Pulse propagation and soliton formation in nonlinear Photonic Band Gap materials

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Periodically microstructured dielectric materials whose linear properties are characterized through a photonic bandstructure that - for appropriate choices of the relevant parameters - may exhibit a photonic band gap (PBG), a frequency range where ordinary (linear) propagation is disallowed. However, in the presence of optical nonlinearities, wave propagation for frequencies inside the PBG may be realized for sufficiently intense pulses in the form of gap-solitons. Recent progress in mircofabrication technology allows one to manufacture Photonic Band Gap materials whose constituents exhibit sizeable nonlinearities so that nonlinear PBG materials will become increasingly important both in fundamental studies of nonlinear effects and advanced applications in all-optical information processing and logic gates. Within this project, we will investigate the propagation of pulses in nonlinear PBG materials and their interaction with defects as well as with each other. Through a combination of numerical simulations and variational techniques, we will study the evolution of nonlinear pulses into gap-solitons where - due to the strong multiple scattering near the PBG - we expect strongly non-Markovian radiation dynamics to occur. We will carry out similar investigations for the trapping of soliton at linear and nonlinear defects within the PBG material and how to control trapped solitons through interactions with propagating gap-solitons. These investigations will be of significance for the realization of practical all-optical technologies as well as provide novel insights into basic nonlinear phenomena which -owing to the universal nature of nonlinear processes - may have implications to other nonlinear systems such as solitons in Bose-Einstein condensates in optical lattices.