It is easy to understand that according to the technical solution of the present invention, without changing the essential spirit of the present invention, a person skilled in the art can propose a variety of interchangeable structural modes and implementation modes. Therefore, the following specific implementation modes and drawings are only exemplary descriptions of the technical solution of the present invention, and should not be regarded as the whole of the present invention or as a limitation or restriction to the technical solution of the present invention.

[0024] The present invention is further described in detail below with reference to the accompanying drawings, but is not intended to limit the present invention.

[0025] As an embodiment of the present invention, a circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens is proposed, the purpose of which is to compensate for the defocusing of different light rings arriving at the focal plane, increase the focal spot energy, reduce the divergence of energy in free space, and ultimately greatly improve the self-focusing ability of the light beam.

[0026] In one embodiment of the present invention, since the prior art adopts the CAB spectrum high-pass filtering method, it can effectively improve the self-focusing performance of the light beam, but there are still limitations in the focal spot energy. Based on this, it should be noted that we propose a spectrum amplitude envelope modulation method on this basis. Compared with the ordinary spectrum filtering method, spectrum envelope modulation can flexibly control the width of the spectrum and the energy proportion of different frequency bands in the spectrum. This effect is as follows Figure 2a and Figure 2b As shown, the modulation effect of the CAB spectrum is demonstrated. Figure 2a The unmodulated CAB spectrum is depicted, showing a typical ring distribution, while Figure 2b The spectrum after envelope modulation with different parameters is shown, in which the width and energy distribution of the spectrum are effectively controlled, which shows that the self-focusing performance of CAB can be significantly improved through spectrum modulation. However, the process of spectrum modulation is not without challenges. Spectrum modulation not only involves careful adjustment of the beam spectrum, but also inevitably affects the initial surface distribution of the beam. Specifically, the distribution of the modulated beam on the initial surface becomes more complicated. This is because the increase in high-frequency components leads to a significant change in the light field structure. This change makes the initial shape of the beam significantly different from that before modulation, affecting the subsequent propagation and focusing characteristics of the beam. The following is an example analysis of the modulation process of the entire spectrum of the beam, which is an expansion of the previous problem:

[0027] The initial surface light field of CAB in the cylindrical coordinate system can be expressed as:

[0028]

[0029] In the formula, A0 is the amplitude constant, Ai(*) represents the Airy function, r0 represents the radius of the main ring, w represents the scale factor, which controls the density of the ring, and α is the exponential decay factor (0<α<1). It should be noted that there is currently no strict analytical expression for the spectrum of CAB, so it is usually calculated using Fourier transform:

[0030]

[0031] Where k represents the radial spatial frequency, J0(*) represents the 0th order Bessel function, and the radial distribution of CAB after Fourier transform is shown in Figure 2(a). The modulated spectrum can be expressed as follows:

[0032]

[0033] In the formula, C represents the amplitude constant to maintain the spectrum energy conservation before and after modulation, E V(k) is the envelope function of the absolute value of the spectrum function |F(k)|, where EV(k) is the spectrum amplitude envelope function. Figure 2(b) shows the spectrum of the light beam modulated by modulation functions with different parameters. It can be understood that as long as the appropriate EV(k) function is selected, the self-focusing performance of the light beam can be greatly improved. The experimental results show that the main focal spot energy accounts for about 30% of the initial light field energy, which is the best result known so far. However, since the spectrum modulation greatly increases the high-frequency component of the light field, it will also change the initial surface distribution of the light beam, making the light field structure more complex, which may be an undesirable effect in some applications, such as Figure 3a and Figure 3b shown.

[0034] Further, Figure 3a and Figure 3b The modulation effect of CAB initial surface light field distribution is further demonstrated. Figure 3a The initial light field distribution of the unmodulated CAB is shown in Figure 1. The light intensity distribution is relatively uniform. Figure 3b The initial surface light field distribution after spectral envelope modulation is presented. It can be observed that the light field structure becomes more complex. This is because the modulation increases the high-frequency component of the light field, thereby changing the initial surface distribution of the light beam to achieve more effective self-focusing.

[0035] Based on the above example analysis, it can be concluded that the focusing ability of different light rings of CAB is different. The main ring has the largest energy share, but its focusing ability is the weakest and the focal length is the longest. The light ring at the edge of the beam has a small energy share, but its focusing ability is stronger and the focal length is smaller. Therefore, the focal length of different light rings can be adjusted by using a multi-focal lens on the wavefront to focus them on the same area as much as possible to increase their coherence in the focal area, thereby improving the focusing ability of the beam. Considering the different focusing abilities of different light ring areas, lenses with different focal lengths are required for phase modulation.

[0036] Based on this, the present invention proposes to integrate the basic characteristics of the Airy beam and realize wavefront phase modulation through the modulation function t(r), so as to further optimize the focusing characteristics of the beam, enhance the focal spot energy, and improve the application efficiency and effect of the beam.

[0037] When implementing it, Fig. 9 As shown, the wavefront phase modulation method proposed in the present invention comprises the following steps:

[0038] S1. Determine the beam parameters of CAB. It can be understood that the beam parameters of CAB include the radius r0 of the main light ring, the proportional factor w, the working wavelength λ of the beam, and the exponential decay factor α.

[0039] S2. It should be noted that the calculation of the self-focusing focal length in this step is a key step to improve the self-focusing ability of the circular Airy beam (CAB). The calculation is based on the preset error tolerance to calculate the self-focusing focal length d of the CAB. The preset error tolerance includes low error tolerance and high error tolerance. Under low error tolerance, a high-precision numerical calculation method is used to determine the self-focusing focal length d of the CAB; under high error tolerance, an approximate formula d= To estimate the self-focusing focal length d of CAB, where r0, w, and λ are the beam parameters of CAB, representing the radius of the main light ring, the scale factor, and the working wavelength of the beam, respectively. Example: If the calculation result of the focal length needs to be within an error of 1%, then it can be considered that this is a high-precision requirement. On the contrary, if an error of 5% or more is allowed, then it can be considered that the accuracy requirement is not very high. Based on the above method, it can ensure that the self-focusing focal length calculation of CAB meets both the accuracy requirements and adapts to different application requirements.

[0040] S3. The nth-order light ring is selected as the research object from among the multiple light rings of CAB. This selection is based on the in-depth analysis of the characteristics of CAB light beams and the consideration of the differences in focusing capabilities of different light rings. Then, in the numerical simulation, all other light rings except the nth-order light ring are blocked or ignored by setting the calculation model to ensure that the focus of the calculation is concentrated on the selected light ring, thereby improving the efficiency and accuracy of the calculation. The selected nth-order light ring is numerically calculated to solve the single light ring diffraction integral. This process involves a mathematical description of the light field distribution of the light ring and the application of relevant physical and optical principles to simulate the propagation of light waves. At the same time, in the calculation process of the diffraction integral, the extreme points of the light intensity distribution are searched by an algorithm. It can be understood that these extreme points correspond to the focusing points of the light beam during the propagation process, that is, the focal position. According to the positions of these light intensity extremes, the focal position of the nth-order single light ring can be determined, thereby obtaining the focal length d n It should be noted that this focal position is the area where the energy of the beam is most concentrated during propagation, which is crucial for achieving self-focusing. In specific implementation, the distance from the focal position to the initial surface is defined as the focal length d n , which is a key parameter for evaluating and comparing the focusing capabilities of different light rings, and is also the basis for estimating the subsequent modulation focal length. Through this step, the focusing characteristics of each light ring in the CAB can be accurately evaluated and optimized, thereby improving the focusing accuracy of the self-focusing beam and providing the possibility for optimizing the performance of the beam in various applications.

[0041] S4, according to the self-focus focal length d and the single light ring focal length d n The difference between n , so that the focal length of the single light ring of the nth light ring plus the phase modulation of the lens changes from d n becomes d.

[0042] S5, based on the obtained levels of light ring modulation focal length f n , by calculating the modulation effect of the overall beam on the modulation focal length f of each level of light ring n Make fine adjustments to achieve the best modulation effect. The phase distribution of the modulated wavefront is given by the formula Definition, where A0 is the amplitude constant, Ai(*) represents the Airy function, r is the radial distance from a point in the beam to the center of the beam, t(r) is the modulation function that varies according to the radius r of the ring, and for different ring regions, contains different modulation focal lengths f n , specifically:

[0043]

[0044] In the formula, r n is the radius of the nth dark ring, f n is the corresponding modulation focal length, and exp(*) is the exponential decay factor.

[0045] It can be understood that the above-mentioned change in the radius r of the light ring is achieved by applying different phase modulations on each light ring to ensure that they can focus on the same focal plane and achieve self-focusing. Through this modulation, each part of the light beam (i.e., each light ring) is given an appropriate phase change, so that they can be concentrated on one point after propagating to a certain distance. This point is the focus, and the light intensity at the focus is thereby enhanced, while the light intensity outside the focal area is relatively weak, thereby achieving a self-focusing effect. At the same time, the modulated wavefront phase distribution also needs to be optimized through numerical simulation and experimental verification to ensure that the light beam can achieve the best focusing effect.

[0046] Based on the above technical concept, in one embodiment of the present invention, after estimating the modulation focal length f n That is, between the above steps S4 and S5, it is also necessary to apply the Fresnel diffraction integral to calculate the distribution of the modulated light field, and calculate the integral by numerical methods to obtain the phase and amplitude distribution of the light field during propagation, so as to predict and optimize the effect of wavefront phase modulation. It should be noted that the Fresnel diffraction integral is the basis for numerical simulation. By numerically calculating this integral, the detailed distribution of the light field during propagation can be obtained, including the light intensity distribution in the focal area, which helps to predict the effect of wavefront phase modulation before the experiment, thereby guiding the experimental design. The numerical simulation results obtained by the Fresnel diffraction integral can be used as the basis for experimental verification. In specific implementation,

[0047] The specific operation of the method of realizing wavefront phase modulation using Fresnel diffraction integral is as follows:

[0048] First, the initial light field is set, and the light field distribution u(x′, y′, 0) of the light beam at the initial plane z=0 is set as the starting point of the wavefront phase modulation, where u(x′, y′, 0) contains the modulated phase information;

[0049] Secondly, the Fresnel diffraction integral formula is used to calculate the light field distribution propagating from the initial surface to any distance z,

[0050]

[0051] In the formula, λ is the wavelength of light, k is the wave number, and i is the imaginary unit;

[0052] Finally, the phase distribution of the modulation function, in the calculation process, substitutes the phase distribution of the modulation function t(r) into u(x′, y′, 0), and numerically calculates the above integral to obtain the phase and amplitude distribution of the light field during propagation.

[0053] Furthermore, after the wavefront phase modulation method is implemented based on the Fresnel diffraction integral, the calculated phase distribution is realized through the spatial light modulator, and the light intensity distribution of the light beam at different propagation positions is recorded using a CCD camera to evaluate the effectiveness of the wavefront phase modulation method. In order to facilitate the explanation of the technical effect of the invention, numerical simulation results are given, and then the simulation results are experimentally verified. In the specific implementation,

[0054] In terms of parameter selection, the model of the helium-neon laser used in the experiment is Daheng Optoelectronics DHN250P, with a power of about 2.4mW and an operating wavelength of 632.8nm. The short-focus lens used in the beam expansion system is Daheng Optoelectronics' GCO-2102 objective lens, with a magnification of 10 times, a numerical aperture of 0.25, and a working distance of 7.3mm. Both the telephoto lens and the Fourier lens use Daheng Optoelectronics' GCL-010117 plano-convex lens with a focal length of 300mm. The pinhole filter size is 25μm. The CCD camera uses Sorebo's BC207VIS / M spot analyzer, with a pixel size of 3.45μm, a resolution of 2448*2048, and a sensor size of 8.45mm7.07mm. The SLM (spatial light modulator) uses Holoeye's GAEA-2 pure phase LCOS spatial light modulator with a resolution of 3840*2160, a pixel size of 3.74μm, and a phase surface size of 15.32mm*9.22mm.

[0055] The steps are as follows:

[0056] First, the initial energy of the beam is normalized, that is, In order to compare the focal spot energy, at the same time, the beam parameters of CAB are determined. In this embodiment, the wavelength is set to 632.8nm, r0=1mm, w=0.08mm, α=0.1, and remain unchanged;

[0057] The process of light field wavefront propagating from the initial surface to the focal area can be calculated using the Fresnel diffraction integral:

[0058]

[0059] In this embodiment, a relatively simple 4-ring structure is used as an example to demonstrate the wavefront phase modulation effect. In actual use, any ring structure can be designed as needed. The phase distribution of the 4-ring structure in this example is as follows:

[0060]

[0061] According to calculation, the modulation focal length of the first ring (main light ring) is f1 = 0.93d; the modulation focal length of the second ring is f2 = 1.08d; the modulation focal length of the third to sixth rings is f3 = 5.26d; the modulation focal length of the sixth ring and beyond is f4 = 5.6d, where d is the self-focusing focal length of CAB. The phase distribution of the modulated beam is as follows: Figure 4 As shown; also refer to Figure 5 As shown, Figure 5 The axial intensity distribution of the light beam before and after modulation is given. It can be seen from the figure that the focal length of the light beam after modulation is slightly reduced compared to the modulation, and the light intensity at the focus increases from less than 30 to 122. The focus area still maintains a very low light intensity peak, and a large light intensity gradient is generated in the focus area, and the sudden self-focusing characteristics are still retained. Figure 6 As shown, the focus spot intensity distribution of the light beam before modulation (line A) and after modulation (line B) is compared. It can be obtained that the focus spot size increases slightly after the light beam is modulated, and the focus spot energy reaches 39% of the initial light field, which is nearly 5 times the 8% of the CAB focus spot energy before modulation.

[0062] Based on this, it can be concluded that: compared with the spectrum modulation method, the wavefront phase modulation proposed in the present invention only changes the phase of the initial light field without changing the light intensity distribution, such as Figure 8 As shown in (a), the focal spot size obtained by the spectrum modulation method is slightly smaller than the focal spot of the original CAB. This is because the spectrum modulation increases the high-frequency component of the light field, while the focal spot radius obtained by the wavefront phase modulation method proposed in the present invention is slightly larger than the focal spot of the original CAB. Therefore, the working principle of the present invention is different from the spectrum high-pass filtering method proposed in the prior art (refer to Figure 1 ), on the other hand, the focal spot energy obtained by the spectrum modulation method can reach 30% of the initial light field, while the focal spot energy obtained by the wavefront phase modulation method proposed in the present invention can reach 39% of the initial light field, which more effectively utilizes the energy of the incident light source, and the present invention does not change the initial light intensity distribution of CAB, which is easier to implement than the existing spectrum modulation method.

[0063] During the above operation steps, the experimental optical path constructed by the present invention is as follows Figure 7 As shown, that is, a 632.8nm helium-neon laser is used as the light source. In practical applications, light sources of different wavelengths can be replaced according to actual needs. The light beam passes through a half-wave plate to adjust the polarization direction to be consistent with the working direction of the spatial light modulator (SLM), and then enters the SLM after being expanded by a lens group and a pinhole filter. The SLM is used to load the wavefront information encoded by the numerically calculated phase holographic algorithm and is placed on the front focal plane of the first Fourier lens. The pinhole aperture is placed on the spectrum plane to selectively filter the spectrum, allowing only the first-order diffraction light to pass through. The light beam passes through the second Fourier lens to generate the required light beam on its rear focal plane. The CCD can move along the optical axis to record the intensity distribution of the light beam at different propagation positions. When the working wavelength is changed, since the modulation focal length is related to the working wavelength, it is necessary to repeat the above steps, recalculate and select values, and obtain the phase distribution of the new modulation function. At this time, the experimental optical path constructed is the same as Figure 7 The same, but the optical devices need to be re-selected according to the working wavelength, and the experimental steps remain unchanged. Figure 8 , is a schematic diagram of the cross-sectional light intensity distribution of the modulated light beam at different propagation distances, Figure 8 (ad) are experimental results; (ef) are corresponding theoretical calculation results, (a) (e) are initial plane z = 0; (b) (f) are z = 100mm; (c) (g) are z = 285mm; (a) (e) are focal planes. For the convenience of comparison, the corresponding theoretical calculation results are also given in the figure. It can be seen from the figure that the experimental light intensity distribution obtained at different positions is very consistent with the light intensity distribution expected by theoretical calculation, which proves that the experimental results are consistent with the theoretical calculation results, and proves the credibility and feasibility of this modulation method. Compared with the theoretical focal spot, the experimental focal spot is elliptical. The reason for this phenomenon may be that the coaxial collimation of each device in the optical path is not adjusted well, and the light beam is deformed after passing through the device, making the focal spot elliptical after focusing.

[0064] As an embodiment of the present invention, a cage coaxial system may be used to construct an optical path, which can better solve the coaxial alignment problem, but will also increase the optical path cost accordingly.

[0065] The technical scope of the present invention is not limited to the contents in the above description. Those skilled in the art can make various deformations and modifications to the above embodiments without departing from the technical idea of ​​the present invention, and these deformations and modifications should all fall within the protection scope of the present invention.

Claims

1. A circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens, characterized in that: Includes steps: Determine the beam parameters of CAB; According to the preset error tolerance, the autofocus focal length d of the CAB is calculated; The nth order light ring is selected as the research object among multiple light rings of CAB. In the numerical simulation, all other light rings except the nth order light ring are blocked, and the selected nth order light ring is numerically calculated to solve the single light ring diffraction integral. At the same time, in the calculation process of the diffraction integral, the focal position of the nth order single light ring is determined by searching the extreme point of the light intensity distribution, so as to obtain the focal length d n ; According to the self-focus focal length d and the single light ring focal length d n The difference between n , so that the focal length of the single light ring of the nth light ring plus the phase modulation of the lens changes from d n becomes d; Based on the obtained light ring levels, the focal length f is modulated n , by calculating the modulation effect of the overall beam on the modulation focal length f of each level of light ring n Make subtle adjustments for optimal modulation.

2. The circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens according to claim 1, characterized in that: The preset error tolerance includes low error tolerance and high error tolerance, where: Under low error tolerance, a high-precision numerical calculation method is used to determine the self-focusing focal length d of CAB; Under high error tolerance, use the approximate formula To estimate the self-focusing focal length d of CAB, where r0, w, and λ are the beam parameters of CAB, representing the main light ring radius, scale factor, and working wavelength of the beam, respectively.

3. The circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens according to claim 1, characterized in that: The phase distribution of the modulated wavefront is given by the formula Definition, where t(r) is the modulation function that varies according to the ring radius r, and contains different modulation focal lengths f for different ring regions. n , specifically: In the formula, r n is the radius of the nth dark ring, f n is the corresponding modulation focal length, and exp(*) is the exponential decay factor.

4. The circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens according to claim 1 or 3, characterized in that: After estimating the modulation focal length f n , it is also necessary to apply the Fresnel diffraction integral to calculate the modulated light field distribution, and calculate the integral through numerical methods to obtain the phase and amplitude distribution of the light field during propagation, so as to predict and optimize the effect of wavefront phase modulation.

5. The circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens according to claim 4, characterized in that: The specific operation of the method of realizing wavefront phase modulation using Fresnel diffraction integral is as follows: Initial light field setting: setting the light field distribution u(x′, y′, 0) of the light beam at the initial plane Z=0 as the starting point of the wavefront phase modulation, where u(x′, y′, 0) contains the modulated phase information; The Fresnel diffraction integral formula is used to calculate the light field distribution from the initial surface to any distance Z. In the formula, λ is the wavelength of light, k is the wave number, and i is the imaginary unit; The phase distribution of the modulation function, in the calculation process, the phase distribution of the modulation function t(r) is substituted into u(x′, y′, 0), and the above integral is calculated numerically to obtain the phase and amplitude distribution of the light field during the propagation process.

6. The circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens according to claim 5, characterized in that: After implementing the wavefront phase modulation method based on the Fresnel diffraction integral, the calculated phase distribution is realized through the spatial light modulator, and the light intensity distribution of the light beam at different propagation positions is recorded using a CCD camera to evaluate the effectiveness of the wavefront phase modulation method.

7. The circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens according to claim 6, characterized in that: The specific operations to evaluate the effectiveness of the wavefront phase modulation method are as follows: First, a helium-neon laser was used as the light source; Secondly, the light beam output by the laser is expanded by a group of lenses, and the expanded light beam is spatially filtered by a pinhole filter; Thirdly, the beam after expansion and filtering is guided to be incident on a spatial light modulator, and the required beam is generated based on the wavefront information encoded by the phase holographic algorithm loaded on the spatial light modulator, and the light intensity distribution of the beam at different propagation positions is recorded using a CCD; Finally, by adjusting the phase pattern on the spatial light modulator, each light ring is modulated independently to ensure that all light rings are optimally focused at the focal point.

8. The circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal length lens according to claim 7, characterized in that: The helium-neon laser model is Daheng Optoelectronics DH-HN250P.

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