160 research outputs found
Recurrence in the high-order nonlinear Schr\"odinger equation: a low dimensional analysis
We study a three-wave truncation of the high-order nonlinear Schr\"odinger
equation for deepwater waves (HONLS, also named Dysthe equation). We validate
our approach by comparing it to numerical simulation, distinguish the impact of
the different fourth-order terms and classify the solutions according to their
topology. This allows us to properly define the temporary spectral upshift
occurring in the nonlinear stage of Benjamin-Feir instability and provides a
tool for studying further generalizations of this model
Spin-Glass Model Governs Laser Multiple Filamentation
We show that multiple filamentation patterns in high-power laser beams, can
be described by means of two statistical physics concepts, namely
self-similarity of the patterns over two nested scales, and nearest-neighbor
interactions of classical rotators. The resulting lattice spin model perfectly
reproduces the evolution of intense laser pulses as simulated by the Non-Linear
Schr\"odinger Equation, shedding a new light on multiple filamentation. As a
side benefit, this approach drastically reduces the computing time by two
orders of magnitude as compared to the standard simulation methods of laser
filamentation.Comment: 8 pages, 4 figure
Laser filamentation as a new phase transition universality class
We show that the onset of laser multiple filamentation can be described as a
critical phenomenon that we characterize both experimentally and numerically by
measuring a set of seven critical exponents. This phase transition deviates
from any existing universality class, and offers a unique perspective of
conducting two-dimensional experiments of statistical physics at a human scale.Comment: 8 pages, 9 figure
Nonlinear stage of Benjamin-Feir instability in forced/damped deep water waves
We study a three-wave truncation of a recently proposed damped/forced
high-order nonlinear Schr\"odinger equation for deep-water gravity waves under
the effect of wind and viscosity. The evolution of the norm (wave-action) and
spectral mean of the full model are well captured by the reduced dynamics.
Three regimes are found for the wind-viscosity balance: we classify them
according to the attractor in the phase-plane of the truncated system and to
the shift of the spectral mean. A downshift can coexist with both net forcing
and damping, i.e., attraction to period-1 or period-2 solutions. Upshift is
associated with stronger winds, i.e., to a net forcing where the attractor is
always a period-1 solution. The applicability of our classification to
experiments in long wave-tanks is verified.Comment: 8 pages, 4 figure
Non-homogeneous approximation for the kurtosis evolution of shoaling rogue waves
Bathymetric changes have been experimentally shown to affect the occurrence
of rogue waves. We recently derived a non-homogeneous correction to the
spectral analysis, allowing to describe the evolution of the rogue wave
probability over a shoal. Here, we extend this work to the evolution of the
excess kurtosis of the surface elevation, that plays a central role in
estimating rare event probabilities. Furthermore, we provide an upper bound to
the excess kurtosis. In intermediate and deep water regimes, a shoal does not
affect wave steepness nor bandwidth significantly, so that the vertical
asymmetry between crests and troughs, the excess kurtosis, and the exceedance
probability of wave height stay rather constant. In contrast, in shallower
water, a sharp increase in wave steepness increases the vertical asymmetry,
resulting in a growth of both the tail of the exceedance probability and the
excess kurtosis
Energy conservation in self-phase modulation
Spectral broadening of ultrashort laser pulses is simultaneously described by
either self-phase modulation (SPM) or four-wave mixing (FWM). The latter
implies the instantaneous conservation of both the photon number and energy,
while the former describes a time-dependent frequency shift, implying a
violation of the energy conservation if the number of photons is to be
conserved in each time slice. We resolve this paradox by considering the
transient energy storage in the propagation medium, that can be calculated in
the SPM formalism via the dephasing between the incident pulse and the medium
polarization leading to an effective imaginary part in the third-order
susceptibility. In parallel, considering the temporal variation of the incident
intensity in FWM offsets the instantaneous frequency.Comment: 6 page
Reversibility of laser filamentation
We investigate the reversibility of laser filamentation, a self-sustained,
non-linear propagation regime including dissipation and time-retarded effects.
We show that even losses related to ionization marginally affect the
possibility of reverse propagating ultrashort pulses back to the initial
conditions, although they make it prone to finite-distance blow-up susceptible
to prevent backward propagation.Comment: 12 pages, 3 figure
Arbitrary-order non-linear contribution to self-steepening
Based on the recently published generalized Miller formula, we derive the
spectral dependence of the contribution of arbitrary-order non-linear indices
to the group-velocity index. We show that in the context of laser filamentation
in gases all experimentally-accessible orders (up to the -order
non-linear susceptibility in air and in argon) have
contributions of alternative signs and similar magnitudes. Moreover, we show
both analytically and numerically that the dispersion term of the non-linear
indices must be considered when computing the intensity-dependent group
velocity.Comment: 10 pages, 3 figures (14 panels
Free space laser telecommunication through fog
Atmospheric clearness is a key issue for free space optical communications
(FSO). We present the first active method to achieve FSO through clouds and
fog, using ultrashort high intensity laser filaments. The laser filaments
opto-mechanically expel the droplets out of the beam and create a cleared
channel for transmitting high bit rate telecom data at 1.55 microns. The low
energy required for the process allows considering applications to
Earth-satellite FSO and secure ground based optical communication, with
classical or quantum protocols.Comment: 4 pages + 2 pages supplementary text and movie
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