Prevalence and inverse design of topological photonic crystals

Broadly applicable symmetry-based techniques for band topological analysis, first introduced by the condensed-matter community, have recently been applied in photonic settings. I will highlight a few interesting examples of the opportunities that this brings. As a first example, I will discuss the prevalence of band topology in two-dimensional photonic crystals, assessed by sampling across a very large set of randomly generated unit cells, and evaluating across stable, fragile, and higher-order topological properties [1]. As a second example, I will describe our efforts to deal with the “practical” problem of photonic topological design – not merely finding a given topological property but finding it in combination with desirable spectral properties, a task that is typically an arduous, manual process. Using a simple inverse design technique based on global and subsequent local, gradient-free optimization of a well-parameterized, symmetry-adapted level-set function, we demonstrate that it is possible to automate this design process, with examples spanning photonic Chern, Weyl, and nodal line phases [2].

[1] Ghorashi, Vaidya, Rechtsman, Benalcazar, Soljačić, & Christensen, arXiv:2307.15701 (2023)
[2] Kim, Christensen, Johnson, & Soljačić, ACS Photonics 10, 861 (2023)