New Regimes for Topology Optimization in Photonics

Abstract

Inverse design is a powerful methodology to obtain non-trivial and non-intuitive photonic structures of unprecedented performance. Topology optimization is a particular class of inverse design method that has been increasingly popular in photonics. Numerous topology optimization tools and frameworks have been developed and often yield satisfying results for various engineering problems. This work explores the subtleties involved in the development and application of topology optimization, and presents new regimes for photonic design, where the key to finding the right solutions lies in posing the right questions. To begin with, we first review the current frameworks for photonic topology optimization. We point out that, as new algorithms emerge, the lack of standardized validation methods presents a challenge for further advancements. To address this, we provide a comprehensive suite of test problems along with a length-scale metric for comparing designs across different algorithms, aiming to facilitate the development and validation of future inverse design approaches. However, a functioning inverse design algorithm alone is not sufficient to guarantee satisfying designs. We present two case studies highlighting the importance of careful formulation for achieving mathematical robustness and tractability that is crucial to the success of optimization. The first case examines the inverse design of 3D-printable metalenses with complementary dispersion for terahertz imaging. It illustrates a physical dichotomy between achieving two distinct dispersion behaviors in a thin structure. We demonstrate that a key aspect in making such design tractable is carefully balancing the trade-offs between focal quality and scanning rate in the optimization problem formulation. The second case focuses on the inverse design of multiresonance filters via quasi-normal mode theory. Traditional filter design approaches have various limitations, and directly applying topology optimization leads to numerically stiff formulations. We propose a new practical high-order-filter design method based on a minimal set of analytical design criteria derived from quasi-normal mode theory. We illustrate our approach by designing 3rd and 4th-order elliptic and Chebyshev dielectric filters.