# Inverse design of photonic crystals through automatic differentiation

arXiv: https://arxiv.org/abs/2003.00379 · HTML: https://mlsanity.com/paper/2003.00379/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2020.

## Built on by (most cited first, 10 of 10)

- [A neural operator-based surrogate solver for free-form electromagnetic inverse design](https://mlsanity.com/paper/2302.01934/) (2023)
- [Inverse design of photonic devices with strict foundry fabrication constraints](https://mlsanity.com/paper/2201.12965/) (2022)
- [Inverse Design in Nanophotonics via Representation Learning](https://mlsanity.com/paper/2507.00546/) (2025)
- [Inverse Design of Grating Couplers Using the Policy Gradient Method from Reinforcement Learning](https://mlsanity.com/paper/2107.00088/) (2021)
- [SPDCinv: Inverse Quantum-Optical Design of High-Dimensional Qudits](https://mlsanity.com/paper/2112.05934/) (2021)
- [Advancing Machine Learning Optimization of Chiral Photonic Metasurface: Comparative Study of Neural Network and Genetic Algorithm Approaches](https://mlsanity.com/paper/2512.13656/) (2025)
- [Democratizing Electronic-Photonic AI Systems: An Open-Source AI-Infused Cross-Layer Co-Design and Design Automation Toolflow](https://mlsanity.com/paper/2601.00130/) (2025)
- [Inverse-designed meta processing units for multi-task near-field photonic computing](https://mlsanity.com/paper/2607.08360/) (2026)
- [When Every Simulation Counts: Value-Based Reinforcement Learning for Accelerated Photonics Inverse Design](https://mlsanity.com/paper/2607.23469/) (2026)
- [Inductively Scalable, Single-Step Neural Surrogates for Wave-Scattering Inverse Problems](https://mlsanity.com/paper/2608.17344/) (2026)

## Abstract (arXiv)

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 approach to studying periodic optical structures like 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 through the use of automatic differentiation, which is a generalization of the adjoint variable method to arbitrary computational graphs. We implement the plane-wave expansion and the guided-mode expansion methods using an automatic differentiation library, and 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 ultra-small cavity in a lithium niobate slab. This extends photonic inverse design to a whole 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.