We have generalized the concept of nonlinear periodic structures to dielectric systems that show
arbitrary spatial and temporal variations of the refractive index. Nonlinear pulse propagation
through these spatiotemporal photonic crystals can be described, for shallow nonstationary
gratings, by coupled mode equations which are a generalization of the traditional equations
used for stationary Bragg gratings. Novel gap soliton solutions are found analytically. They
represent a generalization of the gap solitons in static photonic crystals and resonance solitons
found in dynamic gratings.
We theoretically investigate the possibility of realizing a nonlinear all-optical diode by using the
unique field-localization properties (known as Anderson-Kohmoto localization) of Thue-Morse
quasiperiodic 1D photonic crystals. The interplay between the intrinsic spatial asymmetry in
odd-order Thue-Morse lattices and Kerr nonlinearity gives rise to sharp resonances of perfect
transmission that can be used to give a polarization-insensitive, nonreciprocal propagation with
a contrast close to unity for low optical intensities. Such nonlinear diode would also represent
the first all-optical device which is crucially based on Anderson-like localization.
We have carried out a feasibility study of the excitation of π and 2π Raman solitons in gas filled hollow-core photonic crystal fibers. Using typical fiber parameters we present estimates for the soliton durations and powers and investigate the role played by first and second order fiber dispersions.
Optical waveguides provide rich environment for various nonlinear
processes thanks to the long interaction lengths, sustained high
intensities and diverse dispersion regimes. Nonlinear and dispersion
properties of fibers and waveguides can be widely controlled through
microstructuring resulting in a broad family of photonic crystal and
bandgap waveguides. This flexibility can be used to realize
previously impossible nonlinear interaction regimes for solitons and
quasi-continuous waves. The dynamics of femtosecond optical pulses
in such dispersive and nonlinear materials provide a truly
challenging measurement task, but reward us with most spectacular
images of nonlinear wave interactions. We visualized the dynamics of
solitons and continua in several such structures using cross- correlation frequency-resolved optical gating, the technique which provides experimentally the most complete information about an optical pulse. These detailed time and frequency-resolved measurements infinitely surpass the simple spectral measurements or
even the time axis-symmetric FROG spectrograms. Soliton dynamics in
the vicinity of the second zero-dispersion point of a silica PC
fiber, Cherenkov continuum generation, stabilization against the
Raman self-frequency shift and other resonant interactions as well
as the supercontinuum generation in soft-glass fibers were characterized. Recent theoretical studies were brought about to
develop a fundamental understanding of these resonant interactions
and excellent agreement was found.
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