CN104297925A

CN104297925A - Design method of hybrid refractive-diffractive element for achieving femtosecond laser long focal depth

Info

Publication number: CN104297925A
Application number: CN201410535729.9A
Authority: CN
Inventors: 陈涛; 梁晓莉; 朱航欧
Original assignee: Beijing University of Technology
Current assignee: Beijing University of Technology
Priority date: 2014-10-11
Filing date: 2014-10-11
Publication date: 2015-01-21
Anticipated expiration: 2034-10-11
Also published as: CN104297925B

Abstract

A design method of a refraction-diffraction hybrid element for realizing femtosecond laser long focal depth, which relates to the field of laser beam shaping. The invention discloses a design method of a refraction-diffraction mixing element capable of realizing a long focal depth of an 800nm femtosecond laser beam. The element is composed of plano-convex lens base and binary microstructured diffractive optical surface. The schematic structure is shown in Figure 1, (1) is the plano-convex lens base, and (2) is the binary microstructured diffractive optical surface. The 800nm femtosecond laser beam passes through the element, the plano-convex lens undertakes the focal power of the system, and the microstructured diffractive optical surface is used to adjust the light field distribution, and finally a laser beam with a long focal depth and a small focal spot can be obtained. This method provides a feasible design scheme for the femtosecond laser microfabrication lens with long focal depth.

Description

A Design Method of Refractive-Diffractive Hybrid Elements Realizing Long Focal Depth of Femtosecond Laser

技术领域：Technical field:

本发明涉及激光领域，具体为激光光束整形领域。The invention relates to the field of lasers, in particular to the field of laser beam shaping.

背景技术：Background technique:

自1960年激光器问世以来，激光在加工方面的应用不断拓展，特别是在激光打孔、切割、光刻等方面起了非常重要的作用。在激光打孔和切割实验中，光束聚焦后的尺寸及焦深是决定实验准确度和切割精度的关键。相比于传统的加工方法，飞秒激光微加工具有材料适应性广、非接触、无污染、高精度、高效率等优点，对于微纳尺度的高品质加工，飞秒激光加工是一种更加有效的加工手段。因此实现飞秒激光光束的长焦深有着重要的意义。Since the advent of lasers in 1960, the application of lasers in processing has continued to expand, especially in laser drilling, cutting, and photolithography. In laser drilling and cutting experiments, the size and depth of focus of the beam after focusing are the key to determining the accuracy of the experiment and cutting precision. Compared with traditional processing methods, femtosecond laser micromachining has the advantages of wide material adaptability, non-contact, pollution-free, high precision, and high efficiency. For high-quality processing of micro-nano scale, femtosecond laser processing is a more effective means of processing. Therefore, it is of great significance to realize the long focal depth of the femtosecond laser beam.

实现长焦深的方法有很多种，主要有以下六种方法：There are many ways to achieve a long focal depth, mainly the following six methods:

1.传统的方法是通过减小数值孔径来扩展焦深，但是透镜焦深与焦斑大小的矛盾关系使得分辨率与加工深度很难同时获得提升，增加焦深必然会引起焦斑尺寸的增大。1. The traditional method is to expand the focal depth by reducing the numerical aperture, but the contradictory relationship between the focal depth of the lens and the focal spot size makes it difficult to improve the resolution and processing depth at the same time, and increasing the focal depth will inevitably lead to an increase in the focal spot size big.

2.利用轴锥镜来实现长焦深，轴锥镜能将入射平面波变换为光强沿轴锥镜光轴成线性分布的锥面波，并且可以无扩散的传播很远的距离。然而形成的锥面波在轴上的光强随传播距离呈线性趋势增长，并伴有激烈振荡。2. Use the axicon to achieve a long focal depth. The axicon can transform the incident plane wave into a cone wave whose light intensity is linearly distributed along the optical axis of the axicon, and can propagate a long distance without diffusion. However, the light intensity of the formed cone wave on the axis increases linearly with the propagation distance, and is accompanied by violent oscillation.

3.无衍射光束实现激光长焦深，如圆锥镜法、无限窄圆法等，但这些方法存在焦深范围不易控制和焦深范围内轴上光强振荡厉害，或者能量利用率低等问题。3. Non-diffraction beams can achieve laser long focal depth, such as conical mirror method, infinite narrow circle method, etc., but these methods have problems such as difficult control of the focal depth range, strong oscillation of axial light intensity within the focal depth range, or low energy utilization .

4.利用能量守恒法设计对数光锥实现无衍射光束，该方法有效增加了焦深，但是焦深范围内的能量利用率太低。4. Use the energy conservation method to design the logarithmic light cone to realize the non-diffraction beam. This method effectively increases the focal depth, but the energy utilization rate within the focal depth range is too low.

5.随着二元光学技术的发展，利用折衍混合光学元件实现长焦深成为人们研究的热点，这一方法是将轴上光强分布作为目标函数，通过采用优化算法求解衍射面的相位分布函数或光强分布函数来获得长焦深。5. With the development of binary optical technology, the use of refraction-diffraction hybrid optical elements to achieve long focal depths has become a research hotspot. This method uses the optical intensity distribution on the axis as the objective function, and solves the phase of the diffraction surface by using an optimization algorithm. Distribution function or light intensity distribution function to obtain a long depth of focus.

6.波前编码技术，该方法是将光学技术与图像处理相结合的一种扩大焦深的新技术方法。目前，该方法在光学系统中的应用也取得了长足的进展。6. Wavefront coding technology, which is a new technology method to expand the depth of focus by combining optical technology and image processing. At present, the application of this method in optical systems has also made great progress.

发明内容：Invention content:

本发明利用折衍混合元件实现800nm飞秒激光光束长焦深，公开该折衍混合元件的设计方法。The invention utilizes a refraction-diffraction mixing element to realize a long focal depth of an 800nm femtosecond laser beam, and discloses a design method of the refraction-diffraction mixing element.

折衍混合元件的设计基于已成熟的标量衍射理论。该元件由平凸透镜基底和二元微结构衍射光学表面两部分组成，平凸透镜承担系统的光焦度，微结构衍射光学表面用于调整光场分布。The design of the refraction-diffraction mixing element is based on the well-established scalar diffraction theory. The element is composed of a plano-convex lens base and a binary microstructure diffractive optical surface. The plano-convex lens bears the optical power of the system, and the microstructure diffractive optical surface is used to adjust the light field distribution.

设计长焦深折衍混合元件是相位的恢复问题。因此，本发明的设计步骤如下：Designing a telephoto deep refraction-diffraction hybrid element is a phase recovery problem. Therefore, the design steps of the present invention are as follows:

(1)根据所用激光器的参数和设计焦深焦斑的要求确定折衍混合元件的材料、元件初始孔径值、衍射面初始孔径值、元件厚度、入射光场能量分布、出射光场能量分布。(1) Determine the material of the refraction-diffraction hybrid element, the initial aperture value of the element, the initial aperture value of the diffraction surface, the thickness of the element, the energy distribution of the incident light field, and the energy distribution of the exit light field according to the parameters of the laser used and the requirements for designing the focal depth and focal spot.

(2)计算衍射面初始相位函数矩阵。编写折衍混合元件衍射面初始相位的计算程序，取步骤1中确定的入射光场能量分布、出射光场能量分布作为输入输出光场，计算得到衍射面初始相位函数矩阵。(2) Calculate the initial phase function matrix of the diffraction surface. Write the calculation program for the initial phase of the diffraction surface of the refraction-diffraction hybrid element, take the energy distribution of the incident light field and the energy distribution of the outgoing light field determined in step 1 as the input and output light fields, and calculate the initial phase function matrix of the diffraction surface.

(3)曲线拟合。将衍射面初始相位函数矩阵与光学设计软件Zemax中二元光学元件的相位函数表达式进行拟合，得到衍射面归一化径向孔径坐标的系数值，并将得到的系数值和步骤1中确定的元件材料、元件初始孔径值、衍射面初始孔径值、元件厚度输入Zemax软件中。(3) Curve fitting. Fit the initial phase function matrix of the diffraction surface with the phase function expression of the binary optical element in the optical design software Zemax to obtain the coefficient value of the normalized radial aperture coordinates of the diffraction surface, and compare the obtained coefficient value with that in step 1 The determined element material, initial aperture value of the element, initial aperture value of the diffraction surface, and element thickness are input into the Zemax software.

(4)优化结构参数。提出了一种改进的能量守恒法，根据这种方法编写试用于Zemax软件的宏文件，对元件的孔径值、衍射面孔径值、凸面曲率、元件厚度和二元面归一化径向孔径坐标的系数值进行优化，得到上述元件参数的最终值。(4) Optimize the structural parameters. An improved energy conservation method is proposed. According to this method, the macro file for trial use in Zemax software is written, and the aperture value of the element, the aperture value of the diffraction surface, the curvature of the convex surface, the thickness of the element, and the normalized radial aperture coordinates of the binary surface The coefficient values of the parameters are optimized to obtain the final values of the above-mentioned component parameters.

所述改进的能量守恒法主要思路如下：The main ideas of the improved energy conservation method are as follows:

设P_r(r)为入射光在元件表面的能量密度，P_z(z)为经过折衍混合元件后出射光在焦深前焦面与光轴交点d₁到焦深后焦面与光轴交点d₂之间各个平面上的能量密度。设定高斯光束入射到相位器件表面后，出射能量全部集中在侧面高度为d₁d₂、底面半径为ω的圆柱体内，且在焦深范围内光强分布均匀。下面对核心公式进行推导。Let P _r (r) be the energy density of the incident light on the surface of the element, and P _z (z) be the intersection point d ₁ of the outgoing light after passing through the refraction-diffraction hybrid element between the focal plane and the optical axis at the depth of focus and the distance between the focal plane and the light at the depth of focus Energy densities in the respective planes between the axis intersections _d2 . After the Gaussian beam is set to be incident on the surface of the phase device, all the outgoing energy is concentrated in a cylinder with a side height of d ₁ d ₂ and a bottom radius of ω, and the light intensity distribution is uniform within the focal depth range. The core formula is derived below.

设输入光场能量呈高斯分布，其能量密度分布函数为Assuming that the energy of the input light field is Gaussian distributed, its energy density distribution function is

${P P}_{r r} ((r r)) = = {Pe Pe}^{- - \frac{{22 r r}^{22}}{{ω ω}_{00}^{22}}} - - - - - - ((11))$

式中ω₀为高斯光束束腰半径值；P为输入高斯光束单脉冲最大能量密度值；r为高斯光束半径坐标值。where ω ₀ is the Gaussian beam waist radius value; P is the maximum energy density value of the input Gaussian beam single pulse; r is the Gaussian beam radius coordinate value.

设输出光场能量呈平顶分布，其能量密度为常数，即P_z(z)＝C，为方便计算，一般取值为1。Suppose the energy of the output light field has a flat-top distribution, and its energy density is constant, that is, P _z (z)=C. For the convenience of calculation, the value is generally set to 1.

根据能量守恒原理有According to the principle of energy conservation, there are

$22 {&Integral; &Integral;}_{00}^{x x} {πrPe πrPe}^{- - \frac{{22 r r}^{22}}{{ω ω}_{00}^{22}}} dr dr = = {&Integral; &Integral;}_{{d d}_{11}}^{z z} {Cπω Cπω}^{22} zdz zdz - - - - - - ((22))$

式中ω为出射光束束腰半径值，z为光波在光轴上的传输距离。In the formula, ω is the value of the beam waist radius of the outgoing beam, and z is the transmission distance of the light wave on the optical axis.

求解式(2)则可以得到z的表达式Solving formula (2) can get the expression of z

$z z = = \sqrt{\frac{{ω ω}_{00}^{22} P P}{{Cω Cω}^{22}} ((11 - - {e e}^{- - \frac{{22 x x}^{22}}{{ω ω}_{00}^{22}}})) + + {d d}_{11}^{22}} - - - - - - ((33))$

将表达式(3)作为核心公式，将入射光束看做是由很多条光线组成，对每条光线经过元件出射后在光轴上的交点位置坐标进行控制。根据该思路编写适用于Zemax软件的宏文件。The expression (3) is used as the core formula, and the incident light beam is considered to be composed of many rays, and the coordinates of the intersection point on the optical axis after each ray passes through the component are controlled. Write a macro file suitable for Zemax software according to this idea.

首先，设置初值。根据表达式(3)设置编写宏文件所需输入的初值：输入光束束腰半径值ω₀、输出光束束腰半径值ω、焦深前焦点在光轴上的位置d₁、输入高斯光束单脉冲最大能量密度值P。由于是将入射光束看做是由很多条光线组成，对每条光线经过元件出射后在光轴上的交点位置坐标进行控制。而每条光线的初始位置由在入射光束束腰直径处的垂轴坐标表示，即表达式(3)中的x。因此，为了得到x的取值，设置在入射光束束腰直径内x的抽样个数，并在入射光束束腰直径内进行等距离抽样。First, set the initial value. According to the expression (3), set the initial value required to input the macro file: the input beam waist radius value ω ₀ , the output beam waist radius value ω, the position of the focus on the optical axis before the focal depth d ₁ , the input Gaussian beam Single pulse maximum energy density value P. Since the incident light beam is considered to be composed of many rays, the coordinates of the intersection position on the optical axis after each ray passes through the component are controlled. And the initial position of each ray is represented by the vertical axis coordinate at the waist diameter of the incident beam, that is, x in the expression (3). Therefore, in order to obtain the value of x, the sampling number of x within the incident beam waist diameter is set, and equidistant sampling is performed within the incident beam waist diameter.

然后，编写表达式(3)。Then, write expression (3).

最后，优化参数。按照以上两步将宏文件编写完毕后，将其加载到Zemax软件中，利用软件自身的优化功能对元件的孔径值、衍射面孔径值、凸面曲率、元件厚度和二元面归一化径向孔径坐标的系数值进行优化，从而得到元件各参数的最终值。Finally, optimize the parameters. After the macro file is written according to the above two steps, it is loaded into the Zemax software, and the aperture value of the element, the aperture value of the diffractive surface, the curvature of the convex surface, the thickness of the element, and the normalized radial direction of the binary surface are normalized by using the software's own optimization function. The coefficient values of the aperture coordinates are optimized to obtain the final values of each parameter of the component.

该元件可使出射光束焦深增加到1mm～2mm范围内，焦斑半径大小保持在50μm以内。The component can increase the depth of focus of the outgoing beam to within the range of 1 mm to 2 mm, and keep the radius of the focal spot within 50 μm.

附图说明：Description of drawings:

图1折衍混合元件面型示意图Figure 1 Schematic diagram of the surface shape of the fractal-diffractive mixing element

图2改进的能量守恒法原理图Figure 2 Schematic diagram of the improved energy conservation method

图3衍射面初始结构函数图Figure 3 The initial structure function diagram of the diffraction surface

图4初始结构的光斑离焦情况Figure 4 Defocus of the light spot of the initial structure

图5优化后的光斑离焦情况Figure 5 Optimum spot defocus

图6优化后的光斑能量分布图Figure 6 Optimized spot energy distribution diagram

具体实施方案：Specific implementation plan:

下面结合附图和具体实施方式，对本发明做进一步说明。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

设r₀为输入光场光斑半径坐标，r_i为输出光场光斑半径坐标。Let r ₀ be the radius coordinate of the input light field spot, and _ri be the radius coordinate of the output light field spot.

本发明针对800nm飞秒激光器，该激光器各项参数如表1所示。The present invention is aimed at an 800nm femtosecond laser, and the parameters of the laser are shown in Table 1.

表1800nm飞秒激光器相关参数Table 1800nm femtosecond laser related parameters

根据表1所示参数，可确定折衍混合元件的材料采用BK7玻璃，元件初始孔径值为20mm，衍射面初始孔径值为10mm，元件厚度为2mm。800nm飞秒激光器的输出光斑能量呈高斯分布，选取高斯光束作为GS算法的输入光场，经过传播距离z后其表达式为：According to the parameters shown in Table 1, it can be determined that the material of the refraction-diffraction mixing element is BK7 glass, the initial aperture value of the element is 20 mm, the initial aperture value of the diffraction surface is 10 mm, and the thickness of the element is 2 mm. The output spot energy of the 800nm femtosecond laser has a Gaussian distribution. The Gaussian beam is selected as the input light field of the GS algorithm. After the propagation distance z, its expression is:

E(r₀,z)＝A(r₀,z)exp(-ikz) (4)E(r ₀ ,z)=A(r ₀ ,z)exp(-ikz) (4)

$A A (({r r}_{00},, z z)) = = \frac{{A A}_{00} {ω ω}_{00}}{ω ω ((z z))} exp exp [[- - \frac{{r r}_{00}^{22}}{{ω ω}^{22} ((z z))}]] exp exp {{- - i i [[\frac{{kr kr}_{00}^{22}}{22 R R ((z z))} - - Ψ Ψ]]}} - - - - - - ((55))$

其中A₀为振幅常量；ω₀为高斯光束束腰半径值；ω(z)为高斯光束的束宽，其表达式为：where A ₀ is the amplitude constant; ω ₀ is the beam waist radius of the Gaussian beam; ω(z) is the beam width of the Gaussian beam, and its expression is:

$ω ω ((z z)) = = {ω ω}_{00} \sqrt{11 + + {((z z / / {Z Z}_{00}))}^{22}} - - - - - - ((66))$

${Z Z}_{00} = = \frac{11}{22} k k {ω ω}_{00}^{22} = = \frac{π π {ω ω}_{00}^{22}}{λ λ} - - - - - - ((77))$

R(z)为高斯光束等相面曲率半径，表达式为：R(z) is the radius of curvature of the Gaussian beam isophase surface, the expression is:

$R R ((z z)) = = {Z Z}_{00} ((\frac{z z}{{Z Z}_{00}} + + \frac{{Z Z}_{00}}{z z})) - - - - - - ((88))$

Ψ为高斯光束相位因子，表达式为：Ψ is the Gaussian beam phase factor, the expression is:

$Ψ Ψ = = {tan the tan}^{- - 11} \frac{z z}{{Z Z}_{00}} - - - - - - ((99))$

要求出射光斑能量呈平顶分布，因此选取超高斯光束作为GS算法的输出光场，其在自由空间中的传播可由柯林斯公式描述，通过距离z后的传输公式为：It is required that the output spot energy has a flat-top distribution, so the super-Gaussian beam is selected as the output light field of the GS algorithm, and its propagation in free space can be described by the Collins formula, and the transmission formula after passing the distance z is:

E(r_i,z)＝U(r_i,z)exp{i[kz+Φ(r_i,z)]} (10)E(r _i ,z)=U(r _i ,z)exp{i[kz+Φ(r _i ,z)]} (10)

其中in

$U u (({r r}_{i i},, z z)) = = 22 πF πF {&Integral; &Integral;}_{00}^{+ + \infty \infty} exp exp (({- - &upsi; &upsi;}^{N N})) {J J}_{00} ((22 πF&upsi; πF&upsi; \frac{{r r}_{i i}}{ω ω})) exp exp (({iπF&upsi; iπF&upsi;}^{22})) &upsi;d&upsi; &upsi;d&upsi; - - - - - - ((1111))$

$Φ Φ (({r r}_{i i},, z z)) = = \frac{{kr kr}_{i i}^{22}}{22 z z} + + arg arg {{{&Integral; &Integral;}_{00}^{+ + \infty \infty} exp exp (({- - &upsi; &upsi;}^{N N})) {J J}_{00} ((22 πF&upsi; πF&upsi; \frac{{r r}_{i i}}{ω ω})) exp exp (({iπF&upsi; iπF&upsi;}^{22})) &upsi;d&upsi; &upsi;d&upsi;}} - - - - - - ((1212))$

式中，k为波数；ω为超高斯光束束腰半径值；N为超高斯光束的阶数；J₀为零阶贝塞尔函数；F为与光束有关的菲涅耳数，其表达式为：In the formula, k is the wave number; ω is the beam waist radius value of the super-Gaussian beam; N is the order of the super-Gaussian beam; J ₀ is the zero-order Bessel function; F is the Fresnel number related to the beam, and its expression for:

$F f = = \frac{{ω ω}^{22}}{λz λz} - - - - - - ((1313))$

根据设计要求与表1所示激光器基本参数，上述公式及表达式中参数取值如下：According to the design requirements and the basic parameters of the laser shown in Table 1, the values of the parameters in the above formulas and expressions are as follows:

ω₀＝3.5mm，A₀＝1，ω＝50μm，N＝36，z＝200mm。ω ₀ =3.5 mm, A ₀ =1, ω=50 μm, N=36, z=200 mm.

因此可确定GS算法基本过程为：高斯光束经过折衍混合元件，进行一次菲涅尔衍射积分变换，得到输出平面光场分布，此时以超高斯光束的振幅分布取代原光场振幅分布，同时保持相位不变，然后做菲涅尔逆衍射积分变换，得到输入平面光场分布，在输入平面以高斯光束振幅分布取代原光场振幅分布，同时保持相位不变，接着再做菲涅尔衍射积分变换……如此循环，直到得到满意的结果或达到足够多的循环次数为止。为达到长焦深的效果，迭代时在目标焦深范围内建立多个输出面，以使每个面输出后都影响随后的另一个输出面。Therefore, it can be determined that the basic process of the GS algorithm is as follows: the Gaussian beam passes through the refraction-diffraction mixing element, and performs a Fresnel diffraction integral transformation to obtain the output plane light field distribution. At this time, the amplitude distribution of the super-Gaussian beam is used to replace the original light field amplitude distribution. Keep the phase unchanged, and then perform Fresnel inverse diffraction integral transformation to obtain the input plane light field distribution, replace the original light field amplitude distribution with the Gaussian beam amplitude distribution on the input plane, while keeping the phase unchanged, and then do Fresnel diffraction Integral transformation...Loop in this way until a satisfactory result is obtained or a sufficient number of loops is reached. In order to achieve the effect of long focal depth, multiple output surfaces are established within the target focal depth range during iteration, so that each output surface affects another subsequent output surface.

GS算法选取如下初值：x、y坐标分别在-50mm到50mm之间等距离取500个数值；焦深范围2mm内等距离取200个输出面；循环500次；元件结构周期为10mm。The GS algorithm selects the following initial values: 500 values are taken equidistantly between the x and y coordinates of -50mm and 50mm respectively; 200 output surfaces are taken equidistantly within the focal depth range of 2mm; the cycle is 500 times; the component structure cycle is 10mm.

为了加快迭代计算的速度，进行菲涅尔衍射积分和逆衍射积分时，采用傅里叶变换形式的表达式，傅里叶变换形式的菲涅尔衍射公式为：In order to speed up the iterative calculation, when performing Fresnel diffraction integral and inverse diffraction integral, the expression in the form of Fourier transform is used. The Fresnel diffraction formula in the form of Fourier transform is:

傅里叶变换形式的菲涅尔逆衍射积分公式为：The Fresnel inverse diffraction integral formula in Fourier transform form is:

上述两式中，λ为元件工作波长，取800nm；k为波数；z为在菲涅尔衍射变换和逆衍射变换时光场输出面到输入面的距离，取值为2mm。In the above two formulas, λ is the working wavelength of the element, which is 800nm; k is the wave number; z is the distance from the output surface to the input surface of the light field during Fresnel diffraction transformation and inverse diffraction transformation, and the value is 2mm.

通过以上GS算法过程得到一个500×500的衍射面型初始相位函数矩阵，如图3所示。再通过Matlab中的曲线拟合工具箱将该矩阵与Zemax中描述二元光学面相位的公式进行拟合。Through the above GS algorithm process, a 500×500 diffraction surface initial phase function matrix is obtained, as shown in Figure 3. Then, the matrix is fitted with the formula describing the phase of the binary optical surface in Zemax through the curve fitting toolbox in Matlab.

在Zemax软件中二元光学面2(binary2)根据下面的多项式将相位添加到光线上：In the Zemax software, the binary optical surface 2 (binary2) adds the phase to the light according to the following polynomial:

$φ φ = = M m {Σ Σ}_{i i = = 11}^{N N} {A A}_{i i} {ρ ρ}^{22 i i} - - - - - - ((1616))$

式中N是级数中多项式系数的序号，M是衍射级次，令其等于1，A_i是ρ的第2i次幂的系数，ρ是归一化的径向孔径坐标，即In the formula, N is the serial number of the polynomial coefficient in the series, M is the diffraction order, which is equal to 1, A _i is the coefficient of the 2ith power of ρ, and ρ is the normalized radial aperture coordinate, namely

$ρ ρ = = \frac{\sqrt{(({x x}^{22} + + {y the y}^{22}))}}{{ρ ρ}_{N N}} - - - - - - ((1717))$

其中，ρ_N为归一化半径。Among them, ρ _N is the normalized radius.

将GS算法得到的初始相位函数矩阵按照式(16)进行拟合，取表达式的前五项，得到拟合表达式如下：The initial phase function matrix obtained by the GS algorithm is fitted according to formula (16), and the first five terms of the expression are taken to obtain the fitting expression as follows:

φ＝-163.6ρ²+496.4ρ⁴-628.6ρ⁶+350.6ρ⁸-71.09ρ¹⁰ (18)φ＝-163.6ρ ² +496.4ρ ⁴ -628.6ρ ⁶ +350.6ρ ⁸ -71.09ρ ¹⁰ (18)

将五个系数-163.6、496.4、-628.6、350.6、-71.09分别输入到Zemax软件的额外数据编辑器(Extra Data Editor)中，在Analysis—Spots Diagrams—Through Focus中查看离焦状况如图4所示。Input the five coefficients -163.6, 496.4, -628.6, 350.6, -71.09 respectively into the Extra Data Editor of Zemax software, and check the defocus status in Analysis—Spots Diagrams—Through Focus, as shown in Figure 4 Show.

由图4可看出高斯光束经过所设计的透镜后，发散有所减缓，焦深增加到1.5mm左右，均方根半径在36.48μm左右。It can be seen from Figure 4 that after the Gaussian beam passes through the designed lens, the divergence is slowed down, the focal depth is increased to about 1.5mm, and the root mean square radius is about 36.48μm.

为了减小焦斑的均方根半径，根据所提出的改进的能量守恒法求得光波在光轴上的传播距离z的表达式(3)，通过控制出射光束在光轴上的交点位置来实现在达到长焦深小焦斑效果的同时保持出射光场在焦深范围内能量呈平顶分布。根据表达式(3)编写Zemax中用于优化的宏文件，取ω₀＝3.5mm；ω＝50μm；C＝1；P＝0.091；d₁＝200mm；使用操作数REAZ，并设置其权重为1；在入射光束束腰直径内取100个抽样点，即x在入射光束束腰直径内等距离取100个值。In order to reduce the root mean square radius of the focal spot, the expression (3) of the propagation distance z of the light wave on the optical axis is obtained according to the proposed improved energy conservation method, by controlling the intersection position of the outgoing beam on the optical axis It achieves the effect of long focal depth and small focal spot while maintaining the flat-top energy distribution of the outgoing light field within the focal depth range. According to expression (3) write the macrofile that is used for optimization in Zemax, get ω ₀ =3.5mm; ω=50 μ m; C= ₁ ; P=0.091; 1; Take 100 sampling points within the diameter of the incident beam waist, that is, take 100 values of x equidistantly within the diameter of the incident beam waist.

将编写好的宏文件加载入Zemax软件中，对透镜折射面和衍射面的结构进行优化，经过优化后5个参数分别变为：-377.35、355.12、-1174.46、544.83、-130.27。元件其他参数输出如表2所示。Load the prepared macro file into the Zemax software to optimize the structure of the lens refraction surface and diffraction surface. After optimization, the five parameters become: -377.35, 355.12, -1174.46, 544.83, -130.27. The output of other parameters of the component is shown in Table 2.

表2优化后元件的基本参数Table 2 Basic parameters of optimized components

由图5可以看出，最终得到的折衍混合元件可使飞秒激光光束的焦深在理论上增加到1.5mm，且光斑均方根半径为13.16μm左右，实现了出射光束的长焦深与小焦斑。It can be seen from Figure 5 that the final refraction-diffraction hybrid element can theoretically increase the focal depth of the femtosecond laser beam to 1.5 mm, and the root mean square radius of the spot is about 13.16 μm, realizing the long focal depth of the outgoing beam with small focal spots.

出射光斑能量如图6所示，可以看出出射光斑能量呈锥形的平顶分布，效果较理想。The output spot energy is shown in Figure 6. It can be seen that the output spot energy is distributed in a cone-shaped flat top, and the effect is ideal.

基于本发明中的实施方案的具体展示和介绍，本领域技术人员在没有做出创新性劳动前提下所获得的所有其他实施例，均为本发明的保护范围。Based on the specific demonstration and introduction of the embodiments of the present invention, all other embodiments obtained by those skilled in the art without innovative efforts are within the protection scope of the present invention.

Claims

1. the folding realizing femtosecond laser beam Diode laser spreads out the method for designing of hybrid element, it is characterized in that step is as follows:

(1) determine to roll over according to the requirement of the parameter of laser instrument used and design depth of focus focal spot the spread out material of hybrid element, element initial aperture value, diffraction surfaces initial aperture value, component thickness, incident field energy distribution, the distribution of emergent light field energy;

(2) diffraction surfaces initial phase Jacobian matrix is calculated: write the calculation procedure rolling over the hybrid element diffraction surfaces initial phase that spreads out, get determine in step (1) incident field energy distribution, emergent light field energy distribution as input and output light field, calculate diffraction surfaces initial phase Jacobian matrix;

(3) curve: the phase function expression formula of binary optical elements in diffraction surfaces initial phase Jacobian matrix and optical design software Zemax is carried out matching, obtain the coefficient value of the radial aperture coordinate of diffraction surfaces normalization, and the element material determined in the coefficient value obtained and step (1), element initial aperture value, diffraction surfaces initial aperture value, component thickness are inputted in Zemax software;

(4) optimum structural parameter; If P _r(r) for incident light is in the energy density of element surface, P _zz () is for the emergent light that to spread out through folding after hybrid element is at depth of focus front focal plane and optical axes crosspoint d ₁to depth of focus back focal plane and optical axes crosspoint d ₂between energy density in each plane; After setting Gaussian beam incides phase place device surface, it is d that emanated energy all concentrates on profile height ₁d ₂, bottom surface radius is in the right cylinder of ω, and light distribution is even in focal depth range;

Below core formula is derived:

If input Light Energy is Gaussian distribution, its energy density distribution function is

P_{r} (r) = {Pe}^{- \frac{2 r^{2}}{{ω_{0}}^{2}}} - - - (1)

ω in formula ₀for gauss light beam waist radius value; P is input Gaussian beam monopulse maximum energy-density value; R is Gaussian beam radial coordinate value;

If output light field energy is flat-top distribution, its energy density is constant, i.e. P _z(z)=C, for convenience of calculating, C value is 1;

Have according to conservation of energy principle

2 {&Integral;}_{0}^{x} πrP e^{- \frac{2 r^{2}}{{ω_{0}}^{2}}} dr = {&Integral;}_{d_{1}}^{z} Cπ ω^{2} zdz - - - (2)

In formula, ω is outgoing beam waist radius value, and z is the transmission range of light wave on optical axis;

Solve the expression formula that formula (2) then can obtain z

z = \sqrt{\frac{{ω_{0}}^{2} P}{C ω^{2}} (1 - e^{- \frac{2 x^{2}}{{ω_{0}}^{2}}}) + d_{1}^{2}} - - - (3)

Write the macro document being applicable to Zemax software, specific as follows:

First, initial value is set: the initial value writing macro document required input is set according to expression formula (3): input beam waist radius value ω ₀, output beam waist radius value ω, the position d of depth of focus front focus on optical axis ₁, input Gaussian beam monopulse maximum energy-density value P; Owing to being incident beam is regarded as be made up of a lot of bar light, the position of intersecting point coordinate of every bar light after element outgoing on optical axis is controlled; And the initial position of every bar light is represented by the vertical axial coordinate at incident beam beam waist diameter, the x namely in expression formula (3); Therefore, in order to obtain the value of x, being arranged on the sampling number of x in incident beam beam waist diameter, and carrying out equidistant sampling in incident beam beam waist diameter;

Then, expression formula (3) is write;

Finally, Optimal Parameters: after macro document being write according to above two steps, be loaded in Zemax software, utilize the coefficient value of the radial aperture coordinate of the aperture value of optimizational function to element of software self, diffraction surfaces aperture value, convex curvature, component thickness and the normalization of binary face to be optimized, thus obtain the end value of each parameter of element.