Circularly symmetric airy beam wavefront phase modulation method based on multi-focal length lens

Abstract

The application provides a circularly symmetric Airy beam wavefront phase modulation method based on a multi-focal lens, which comprises the following steps: determining the beam parameter of a CAB; calculating the self-focusing focal length d of the CAB; shielding all other light rings except the nth light ring, solving a single light ring diffraction integral, thereby obtaining the focal length d n ; reasonably estimating the modulation focal length f n according to the difference between the self-focusing focal length d and the single light ring focal length d n ; and finely adjusting the modulation focal length f n of each light ring based on the obtained modulation focal length f n of each light ring, so as to achieve the best modulation effect. The application realizes higher energy concentration and better focusing characteristics without changing the initial light intensity distribution of the CAB, and improves the focusing precision of the light beam.

Description

Technical Field

[0001] This invention relates to the field of wavefront phase modulation technology for multifocal lenses, specifically to a wavefront phase modulation method for circularly symmetric Airy beams based on multifocal lenses. Background Technology

[0002] A circular Airy beam (CAB) is a self-focusing beam that does not require a lens for focusing. Its characteristic is that when propagating in free space, the beam maintains the self-accelerating properties of an Airy beam, and the light field energy converges along the parabolic surface to the focal point. Thus, it can maintain the intensity distribution of the pole before the focal point, while the light intensity suddenly increases by tens or even hundreds of times when it reaches the vicinity of the focal point. Therefore, it is also known as an abruptly autofocusing beam (AAB).

[0003] As shown in the attached diagram of the instruction manual. Figure 1 As shown, compared to Gaussian focused beams, CAB (Cyclic Aperture Blower) has unparalleled natural advantages in fields such as photodynamic therapy, nonlinear optics, laser 3D micromachining, and optical tweezers manipulation. However, most of the energy of CAB is diffused in space during propagation, and only about 8% of the initial light field energy is focused at the focal point, which seriously hinders the application of the beam. Therefore, how to maximize the self-focusing ability of CAB has become one of the core issues of concern to researchers.

[0004] To improve the self-focusing performance of CAB (Cyclic Aperture Beam), researchers proposed a spectral high-pass filtering method, which effectively enhances the beam's focusing ability. Furthermore, a spectral amplitude envelope modulation method was developed, optimizing the beam's focusing characteristics by flexibly controlling the spectral width and energy ratio. However, a problem arises because this spectral modulation method yields a smaller focal spot size, with the total energy of the focal spot only about 30% of the initial optical field, less than the 39% achieved by wavefront phase modulation. This limits the current technology's ability to increase focal spot energy. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the purpose of this invention is to provide a wavefront phase modulation method for circularly symmetric Airy beams based on multifocal lenses, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a wavefront phase modulation method for a circularly symmetric Airy beam based on a multifocal lens, comprising the following steps.

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

[0008] Among the multiple rings in CAB, the nth-order ring is selected as the research object. In the numerical simulation, all other rings except the nth-order ring are blocked, and numerical calculations are performed on the selected nth-order ring to solve for the single-ring diffraction integral. Simultaneously, during the calculation of this diffraction integral, the focal position of the nth-order single ring is determined by searching for the extreme points of the light intensity distribution, thereby obtaining the focal length d. n Based on the self-focusing focal length d and the single-ring focal length d n The difference, reasonably estimate the modulation focal length f n This causes the focal length of the single ring of the nth order optical ring, after phase modulation by the lens, to be reduced from d. n It becomes d; based on the obtained aperture rings at each level, the focal length f is modulated. n The modulation focal length f of each level of the optical ring is calculated by the overall beam modulation effect. n Make fine adjustments to achieve the best modulation effect.

[0009] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0010] The wavefront phase modulation method proposed in this invention significantly enhances the self-focusing capability of a circular Airy beam (CAB). By precisely calculating and adjusting the focal length of each ring in the CAB, this method ensures that different rings converge at the same focal point during propagation, thereby greatly enhancing the energy of the focal spot. Experimental results show that the intensity of the modulated beam at the focal point is significantly increased, with the focal spot energy reaching 39% of the initial intensity—nearly five times the 8% of the unmodulated CAB focal spot energy. Compared to existing spectral modulation methods, this invention achieves higher energy concentration and superior focusing characteristics without altering the initial intensity distribution of the CAB. It not only improves the focusing accuracy of the beam but also, due to its ease of implementation and efficient utilization of light source energy, provides new possibilities for performance optimization of CABs in various application areas such as photodynamic therapy, nonlinear optics, laser 3D micromachining, and optical tweezers manipulation. Attached Figure Description

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

[0012] Figure 1 This is a schematic diagram of the sudden self-focusing characteristic of CAB in the prior art;

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

[0014] Figure 2bThis is a schematic diagram of the spectrum modulated by envelopes with different parameters according to one embodiment of the present invention;

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

[0016] Figure 3b This is a schematic diagram of the initial surface light field distribution after spectral envelope modulation, as proposed in one embodiment of the present invention;

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

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

[0019] Figure 6 This is a schematic diagram comparing the focal spot intensity distribution of the beam before modulation (line A) and after modulation (line B) in one embodiment of the present invention.

[0020] Figure 7 This is a schematic diagram of the experimental optical path constructed for evaluating the effectiveness of the wavefront phase modulation method proposed in one embodiment of the present invention.

[0021] Figure 8 This is a schematic diagram of the cross-sectional light intensity of the modulated beam at different propagation distances according to an embodiment of the present invention;

[0022] Figure 9 This is a schematic flowchart of the wavefront phase modulation method proposed in one embodiment of the present invention. Detailed Implementation

[0023] It is readily understood that, based on the technical solution of this invention, those skilled in the art can propose various interchangeable structural methods and implementations without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention.

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

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

[0026] In one embodiment of the present invention, since the existing technology uses CAB spectral high-pass filtering, which can effectively improve the self-focusing performance of the beam, it still has limitations in terms of focal spot energy. Therefore, it should be noted that we propose an envelope modulation method for spectral amplitude based on this. Compared with ordinary spectral filtering methods, spectral 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 illustrated. Figure 2a The unmodulated CAB spectrum was depicted, exhibiting a typical ring distribution, while... Figure 2b This demonstrates the spectra after envelope modulation with different parameters, where the spectral width and energy distribution are effectively controlled, indicating that spectral modulation can significantly improve the self-focusing performance of CAB. However, spectral modulation is not without its challenges. It involves not only meticulous adjustments to 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 complex because the increase in high-frequency components leads to significant changes in the optical field structure. This change results in a significantly different initial beam shape compared to the unmodulated form, affecting the subsequent beam propagation and focusing characteristics. The following is an example analysis of the modulation process across the entire beam spectrum, extending from the preceding issues:

[0027] The initial surface light field of CAB in cylindrical coordinates 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 scaling factor, controlling the density of the rings, and α is the exponential decay factor (0 < α < 1). It should be noted that there is currently no rigorous analytical expression for the CAB spectrum; therefore, it is usually obtained using Fourier transform calculations.

[0030]

[0031] In the formula, 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 by the following formula:

[0032]

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

[0034] Furthermore, Figure 3a and Figure 3b The modulation effect of the initial surface light field distribution of CAB was further demonstrated. Figure 3a The image shows the initial surface light field distribution of the unmodulated CAB, which has a relatively uniform intensity distribution. In contrast, 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 components of the light field, thereby changing the initial surface distribution of the beam to achieve more effective self-focusing.

[0035] Based on the above example analysis, it can be concluded that the focusing capabilities of different rings in a CAB beam vary. The main ring has the largest energy proportion but the weakest focusing capability and the longest focal length, while the rings at the beam edges have a smaller energy proportion but stronger focusing capability and shorter focal lengths. Therefore, by using a multifocal lens on the wavefront, the focal lengths of different rings can be adjusted to focus them as much as possible into the same region, thereby increasing their coherence in the focusing area and improving the beam's focusing capability. Considering the different focusing capabilities of different ring regions, lenses with different focal lengths are needed for phase modulation.

[0036] Based on this, the present invention proposes to integrate the basic characteristics of Airy beams and achieve wavefront phase modulation through modulation function t(r), thereby further optimizing the focusing characteristics of the beam, enhancing the focal spot energy, and improving the application efficiency and effect of the beam.

[0037] In specific implementation, such as Figure 9 As shown, the wavefront phase modulation method proposed in this invention includes the following steps:

[0038] S1. Determine the beam parameters of the CAB; it is understood that the beam parameters of the CAB include the main ring radius r0, the scaling factor w, the operating wavelength λ of the beam, and the exponential attenuation factor α.

[0039] S2. It should be noted that calculating the self-focusing focal length in this step is crucial for improving the self-focusing capability of the circular Airy beam (CAB). The calculation is performed based on a preset error tolerance, determining the CAB's self-focusing focal length d. The preset error tolerance includes low and high tolerances. Under low tolerance, a high-precision numerical calculation method is used to determine the CAB's self-focusing focal length d; under high tolerance, an approximate formula d = ... The self-focusing focal length d of the CAB is estimated using the formula, where r0, w, and λ are the beam parameters of the CAB, representing the principal ring radius, scaling factor, and operating wavelength of the beam, respectively. Example: If the required focal length calculation error is within 1%, then this can be considered a high-precision requirement. Conversely, if an error of 5% or greater is acceptable, then the precision requirement can be considered less stringent. Based on the above method, it can be ensured that the self-focusing focal length calculation of the CAB meets both precision requirements and adapts to different application needs.

[0040] S3. The nth-order ring is selected as the research object from among the multiple rings of the CAB beam. This selection is based on an in-depth analysis of the CAB beam characteristics and consideration of the differences in focusing capabilities among different rings. Then, in the numerical simulation, by setting the computational model, all other rings except the nth-order ring are blocked or ignored to ensure that the focus of the calculation is concentrated on the selected ring, thereby improving computational efficiency and accuracy. Numerical calculations are performed on the selected nth-order ring to solve for the single-ring diffraction integral. This process involves a mathematical description of the ring's light field distribution and the application of relevant physical and optical principles to simulate light wave propagation. Simultaneously, during the calculation of this diffraction integral, an algorithm is used to search for extreme points in the light intensity distribution. These extreme points correspond to the focal points of the beam during propagation, i.e., the focal positions. Based on the positions of these extreme light intensity points, the focal position of the nth-order single ring can be determined, thus obtaining the focal length d. n It should be noted that this focal position is the region where the energy of the light beam is most concentrated during propagation, which is crucial for achieving self-focusing. In practice, the distance from the focal position to the initial surface is defined as the focal length d. n Focusing is a key parameter for evaluating and comparing the focusing capabilities of different rings, and it is also the basis for subsequent modulation focal length prediction. Through this step, the focusing characteristics of each ring in CAB can be accurately evaluated and optimized, thereby improving the focusing accuracy of the self-focusing beam and providing the possibility for beam performance optimization in various applications.

[0041] S4. Based on the self-focusing focal length d and the single-ring focal length d n The difference, reasonably estimate the modulation focal length f n This causes the focal length of the single ring of the nth order optical ring, after phase modulation by the lens, to be reduced from d. n It becomes d.

[0042] S5. Based on the obtained focal length f of each level of optical ring modulation n The modulation focal length f of each level of the optical ring is calculated by the overall beam modulation effect. n Fine-tuning is performed to achieve the best modulation effect. The modulated wavefront phase distribution is given by the formula. Defined as follows: where A0 is the amplitude constant, Ai(*) represents the Airy function, r is the radial distance from a point in the beam to the beam center, and t(r) is the modulation function that varies according to the radius r of the halo. Furthermore, different halo regions contain different modulation focal lengths f. n Specifically:

[0043]

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

[0045] Understandably, the aforementioned variation in the halo radius r is achieved by applying different phase modulations to each halo to ensure that they can be focused on the same focal plane, thus achieving self-focusing. Through this modulation, each part of the beam (i.e., each halo) is given an appropriate phase change, allowing them to converge at a point after propagating a certain distance. This point is the focal point, and the light intensity at the focal point is thus enhanced, while the light intensity outside the focal region is relatively weak, achieving the self-focusing effect. At the same time, the modulated wavefront phase distribution needs to be optimized through numerical simulation and experimental verification to ensure that the 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 steps S4 and S5 above, Fresnel diffraction integrals need to be applied to calculate the modulated light field distribution, and the integral is calculated numerically to obtain the phase and amplitude distribution of the light field during propagation, in order to predict and optimize the effect of wavefront phase modulation. It should be noted that Fresnel diffraction integrals are the foundation for numerical simulation. By numerically calculating this integral, a detailed distribution of the light field during propagation can be obtained, including the light intensity distribution in the focal region, which helps to predict the effect of wavefront phase modulation before the experiment, thus guiding experimental design. The numerical simulation results obtained through Fresnel diffraction integrals can serve as the basis for experimental verification. In specific implementation,

[0047] The specific operation of the wavefront phase modulation method 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 beam on the initial surface z=0 is set as the starting point of 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 an arbitrary 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 is obtained by substituting the phase distribution of the modulation function t(r) into u(x′,y′,0) during the calculation process and calculating the above integral numerically to obtain the phase and amplitude distribution of the light field during propagation.

[0053] Furthermore, after implementing the wavefront phase modulation method based on Fresnel diffraction integral, the calculated phase distribution is realized using a spatial light modulator, and the light intensity distribution of the beam at different propagation positions is recorded using a CCD camera to evaluate the effectiveness of the wavefront phase modulation method. To facilitate the illustration of the invention's technical effects, numerical simulation results are presented, followed by experimental verification of the simulation results. In specific implementation...

[0054] Regarding parameter selection, the helium-neon laser used in the experiment was the Daheng Optoelectronics DHN250P, with a power of approximately 2.4mW and a working wavelength of 632.8nm. The beam expander system used a Daheng Optoelectronics GCO-2102 objective lens with a magnification of 10x, a numerical aperture of 0.25, and a working distance of 7.3mm. Both the long-focus and Fourier lenses were Daheng Optoelectronics GCL-010117 plano-convex lenses with a focal length of 300mm. The pinhole filter size was 25μm. The CCD camera used was a Solvay BC207VIS / M spot analyzer with a pixel size of 3.45μm, a resolution of 2448*2048, and a sensor size of 8.45mm x 7.07mm. 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 plane size of 15.32mm*9.22mm.

[0055] The operation steps are as follows:

[0056] First, the initial energy of the beam is normalized, that is, let... To facilitate the comparison of focal spot energy and determine the beam parameters of CAB, in this embodiment, the wavelength is set to 632.8 nm, r0 = 1 mm, w = 0.08 mm, α = 0.1, and remains unchanged;

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

[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 calculations, the modulation focal length of the first ring (main ring) is f1 = 0.93d; the modulation focal length of the second ring is f2 = 1.08d; the modulation focal length of rings 3-6 is f3 = 5.26d; and the modulation focal length of rings 6 and beyond is f4 = 5.6d, where d is the self-focusing focal length of the 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 beam before and after modulation is shown in the figure. As can be seen from the figure, the focal length of the modulated beam is slightly reduced compared to the modulated beam, and the intensity at the focal point increases from less than 30 to 122. Furthermore, the focal region still maintains a very low peak intensity, creating a large intensity gradient in the focal region, thus preserving the sudden self-focusing characteristic. (See also...) Figure 6 As shown, the focal spot intensity distribution of the beam before modulation (line A) and after modulation (line B) is compared. It can be seen that the focal spot size of the beam is slightly increased after modulation, and the focal spot energy reaches 39% of the initial light field, which is nearly 5 times the 8% of the focal spot energy of CAB before modulation.

[0062] Based on this, it can be concluded that: compared with the spectral modulation method, the wavefront phase modulation proposed in this 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 spectral modulation method is slightly smaller than that of the original CAB. This is because spectral modulation increases the high-frequency components of the optical field, while the focal spot radius obtained by the wavefront phase modulation method proposed in this invention is slightly larger than that of the original CAB. Therefore, the working principle of this invention is similar to that of the spectral high-pass filtering method proposed in the prior art (see reference). Figure 1 The theoretical principles are completely different. 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 this invention can reach 39% of the initial light field, which makes more effective use of the energy of the incident light source. Moreover, this invention does not change the initial light intensity distribution of CAB, and is easier to implement than the existing spectrum modulation method.

[0063] During the above-described operational steps, the experimental optical path constructed by this invention is as follows: Figure 7 As shown, a 632.8nm helium-neon laser is used as the light source. In practical applications, different wavelengths of light sources can be used according to actual needs. The beam passes through a half-wave plate to adjust its polarization direction to be consistent with the working direction of the spatial light modulator (SLM). Then, after passing through a lens group and pinhole filter, the beam is expanded and incident on the SLM. 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 spectral plane to selectively filter the spectrum, allowing only the first-order diffracted light to pass through. The beam passes through a second Fourier lens and generates the desired beam on its rear focal plane. The CCD can be moved along the optical axis to record the light intensity distribution of the beam at different propagation positions. When the working wavelength is changed, since the modulation focal length is related to the working wavelength, the above steps need to be repeated to recalculate and select values ​​to obtain the phase distribution of the new modulation function. The experimental optical path built at this time is the same as... Figure 7 The procedures are the same, but the optical components need to be reselected based on the operating wavelength; the experimental steps remain unchanged. (Reference) Figure 8 This is a schematic diagram of the cross-sectional light intensity distribution of the modulated beam at different propagation distances. Figure 8 In the figure, (ad) represents the experimental results; (ef) represents the corresponding theoretical calculation results. (a) and (e) represent the initial plane z = 0; (b) and (f) represent z = 100 mm; (c) and (g) represent z = 285 mm. (a) and (e) represent the focal plane. For ease of comparison, the corresponding theoretical calculation results are also given in the figure. As can be seen from the figure, the experimental light intensity distribution obtained at different positions matches the theoretically expected light intensity distribution very well, proving that the experimental results are consistent with the theoretical calculation results, and demonstrating 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 the various devices in the optical path was not properly adjusted, and the beam was deformed after passing through the devices, resulting in an elliptical focal spot after focusing.

[0064] As an embodiment of the present invention, a cage-type coaxial system can also be used to build the optical path, which can better solve the coaxial collimation problem, but will also increase the cost of the optical path.

[0065] The technical scope of this invention is not limited to the content described above. Those skilled in the art can make various modifications and variations to the above embodiments without departing from the technical concept of this invention, and all such modifications and variations should fall within the protection scope of this invention.

Claims

1. A wavefront phase modulation method for circularly symmetric Airy beams based on multifocal lenses, characterized in that: Including the following steps: Determine the beam parameters of the circular Airy beam; Calculate the self-focusing focal length of the circular Airy beam based on the preset error tolerance. ; In a circular Airy beam, the nth-order ring is selected as the research object. In the numerical simulation, all other rings except the nth-order ring are blocked. Numerical calculations are performed on the selected nth-order ring to solve for the single-ring diffraction integral. Simultaneously, during the calculation of this diffraction integral, the focal position of the nth-order single ring is determined by searching for the extreme points of the light intensity distribution, thereby obtaining the focal length. ; Based on self-focusing focal length With single-ring focal length The difference, reasonably estimate the modulation focal length This causes the focal length of the single ring of the nth order optical ring, after phase modulation by the lens, to be from... Become ; Based on the obtained focal length modulation of each level of the optical ring The modulation focal length of each level of the optical ring is calculated by the modulation effect of the overall beam. Make fine adjustments to achieve the best modulation effect; The modulated wavefront phase distribution is given by the formula Define, where, The modulation function is based on the variation of the halo radius r, and includes different modulation focal lengths for different halo regions. , Represents the Airy function, Represents the radius of the main halo. Represents the scaling factor. The exponential decay factor is as follows: In the formula, Let the radius be the nth dark ring. For the corresponding modulated focal length, It is an exponential decay factor.

2. The wavefront phase modulation method for a circularly symmetric Airy beam based on a multifocal 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 of the circular Airy beam. ; Under high error tolerance, an approximate formula is used. To estimate the self-focusing focal length of the circular Airy beam. In the formula, , , These are all beam parameters for a circular Airy beam, representing the main ring radius, scaling factor, and operating wavelength of the beam, respectively.

3. The wavefront phase modulation method for a circularly symmetric Airy beam based on a multifocal lens according to claim 1, characterized in that: After estimating the modulation focal length Furthermore, Fresnel diffraction integrals are needed to calculate the modulated light field distribution, and numerical methods are used to calculate the integrals to obtain the phase and amplitude distribution of the light field during propagation, in order to predict and optimize the effect of wavefront phase modulation.

4. The wavefront phase modulation method for a circularly symmetric Airy beam based on a multifocal lens according to claim 3, characterized in that: The specific operation of the wavefront phase modulation method using Fresnel diffraction integral is as follows: Initial light field setting: Setting the light field distribution of the beam at the initial surface z=0. This is the starting point for wavefront phase modulation, where, It contains modulated phase information; The light field distribution propagating from the initial surface to an arbitrary distance z is calculated using the Fresnel diffraction integral formula. 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 is used in the calculation process. Substituting the phase distribution In this process, the phase and amplitude distribution of the light field during propagation are obtained by numerically calculating the above integral.

5. The wavefront phase modulation method for a circularly symmetric Airy beam based on a multifocal lens according to claim 4, characterized in that: After realizing the wavefront phase modulation method based on Fresnel diffraction integral, the calculated phase distribution is realized through a spatial light modulator, and the light intensity distribution of the beam at different propagation positions is recorded using a CCD camera to evaluate the effectiveness of the wavefront phase modulation method.

6. The wavefront phase modulation method for a circularly symmetric Airy beam based on a multifocal lens according to claim 5, characterized in that: The specific steps for evaluating the effectiveness of wavefront phase modulation methods are as follows: First, a helium-neon laser is used as the light source; Secondly, the beam output by the laser is expanded by a set of lenses, and the expanded beam is spatially filtered by a pinhole filter. Next, the expanded and filtered beam is guided into the spatial light modulator. Based on the wavefront information encoded by the phase holographic algorithm loaded into the spatial light modulator, the required beam is generated, and the 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, independent modulation of each light ring is achieved, ensuring that all light rings are optimally focused at the focal point.

7. The wavefront phase modulation method for a circularly symmetric Airy beam based on a multifocal lens according to claim 6, characterized in that: The helium-neon laser is model DH-HN250P from Daheng Optoelectronics.

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