Accelerating numerical methods for gradient-based photonic optimization and novel plasmonic functionalities

Optimizing the design and performance of photonic systems has been an active and growing area of research over the past decade with many practical applications such as image sensors, augmented reality and virtual reality, on-chip photonic systems, and more. Moreover, gradient-based methods, such as the adjoint variable method (AVM), have led to very distinctive and complex designs for on-chip multiplexers, tapers, dielectric laser accelerators, and more, while yielding much higher performance metrics which classical design approaches using first principles physics cannot match. However, less research has been dedicated in the photonics community to understanding and improving the underlying numerical methods which are critical for the success of these applications. In this thesis, we will demonstrate four key numerical advancements in the use of gradient-based design methods using frequency domain numerical solvers of Maxwell's equations, particularly finite difference frequency domain (FDFD) solvers. The first is the application of domain decomposition techniques to gradient-based optimization, allowing us to reduce the effective system size for a gain in efficiency. The second exploits the physics of perturbative series expansions to efficiently determine the optimal learning rate essential to gradient-based optimization. The third leverages the fundamental similarities of the previous two methods, allowing us to combine the two to achieve a further multiplicative acceleration. The fourth is exploiting the choice of boundary condition in the context of perfectly matched layers to minimize overhead and optimize the efficiency of the simulations required during the optimization procedure. Furthermore, we will demonstrate one novel practical application in designing a next generation replacement for traditional filter-based image sensors that we term a 'color router'. By using a gradient-based approach, we demonstrate not only can we overcome the traditional limitations of filter-based approaches, but we can approach the absolute physical limit of color separation efficiency. In the context of this problem as well, we also demonstrate one further novel method to accelerate optimization, using an L1-like penalty method inspired by L1-regularization popularized in machine learning to improve the robustness to manufacturing errors and other perturbations to the device design. Finally, as a contrast to the gradient-based technique of optimization, we also showcase two examples of more traditional device optimization using the theoretical principles of Maxwell's equations. The first is to exploit analytic continuation and the band-structure of insulator-metal-insulator waveguides to design a reflector with superior reflection properties to that of a uniform metal but with lower loss (essentially a nearly metal-less metallic metamaterial). The second is to engineer interesting radiative properties and extraordinarily high reflection in atomically-thin monolayer graphene nano-ribbon system

Keywords: Applied Physics.
Advisor: Fan Shanhui
Brongersma Mark L.
Fan Jonathan Albert