230 research outputs found
Bifurcation of gap solitons through catastrophe theory
In the theory of optical gap solitons, slowly-moving finite-amplitude
Lorentzian solutions are found to mediate the transition from bright to
coexistent dark-antidark solitary wave pairs when the laser frequency is
detuned out of the proper edge of a dynamical photonic bandgap. Catastrophe
theory is applied to give a geometrical description of this strongly
asymmetrical 'morphing' process.Comment: 6 pages, 3 figures, submitted to Phys. Rev.
Mechanism of wave breaking from a vacuum point in the defocusing nonlinear Schrödinger equation
We study the wave breaking mechanism for the weakly dispersive defocusing nonlinear Schrödinger equation with a constant phase dark initial datum that contains a vacuum point at the origin. We prove by means of the exact solution to the initial value problem that, in the dispersionless limit, the vacuum point is preserved by the dynamics until breaking occurs at a finite critical time. In particular, both Riemann invariants experience a simultaneous breaking at the origin. Although the initial vacuum point is no longer preserved in the presence of a finite dispersion, the critical behavior manifests itself through an abrupt transition occurring around the breaking time
Resonant radiation shed by dispersive shock waves
We show that dispersive shock waves resulting from the nonlinearity
overbalancing a weak leading-order dispersion can emit resonant radiation owing
to higher-order dispersive contributions. We analyze such phenomenon for the
defocusing nonlinear Schroedinger equation, giving criteria for calculating the
radiated frequency based on the estimate of the shock velocity, revealing also
a diversity of possible scenarios depending on the order and magnitude of the
dispersive corrections
Shocks in nonlocal media
We investigate the formation of collisionless shocks along the spatial
profile of a gaussian laser beam propagating in nonlocal nonlinear media. For
defocusing nonlinearity the shock survives the smoothing effect of the nonlocal
response, though its dynamics is qualitatively affected by the latter, whereas
for focusing nonlinearity it dominates over filamentation. The patterns
observed in a thermal defocusing medium are interpreted in the framework of our
theory.Comment: 5 pages, 5 figure
Modulational instability in dispersion oscillating fiber ring cavities
We show that the use of a dispersion oscillating fiber in passive cavities
significantly extend modulational instability to novel high-frequency bands,
which also destabilize the branches of the steady response which are stable
with homogeneous dispersion. By means of Floquet theory, we obtain exact
explicit expression for the sideband gain, and a simple analytical estimate for
the frequencies of maximum gain. Numerical simulations show that stable
stationary trains of pulses can be excited in the cavity
Parametric excitation of multiple resonant radiations from localized wavepackets
Fundamental physical phenomena such as laser-induced ionization, driven
quantum tunneling, Faraday waves, Bogoliubov quasiparticle excitations, and the
control of new states of matter rely on time-periodic driving of the system. A
remarkable property of such driving is that it can induce the localized (bound)
states to resonantly couple to the continuum. Therefore experiments that allow
for enlightening and controlling the mechanisms underlying such coupling are of
paramount importance. We implement such an experiment in a special fiber optics
system characterized by a dispersion oscillating along the propagation
coordinate, which mimics "time". The quasi-momentum associated with such
periodic perturbation is responsible for the efficient coupling of energy from
the localized wave-packets sustained by the fiber nonlinearity into
free-running linear dispersive waves (continuum), at multiple resonant
frequencies. Remarkably, the observed resonances can be explained by means of a
unified approach, regardless of the fact that the localized state is a
soliton-like pulse or a shock front
Dispersive dam-break flow of a photon fluid
We investigate the temporal photonic analogue of the dam-break phenomenon for
shallow water by exploiting a fiber optics setup. We clearly observe the decay
of the step-like input (photonic dam) into a pair of oppositely propagating
rarefaction wave and dispersive shock wave. Our results show evidence for a
critical transition of the dispersive shock into a self-cavitating state. The
detailed observation of the cavitating state dynamics allows for a fully
quantitative test of the Whitham modulation theory applied to the universal
defocusing nonlinear Schroedinger equation
Competing Turing and Faraday instabilities in longitudinally modulated passive resonators
We experimentally investigate the interplay of Turing and Faraday
(modulational) instabilities in a bistable passive nonlinear resonator. The
Faraday branch is induced via parametric resonance owing to a periodic
modulation of the resonator dispersion. We show that the bistable switching
dynamics is dramatically affected by the competition between the two
instability mechanisms, which dictates two completely novel scenarios. At low
detunings from resonance switching occurs between the stable stationary lower
branch and the Faraday-unstable upper branch, whereas at high detunings we
observe the crossover between the Turing and Faraday periodic structures. The
results are well explained in terms of the universal Lugiato-Lefever model
A collective modulation instability of multiple four-wave mixing
We investigate the modulation instability of multiple four-wave mixing
arising from a dual-frequency pump in a single-mode fiber or waveguide. By
applying the Floquet theory on account of the periodic nature of four-wave
mixing, we reveal a collective type of instability occurring in the anomalous
dispersion regime. Our interpretation of the linear stability analysis is
validated by the numerical solution of the nonlinear Schroedinger equationComment: 4 pages, 3 figure
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