Development of Numerical Optimization Techniques for Optimal Design of Nanophotonic and Nanoplasmonic Systems

Abstract

There is a steadily growing interest in building new photonic and plasmonic nanosystems capable of tailoring the electromagnetic properties of light. An optimal design of these nanosystems is critical for their efficiency. One essential component of optimal design of nanodevices is numerical simulation and optimization that provide the optimal structure to be tested experimentally, and eventually implemented as actual device. This dissertation focuses on the development of numerical optimization techniques to analyze and design efficient nanoplasmonic and nanophotonic systems. In this work the electromagnetic field is modeled through the numerical solution of Maxwell's equations in the frequency domain, and numerical techniques that address optimization problems with these PDE constraints are developed. Application of the techniques to problems of i) maximization of light absorption by metal nanoparticle and ii) efficient surface plasmon generation demonstrate considerable practical value of the developed methodology No preferred strategy has yet emerged from the nanophotonic research community to solve optimization problems with partial differential equation constraints, despite continuous theoretical developments in topology and shape optimization, large-scale nonlinear optimization and sensitivity analysis. This dissertation considers two approaches to the problem. The first approach is to discretize and incorporate the PDE into a constrained optimization problem to solve with an appropriate nonlinear programming algorithm. The second optimization approach is to formulate and compute the gradient and modify the parameters accordingly, using the current data and PDE solution obtained from the solver. The first approach has been implemented in AMPL modeling language for problem i). The second numerical optimization approach is the main strategy implemented for both problems i)and ii) using COMSOL Multiphysics and MATLAB. Although this effort to solve a design optimization problem is specific to nanophotonic/nanoplasmonic systems, the result of this work afford computational tools with broader applications to advance the wider problem of optimization with PDE constraints.