We introduce a model of nonlinear multimode fibers with losses and gain. The model is based on the (3+1)-dimensional cubic-quantic complex Ginzburg-Landau equation (CGLE) with conservative and dissipative nonlinearities and a 2- dimensional transverse trapping potential. It applies to passively mode-locked lasers in the short-pulse operation regime. Systematic numerical analysis of the model reveals a variety of stable modes, including stable fundamental solitons and breathers, as well as solitary vortices with winding number n =1 , while vortices with n = 2 are unstable, splitting into persistently rotating bound states of two unitary vortices. An essential finding is biostability between the fundamental and vortex solitons.
A mechanism of creating a Newton's cradle (NC) in the form of a chain of solitons is proposed for understanding fission of higher-order soliton in optical fibers caused by higher-order dispersion. After the transformation of the initial Nsoliton into a chain of fundamental quasi-solitons, the tallest one travels along the chain through elastic collisions with other solitons, and then escapes, while the other solitons remain in a bound state. Multiple releases of solitons take place if N is sufficiently large. The NC effect is robust against inclusion of the Raman and self-steepening terms.
Four-wave mixing (FWM) has been extensively explored in optical fibers and more recently in on-chip silicon-oninsulator (SOI) waveguides. A phase-matched FWM with a pair of degenerate pump photons generating and amplifying signal and idler photons is referred as modulational instability (MI). Following theory of FWM in waveguide arrays, we utilize evanescent couplings between neighboring waveguides to control the phase-matching condition in FWM. In experiments, a set of single-channel SOI nanowaveguides with the waveguide width decreasing from 380nm to 340nm demonstrate that changing the waveguide group velocity dispersion (GVD) at the pump wavelength from being anomalous to being normal makes MI gain gradually disappear. We also perform the same experiment with an array of two 380nm-wide SOI waveguide, and demonstrate that for the large separation of 900nm and 800nm, MI gain is present as for the single waveguide; while for the small separation of 400nm, the MI gain disappears. This transformation of phase-matching in FWM is attributed to the fact that the coupling induced dispersion changes the net GVD of the symmetric supermode from being anomalous for large separation to being normal for small separation. Our observation illustrates that the coupling-induced GVD can compete and exceed in value the GVD of a single SOI nanowaveguide. This creates a new previously unexplored degree of freedom to control FWM on chips.
We study theoretically the non-phase-matched degenerate four-wave mixing of type ωs = 2ω1 ωω2 , involving beams
carrying two-dimensional spatial phase dislocations in the form of singly-charged optical vortices (OVs).
Accompanying third-order nonlinear processes in the non-resonant nonlinear medium (NLM), which are accounted
for, are self- and cross-phase modulation. In the case of pump OV beams with identical topological charges the
model predicts the generation of signal beams carrying OVs of the same charge. If the pump beams carry OVs with
opposite charges, the generated signals are predicted to carry triply charged vortices which, in the case of a nonnegligible
initial free-space propagation from the plane of vortex generation to the NLM, decay inside the NLM into
three singly-charged vortices with highly overlapping cores.
We derive nonlinear evolution equations describing parametric up- and down-conversion under the conditions when either of the two interacting waves is in resonance with a material transition, e.g., with plasmonic oscillations. Using perturbation theory in the limit of the large wave-number mismatch we drive analytical expressions for two families of quasi-solitonic solutions. If material transition is in resonance with the second-harmonic then the quasi-solitons are of the Nonlinear-Schrodinger type. If the fundamental frequency is in resonance then the reduced system is the paraxial wave equation coupled to the nonlinear classical oscillator. The latter system is integrated analytically and localized solutions are presented.
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.
The dynamics of free and optically induced decay of quasi-one-dimensional atomic Bose-Einstein condensates (BECs) is considered. The main characteristics of BEC modulation instability were found and compared for the cases of local and non-local interatomic interaction potential. The dynamics of BEC decay was studied numerically for the cases of positive and negative scattering length, absence or presence of optical standing wave, and for different shapes of initial BEC density distribution.
Model equations for a ring class B laser operating in three Gauss-Laguerre modes are derived and studied. Bifurcation mechanisms leading to the appearance of low-frequency antiphase oscillations of mode intensities are investigated. The spontaneous phase symmetry breaking effect leading to transverse patterns with rotating crystal generated by four optical vortices is described.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.