Theory and Applications of Nonlinear Optics in Optically-Induced Photonic Lattices.

摘要

In this funding period, the P.I. investigated nonlinear light propagation in one- and two-dimensional optically-induced photonic lattices both theoretically and experimentally. Photonic lattices in these works were created by optical induction and were highly tunable in real time, thus they provided a convenient medium to study novel physical phenomena of light propagation in periodic and quasiperiodic media. P.I. discovered many new types of nonlinear localized modes (optical solitons) in photonic lattices, such as saddle solitons, truncated-Bloch-mode solitons, two-dimensional embedded solitons, soliton trains, and arbitrary-shape solitons. The finding of these new types of optical solitons offers new possibilities for nonlinear light localization in photonic lattices. His theoretical discovery of arbitrary-shape solitons in photonic lattices also led to a novel image transmission scheme through nonlinear media, and this scheme was successfully demonstrated experimentally. He demonstrated that a nonlinear beam can be reflected by a negative (repulsive) defect in a photonic lattice if the incident angle is below a threshold value. Above this threshold angle, the beam simply passes through the defect. This phenomenon provides a way to use the incident angle to control beam propagation in a lattice network. Furthermore, a negative defect can guide various linear defect modes (such as vortex modes) without any diffraction. P.I. also developed a mathematical technique (the exponential asymptotics method) for the study of existence and linear stability of solitons in photonic lattices. P.I. invented a new numerical method--the Newton-conjugate-gradient method, which can efficiently determine solitons in photonic lattices.