| Whether over micron-long or kilometer-long distances, periodic phenomena can strongly affect both the propagation and the confinement of optical pulses. Periodicities can be engineered through the structural design of optical waveguides, or they may manifest self-consistently from induced nonlinear polarizations. In light of recent developments in fabrication technologies for semiconductor waveguides, polymeric materials, and optical fiber, we show that both strongly- and weakly-nonlinear channels are promising for new devices and systems in optical communications. This thesis proposes and discusses applications of guided wave periodicities in the framework of photonic crystals (coupled-resonator optical waveguides as well as transverse Bragg resonance waveguides and amplifiers), nonlinear phenomena in photorefractive semiconductors, and the nonlinear evolution of temporal solitons in dispersion-managed fibers.; Coupled-resonator optical waveguides (CROWs) are composed of a periodic array of electromagnetic resonators, typically on the micron or sub-micron length scales. A photon in such a waveguide sees a periodic potential, and according to the Floquet-Bloch theorems, has a wavefunction that reflects this periodicity. CROWs have a unique dispersion relationship compared to other semiconductor waveguides, and can be used to slow down the speed of propagation, enhance nonlinear interactions such as second-harmonic generation and four-wave mixing, and form frozen soliton-type field distributions that use the optical Kerr nonlinearity to stabilize themselves against decay via adjacent-resonator or waveguide-resonator coupling.; In optical fibers that possess the optical Kerr nonlinearity in addition to group-velocity dispersion, it is possible to propagate pulses with envelopes that “breathe” with distance, typically at kilometer or longer length scales. Such waveforms are characterized by a set of parameters—e.g., amplitude, chirp, etc.—that vary in a periodic manner as the pulse propagates. Borrowing an idea from field theory, e.g., of classical pendulums, or quantum-mechanical elementary particles, the pulse envelope may be viewed as a particle traversing a trajectory in a phase space defined by its characteristic parameters. Distinct, non-overlapping trajectories are assigned as symbols of a multilevel communication code. Since it is the periodicity, arising from the Kerr nonlinearity, that generates this diversity in phase-space, there is no analog of this multiplexed system in linear optical transmission links. The overall bit-rate can be improved several fold above the current limits. |
