Linear and nonlinear optical processes in artificially structured materials

We discuss optical effects in two channel micro-resonator structures, identify the underlying physics through a study of their dispersion relations, and present an efficient numerical technique that can be used to analyze pulse propagation within these structures when a Kerr nonlinearity is present. We show that these structures are ideal candidates for a number of photonic applications, such as optical buffers and optical AND-gates. The proposed applications are of interest to practitioners in the field of integrated optics. Following the discussion of numerical results, we present a Lorentzian model to describe transmission across short, Kerr nonlinear micro-resonator structures. Based on this model we derive a set of coupled differential equations that describe Kerr nonlinear pulse propagation and optical switching in systems coupled by a few cavities. The resulting equations greatly facilitate numerical investigations of intensity-dependent switching and optical bistability in such systems. We then consider a relation between the band structure and real space symmetry of a general class of quasi-lD dielectric structures. We show that by transforming the dielectric profile of these structures to an appropriate mirror image, time-reversed electromagnetic pulse propagation can be achieved. Our scheme provides a general recipe for obtaining time-reversed propagation in quasi-lD structures. In order to gain a deeper insight into pulse dynamics in periodic micro-resonator structures, we derive, for the first time, a set of coupled mode equations that describe pulse dynamics in the vicinity of the associated indirect band gaps. We employ an effective-field method and use a phenomenological Hamiltonian as the starting point. The resulting coupled mode equations are applicable to a wide class of side-coupled cavity structures, and lead to a more intuitive understanding of their dispersion relations. Lastly, we develop a rigorous Hamiltonian formulation for coupling problems commonly encountered in the study of artificially structured materials. We employ a "dressed mode" approach, which differs from coupled mode formalisms commonly used in the literature. The proposed formalism can be extended to include nonlinear effects in a systematic manner, and facilitate the analysis of optical processes in artificially structured materials in the quantum and nonlinear regimes.Ph.D