技术领域Technical field
本发明属于光学设计和机器学习领域，具体涉及一种基于D2NN超构表面的激光光束整形方法。The invention belongs to the field of optical design and machine learning, and specifically relates to a laser beam shaping method based on D2NN metasurface.
背景技术Background technique
激光光束整形是一种利用激光技术对光束进行改变的过程，它可以调整和优化光束的形状、强度和分布，在激光加工、医疗、光通信等方面都有重要应用。Zhang等人根据ZEMAX上非球面镜子午截面曲线表达式，拟合得到误差尽可能小的双凸非球面镜系统来实现高斯光束到平顶光束的激光光束整形。但是非球面镜等传统透镜实现光束整形，需要逐渐积累相位从而改变光波前，导致镜面具有体积大、质量重的缺陷，无法满足现代光学系统对于小型化、集成化的要求。并且传统透镜的面型都是根据其面型公式进行设计的，自由度不够高，无法实现复杂的光束整形效果。Laser beam shaping is a process that uses laser technology to change the beam. It can adjust and optimize the shape, intensity and distribution of the beam. It has important applications in laser processing, medical treatment, optical communications, etc. According to the expression of the meridional cross-section curve of the aspherical mirror on ZEMAX, Zhang et al. fitted a biconvex aspherical mirror system with the smallest possible error to achieve laser beam shaping from Gaussian beam to flat-top beam. However, traditional lenses such as aspheric mirrors need to gradually accumulate phases to change the light wavefront to achieve beam shaping. This results in the mirror being large in size and heavy in mass, and cannot meet the requirements of modern optical systems for miniaturization and integration. Moreover, the surface shape of traditional lenses is designed based on its surface shape formula, and the degree of freedom is not high enough to achieve complex beam shaping effects.
深度学习是目前用于光束整形领域的常见手段。Shao等人将衍射光学元件的相位分布数据拟合为多项式，通过神经网络构建系统参数与多项式系数之间的映射关系来实现激光光束整形。但是传统深度学习需要大量的先验数据集，数据集的采集通常要数天甚至数个月的时间，花费时间长，并且深度学习最终的训练效果取决于网络的性能，具有不确定性。Deep learning is a common method currently used in the field of beam shaping. Shao et al. fit the phase distribution data of diffractive optical elements into polynomials, and used neural networks to construct a mapping relationship between system parameters and polynomial coefficients to achieve laser beam shaping. However, traditional deep learning requires a large amount of prior data sets. The collection of data sets usually takes days or even months, which is a long time. Moreover, the final training effect of deep learning depends on the performance of the network and is uncertain.
发明内容Contents of the invention
本发明的目的在于提供一种基于D2NN超构表面的激光光束整形方法，实现了独立设计超构表面上每个原子的相位分布，不受面型公式的设计约束，具有更高的光束整形能力。The purpose of the present invention is to provide a laser beam shaping method based on D2NN metasurface, which realizes the independent design of the phase distribution of each atom on the metasurface, is not subject to the design constraints of the surface formula, and has higher beam shaping capabilities. .
实现本发明目的的技术解决方案为：一种基于D2NN超构表面的激光光束整形方法，包括以下步骤：The technical solution to achieve the purpose of the present invention is: a laser beam shaping method based on D2NN metasurface, including the following steps:
S1、设计基于D2NN超构表面的激光光束整形光路：S1. Design the laser beam shaping optical path based on D2NN metasurface:
所述基于D2NN超构表面的激光光束整形光路包括沿光路依次设置的激光器、准直扩束镜、D2NN超构表面、CCD相机，CCD相机与计算机连接。The laser beam shaping optical path based on the D2NN metasurface includes a laser, a collimating beam expander, a D2NN metasurface, and a CCD camera that are sequentially arranged along the optical path. The CCD camera is connected to a computer.
激光器发出10.6um的远红外光，并经准直扩束镜准直并扩束为平行光，作为输入光场。平行光入射到D2NN超构表面被整形，整形后在空间中传播最终被CCD相机接收。转入S2。The laser emits 10.6um far-infrared light, which is collimated and expanded into parallel light by a collimating beam expander as the input light field. Parallel light is incident on the D2NN metasurface and is shaped. After shaping, it propagates in space and is finally received by the CCD camera. Go to S2.
S2、确定光束整形目标，即目标光场，转入S3。S2. Determine the beam shaping target, that is, the target light field, and transfer to S3.
S3、在计算机中通过相位层表征D2NN超构表面的相位调制，进而构建基于衍射传播模型的D2NN，模拟激光光束整形光路中光场的传播过程，将输入光场送入D2NN，得到输出光场，转入S4。S3. Characterize the phase modulation of the D2NN metasurface through the phase layer in the computer, and then construct a D2NN based on the diffraction propagation model, simulate the propagation process of the light field in the laser beam shaping optical path, send the input light field to the D2NN, and obtain the output light field. , transfer to S4.
S4、根据输出光场和目标光场的差值训练D2NN，训练完成后得到相位层的相位分布，即D2NN超构表面的相位分布，转入S5。S4. Train D2NN based on the difference between the output light field and the target light field. After the training is completed, the phase distribution of the phase layer is obtained, that is, the phase distribution of the D2NN supersurface. Transfer to S5.
S5、D2NN超构表面由若干超构原子排列组合而成，基于FDTD仿真超构原子在光路中的调制相位，以实现超构原子相位全覆盖，转入S6。S5 and D2NN metasurfaces are composed of a number of superstructured atoms arranged and combined. Based on FDTD, the modulation phase of superstructured atoms in the optical path is simulated to achieve full coverage of the superstructured atom phase, which is transferred to S6.
S6、将D2NN超构表面的相位分布和超构原子的调制相位进行配对，排布超构原子生成D2NN超构表面，转入S7。S6. Pair the phase distribution of the D2NN metasurface with the modulation phase of the superstructure atoms, arrange the superstructure atoms to generate the D2NN superstructure, and transfer to S7.
S7、将得到的D2NN超构表面放入激光光束整形光路，以实现激光光束整形。S7. Put the obtained D2NN metasurface into the laser beam shaping optical path to achieve laser beam shaping.
本发明与现有技术相比，其显著优点在于：Compared with the prior art, the significant advantages of the present invention are:
(1)使用D2NN超构表面实现光束整形，超构表面不受面型公式的约束，具有更高的光束整形能力；超构表面由亚波长结构组成，体积小、重量轻，有利于系统集成化。(1) Use D2NN metasurface to achieve beam shaping. The metasurface is not constrained by surface formulas and has higher beam shaping capabilities. The metasurface is composed of sub-wavelength structures, is small in size and light in weight, and is conducive to system integration. change.
(2)本发明基于衍射传播的物理模型进行相位设计，与其他的深度学习方法相比，设计过程可解释，有更好的训练效果；训练过程不需要大量的数据集，将训练集的采集时间节省了千倍以上。(2) The present invention performs phase design based on the physical model of diffraction propagation. Compared with other deep learning methods, the design process is interpretable and has better training effects; the training process does not require a large number of data sets, and the collection of training sets is Time is saved more than a thousand times.
附图说明Description of the drawings
图1是基于D2NN超构表面的激光光束整形方法。Figure 1 is a laser beam shaping method based on D2NN metasurface.
图2是基于D2NN超构表面的激光光束整形光路图。Figure 2 is a laser beam shaping optical path diagram based on D2NN metasurface.
图3是输入光场的振幅分布图。Figure 3 is the amplitude distribution diagram of the input light field.
图4是目标光场的振幅分布图。Figure 4 is an amplitude distribution diagram of the target light field.
图5是D2NN网络结构图。Figure 5 is the D2NN network structure diagram.
图6是训练后的网络输出光场振幅分布图。Figure 6 is the network output light field amplitude distribution diagram after training.
图7是训练后得到的超构表面相位分布图。Figure 7 is the metasurface phase distribution diagram obtained after training.
图8是扫描的超构原子模型。Figure 8 is a scanned superstructural atomic model.
图9是FDTD仿真界面截面图。Figure 9 is a cross-sectional view of the FDTD simulation interface.
图10是扫描得到的超构原子直径与相位变化曲线图。Figure 10 is a graph of diameter and phase changes of superstructured atoms obtained by scanning.
图11是超构原子排布方法示意图。Figure 11 is a schematic diagram of the superstructural atomic arrangement method.
具体实施方式Detailed ways
下面结合附图对本发明作详细说明。The present invention will be described in detail below with reference to the accompanying drawings.
结合图1，本发明所述的一种基于D2NN(Deep Diffraction Neural Network)超构表面的激光光束整形方法，能够独立设计超构表面上各个超构原子的相位，设计过程基于物理模型可解释，包括以下步骤：With reference to Figure 1, the laser beam shaping method based on D2NN (Deep Diffraction Neural Network) metasurface described in the present invention can independently design the phase of each metastructured atom on the metastructured surface. The design process can be explained based on the physical model. Includes the following steps:
S1、设计基于D2NN超构表面的激光光束整形光路，转入S2。S1. Design the laser beam shaping optical path based on D2NN metasurface and transfer to S2.
所述基于D2NN超构表面的激光光束整形光路包括沿光路依次设置的激光器1、准直扩束镜2、D2NN超构表面3、CCD相机4，CCD相机4与计算机连接，如图2所示。The laser beam shaping optical path based on the D2NN metasurface includes a laser 1, a collimating beam expander 2, a D2NN metasurface 3, and a CCD camera 4. The CCD camera 4 is connected to a computer, as shown in Figure 2. .
激光器1发出10.6um的远红外光，并经准直扩束镜2准直并扩束为平行光。平行光入射到D2NN超构表面3被整形，整形后在空间中传播最终被CCD相机4接收。Laser 1 emits 10.6um far-infrared light, which is collimated and expanded into parallel light by the collimating beam expander 2. Parallel light is incident on the D2NN metasurface 3 and is shaped. After shaping, it propagates in space and is finally received by the CCD camera 4.
S2、确定光束整形目标，即目标光场，转入S3。S2. Determine the beam shaping target, that is, the target light field, and transfer to S3.
激光器1出射光为高斯光束，截面半径为ω1，准直扩束镜2的扩束倍数为β，故输入光场是截面半径为ω2的高斯光束，ω2＝βω1，其振幅分布为A′为光束截面中心的振幅，r为点(x0，y0)距光束截面中心的距离，输入光场的振幅分布图如图3所示。光束经准直扩束镜2后发散角缩减为原来的β倍，所以输入光场可近似看成平行光，其相位分布表示为/>The emitted light of laser 1 is a Gaussian beam with a cross-sectional radius of ω1 , and the beam expansion factor of the collimating beam expander 2 is β. Therefore, the input light field is a Gaussian beam with a cross-sectional radius of ω2 , ω2 =βω1 , and its amplitude distribution for A′ is the amplitude of the beam cross-section center, r is the distance between the point (x0 , y0 ) and the beam cross-section center. The amplitude distribution diagram of the input light field is shown in Figure 3. After the beam passes through the collimating beam expander 2, the divergence angle is reduced to β times the original, so the input light field can be approximately regarded as parallel light, and its phase distribution is expressed as/>
目标光场为半径r0的圆形平项光束，其振幅分布A″为常数，(x，y)为目标光场的坐标，目标光场振幅分布图如图4所示。由于CCD相机4相机接收的信息为光强信息，与相位无关，所以目标光场的相位不做要求。The target light field is a circular flat-term beam with radius r0 , and its amplitude distribution A″ is a constant, (x, y) is the coordinates of the target light field, and the target light field amplitude distribution diagram is shown in Figure 4. Since the information received by the CCD camera 4 is light intensity information, which has nothing to do with the phase, the target light field The phase is not required.
S3、在计算机中通过相位层表征D2NN超构表面3的相位调制，进而构建基于衍射传播模型的D2NN，模拟激光光束整形光路中光场的传播过程，将输入光场送入D2NN，得到输出光场，转入S4。S3. Characterize the phase modulation of the D2NN metasurface 3 through the phase layer in the computer, and then construct a D2NN based on the diffraction propagation model, simulate the propagation process of the light field in the laser beam shaping optical path, send the input light field to the D2NN, and obtain the output light field, transfer to S4.
图5绘出了D2NN网络模型，由输入层、输出层和至少一个相位层组成，单个相位层表征单个超构表面的相位调制作用。将输入光场送入输入层，输入光场的复振幅分布U0(x0，y0)表示为：Figure 5 depicts the D2NN network model, which consists of an input layer, an output layer and at least one phase layer. A single phase layer represents the phase modulation effect of a single metasurface. The input light field is sent to the input layer, and the complex amplitude distribution U0 (x0 , y0 ) of the input light field is expressed as:
其中(x0，y0)为输入光场的坐标，A0(x0，y0)为输入光场的振幅分布，为输入光场的相位分布，i表示虚部。Where (x0 , y0 ) is the coordinates of the input light field, A0 (x0 , y0 ) is the amplitude distribution of the input light field, is the phase distribution of the input light field, i represents the imaginary part.
输入光场经过第一段空间中的自由传播后到达第一个相位层的前表面，即第一个超构表面的前表面，该过程表示为：After free propagation in the first space, the input light field reaches the front surface of the first phase layer, that is, the front surface of the first metasurface. This process is expressed as:
U1f(x1，y1)＝f[U0(x0，y0)，z1]U1f (x1 , y1 )=f [U0 (x0 , y0 ), z1 ]
其中(x1，y1)表示第一个相位层的前表面坐标，U1f(x1，y1)表示第一个相位层前表面光场的复振幅分布，z1表示从输入层到第一个相位层前表面的传播距离，f[·]表示光场自由传播过程的自由空间衍射传播函数。Where (x1 , y1 ) represents the front surface coordinates of the first phase layer, U1f (x1 , y1 ) represents the complex amplitude distribution of the light field on the front surface of the first phase layer, z1 represents the transition from the input layer to the first phase layer. The propagation distance of the front surface of a phase layer, f[·] represents the free space diffraction propagation function of the free propagation process of the light field.
根据角谱与复振幅之间存在的傅里叶变换关系，通过频谱来表征自由空间的衍射传播函数，计算过程为：According to the Fourier transform relationship between the angular spectrum and the complex amplitude, the diffraction propagation function of the free space is characterized by the spectrum. The calculation process is:
O1f(fx，fy)＝O0(fx，fy)H(fx，fy)O1f (fx , fy )=O0 (fx , fy )H (fx , fy )
其中，O1f(fx，fy)和O0(fx，fy)分别为光场自由传播过程的输出频谱和输入频谱，(fx，fy)为频谱坐标，j为虚部，H(fx，fy)是光场传递函数。Among them, O1f (fx , fy ) and O0 (fx , fy ) are the output spectrum and input spectrum of the light field free propagation process respectively, (fx , fy ) is the spectrum coordinate, and j is the imaginary part , H(fx , fy ) is the light field transfer function.
自由空间衍射传播为线性不变系统，且在频域上的传递函数为Free space diffraction propagation is a linear invariant system, and the transfer function in the frequency domain is
其中k为波矢，λ为波长。where k is the wave vector and λ is the wavelength.
光场从第一个相位层的前表面入射到其后表面会受到相位层的相位调制作用，该过程表示为：The light field incident from the front surface of the first phase layer to its rear surface will be phase modulated by the phase layer. This process is expressed as:
其中U1b(x1，y1)表示第一个相位层后表面的光场复振幅分布，表示第一个相位层的相位分布。Where U1b (x1 , y1 ) represents the complex amplitude distribution of the light field on the back surface of the first phase layer, Represents the phase distribution of the first phase layer.
经过相位层调制后的光场继续在空间中自由传播，直至传播到第二个相位层，接受第二个相位层的相位调制后在空间中自由传播，以此进行循环往复，直至到达输出层，由输出层输出光场。因此，D2NN的物理模型表示为：The light field modulated by the phase layer continues to propagate freely in space until it propagates to the second phase layer. After receiving the phase modulation of the second phase layer, it propagates freely in space and repeats this cycle until it reaches the output layer. , the light field is output from the output layer. Therefore, the physical model of D2NN is expressed as:
其中N为相位层的总数，n为相位层的序号，n＝1，2，...，N，Unf(xn，yn)表示第n个相位层前表面的光场复振幅分布，Unb(xn，yn)为第n个相位层后表面的光场复振幅分布，为第n个相位层的相位分布，zn为光场从第n-1个相位层到第n个相位层的传播距离，zN+1为光场从最后一个相位层到像面的传播距离，U0b(x0，y0)为输入光场的复振幅分布，U(x，y)为输出光场的复振幅分布。Where N is the total number of phase layers, n is the sequence number of the phase layer, n=1, 2,...,N, Unf (xn , yn ) represents the complex amplitude distribution of the light field on the front surface of the nth phase layer , Unb (xn , yn ) is the complex amplitude distribution of the light field on the rear surface of the nth phase layer, is the phase distribution of the nth phase layer, zn is the propagation distance of the light field from the n-1th phase layer to the nth phase layer, zN+1 is the propagation distance of the light field from the last phase layer to the image plane , U0b (x0 , y0 ) is the complex amplitude distribution of the input light field, and U (x, y) is the complex amplitude distribution of the output light field.
D2NN输出光场的光强分布为The light intensity distribution of the D2NN output light field is
I(x，y)＝U(x，y)·U*(x，y) (5)I(x,y)=U(x,y)·U* (x,y) (5)
其中U*(x，y)为U(x，y)的共轭。D2NN的输出光场即为CCD相机4探测到的输出光场。Where U* (x, y) is the conjugate of U (x, y). The output light field of D2NN is the output light field detected by the CCD camera 4.
S4、根据输出光场和目标光场的差值训练D2NN，训练完成后得到相位层的相位分布，即D2NN超构表面3的相位分布。S4. Train D2NN based on the difference between the output light field and the target light field. After the training is completed, the phase distribution of the phase layer is obtained, that is, the phase distribution of the D2NN metasurface 3.
在本例中，由于样本集只需要一对样本，因此不需要将样本分批次，每次训练只需要将同一输入光场送入网络进行训练，共训练了6000轮(epoch_num)，训练过程中将目标光场的振幅与输出光场的振幅做MSE得到损失值，并使用Adam优化算法对网络中的相位层进行优化，采用的学习率(lr)为0.01，训练完成后最终输出光场和目标广场的损失值达到10-4，此时输出光场与目标光场接近一致，相位层的相位分布即为D2NN超构表面的相位分布。图6为训练后输出光场的振幅分布图，图7为训练得到的光束整形超构表面相位分布图。In this example, since the sample set only requires a pair of samples, there is no need to divide the samples into batches. Each training only needs to send the same input light field to the network for training. A total of 6000 rounds (epoch_num) are trained. The training process The amplitude of the target light field and the amplitude of the output light field are done by MSE to obtain the loss value, and the Adam optimization algorithm is used to optimize the phase layer in the network. The learning rate (lr) used is 0.01. After the training is completed, the final output light field is The loss value of the target square reaches 10-4 . At this time, the output light field is close to the target light field, and the phase distribution of the phase layer is the phase distribution of the D2NN metasurface. Figure 6 is the amplitude distribution diagram of the output light field after training, and Figure 7 is the phase distribution diagram of the beam shaping metasurface obtained by training.
S5、D2NN超构表面3由若干超构原子排列组合而成，基于FDTD(Finite DifferenceTime Domain)仿真超构原子在光路中的调制相位，以实现超构原子相位全覆盖。S5 and D2NN metasurface 3 are composed of a number of superstructured atoms arranged and combined. The modulation phase of superstructured atoms in the optical path is simulated based on FDTD (Finite DifferenceTime Domain) to achieve full coverage of the superstructured atom phase.
S51、设置超构原子。由于本例光束整形的光场为非偏振光，所以将超构原子的形状定为具有高度对称性的纳米圆柱体，材料定为在远红外波段具有高折射率、高透过率、价格低廉等优点的单晶硅，纳米圆柱体置于基底之上。描述纳米圆柱体尺寸的参数有直径D、高度H，描述基底尺寸的参数有周期P，超构原子的形状如图8所示。S51. Set up superstructure atoms. Since the light field used for beam shaping in this example is non-polarized light, the shape of the superstructure atoms is determined to be a highly symmetrical nanocylinder, and the material is determined to have high refractive index, high transmittance, and low price in the far-infrared band. Single crystal silicon with equal advantages, nanocylinders are placed on the substrate. The parameters describing the size of the nanocylinder are diameter D and height H, and the parameters describing the size of the substrate are period P. The shape of the superstructured atom is shown in Figure 8.
S52、设置仿真空间。仿真空间在XY截面的大小与超构原子基底的周期P大小一致，Z方向的大小比超构原子的高度H至少长一个光波，XY方向的边界条件设置为周期性边界条件来模拟超构表面上单个原子与其他原子的耦合关系，Z方向的边界条件设置为完美吸收层来模拟无限传播的真实世界，FDTD仿真截面界面图如图9所示。S52. Set up the simulation space. The size of the simulation space in the XY cross-section is consistent with the period P of the metaatomic base. The size in the Z direction is at least one light wave longer than the height H of the metaatomic. The boundary conditions in the XY direction are set to periodic boundary conditions to simulate the metasurface. On the coupling relationship between a single atom and other atoms, the boundary condition in the Z direction is set to a perfect absorption layer to simulate the real world of infinite propagation. The FDTD simulation cross-sectional interface diagram is shown in Figure 9.
S53、设置光源。光源的类型为平面波，波长10.6um，方向沿Z轴正向传播。S53. Set the light source. The type of light source is a plane wave with a wavelength of 10.6um and a direction propagating forward along the Z-axis.
S54、相位扫描。通过FDTD自带的优化和扫描模块，将超构原子的直径D和高度H设置为变量进行扫描，得到随直径和高度变化的透过率和相位分布，选取在高度H一定时，随着直径D的变化能够实现2pi相位全覆盖以及平均透过率达到70％以上的超构原子，扫描得到的超构原子直径D与相位变化关系如图10所示。S54, phase scan. Through the optimization and scanning module that comes with FDTD, the diameter D and height H of the superstructure atoms are set as variables for scanning, and the transmittance and phase distribution that change with the diameter and height are obtained. When the height H is constant, the transmittance and phase distribution are obtained with the diameter. The change of D can achieve full coverage of the 2pi phase and a superatom with an average transmittance of more than 70%. The relationship between the scanned superatom diameter D and the phase change is shown in Figure 10.
S6、将D2NN超构表面3的相位分布和超构原子的调制相位进行配对，排布超构原子生成D2NN超构表面3。S6. Pair the phase distribution of the D2NN supersurface 3 with the modulation phase of the superstructured atoms, and arrange the superstructured atoms to generate the D2NN superstructured surface 3.
由于超构表面加工条件的限制，超构原子实际加工与设计会有一定的偏差，为了回避这个问题且保证超构表面的性能，一般将超构表面的相位分成8段。将S4中得到的光束整形超构表面以pi/4为步长进行分段，0～pi/4范围内的相位变更为0，pi/4～pi/2范围内的相位变更为pi/4，以此类推共分为八段。坐标为(rm，sn)位置处的相位为phase(rm，sn)，通过FDTD扫描得到的直径-相位变换关系f(D)，得到对应的超构原子直径D(Rm，Sn)＝f-1(phase(rm，sn))，将直径为D(Rm，Sn)的超构原子的中心放置在(Rm，Sn)位置处，此处Rm＝rm*P，Sn＝sn*P，即超构原子中心之间的距离为周期P，排布规律示意图如图11所示。Due to the limitations of metasurface processing conditions, there will be a certain deviation between the actual processing and design of metastructure atoms. In order to avoid this problem and ensure the performance of the metasurface, the phase of the metasurface is generally divided into eight segments. The beam shaping metasurface obtained in S4 is segmented in steps of pi/4. The phase in the range of 0 to pi/4 is changed to 0, and the phase in the range of pi/4 to pi/2 is changed to pi/4. , and so on, it is divided into eight sections. The phase at the position where the coordinates are (rm , sn ) is phase (rm , sn ). Through the diameter-phase transformation relationship f(D) obtained by FDTD scanning, the corresponding superstructured atom diameter D(Rm , Sn )=f-1 (phase (rm , sn) ), place the center of the superstructured atom with diameter D (Rm , Sn ) at the position (Rm , Sn ), where Rm =rm *P, Sn =sn *P, that is, the distance between the centers of superstructure atoms is period P. The schematic diagram of the arrangement is shown in Figure 11.
综上所述，本方法使用D2NN超构表面实现光束整形，超构表面不受面型公式的约束，具有更高的光束整形能力，在光束整形领域具有广泛的应用前景。To sum up, this method uses D2NN metasurface to achieve beam shaping. The metasurface is not constrained by the surface formula, has higher beam shaping capabilities, and has broad application prospects in the field of beam shaping.
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