Generalized Lorenz Mie theory application to scattering and resonances of photonic complexes
Complex photonic media mold the flow of light at the wavelength scale using multiple scattering and interference effects. This functionality at the nano scale level paves the way for various applications, ranging from optical communications to biosensing. This thesis is mainly concerned with the numerical modeling of photonic complexes based on twodimensional arrays of cylindrical scatterers. Two applications are considered, namely the use of photonic crystal like devices for the design of integrated beam shaping elements, as well as active photonic molecules for the realization of compact laser sources. These photonic structures can be readily analyzed using the 2D Generalized Lorenz Mie theory (2D GLMT) a numerical scheme which exploits the symmetry of the underlying cylindrical structures. We begin this thesis by presenting the electromagnetic theory behind 2D GLMT. Other useful frameworks are also presented, including a recently formulated stationary version of the Maxwell Bloch equations called steady state ab initio laser theory (SALT) Metaheuristics, optimization algorithms based on empirical rules for exploring large solution spaces, are also discussed. After laying down the theoretical content, we proceed to the design and optimization of beam shaping devices based on engineered photonic crystal like structures. The combinatorial optimization problem associated to beam shaping is tackled using the genetic algorithm (GA) as well as tabu search (TS) Our results show the possibility to design integrated beam shapers tailored for the control of the amplitude, phase and polarization profile of the output beam. A theoretical and numerical study of the lasing characteristics of photonic molecules composed of a few coupled optically active cylinders is also presented. Using a combination of 2D GLMT and SALT, it is shown that the physical properties of photonic molecule lasers, specifically their threshold, spectrum and emission profile, can be significantly affected by the underlying gain medium parameters. These findings are out of reach of the established approach of computing the meta stable states of the Helmholtz equation and their quality factor. This dissertation is concluded with a research outlook concerning the modeling of disordered photonic media.