A laser beam shaping method based on D2NN metasurface

Abstract

This invention discloses a laser beam shaping method based on a D2NN metasurface. The specific steps are as follows: designing a laser beam shaping optical path and a target optical field based on a D2NN metasurface; simulating the propagation process of the optical field in the laser beam shaping optical path using a D2NN, inputting the optical field into the D2NN to obtain the output optical field; training the D2NN based on the difference between the output and target optical fields to obtain the phase distribution of the D2NN metasurface; simulating the modulation phase of metaatoms using FDTD to achieve full phase coverage of metaatoms; pairing the phase distribution of the D2NN metasurface with the modulation phase of the metaatoms to arrange the metaatoms and generate the D2NN metasurface; and using the D2NN metasurface to achieve laser beam shaping. This method uses a D2NN metasurface to achieve beam shaping. The metasurface is not constrained by surface shape formulas, has higher beam shaping capabilities, and has broad application prospects in the field of beam shaping.

Description

Technical Field

[0001] This invention belongs to the fields of optical design and machine learning, and specifically relates to a laser beam shaping method based on a D2NN metasurface. Background Technology

[0002] Laser beam shaping is a process that uses laser technology to modify a light beam. It can adjust and optimize the shape, intensity, and distribution of the beam, and has important applications in laser processing, medicine, and optical communication. Zhang et al. fitted a biconvex aspherical mirror system with the smallest possible error based on the expression of the meridional section curve of an aspherical mirror on ZEMAX to achieve laser beam shaping from a Gaussian beam to a flat-top beam. However, beam shaping using traditional lenses such as aspherical mirrors requires gradually accumulating phase to change the wavefront, resulting in large size and heavy weight of the mirror, which cannot meet the miniaturization and integration requirements of modern optical systems. Furthermore, the surface shape of traditional lenses is designed according to their surface shape formulas, which lacks sufficient freedom and cannot achieve complex beam shaping effects.

[0003] Deep learning is a common technique used in beam shaping. Shao et al. fitted the phase distribution data of diffractive optical elements into a polynomial and used a neural network 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, which typically takes days or even months to collect, making it time-consuming. Furthermore, the final training effect of deep learning depends on the network's performance and is therefore uncertain. Summary of the Invention

[0004] The purpose of this invention is to provide a laser beam shaping method based on D2NN metasurfaces, which enables independent design of the phase distribution of each atom on the metasurface, is not constrained by the design of the surface shape formula, and has higher beam shaping capability.

[0005] The technical solution to achieve the purpose of this invention is: a laser beam shaping method based on a D2NN metasurface, comprising the following steps:

[0006] S1. Design of laser beam shaping optical path based on D2NN metasurface:

[0007] 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 arranged sequentially along the optical path. The CCD camera is connected to a computer.

[0008] The laser emits 10.6µm far-infrared light, which is collimated and expanded into parallel light by a collimating and expanding lens, serving as the input light field. The parallel light is incident on the D2NN metasurface and shaped, then propagates in space and is finally received by a CCD camera. Proceed to S2.

[0009] S2. Determine the beam shaping target, i.e. the target light field, and proceed to S3.

[0010] S3. In the computer, the phase modulation of the D2NN metasurface is characterized by a phase layer, and then a D2NN based on the diffraction propagation model is constructed to simulate the propagation process of the optical field in the laser beam shaping optical path. The input optical field is sent into the D2NN to obtain the output optical field, and then proceeds to S4.

[0011] S4. Train the D2NN based on the difference between the output light field and the target light field. After training, obtain the phase distribution of the phase layer, i.e. the phase distribution of the D2NN metasurface, and proceed to S5.

[0012] S5 and D2NN metasurfaces are composed of several metaatoms arranged and combined. Based on FDTD simulation, the modulation phase of metaatoms in the optical path is achieved to realize full coverage of metaatomic phase. Then proceed to S6.

[0013] S6. Pair the phase distribution of the D2NN metasurface with the modulation phase of the meta atoms, arrange the meta atoms to generate the D2NN metasurface, and proceed to S7.

[0014] S7. Place the obtained D2NN metasurface into the laser beam shaping optical path to achieve laser beam shaping.

[0015] Compared with the prior art, the significant advantages of this invention are:

[0016] (1) D2NN metasurfaces are used to achieve beam shaping. Metasurfaces are not constrained by surface shape formulas and have higher beam shaping capabilities. Metasurfaces are composed of subwavelength structures, which are small in size and light in weight, which is conducive to system integration.

[0017] (2) The present invention designs phase based on the physical model of diffraction propagation. Compared with other deep learning methods, the design process is interpretable and has better training effect. The training process does not require a large amount of data, saving more than a thousand times the time of collecting training sets. Attached Figure Description

[0018] Figure 1 It is a laser beam shaping method based on D2NN metasurfaces.

[0019] Figure 2 This is a laser beam shaping optical path diagram based on D2NN metasurface.

[0020] Figure 3This is a diagram showing the amplitude distribution of the input light field.

[0021] Figure 4 This is the amplitude distribution diagram of the target light field.

[0022] Figure 5 This is a diagram of the D2NN network structure.

[0023] Figure 6 This is a diagram showing the amplitude distribution of the output light field of the trained network.

[0024] Figure 7 It is the phase distribution map of the metasurface obtained after training.

[0025] Figure 8 It is a scanning superatomic model.

[0026] Figure 9 This is a cross-sectional view of the FDTD simulation interface.

[0027] Figure 10 This is a graph showing the change in diameter and phase of the superatoms obtained from the scan.

[0028] Figure 11 This is a schematic diagram of the meta-atomic arrangement method. Detailed Implementation

[0029] The present invention will now be described in detail with reference to the accompanying drawings.

[0030] Combination Figure 1 The present invention discloses a laser beam shaping method based on a D2NN (Deep Diffraction Neural Network) metasurface, which can independently design the phase of each metaatom on the metasurface. The design process is based on a physically interpretable model and includes the following steps:

[0031] S1. Design the laser beam shaping optical path based on the D2NN metasurface, then proceed to S2.

[0032] The laser beam shaping optical path based on the D2NN metasurface includes a laser 1, a collimating and beam expanding lens 2, a D2NN metasurface 3, and a CCD camera 4 arranged sequentially along the optical path. The CCD camera 4 is connected to a computer. Figure 2 As shown.

[0033] Laser 1 emits 10.6µm far-infrared light, which is collimated and expanded into parallel light by collimating and beam-expanding lens 2. The parallel light is incident on the D2NN metasurface 3 and shaped. After shaping, it propagates in space and is finally received by CCD camera 4.

[0034] S2. Determine the beam shaping target, i.e. the target light field, and proceed to S3.

[0035] The output light from laser 1 is a Gaussian beam with a cross-sectional radius of ω1. The collimating and beam-expanding lens 2 has a beam-expanding factor of β. Therefore, the input light field is a Gaussian beam with a cross-sectional radius of ω2, where ω2 = βω1, and its amplitude distribution is as follows: A′ represents the amplitude at the center of the beam cross-section, and r is the distance from point (x0, y0) to the center of the beam cross-section. The amplitude distribution diagram of the input light field is shown below. Figure 3 As shown. After passing through collimating and expanding lens 2, the divergence angle of the beam is reduced to β times its original value. Therefore, the input light field can be approximated as parallel light, and its phase distribution is expressed as follows.

[0036] The target light field is a circular, flat-headed beam with radius r0, and its amplitude distribution is... A″ is a constant, (x, y) are the coordinates of the target light field, and the amplitude distribution diagram of the target light field is shown below. Figure 4 As shown. Since the information received by the CCD camera is light intensity information, which is independent of phase, the phase of the target light field is not required.

[0037] S3. In the computer, the phase modulation of the D2NN metasurface 3 is characterized by a phase layer, and then a D2NN based on the diffraction propagation model is constructed to simulate the propagation process of the optical field in the laser beam shaping optical path. The input optical field is sent into the D2NN to obtain the output optical field, and then proceeds to S4.

[0038] Figure 5 The D2NN network model was drawn, consisting of an input layer, an output layer, and at least one phase layer. Each phase layer represents the phase modulation effect of a single metasurface. The complex amplitude distribution U0(x0, y0) of the input light field, fed into the input layer, is expressed as:

[0039]

[0040] Where (x0, y0) are the coordinates of the input light field, and A0(x0, y0) is the amplitude distribution of the input light field. Let i represent the phase distribution of the input light field, where i denotes the imaginary part.

[0041] After the input light field propagates freely in the first segment of space, it reaches the front surface of the first phase layer, i.e., the front surface of the first metasurface. This process can be represented as:

[0042] U 1f (x1,y1)=f[U0(x0,y0),z1]

[0043] Where (x1, y1) represents the coordinates of the front surface of the first phase layer, U 1f(x1, y1) represents the complex amplitude distribution of the light field on the front surface of the first phase layer, z1 represents the propagation distance from the input layer to the front surface of the first phase layer, and f[·] represents the free space diffraction propagation function of the free propagation process of the light field.

[0044] Based on the Fourier transform relationship between the angular spectrum and the complex amplitude, the diffraction propagation function in free space is characterized by the spectrum. The calculation process is as follows:

[0045]

[0046] O 1f (f x f y )=O0(f x f y )H(f x f y )

[0047]

[0048] Among them, O 1f (f x f y ) and O0(f x f y (f) represents the output spectrum and input spectrum of the free propagation process of the light field, respectively. x f y H(f) represents the spectral coordinates, j represents the imaginary part, and H(f) represents the spectral coordinates. x f y ) is the light field transfer function.

[0049] Free-space diffraction propagation is a linearly invariant system, and its transfer function in the frequency domain is...

[0050]

[0051] Where k is the wave vector and λ is the wavelength.

[0052] When a light field is incident from the front surface of the first phase layer to its rear surface, it is subject to phase modulation by the phase layer. This process can be represented as follows:

[0053]

[0054] Among them U 1b (x1, y1) represents the complex amplitude distribution of the optical field on the back surface of the first phase layer. This represents the phase distribution of the first phase layer.

[0055] The light field, modulated by the phase layer, continues to propagate freely in space until it reaches the second phase layer. There, it receives phase modulation from the second phase layer and continues propagating freely again. This cycle repeats until it reaches the output layer, where the light field is output. Therefore, the physical model of D2NN can be represented as:

[0056]

[0057] Where N is the total number of phase layers, and n is the sequence number of the phase layer, n = 1, 2, ..., N, U nf (x n y n U represents the complex amplitude distribution of the optical field on the front surface of the nth phase layer. nb (x n y n () represents the complex amplitude distribution of the optical field on the back surface of the nth phase layer. Let zn be the phase distribution of the nth phase layer, and zn be the propagation distance of the light field from the (n-1)th phase layer to the nth phase layer. N+1 U is the propagation distance of the light field from the last phase layer to the image plane. 0b (x0, y0) represents the complex amplitude distribution of the input light field, and U(x, y) represents the complex amplitude distribution of the output light field.

[0058] The light intensity distribution of the D2NN output light field is as follows:

[0059] I(x, y) = U(x, y) · U * (x, y) (5)

[0060] Among them U * (x, y) is the conjugate of U(x, y). The output light field of D2NN is the same as the output light field detected by CCD camera 4.

[0061] S4. Train the D2NN based on the difference between the output light field and the target light field. After training, the phase distribution of the phase layer is obtained, that is, the phase distribution of the D2NN metasurface 3.

[0062] In this example, since the sample set only requires one pair of samples, there is no need to batch the samples. Each training session only requires feeding the same input light field into the network for training, for a total of 6000 epochs (epoch_num). During training, the MSE (Mean Squared Error) of the target light field amplitude and the output light field amplitude is used to obtain the loss value. The Adam optimization algorithm is then used to optimize the phase layer in the network, with a learning rate (lr) of 0.01. After training, the final loss value of the output light field and the target square reaches 10. -4 At this point, the output light field is nearly identical to the target light field, and the phase distribution of the phase layer is the same as the phase distribution of the D2NN metasurface. Figure 6This is the amplitude distribution diagram of the output light field after training. Figure 7 The phase distribution map of the beam-shaping metasurface obtained during training.

[0063] S5 and D2NN metasurface 3 are composed of several meta atoms arranged and combined. The modulation phase of meta atoms in the optical path is simulated based on FDTD (Finite Difference Time Domain) to achieve full coverage of meta atom phase.

[0064] S51. Setting up the meta-atoms. Since the light field for beam shaping in this example is unpolarized light, the shape of the meta-atoms is defined as highly symmetrical nanocylinders. The material is single-crystal silicon, which has advantages such as high refractive index, high transmittance, and low cost in the far-infrared band. The nanocylinders are placed on the substrate. The parameters describing the size of the nanocylinders are diameter D and height H, and the parameter describing the size of the substrate is period P. The shape of the meta-atoms is as follows: Figure 8 As shown.

[0065] S52. Set up the simulation space. The size of the simulation space in the XY section is consistent with the period P of the metaatomic substrate. The size in the Z direction is at least one light wave longer than the height H of the metaatomic atom. The boundary conditions in the XY direction are set as periodic boundary conditions to simulate the coupling relationship between a single atom and other atoms on the metaatomic surface. The boundary condition in the Z direction is set as a perfect absorption layer to simulate the infinite propagation in the real world. The FDTD simulation cross-section interface diagram is shown below. Figure 9 As shown.

[0066] S53. Set the light source. The light source type is a plane wave with a wavelength of 10.6 μm and a direction of propagation along the positive Z-axis.

[0067] S54. Phase Scan. Using the optimization and scanning modules built into FDTD, the diameter D and height H of the metaatom are set as variables for scanning to obtain the transmittance and phase distribution as the diameter and height change. Metaatoms that achieve full 2pi phase coverage and an average transmittance of over 70% with varying diameter D at a constant height H are selected. The relationship between the diameter D and phase change of the scanned metaatoms is as follows: Figure 10 As shown.

[0068] S6. Pair the phase distribution of the D2NN metasurface 3 with the modulation phase of the meta atoms, and arrange the meta atoms to generate the D2NN metasurface 3.

[0069] Due to limitations in metasurface fabrication conditions, there will be some deviation between the actual fabrication and design of metaatoms. To avoid this problem and ensure the performance of the metasurface, the phase of the metasurface is generally divided into 8 segments. The beam-shaped metasurface obtained in S4 is segmented with a step size of pi / 4. The phase in the range of 0 to pi / 4 is changed to 0, the phase in the range of pi / 4 to pi / 2 is changed to pi / 4, and so on, for a total of eight segments. The coordinates are (r m s n The phase at position ) is phase(r) m s n The diameter-phase transformation relationship f(D) obtained by FDTD scanning is used to obtain the corresponding superatomic diameter D(R). m S n )=f -1 (phase(r m s n )), with a diameter of D(R) m S n The center of the superatoms of ) is placed in (R m S n At this location, R m =r m *P,S n =s n *P, where the distance between the centers of the superatoms is the period P, is illustrated in the diagram below. Figure 11 As shown.

[0070] In summary, this method uses D2NN metasurfaces to achieve beam shaping. Metasurfaces are not constrained by surface shape formulas and have higher beam shaping capabilities, showing broad application prospects in the field of beam shaping.

Claims

1. A laser beam shaping method based on a D2NN metasurface, characterized in that, Includes the following steps: S1. Design of laser beam shaping optical path based on D2NN metasurface: 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) arranged sequentially along the optical path. The CCD camera (4) is connected to a computer. The laser (1) emits far-infrared light of 10.6 μm, which is collimated and expanded into parallel light by the collimating and beam expander (2) and used as the input light field. The parallel light is incident on the D2NN metasurface (3) and shaped. After shaping, it propagates in space and is finally received by the CCD camera (4). Switch to S2; S2. Determine the beam shaping target, i.e. the target light field, and proceed to S3; S3. In the computer, the phase modulation of the D2NN metasurface (3) is characterized by the phase layer, and then the D2NN based on the diffraction propagation model is constructed to simulate the propagation process of the optical field in the laser beam shaping optical path. The input optical field is sent into the D2NN to obtain the output optical field, and then transferred to S4. S4. Train D2NN based on the difference between the output light field and the target light field. After training, obtain the phase distribution of the phase layer, i.e. the phase distribution of the D2NN metasurface (3), and proceed to S5. S5, D2NN metasurface (3) is composed of several meta atoms arranged and combined. Based on FDTD simulation, the modulation phase of meta atoms in the optical path is achieved to realize full coverage of meta atom phase, and then proceed to S6; S6. Pair the phase distribution of the D2NN metasurface (3) with the modulation phase of the meta atoms, arrange the meta atoms to generate the D2NN metasurface (3), and proceed to S7. S7. Place the obtained D2NN metasurface (3) into the laser beam shaping optical path to achieve laser beam shaping.

2. The laser beam shaping method based on a D2NN metasurface according to claim 1, characterized in that, In S2, the beam shaping target, i.e., the target optical field, is determined as follows: The laser (1) emits a Gaussian beam with a cross-sectional radius of . The beam expansion factor of the collimating beam expander (2) is β, therefore the input light field has a cross-sectional radius of β. Gaussian beam, Its amplitude distribution is , The amplitude is at the center of the beam cross-section, and r is the point... The distance from the center of the beam cross-section; since the divergence angle of the beam is reduced to β times its original value after passing through the collimating beam expander (2), the input light field is approximated as parallel light, and its phase distribution is expressed as ; The target light field is a circular flat-top beam with radius r0, and its amplitude distribution is... , It is a constant. The coordinates of the target light field are given. Since the information received by the CCD camera (4) is light intensity information, which is independent of the phase, the phase of the target light field is not required.

3. The laser beam shaping method based on a D2NN metasurface according to claim 1, characterized in that, In S3, the phase modulation of the D2NN metasurface (3) is characterized by a phase layer in the computer, and then a D2NN based on the diffraction propagation model is constructed to simulate the propagation process of the optical field in the laser beam shaping optical path. The input optical field is sent into the D2NN to obtain the output optical field, as follows: S31 and D2NN consist of an input layer, an output layer, and at least one phase layer. A single phase layer characterizes the phase modulation effect of a single metasurface. The input optical field is fed into the input layer, and the complex amplitude distribution of the input optical field... Represented as: ； in The coordinates of the input light field are given. The amplitude distribution of the input light field. The phase distribution of the input light field. Indicates the imaginary part; S32. The process by which the input light field, after free propagation through the first segment of space, reaches the front surface of the first phase layer, i.e., the process of the front surface of the first metasurface, is represented as: ； in This represents the coordinates of the front surface of the first phase layer. This represents the complex amplitude distribution of the optical field on the front surface of the first phase layer. This represents the propagation distance from the input layer to the front surface of the first phase layer. The free-space diffraction propagation function represents the free propagation process of a light field; S33. When a light field is incident from the front surface of the first phase layer to its rear surface, it will be subject to phase modulation by the phase layer. This process can be represented as follows: ； in This represents the complex amplitude distribution of the optical field on the back surface of the first phase layer. This represents the phase distribution of the first phase layer; S34. The light field modulated by the phase layer continues to propagate freely in space until it reaches the second phase layer. After being modulated by the second phase layer, it propagates freely in space again, repeating this cycle until it reaches the output layer, where the light field is output. Therefore, the physical model of D2NN is expressed as: ； in The total number of phase layers, The phase layer number, , Indicates the first The complex amplitude distribution of the optical field on the front surface of each phase layer For the first Complex amplitude distribution of the optical field on the back surface of each phase layer For the first Phase distribution of each phase layer For the light field from the first The phase layer to the first The propagation distance of each phase layer Let be the propagation distance of the light field from the last phase layer to the image plane. The complex amplitude distribution of the output light field; The light intensity distribution of the output light field of S35 and D2NN is as follows: （5） in for Conjugate; The output light field of D2NN is the output light field detected by CCD camera (4).

4. The laser beam shaping method based on a D2NN metasurface according to claim 1, characterized in that, In S4, D2NN is trained based on the difference between the output light field and the target light field. After training, the phase distribution of the phase layer is obtained, that is, the phase distribution of the D2NN metasurface (3), as follows: Amplitude distribution of the target light field The loss value is obtained by performing MSE on the amplitude distribution of the output light field. The Adam optimizer is used for backpropagation to update the phase distribution of the phase layer. After training, the output light field is close to the target light field. At this time, the phase distribution of the phase layer is the phase distribution of the D2NN metasurface (3).

5. The laser beam shaping method based on a D2NN metasurface according to claim 1, characterized in that, The D2NN metasurface (3) is composed of several metaatoms arranged and combined. Based on FDTD simulation, the modulation phase of metaatoms in the optical path is achieved to realize full phase coverage of metaatoms, as follows: S51. Set up a meta-atom; the shape of the meta-atom is a nanocylinder, the material is single-crystal silicon, and the nanocylinder is placed on the substrate; the parameters describing the size of the nanocylinder include diameter D and height H, and the parameter describing the size of the substrate is period P; S52. Set up the simulation space; the size of the simulation space in the XY section is the same as the period P of the meta-atom substrate, and the size in the Z direction is at least one light wavelength longer than the height H of the meta-atom. Set the boundary conditions in the XY direction as periodic boundary conditions, and set the boundary conditions in the Z direction as perfect absorption layer. S53. Set the light source; the light source type is plane wave, wavelength 10.6um, and direction is propagation along the positive Z-axis; S54, Phase Scan: Using the optimization and scanning modules built into FDTD, the diameter D and height H of the meta-atom are set as variables for scanning to obtain the transmittance and phase distribution as the diameter D and height H change. The meta-atom that can achieve full 2pi phase coverage as the diameter D changes when the height H is constant is selected.

6. The method of claim 1, wherein the D2NN metasurface is configured to shape the laser beam. In S6, the phase distribution of the D2NN metasurface (3) and the modulation phase of the metaatoms are paired, and the metaatoms are arranged to generate the D2NN metasurface (3), as follows: The phase distribution of the D2NN metasurface (3) is segmented with a step size of pi / 4. The phase in the range of 0~pi / 4 is changed to 0, the phase in the range of pi / 4~pi / 2 is changed to pi / 4, and so on, for a total of eight segments. According to the phase arrangement obtained in S4, with the period being the interval between the centers of two metaatoms, the metaatoms that realize the phases of 0, pi / 4, pi / 2, 3pi / 4, pi, 5pi / 4, 3pi / 2, and 7pi / 4 are placed in their corresponding positions to form the entire D2NN metasurface (3).

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