A Hierarchical Approach to the Design and Optimization of Photonics
- Author(s): Michaels, Andrew
- Advisor(s): Yablonovitch, Eli
- et al.
Over the last two decades, silicon photonics has rapidly matured, leading to a growing interest in building large complex systems consisting of thousands of integrated optical components. A direct consequence of this push towards large scale integration is the need for high efficiency silicon photonic building blocks.
In this work, we present a concrete path towards realizing these essential photonic building blocks. The foundation of our approach to designing photonic components is gradient-based shape optimization, which employs boundary smoothing based on high numerical precision polygons. In addition to helping us calculate accurate device sensitivities, this method affords us a great amount of flexibility when representing device geometries and enables us to incorporate design constraints directly into optimizations in a simple and intuitive way.
Our approach to gradient-based optimization shares an important similarity to other forms of shape and topology optimization employed in the nanophotonics community: on its own, it is not a complete solution to designing high performance and robust devices. Due to the inherently non-convex nature of electromagnetic optimization problems, we cannot expect convex optimization to universally yield good devices without outside input. In order to overcome this obstacle, we have systematized the process of providing "outside input" through our hierarchical approach to design and optimization. Using a strategic combination of simple physical analysis to find good starting geometries and optimization with both coarse and fine parameterizations, we show that efficient and robust devices can be designed with minimal guesswork.
Using this hierarchical approach, we demonstrate how a variety of silicon photonic components can be designed with superior performance. In particular, we design three port splitters, broadband four port splitters, fabrication-insensitive waveguide crossings, and a variety of efficient grating couplers which set a new standard for device performance. These components form the foundation for an optimized silicon photonic component library which will be important for demanding applications of the future.