Inverse Design of Photonic Crystals through Automatic Differentiation

Abstract

Gradient-based inverse design in photonics has already achieved remarkable results in designing small-footprint, high-performance optical devices. The adjoint variable method, which allows for the efficient computation of gradients, has played a major role in this success. However, gradient-based optimization has not yet been applied to the mode-expansion methods that are the most common approaches to studying periodic optical structures such as photonic crystals. This is because, in such simulations, the adjoint variable method cannot be defined as explicitly as in standard finite-difference or finite-element time-or frequency-domain methods. Here, we overcome this gap through the use of automatic differentiation, which is a generalization of the adjoint variable method to arbitrary computational graphs. We implement the planewave expansion and the guided-mode expansion methods using an automatic differentiation library, and we show that the gradient of any simulation output can be computed efficiently and in parallel, with respect to all input parameters. We then use this implementation to optimize the dispersion of a photonic crystal waveguide, and the quality factor of an ultrasmall cavity in a lithium niobate slab. This extends photonic inverse design to an entirely new class of simulations, and more broadly highlights the importance that automatic differentiation could play in the future for tracking and optimizing complicated physical models.

Arbitrary linear transformations for photons in the frequency synthetic dimension

“…While explicitly defined adjoint variable methods have been widely used for photonic inverse design 39 , automatic differentiation is the generalization of the adjoint variable methods to arbitrary computational graphs. Automatic differentiation has recently been successfully applied to the inverse design of photonic band structures 40 as well as photonic neural networks 41 , where explicit adjoint methods are challenging to implement. Here, automatic differentiation enables the efficient computation of the gradients of a scalar objective function with respect to complex control parameters, which in this case are the coupling constants κ ± l as defined in Eq.…”

Multiobjective and categorical global optimization of photonic structures based on ResNet generative neural networks

“…implemented in finite-difference time domain (FDTD) and finitedifference frequency domain (FDFD) simulators [37,38]. Compared to generalized differentiable electromagnetic solvers, such as these FDTD and FDFD implementations, our analytic TMM-based algorithms are faster without loss of accuracy because the thin films are described as layers instead of voxels.…”

Intelligent designs in nanophotonics: from optimization towards inverse creation

“…AI-algorithm-aided design methodologies are fast becoming fundamental toolboxes to develop high-quality photonic structures. To date, the soaring number of nanoscale applications [139][140][141] have been appreciably benefited from the artificial intelligence such as photonic crystals [142], Fano resonators [143], photon extractors [144], topological insulators [145], and particle accelerators [146], etc. in addition to the aforesaid meta-devices.…”