Inverse design method for micro-nano acceleration structure of medium laser accelerator

Abstract

The invention provides an inverse design method for a micro-nano acceleration structure of a medium laser accelerator, and the method comprises the steps: improving the setting of a target function in the inverse design process of the micro-nano acceleration structure of the medium laser accelerator, introducing the simulation of electron motion, and continuously correcting the target function of each iteration, thereby achieving the inverse design of the micro-nano acceleration structure of the medium laser accelerator. And phase loss of electrons and a light field is reduced, so that the performance of the medium laser accelerator is improved.

Description

Technical Field

[0001] The invention relates to the field of electronic information technology, and in particular to an inverse design method for a micro-nano acceleration structure of a dielectric laser accelerator. Background Art

[0002] Particle accelerators are devices that use electromagnetic fields to accelerate charged particles (electrons, protons, ions, etc.) and are widely used in industries such as industry, agriculture, medicine, and scientific research. Although a variety of acceleration schemes have emerged in the field of accelerators over the past century, their essence is still to transfer the energy of the electromagnetic field to charged particles. Laser-driven on-chip particle accelerators are one of the acceleration schemes to achieve high acceleration gradients and are also a current research hotspot. Laser-driven on-chip particle accelerators use micro-nanoscale dielectric structures to regulate laser-driven light fields, so that charged particles are accelerated by the driving light field in the medium transmission channel. Using laser drive, the acceleration structure can be compressed to the micro-nano scale of the optical wavelength by taking advantage of the short wavelength of the laser, and a higher acceleration gradient can be achieved on the micron-scale structure.

[0003] Compared with traditional RF accelerators, the characteristic structural size of laser-driven on-chip particle accelerators can be reduced by 104 orders of magnitude. Since dielectrics have a higher laser damage threshold, they can withstand an accelerating electric field that is 102 orders of magnitude larger than that of traditional copper RF accelerators. The corresponding acceleration gradient can be increased by 102 orders of magnitude, and a higher energy gain can be obtained within a short distance. At the same time, thanks to the development of laser technology, commercial femtosecond mode-locked lasers with high average power can provide stable drive for laser-driven on-chip particle accelerators, which are easy to implement and maintain. Due to the above advantages, laser-driven on-chip particle accelerators are expected to become an advanced accelerator technology and be applied in many fields. As shown in Figure 2, through its volume advantage, desktop-level high-energy particle beam sources can be realized, and applied to desktop-level ultra-bright ultra-fast light sources, compact radiation imagers, and CT three-dimensional reconstruction. In addition, the ultrashort pulses generated by particle accelerator light sources can also be used for atomic-scale material structure analysis and dynamic imaging at the femtosecond time scale.

[0004] In 2018, Cesar D et al. from the University of California, Los Angeles, studied the nonlinear optical effects and phase control methods in laser-driven on-chip particle accelerators under high electric field strength, and could produce a maximum acceleration gradient of 1.8 GeV / m for electrons with an initial energy of 8 MeV. However, for sub-relativistic electrons, due to the dephasing caused by the increase in electron velocity, in the existing experimental results, for electrons with an initial energy of 96.3 keV, the maximum acceleration gradient is 370 MeV / m; for electrons with an initial energy of 28 keV, the maximum acceleration gradient is 25 MeV / m.

[0005] Patent CN 109600904 B discloses a semiconductor laser accelerator and a laser acceleration unit thereof, providing a semiconductor laser accelerator and an acceleration unit thereof with a simple structure and capable of solving the phase slip problem, such as Figure 1 shown.

[0006] like Figure 2(a) and 2(b) As shown in the literature, “Laser acceleration and deflection of 96.3keV electrons with a silicon dielectric structure” achieved an acceleration gradient of more than 200MeV / m and sub-optical periodic fringes of 96.30keV electrons driven by a 5nJ, 130fs 907nm wavelength mode-locked Ti:sapphire laser.

[0007] like Figure 3 As shown in the literature "Topology optimization of on-chip integrated laser-driven particle accelerator, NUCL SCI TECH (2022) 33:120", this is a method to optimize the material distribution in a specific area based on given load conditions, constraints and performance indicators. Randomly select the dielectric constant value of each grid as 0 or 1, where 0 represents vacuum and 1 represents the dielectric constant of the material, then change the dielectric constant value state of one grid and change the dielectric constant value of another grid to simulate, and record the objective function The value is calculated repeatedly until all combination results are traversed, and finally the optimal structure is selected from all simulation results.

[0008] Considering the energy conversion rate, the acceleration gradient should be as high as possible above the peak value of the incident electric field. This means that the "conversion factor" given by dividing the acceleration gradient by the peak amplitude of the incident electric field needs to be optimized. This quantity will reveal the maximum conversion rate that the structure can achieve. In mathematical language, we express this principle as:

[0009]

[0010] Using periodic conditions, a plane wave (E0 is the initial injection electric field) is introduced from the left into the DLA chip. The laser wavelength used in the simulation is 2000nm. The normalized velocity of the injected electrons is 0.5, and the square grid size used in the simulation is 20nm. The material used in the optimization process is fused silica (SiO2) with a refractive index of n = 1.45. By optimizing the maximum conversion factor, a conversion factor of 0.32 can be achieved. The results of the structural optimization are consistent with those in the reference, such as Figure 4shown.

[0011] When a conventional grating acceleration structure accelerates non-relativistic electrons or sub-relativistic electrons (<500 keV), the dephasing caused by the increase in electron velocity will affect the acceleration performance. Summary of the invention

[0012] In view of this, the present invention provides an inverse design method for a micro-nano acceleration structure of a dielectric laser accelerator, which is an improvement based on the inverse design method. In the process of constructing the objective function, the influence of the increase in electron velocity on the objective function is considered, and part of the phase loss that may occur is offset in the inverse design optimization process, thereby improving the conversion factor, that is, improving the acceleration performance.

[0013] A method for inverse design of a micro-nano acceleration structure of a dielectric laser accelerator, comprising:

[0014] In the DLA system, electrons gain energy through the electric field along their propagation direction, and the acceleration gradient G acc for:

[0015]

[0016] Where L is the interaction distance between the electron and the driving laser, e is the charge of the electron, and E y (x,y,z) is the electric field amplitude along the y direction, and φ 0 (x, y, z) is the initial phase of the electric field, and the angular frequency ω=2πc 0 / λ 0 ; 0 represents the driving laser wavelength, c 0 represents the speed of light in a vacuum;

[0017] Based on the Yee grid size ΔL and G acc Discretize:

[0018]

[0019] Among them, N is the number of grids in the y direction, n is the grid number, and β is the ratio of the electron speed to the speed of light c. 0 The speed factor of the ratio; E yn =E y (x 0 ,y 0 +nΔL,z 0 ), where x 0 ,y 0 ,z 0 It represents the initial position of the electron. It is assumed that the electron moves along the y direction, and the displacement in the x and z directions is negligible. y represents the y-direction component of the electric field; β jRepresents the velocity factor of the electron at the jth grid, which is accumulated by Indicates the time it takes for the electron to move to the nth grid; φ 0n represents the phase of the electric field at the nth grid, G acc Expressed as an inner product:

[0020]

[0021] Among them, <, > represent inner product operation;

[0022] Construct the following two complex one-dimensional matrices to represent the inner product:

[0023]

[0024] X n =E yn exp(φ 0n ) (5)

[0025] C n represents the simplified complex coefficients based on the interaction between electrons and the electric field at the grid n; X n represents the frequency domain electric field distribution at grid n;

[0026] Let X = [X 1 ,X 2 ,...,X N ] is the frequency domain electric field distribution at each grid from FDFD, C = [C 1 , C 2 ,...,C N ] is the simplified complex coefficient based on the interaction between electrons and electric fields at each grid,<C,X> is a complex number, where the real part refers to the acceleration gradient experienced by the electron entering the accelerator at a specific phase, and the modulus refers to the maximum acceleration gradient that can be obtained in all phases; the objective function is defined as:

[0027] f=|<C,X> | (6)

[0028] 2. Optimization Methods

[0029] Obtain the gradient of the objective function relative to the structural parameter p to be optimized The parameter p is updated according to the set step size in the opposite direction of the gradient, thereby updating the objective function; and the gradient of the updated function is calculated again to update the parameter p. This process is repeated many times until the stopping condition is reached and the structural parameters are obtained.

[0030] Preferably, the stopping condition is: the maximum number of iterations or the objective function no longer changes.

[0031] Preferably, the gradient of the objective function relative to the structural parameter p to be optimized is obtained The methods include:

[0032] According to the chain rule:

[0033] Among them, p represents the optimized structural parameter. Gradient optimization first needs to find the gradient of the objective function with respect to the optimized structural parameter. The gradient of the objective function with respect to the electric field is:

[0034]

[0035] Through FDFD electromagnetic field simulation, for a certain p, the corresponding X is obtained, and the FDFD simulation is simplified to solve the following problem:

[0036] A(p)X=b;

[0037] Where A(p) represents the coefficient matrix of the FDFD solution system, and b represents the source of the FDFD solution system;

[0038] Differentiate both sides of the equal sign in the above solution problem:

[0039]

[0040] where p = [p 1 ,p 2 ,...,p M ], M represents the number of structural parameters, p i represents the i-th parameter in the structural parameter p, then:

[0041]

[0042] Can get

[0043]

[0044] in, and are constants after p is determined. As a companion source, a similar problem to that of FDFD simulation can be solved:

[0045]

[0046] in,

[0047] By solving the FDFD system twice, the gradient of the objective function relative to the structural parameter p to be optimized is obtained

[0048] The present invention has the following beneficial effects:

[0049] The present invention provides an inverse design method for a micro-nano acceleration structure of a dielectric laser accelerator. Taking into account the influence of changes in electron velocity, during the inverse design process of the micro-nano acceleration structure of a dielectric laser accelerator, the setting of an objective function is improved, and at the same time, simulation of electron motion is introduced to continuously correct the objective function of each iteration, which is beneficial to reducing the phase difference between electrons and light fields, thereby improving the performance of the dielectric laser accelerator. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The semiconductor laser accelerator and its laser acceleration unit structure diagram disclosed in patent CN109600904B;

[0051] Figure 2(a) is a schematic diagram of the light field of electrons above the accelerating structure;

[0052] Figure 2(b) is a schematic diagram of the acceleration experiment device;

[0053] Figure 3 An optimized design scheme for a double-layer structure with an electron acceleration channel;

[0054] Figure 4 Based on Figure 3 The optimization design results;

[0055] Figure 5 It is the algorithm flow chart of the present invention;

[0056] FIG6(a) and FIG6(b) are comparisons of the design results of the algorithm of the present invention and the acceleration gradient of the electrons by the grating structure in the single-layer optimization region. FIG6(a) shows the design result of the present invention, and the acceleration gradient of the electrons can reach 459 MeV / m. FIG6(b) shows that the acceleration gradient of the electrons by the grating structure under the same conditions is 418 MeV / m.

[0057] Figures 7(a) and 7(b) are comparisons of the design results of the algorithm of the present invention and the results of other inverse design optimization algorithms in the double-layer optimization region. Figure 7(a) shows the design result of the present invention, and the electron acceleration gradient can reach 678MeV / m. Figure 7(b) shows that the acceleration gradient of electrons for other inverse design structures is 331MeV / m. DETAILED DESCRIPTION

[0058] 1. Objective function definition

[0059] In the DLA system, electrons gain energy through the electric field along their propagation direction, and the acceleration gradient G acc for:

[0060]

[0061] Where L is the interaction distance between the electron and the driving laser, e is the charge of the electron, and Ey (x,y,z) is the electric field amplitude along the y direction, and φ 0 (x, y, z) is the initial phase of the electric field, and the angular frequency ω=2πc 0 / λ 0 ; 0 represents the driving laser wavelength, c 0 represents the speed of light in a vacuum;

[0062] Electric field amplitude E y and the initial phase φ 0 It can be solved by the finite difference frequency domain (FDFD) method. acc In the FDFD method, we use the Yee grid size ΔL to acc Discretize.

[0063]

[0064] Where N is the number of grids in the y direction, n is the grid number, and β is the ratio of the electron speed to the speed of light c 0 The speed factor of the ratio. yn =E y (x 0 ,y 0 +nΔL,z 0 ), where x 0 ,y 0 ,z 0 represents the initial position of the electron. It is assumed that the electron moves along the y direction, and the displacements in the x and z directions are negligible; β j Represents the velocity factor of the electron at the jth grid, which is accumulated by Indicates the time it takes for the electron to move to the nth grid; φ 0n represents the phase of the electric field at the nth grid. To simplify the following derivation, G acc It can be expressed as an inner product:

[0065]

[0066] Among them, <, > represent inner product operations.

[0067] We construct two complex one-dimensional matrices to represent the inner product:

[0068]

[0069] X n =E yn exp(φ 0n ) (5)

[0070] Let X = [X 1 ,X 2 ,...,XN ] is the frequency domain electric field distribution at each grid from FDFD, C = [C 1 , C 2 ,...,C N ] is the simplified complex coefficient based on the interaction between electrons and electric fields at each grid,<C,X> is a complex number, where the real part refers to the acceleration gradient experienced by the electron entering the accelerator at a specific phase, and the modulus refers to the maximum acceleration gradient that can be obtained in all phases. Therefore, our objective function is defined as:

[0071] f=|<C,X> | (6)

[0072] 2. Optimization Methods

[0073] According to the chain rule:

[0074] Among them, p represents the optimized structural parameter. Gradient optimization first needs to find the gradient of the objective function with respect to the optimized structural parameter. The gradient of the objective function with respect to the electric field is:

[0075]

[0076] Through FDFD electromagnetic field simulation, for a certain p, the corresponding X can be obtained. FDFD simulation can be simplified to solve the following problems:

[0077] A(p)X=b;

[0078] Where A(p) represents the coefficient matrix of the FDFD solution system, and b represents the source of the FDFD solution system;

[0079] Differentiate both sides of the equal sign in the above solution problem:

[0080]

[0081] where p = [p 1 ,p 2 ,...,p M ], M represents the number of structural parameters, p i represents the i-th parameter in the structural parameter p, then:

[0082]

[0083] Can get

[0084]

[0085] in, and are constants after p is determined. As a companion source, a similar problem to that of FDFD simulation can be solved:

[0086]

[0087] in,

[0088] By solving the FDFD system twice, the gradient of the objective function relative to the structural parameter p to be optimized is obtained

[0089] The gradient represents the rate of change of the objective function under the current structural parameter p to be optimized. The parameter p is updated according to a certain step size in the opposite direction of the gradient, thereby updating the objective function; and the gradient of the updated function is calculated again to update the parameter p. This is repeated many times until the maximum number of iterations is reached or the objective function no longer changes, that is, the structural parameter p that can best accelerate our structural effect is obtained.

[0090] The above process starts from the purpose of improving the acceleration performance, defines the objective function and then optimizes the gradient to solve the optimal structural parameters. This is the inverse design method of the acceleration structure of the present invention. The innovation of the present invention is that the electron velocity is processed in the form of a vector rather than a fixed value in the objective function setting.

[0091] 3. Electronic motion simulation

[0092] According to the electromagnetic field generated by FDFD and the initial velocity v of the electron 0 , we can calculate the Lorentz force acting on the electron and deduce the electron velocity at each moment. In addition, assuming the initial coordinates (x 0 ,y 0 ) we can obtain the electron coordinates (x n sim ,y n sim ).

[0093] Consider the electron motion equation for the relativistic case:

[0094]

[0095] Where m is the mass of the electron, m e is the electron rest mass, and is the relativistic factor γ defined as:

[0096]

[0097] in

[0098]

[0099] The expression for the Lorentz force can be written as

[0100]

[0101] Combining equation (11) and equation (12), we can get

[0102]

[0103] Where m e c 0 2 is a constant, approximately 511keV.

[0104] Assume that the initial state of the electron (x 0 ,y 0 ,z 0 ), then the next moment (x 1 ,y 1 ,v 1 )'s electronic state.

[0105]

[0106] γ 1 =γ 0 +Δγ

[0107]

[0108] v 1 =v 0 +Δv

[0109] (x 1 ,y 1 )=(x 0 ,y 0 )+v 0 Δt (13)

[0110] Here we approximately assume that the electron velocity remains constant over a very small time interval Δt.

[0111] In this way, we are able to simulate the trajectory of the electron and its speed (energy) at different positions along its trajectory.

[0112] 4. Result verification:

[0113] The optimization results and electron energy changes are shown in Figure 6(a). The driving laser is irradiated perpendicular to the paper surface (z direction), the structure has a certain thickness, and the bottom substrate is not shown in the figure. The simulated driving laser is a plane wave with a field strength of 1 GV / m and polarization in the y direction. The final calculated electron acceleration gradient is 459 MeV / m.

[0114] FIG6( b ) shows that the electron acceleration gradient of the common grating structure under the same electron and driving laser conditions is 418 MeV / m, indicating that the inverse design scheme of the present invention is effective.

[0115] As shown in Figure 7(a), the driving laser is irradiated from top to bottom (y direction), and the structure has a certain extension in the direction perpendicular to the paper surface. The 2D simulation assumes that this extension is infinite. The simulated driving laser is a plane wave with a field strength of 1 GV / m and polarized in the y direction. The final calculated electron acceleration gradient is 678 MeV / m.

[0116] FIG. 7( b ) shows the result obtained by other inverse design methods. The electron acceleration gradient is 331 MeV / m. The electron acceleration effect of the present invention is more obvious.

[0117] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for inverse design of a micro-nano acceleration structure of a dielectric laser accelerator, characterized in that: include: In the DLA system, electrons gain energy through the electric field along their propagation direction, and the acceleration gradient G acc for: Where L is the interaction distance between the electron and the driving laser, e is the charge of the electron, and E y (x, y, z) is the electric field amplitude along the y direction, and φ0(x, y, z) is the initial phase of the electric field, angular frequency ω = 2πc0 / λ0; λ0 is the wavelength of the driving laser, and c0 is the speed of light in vacuum; Based on the Yee grid size ΔL and G acc Discretize: Where N is the number of grids in the y direction, n is the grid number, β is the speed factor representing the ratio of the electron speed to the speed of light c0; E yn =E y (x0,y0+nΔL,z0), where x0,y0,z0 represent the initial positions of the electrons. It is assumed that the electrons move along the y direction, and the displacements in the x and z directions are negligible; E y represents the y-direction component of the electric field; β j Represents the electron velocity factor at the jth grid, which is accumulated by Indicates the time it takes for the electron to move to the nth grid; φ 0n represents the phase of the electric field at the nth grid, G acc Expressed as an inner product: Among them, <, > represent inner product operation; Construct the following two complex one-dimensional matrices to represent the inner product: X n =E yn exp(φ 0n ) (5) C n represents the simplified complex coefficients based on the interaction between electrons and the electric field at the grid n; X n represents the frequency domain electric field distribution at grid n; Let X = [X1, X2, ..., X N ] is the frequency domain electric field distribution at each grid from FDFD, C = [C1, C2, ..., C N ] is the simplified complex coefficient based on the interaction between electrons and electric fields at each grid,<C,X> is a complex number, where the real part refers to the acceleration gradient experienced by the electron entering the accelerator at a specific phase, and the modulus refers to the maximum acceleration gradient that can be obtained in all phases; the objective function is defined as: f=|<C,X> | (6) Obtain the gradient of the objective function relative to the structural parameter p to be optimized The parameter p is updated according to the set step size in the opposite direction of the gradient, thereby updating the objective function; and the gradient of the updated function is calculated again to update the parameter p. This process is repeated many times until the stopping condition is reached and the structural parameters are obtained.

2. The inverse design method of a medium laser accelerator micro-nano acceleration structure according to claim 1, characterized in that: The stopping condition is: the maximum number of iterations or the objective function no longer changes.

3. The inverse design method of a medium laser accelerator micro-nano acceleration structure according to claim 1, characterized in that: Obtain the gradient of the objective function relative to the structural parameter p to be optimized The methods include: According to the chain rule: Among them, p represents the optimized structural parameter. Gradient optimization first needs to find the gradient of the objective function with respect to the optimized structural parameter. The gradient of the objective function with respect to the electric field is: Through FDFD electromagnetic field simulation, for a certain p, the corresponding X is obtained, and the FDFD simulation is simplified to solve the following problem: A(p)X=b; Where A(p) represents the coefficient matrix of the FDFD solution system, and b represents the source of the FDFD solution system; Differentiate both sides of the equal sign in the above solution problem: where p=[p1,p2,...,p M ], M represents the number of structural parameters, p i represents the i-th parameter in the structural parameter p, then: Can get in, and are constants after p is determined. As a companion source, a similar problem to that of FDFD simulation can be solved: in, By solving the FDFD system twice, the gradient of the objective function relative to the structural parameter p to be optimized is obtained

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