Method for computationally efficient design of dielectric laser accelerator structures

Abstract

Dielectric microstructures have generated much interest in recent years as a means of accelerating charged particles when powered by solid state lasers. The acceleration gradient (or particle energy gain per unit length) is an important figure of merit. To design structures with high acceleration gradients, we explore the adjoint variable method, a highly efficient technique used to compute the sensitivity of an objective with respect to a large number of parameters. With this formalism, the sensitivity of the acceleration gradient of a dielectric structure with respect to its entire spatial permittivity distribution is calculated by the use of only two full-field electromagnetic simulations, the original and 'adjoint'. The adjoint simulation corresponds physically to the reciprocal situation of a point charge moving through the accelerator gap and radiating. Using this formalism, we perform numerical optimizations aimed at maximizing acceleration gradients, which generate fabricable structures of greatly improved performance in comparison to previously examined geometries.

Reconfigurable Photonic Circuit for Controlled Power Delivery to Laser-Driven Accelerators on a Chip

“…It was shown previously [29] that the gradient of the output of an MZI mesh with respect to the dielectric function of each of the phase shifters may be measured experimentally using adjoint fields [41]. Interestingly, for the case of maximizing the acceleration of a DLA, it was independently shown that the corresponding adjoint fields are given exactly by the fields radiated by the electron beam [8]. This suggests an interesting approach to optimizing the MZI mesh towards maximum acceleration by first measuring the radiation from test electron beam, and then using the protocol from Ref.…”

Adjoint Method and Inverse Design for Nonlinear Nanophotonic Devices

“…In analogy with the linear adjoint method, we can now compute the gradient by solving an additional linear system. We define a complex-valued adjoint field e aj as the solution to ∂f /∂e ∂f /∂e * ∂f * /∂e ∂f * /∂e * T e aj e * aj = − ∂L/∂e T ∂L/∂e * T , (7) and the gradient of the objective function is then…”

“…In recent years, there has been significant interest in using computational optimization tools to design novel nanophotonic devices with a wide range of applications [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Much of this progress [1][2][3][4][5][6][7][8][9][10][11][12] is made possible by the adjoint method [18,19], a technique which allows the gradient of an objective function to be computed with respect to an arbitrarily large number of degrees of freedom using only two full-field simulations. This method makes large-scale gradient-based design of electromagnetic structures possible.…”

Training of Photonic Neural Networks through In Situ Backpropagation

“…In this work, we propose a procedure, which we label the time-reversal interference method (TRIM), to compute the gradient of the cost function of a photonic ANN by use of only in situ intensity measurements. Our procedure works by physically implementing the adjoint variable method (AVM), a technique that has typically been implemented computationally in the optimization and inverse design of photonic structures [18][19][20]. Furthermore, the method scales in constant time with respect to the number of parameters, which allows for backpropagation to be efficiently implemented in a hybrid optoelectronic network.…”