CN114488546A - A method for generating multi-focus self-focusing beams with adjustable focal characteristics - Google Patents

A method for generating multi-focus self-focusing beams with adjustable focal characteristics Download PDF

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CN114488546A
CN114488546A CN202111631722.3A CN202111631722A CN114488546A CN 114488546 A CN114488546 A CN 114488546A CN 202111631722 A CN202111631722 A CN 202111631722A CN 114488546 A CN114488546 A CN 114488546A
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陈钰杰
吴孟霖
林树青
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Sun Yat Sen University
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    • G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
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    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
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Abstract

The invention discloses a method for generating a multifocal self-focusing light beam with adjustable focal point characteristics, which comprises the following steps: constructing a self-focusing light beam by a caustic method; superposing wave fronts corresponding to the multiple groups of self-focusing light beams; encoding the complex amplitude distribution of the wavefront into a pure phase form; loading the obtained phase distribution on a spatial light modulator to modulate an incident light field; and Fourier transform is carried out on the modulated light field by using the lens. The invention has the advantages that the optical field can be converged to a plurality of focuses along different tracks after being modulated once, and the number, the position and the relative strength among the focuses of the focuses can be regulated and controlled simultaneously, thereby realizing more flexible control on the energy of the optical field. The invention provides a method for encoding the complex wavefront required by generating the multi-focus self-focusing light beam into a pure phase form by using a biphase method, thereby reducing the requirements on optical field regulation and control equipment.

Description

一种产生焦点特性可调的多焦点自聚焦光束方法A method for generating multi-focus self-focusing beams with adjustable focal characteristics

技术领域technical field

本发明属于光束调控的技术领域，具体涉及一种产生焦点特性可调的多焦点自聚焦光束方法。The invention belongs to the technical field of beam regulation, and in particular relates to a method for generating a multi-focus self-focusing beam with adjustable focus characteristics.

背景技术Background technique

自从2007年在实验上产生并观测到艾里光束以来，这种光束由于其独特的横向自加速、无衍射传播、可自愈的特性受到了研究人员广泛的关注。为了突破艾里光束只能沿抛物线轨迹传播的限制，研究者提出了光学焦散线方法，使得可以在实空间或傅里叶空间构造沿任意凸轨迹传播的自加速光束。Since the experimental generation and observation of Airy beams in 2007, this beam has attracted extensive attention of researchers due to its unique lateral self-acceleration, diffraction-free propagation, and self-healing properties. In order to break through the limitation that Airy beams can only travel along parabolic trajectories, the researchers proposed the optical caustics method, which makes it possible to construct self-accelerating beams propagating along arbitrary convex trajectories in real space or Fourier space.

对自加速光束的研究引出了另一类具有新奇特性的光束：急剧自聚焦光束。其在2010年被首次提出，并在2011年得到了实验验证。通过构造环形艾里光束，这种光束的能量在初始阶段分布在远离中心的位置，随着光场传播以加速的形式向中心汇聚，并在到达焦点处时能量可以突然增大几个数量级。急剧自聚焦光束很快在需要光场能量突变的领域得到了应用，如微加工、粒子操控、医学激光治疗等。此后，人们提出了许多种方法来进一步提高焦点的强度对比度，或是为急剧自聚焦光束引入其他新特性，如改变相位啁啾、引入涡旋相位、构造其他轨迹的自聚焦光束、从傍轴情况推广到非傍轴情况等。The study of self-accelerating beams has led to another class of beams with novel properties: sharp self-focusing beams. It was first proposed in 2010 and experimentally verified in 2011. By constructing a ring-shaped Airy beam, the energy of this beam is initially distributed away from the center, converges toward the center in an accelerated fashion as the light field propagates, and can suddenly increase by several orders of magnitude when it reaches the focal point. Sharp self-focusing beams soon found applications in fields that require abrupt changes in optical field energy, such as micromachining, particle manipulation, and medical laser therapy. Since then, many methods have been proposed to further improve the intensity contrast of the focal point, or to introduce other new properties for sharp self-focusing beams, such as changing the phase chirp, introducing vortex phase, constructing self-focusing beams of other trajectories, and from paraxial The case generalizes to the non-paraxial case, etc.

针对如何产生多焦点自聚焦光束的问题，中国专利公开号：CN111522140A，申请公开日：2021年03月19日，公开了一种构造对称多周期余弦自加速光束的方法，可以在中轴线上产生多个焦点，但是该方法构造的是二维光束，产生的焦点对比度不高，且无法对焦点的强度和位置进行有效调控。In view of the problem of how to generate a multi-focus self-focusing beam, Chinese Patent Publication No.: CN111522140A, Application Publication Date: March 19, 2021, discloses a method for constructing a symmetrical multi-period cosine self-accelerating beam, which can be generated on the central axis However, this method constructs a two-dimensional beam, resulting in a low contrast of the focus, and cannot effectively control the intensity and position of the focus.

发明内容SUMMARY OF THE INVENTION

针对现有技术的不足，本发明旨在提供一种产生焦点特性可调的多焦点自聚焦光束方法，通过本发明提高自聚焦光束设计的自由度，实现对光场能量更灵活的控制，进一步的，本发明可以同时实现对焦点的个数、位置和焦点间相对强度的调控，且只需使用纯相位器件就可以产生光束。In view of the deficiencies of the prior art, the present invention aims to provide a method for generating a multi-focus self-focusing beam with adjustable focal characteristics. The present invention improves the degree of freedom of self-focusing beam design, realizes more flexible control of light field energy, and further Therefore, the present invention can simultaneously realize the regulation of the number, position and relative intensity of the focus points, and only needs to use a pure phase device to generate a light beam.

为了实现上述目的，本发明采用如下技术方案，In order to achieve the above object, the present invention adopts the following technical solutions:

一种产生焦点特性可调的多焦点自聚焦光束方法，所述方法包括以下步骤：A method for generating a multi-focus self-focusing beam with adjustable focus characteristics, the method comprises the following steps:

S1通过焦散线方法构造自聚焦光束；S1 constructs a self-focusing beam by the caustics method;

S2叠加多组自聚焦光束对应的波前；S2 superimposes the wavefronts corresponding to multiple groups of self-focusing beams;

S3将波前的复振幅分布编码为纯相位形式；S3 encodes the complex amplitude distribution of the wavefront into pure phase form;

S4在空间光调制器加载得到的相位分布，对入射光场进行调制；S4 loads the phase distribution obtained by the spatial light modulator to modulate the incident light field;

S5利用透镜对调制后的光场进行傅里叶变换。S5 uses a lens to perform Fourier transform on the modulated light field.

需要说明的是，所述步骤S1包括在空间频域构造环形抛物线轨迹的自加速光束，其中，焦散线轨迹方程可表示为：It should be noted that the step S1 includes constructing a self-accelerating beam with an annular parabolic trajectory in the spatial frequency domain, wherein the caustics trajectory equation can be expressed as:

Figure BDA0003440437340000031
Figure BDA0003440437340000031

r是极坐标下的径向坐标，r0是中心暗区的半径，z是光场传播方向，zc是焦散线与中轴线的交点，可以近似为产生焦点的位置。r is the radial coordinate in polar coordinates, r 0 is the radius of the central dark area, z is the propagation direction of the light field, and z c is the intersection of the caustics line and the central axis, which can be approximated as the location where the focus is generated.

需要说明的是，所述步骤S2包括对于焦点都在中轴线上的情况，多焦点自聚焦光束波前的复振幅分布可以表示为：It should be noted that the step S2 includes that for the case where the focal points are all on the central axis, the complex amplitude distribution of the wavefront of the multi-focus self-focusing beam can be expressed as:

Figure BDA0003440437340000032
Figure BDA0003440437340000032

式中，n为轨迹/焦点的个数，下标j表示第j组自聚焦光束的参数，cj表示第j组轨迹的附加相位，1/M项是为了保证振幅a(r)不大于1，M可以表示为：

Figure BDA0003440437340000033
通过为每组轨迹选择适当的附加相位，可以使得光场叠加后焦点间的相对强度保持不变。In the formula, n is the number of trajectories/focus, the subscript j represents the parameters of the j-th group of self-focusing beams, c j represents the additional phase of the j-th group of trajectories, and the 1/M term is to ensure that the amplitude a(r) is not greater than 1, M can be expressed as:
Figure BDA0003440437340000033
By choosing an appropriate additional phase for each set of trajectories, the relative intensities between the foci after superposition of the light fields can be kept constant.

进一步的，假设使用焦距为f的透镜进行傅里叶变换，步骤S1中轨迹自聚焦光束在相平面(透镜前焦面)的相位分布为：Further, assuming that a lens with a focal length of f is used for Fourier transform, the phase distribution of the self-focusing beam of the trajectory in the phase plane (front focal plane of the lens) in step S1 is:

Figure BDA0003440437340000034
Figure BDA0003440437340000034

式中，k是光波的波数。为了最大化利用光场的能量，将波前的振幅分布a(r)设置为：在半径为R的圆内振幅为1，在圆外振幅为0。利用傍轴近似下的角谱衍射公式，可以得到中轴线上的光场复振幅为：where k is the wave number of the light wave. In order to maximize the utilization of the energy of the light field, the amplitude distribution a(r) of the wavefront is set to be 1 within the circle of radius R and 0 outside the circle. Using the angular spectrum diffraction formula under the paraxial approximation, the complex amplitude of the light field on the central axis can be obtained as:

Figure BDA0003440437340000035
Figure BDA0003440437340000035

要产生急剧自聚焦效果，选择的光场范围需要满足

Figure BDA0003440437340000041
对上式进行计算可知，在一定范围内，焦点强度随R增大而增大，通过改变R的值可以调控产生焦点的强度。To produce a sharp self-focusing effect, the selected light field range needs to meet the
Figure BDA0003440437340000041
The calculation of the above formula shows that within a certain range, the focus intensity increases with the increase of R, and the intensity of the focus can be regulated by changing the value of R.

需要说明的是，还包括对于焦点离轴的情况，多焦点自聚焦光束波前的复振幅分布可以表示为：It should be noted that, for the case where the focus is off-axis, the complex amplitude distribution of the multi-focus self-focusing beam wavefront can be expressed as:

Figure BDA0003440437340000042
Figure BDA0003440437340000042

式中，(x′j,y′j)是第j组轨迹的偏移量，也是在焦点平面上的坐标。In the formula, (x′ j , y′ j ) is the offset of the jth group of trajectories, and is also the coordinates on the focal plane.

需要说明的是，所述步骤S3包括利用双相法，将多焦点自聚焦光束波前的复振幅分布分解为两个相位分量，该过程可以表示为：It should be noted that the step S3 includes using the dual-phase method to decompose the complex amplitude distribution of the multi-focus self-focusing beam wavefront into two phase components, and the process can be expressed as:

Figure BDA0003440437340000043
Figure BDA0003440437340000043

Figure BDA0003440437340000044
Figure BDA0003440437340000044

同时，将空间光调制器的2×2个像素单元组成一个巨像素单元，对巨像素中心位置的波前复振幅分解为两个相位分量，分别设置在巨像素的两条对角线上。At the same time, the 2×2 pixel units of the spatial light modulator are formed into a giant pixel unit, and the wavefront complex amplitude at the center of the giant pixel is decomposed into two phase components, which are respectively arranged on the two diagonals of the giant pixel.

需要说明的是，所述步骤S4包括假设空间光调制器像素单元边长为p，在实空间中重建的光场必须满足奈奎斯特带宽的限制条件，即

Figure BDA0003440437340000045
It should be noted that the step S4 includes assuming that the side length of the pixel unit of the spatial light modulator is p, and the light field reconstructed in the real space must meet the restriction condition of the Nyquist bandwidth, that is,
Figure BDA0003440437340000045

需要说明的是，透镜前焦面与后焦面处的光场满足傅里叶变换的关系，透镜的前焦面与空间光调制器重合。It should be noted that the light fields at the front focal plane and the back focal plane of the lens satisfy the Fourier transform relationship, and the front focal plane of the lens coincides with the spatial light modulator.

本发明有益效果在于：The beneficial effects of the present invention are:

1、本发明可以使光场经过一次调制后就可以沿不同轨迹汇聚到多个焦点，且能够同时实现对焦点的个数、位置和焦点间相对强度的调控，从而实现了对光场能量更灵活的控制。1. The present invention can make the light field converge to multiple focal points along different trajectories after one modulation, and can realize the regulation of the number, position and relative intensity of the focal points at the same time, thereby realizing the improvement of the energy of the light field. Flexible control.

2、本发明提出将产生多焦点自聚焦光束所需的复波前利用双相法编码为纯相位的形式，降低了对光场调控设备的要求。2. The present invention proposes to encode the complex wavefront required to generate the multi-focus self-focusing beam into the form of pure phase by using the biphase method, which reduces the requirements for the light field control equipment.

附图说明Description of drawings

图1为本发明中的实施例的流程图。FIG. 1 is a flowchart of an embodiment of the present invention.

图2为本发明中的实施例实现多焦点自聚焦光束光路系统示意图。FIG. 2 is a schematic diagram of an optical path system for realizing a multi-focus self-focusing beam according to an embodiment of the present invention.

图3为本发明中的实施例产生多焦点自聚焦光束的仿真的强度分布图；其中，左图是在中轴线上有三个强度一致焦点的多焦点自聚焦光束，右图是在焦平面上有三个强度一致焦点的多焦点自聚焦光束。3 is a simulated intensity distribution diagram of a multi-focus self-focusing beam generated by an embodiment of the present invention; wherein, the left image is a multi-focus self-focusing beam with three focus points of consistent intensity on the central axis, and the right image is on the focal plane A multifocal self-focusing beam with three foci of uniform intensity.

图4为本发明中的实施例对应复波前的振幅和相位图和编码后加载到空间光调制器上的相位图。FIG. 4 is an amplitude and phase diagram of a complex wavefront corresponding to an embodiment of the present invention and a phase diagram loaded onto the spatial light modulator after encoding.

具体实施方式Detailed ways

以下将对结合附图本发明作进一步的描述，需要说明的是，以下实施例以本技术方案为前提，给出了详细的实施方式和具体的操作过程，但本发明的保护范围并不限于本实施例。The present invention will be further described below in conjunction with the accompanying drawings. It should be noted that the following examples are based on the technical solution, and provide detailed implementations and specific operation processes, but the protection scope of the present invention is not limited to this example.

本发明为一种产生焦点特性可调的多焦点自聚焦光束方法，所述方法包括以下步骤：The present invention is a method for generating a multi-focus self-focusing beam with adjustable focus characteristics, which comprises the following steps:

S1通过焦散线方法构造自聚焦光束；S1 constructs a self-focusing beam by the caustics method;

S2叠加多组自聚焦光束对应的波前；S2 superimposes the wavefronts corresponding to multiple groups of self-focusing beams;

S3将波前的复振幅分布编码为纯相位形式；S3 encodes the complex amplitude distribution of the wavefront into pure phase form;

S4在空间光调制器加载得到的相位分布，对入射光场进行调制；S4 loads the phase distribution obtained by the spatial light modulator to modulate the incident light field;

S5利用透镜对调制后的光场进行傅里叶变换。S5 uses a lens to perform Fourier transform on the modulated light field.

进一步的，本发明所述步骤S1包括在空间频域构造环形抛物线轨迹的自加速光束，其中，焦散线轨迹方程可表示为：Further, the step S1 of the present invention includes constructing a self-accelerating beam with a circular parabolic trajectory in the spatial frequency domain, wherein the caustics trajectory equation can be expressed as:

Figure BDA0003440437340000061
Figure BDA0003440437340000061

r是极坐标下的径向坐标，r0是中心暗区的半径，z是光场传播方向，zc是焦散线与中轴线的交点，可以近似为产生焦点的位置。r is the radial coordinate in polar coordinates, r 0 is the radius of the central dark area, z is the propagation direction of the light field, and z c is the intersection of the caustics line and the central axis, which can be approximated as the location where the focus is generated.

进一步的，本发明所述步骤S2包括对于焦点都在中轴线上的情况，多焦点自聚焦光束波前的复振幅分布可以表示为：Further, step S2 of the present invention includes that for the case where the focal points are all on the central axis, the complex amplitude distribution of the wavefront of the multi-focus self-focusing beam can be expressed as:

Figure BDA0003440437340000062
Figure BDA0003440437340000062

式中，n为轨迹/焦点的个数，下标j表示第j组自聚焦光束的参数，cj表示第j组轨迹的附加相位，1/M项是为了保证振幅a(r)不大于1，M可以表示为：

Figure BDA0003440437340000063
通过为每组轨迹选择适当的附加相位，可以使得光场叠加后焦点间的相对强度保持不变。In the formula, n is the number of trajectories/focus, the subscript j represents the parameters of the j-th group of self-focusing beams, c j represents the additional phase of the j-th group of trajectories, and the 1/M term is to ensure that the amplitude a(r) is not greater than 1, M can be expressed as:
Figure BDA0003440437340000063
By choosing an appropriate additional phase for each set of trajectories, the relative intensities between the foci after superposition of the light fields can be kept constant.

进一步的，假设使用焦距为f的透镜进行傅里叶变换，步骤S1中轨迹自聚焦光束在相平面(透镜前焦面)的相位分布为：Further, assuming that a lens with a focal length of f is used for Fourier transform, the phase distribution of the self-focusing beam of the trajectory in the phase plane (front focal plane of the lens) in step S1 is:

Figure BDA0003440437340000071
Figure BDA0003440437340000071

式中，k是光波的波数。为了最大化利用光场的能量，将波前的振幅分布a(r)设置为：在半径为R的圆内振幅为1，在圆外振幅为0。利用傍轴近似下的角谱衍射公式，可以得到中轴线上的光场复振幅为：where k is the wave number of the light wave. In order to maximize the utilization of the energy of the light field, the amplitude distribution a(r) of the wavefront is set to be 1 within a circle of radius R and 0 outside the circle. Using the angular spectrum diffraction formula under the paraxial approximation, the complex amplitude of the light field on the central axis can be obtained as:

Figure BDA0003440437340000072
Figure BDA0003440437340000072

要产生急剧自聚焦效果，选择的光场范围需要满足

Figure BDA0003440437340000073
对上式进行计算可知，在一定范围内，焦点强度随R增大而增大，通过改变R的值可以调控产生焦点的强度。To produce a sharp self-focusing effect, the selected light field range needs to meet the
Figure BDA0003440437340000073
The calculation of the above formula shows that within a certain range, the focus intensity increases with the increase of R, and the intensity of the focus can be regulated by changing the value of R.

进一步的，本发明还包括对于焦点离轴的情况，多焦点自聚焦光束波前的复振幅分布可以表示为：Further, the present invention also includes that for the case where the focus is off-axis, the complex amplitude distribution of the wavefront of the multi-focus self-focusing beam can be expressed as:

Figure BDA0003440437340000074
Figure BDA0003440437340000074

式中，(x′j,y′j)是第j组轨迹的偏移量，也是在焦点平面上的坐标。In the formula, (x′ j , y′ j ) is the offset of the jth group of trajectories, and is also the coordinates on the focal plane.

进一步的，本发明所述步骤S3包括利用双相法，将多焦点自聚焦光束波前的复振幅分布分解为两个相位分量，该过程可以表示为：Further, the step S3 of the present invention includes using the dual-phase method to decompose the complex amplitude distribution of the multi-focus self-focusing beam wavefront into two phase components, and the process can be expressed as:

Figure BDA0003440437340000075
Figure BDA0003440437340000075

Figure BDA0003440437340000076
Figure BDA0003440437340000076

同时，将空间光调制器的2×2个像素单元组成一个巨像素单元，对巨像素中心位置的波前复振幅分解为两个相位分量，分别设置在巨像素的两条对角线上。At the same time, the 2×2 pixel units of the spatial light modulator are formed into a giant pixel unit, and the wavefront complex amplitude at the center of the giant pixel is decomposed into two phase components, which are respectively arranged on the two diagonals of the giant pixel.

进一步的，本发明所述步骤S4包括假设空间光调制器像素单元边长为p，在实空间中重建的光场必须满足奈奎斯特带宽的限制条件，即

Figure BDA0003440437340000081
Further, the step S4 of the present invention includes assuming that the side length of the pixel unit of the spatial light modulator is p, and the light field reconstructed in the real space must meet the restriction condition of the Nyquist bandwidth, that is,
Figure BDA0003440437340000081

进一步的，本发明透镜前焦面与后焦面处的光场满足傅里叶变换的关系，透镜的前焦面与空间光调制器重合。Further, the light fields at the front focal plane and the back focal plane of the lens of the present invention satisfy the Fourier transform relationship, and the front focal plane of the lens coincides with the spatial light modulator.

实施例Example

在一个具体的实施例中，要得到在中轴线上有三个强度一致焦点的多焦点自聚焦光束，选择的三组自聚焦光束参数为：r01＝0.6mm，zc1＝60mm，R1＝2.15mm，c1＝0；r02＝0.9mm，zc2＝90mm，R2＝2.19mm，c2＝0.6π；r03＝1.2mm，zc3＝120mm，R3＝2.25mm，c3＝0.17π，得到的波前振幅、相位分布和编码后的相位分布如图4第一行所示，所产生的多焦点自加速光束如图3左图所示。要得到在焦平面上有三个强度一致焦点的多焦点自聚焦光束，选择自聚焦光束参数为r0＝0.8mm，zc＝80mm，R＝2.25mm，并与沿Y轴平移±4mm后的轨迹叠加，得到的波前振幅、相位分布和编码后的相位分布如图4第二行所示，所产生的多焦点自加速光束如图3右图所示。In a specific embodiment, to obtain a multi-focus self-focusing beam with three focal points of uniform intensity on the central axis, the selected three sets of self-focusing beam parameters are: r 01 =0.6mm, z c1 =60mm, R 1 = 2.15mm, c1 = 0; r02 =0.9mm, zc2=90mm, R2= 2.19mm , c2 = 0.6π ; r03=1.2mm, zc3 =120mm, R3 = 2.25mm , c3 = 0.17π, the obtained wavefront amplitude, phase distribution and encoded phase distribution are shown in the first row of Figure 4, and the resulting multi-focus self-accelerating beam is shown in the left figure of Figure 3. To obtain a multifocal self-focusing beam with three focal points of uniform intensity on the focal plane, the parameters of the self-focusing beam are selected as r 0 =0.8mm, zc =80mm, R=2.25mm, and the parameters of the self-focusing beam are selected as r 0 =0.8mm, z c =80mm, R = 2.25mm, and the The trajectories are superimposed, and the obtained wavefront amplitude, phase distribution and encoded phase distribution are shown in the second row of Figure 4, and the resulting multi-focus self-accelerating beam is shown in the right figure of Figure 3.

对于本领域的技术人员来说，可以根据以上的技术方案和构思，给出各种相应的改变和变形，而所有的这些改变和变形，都应该包括在本发明权利要求的保护范围之内。For those skilled in the art, various corresponding changes and deformations can be given according to the above technical solutions and concepts, and all these changes and deformations should be included within the protection scope of the claims of the present invention.

Claims (7)

1. A method of producing a multifocal self-focusing beam having adjustable focal properties, said method comprising the steps of:
s1 constructing a self-focusing light beam by a caustic method;
s2 superposing wave fronts corresponding to the multiple groups of self-focusing light beams;
s3 encoding the complex amplitude distribution of the wavefront into a pure phase form;
s4, the phase distribution obtained by loading on the spatial light modulator is used for modulating the incident light field;
s5 fourier-transforms the modulated light field using a lens.
2. A method for generating a multifocal self-focusing beam with adjustable focal characteristics according to claim 1, wherein said step S1 comprises constructing a self-accelerating beam with a circular parabolic trajectory in a spatial frequency domain, wherein a caustic trajectory equation can be expressed as:
Figure FDA0003440437330000011
r is the radial coordinate in polar coordinates, r0Is the radius of the central dark space, z is the light field propagation direction, zcIs the intersection of the caustic and the central axis and can be approximated as the location of the focal point.
3. A method for generating a multifocal self-focusing beam with adjustable focal characteristics as claimed in claim 1, wherein said step S2 includes that for the case where the focal points are all on the central axis, the complex amplitude distribution of the wavefront of the multifocal self-focusing beam can be expressed as:
Figure FDA0003440437330000012
where n is the number of tracks/focal points, the index j indicates the parameters of the jth group of self-focusing beams, cjRepresenting the additional phase of the jth group of traces, the term 1/M being to ensure that the amplitude a (r) is not greater than 1, M can be expressed as:
Figure FDA0003440437330000021
by choosing appropriate additional phases for each set of trajectories, the relative intensity between the foci after superposition of the light fields can be kept constant.
4. A method of producing a multifocal self-focusing beam having adjustable focal properties according to claim 3 and further comprising, for the case of off-axis focal points, the complex amplitude profile of the wavefront of the multifocal self-focusing beam is expressed as:
Figure FDA0003440437330000022
wherein (x'j,y′j) Is the offset of the jth group of tracks and is also the coordinate on the focal plane.
5. A method for generating a multifocal self-focusing beam with adjustable focal characteristics as claimed in claim 1, wherein said step S3 includes decomposing the complex amplitude distribution of the wavefront of the multifocal self-focusing beam into two phase components by a bi-phase method, which can be expressed as:
Figure FDA0003440437330000023
Figure FDA0003440437330000024
meanwhile, 2 × 2 pixel units of the spatial light modulator form a giant pixel unit, the complex amplitude of the wavefront at the center position of the giant pixel is decomposed into two phase components, and the two phase components are respectively arranged on two diagonal lines of the giant pixel.
6. A method for generating a multi-focal self-focusing light beam with adjustable focal characteristics as claimed in claim 1, wherein the step S4 comprises assuming that the spatial light modulator pixel unit side length is p, the light field reconstructed in real space must satisfy the nyquist bandwidth limitation, i.e. the nyquist bandwidth limitation is satisfied
Figure FDA0003440437330000025
7. The method of claim 1, wherein the optical field at the front focal plane and the back focal plane of the lens satisfy a fourier transform relationship, and the front focal plane of the lens coincides with the spatial light modulator.
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