Dissertations, Theses, and Capstone Projects

Date of Degree

6-2024

Document Type

Dissertation

Degree Name

Ph.D.

Program

Physics

Advisor

Mohammad-Ali Miri

Committee Members

Andrea Alu

Vinod Menon

Azriel Genack

Myoung-Gyun Suh

Subject Categories

Electromagnetics and Photonics | Non-linear Dynamics | Optics

Keywords

Optical Computing, Photonic Oscillators, Combinatorial Optimization, Nonlinear Dynamics

Abstract

The ever-increasing demand for data processing and the challenges in scaling traditional computing architectures are driving intensive research into alternative computing paradigms. Optical computing has garnered renewed attention since the 2010s, driven by its potential to accelerate specialized computational tasks such as combinatorial optimization and neural networks.

Coherent light sources including lasers and parametric oscillators have been around for decades and become indispensable tools in modern technology, but these photonic oscillators are also nonlinear dynamical systems that can exhibit emergent, complex phenomena, especially when coupled in arrays. These nonlinear optical systems have recently been shown to be capable of doing computation by emulating spin models. Specifically, an optical realization of the Ising model known as the Coherent Ising Machine has attracted attention for its potential capability of solving the NP-hard Ising problem. This has opened up interesting questions about the opportunities that optical oscillator networks can offer as combinatorial optimization solvers.

This thesis primarily explores the potential of networks of nonlinear photonic oscillators for computation. First, we show that a Potts solver can be realized by utilizing multi-stable states of an OPO network, therefore generalizing the Ising machine. Next, through a series of numerical and theoretical investigations, we examine the potential of a coupled laser array as an XY spin model simulator. We show that, under certain conditions, such a system can accurately model the XY Hamiltonian while giving high-quality solutions to the XY optimization problem.

Recognizing that we are dealing with classical physical systems, we took inspiration from the dynamics to develop a photonic-inspired algorithm as a heuristic to solve combinatorial optimization problems on digital hardware. We examine the effectiveness of this algorithm and demonstrate its capability in approximating the ground state of the classical Potts Hamiltonian. This approach streamlines the search within extensive discrete solution spaces, a task traditionally addressed through less efficient greedy algorithms, which typically make locally optimal choices at each step without considering the broader landscape of the cost function.

During the later part of my doctoral studies, I engaged in the design and characterization of integrated silicon photonic devices that can benefit from optical computing methods. These devices exploit the computational potential of optics to enhance various signal processing tasks in the analog domain. Optics can be particularly beneficial for handling tasks that involve matrix-vector multiplications due to its ability to efficiently perform fan-in (summation) and fan-out (copying) operations. These are fundamental operations in parallel processing, while digital processors are limited by capacitive RC and LC delays. We developed photonic integrated devices involving on-chip diffractive and phase shifter layers which can realize arbitrary unitary transformations. Potential applications of such a device beyond direct computational use include scalable, low-power optical beam-steering and switching devices which are discussed in the final chapter of this dissertation.

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