I gave a talk on auto-differentiation, topology optimization and open-source Maxwell solvers for the MetaMat online seminar series. Slides and recording available.
I had the opportunity to present my research at the MetaMat online seminar.
Abstract
Advances in nanofabrication have opened new applications in photonics. Engineering novel functionalities requires rigorous and efficient numerical methods. At the same time, algorithmic differentiation has made great progress, pushed in part by machine learning, and it now enables large-scale optimization of devices with only a few changes to the underlying code.
In this talk I outline the concepts behind automatic differentiation and give details on topology optimization algorithms. I present applications in electromagnetism and metamaterials, such as cloaking and illusion devices (the figure above shows an optimized cloak). Finally, I describe three software libraries for solving Maxwell’s equations:
- a finite element code with a high-level interface for problems common in photonics (gyptis)
- a Fourier modal method for multilayer bi-periodic metasurfaces (nannos)
- a plane wave expansion method for band diagrams of two-dimensional photonic crystals (protis)
All three support automatic differentiation, and I show typical inverse design examples with each.