2,014 research outputs found
Time-Reversal of Nonlinear Waves - Applicability and Limitations
Time-reversal (TR) refocusing of waves is one of fundamental principles in
wave physics. Using the TR approach, "Time-reversal mirrors" can physically
create a time-reversed wave that exactly refocus back, in space and time, to
its original source regardless of the complexity of the medium as if time were
going backwards. Lately, laboratory experiments proved that this approach can
be applied not only in acoustics and electromagnetism but also in the field of
linear and nonlinear water waves. Studying the range of validity and
limitations of the TR approach may determine and quantify its range of
applicability in hydrodynamics. In this context, we report a numerical study of
hydrodynamic TR using a uni-directional numerical wave tank, implemented by the
nonlinear high-order spectral method, known to accurately model the physical
processes at play, beyond physical laboratory restrictions. The applicability
of the TR approach is assessed over a variety of hydrodynamic localized and
pulsating structures' configurations, pointing out the importance of high-order
dispersive and particularly nonlinear effects in the refocusing of hydrodynamic
stationary envelope solitons and breathers. We expect that the results may
motivate similar experiments in other nonlinear dispersive media and encourage
several applications with particular emphasis on the field of ocean
engineering.Comment: 14 pages, 17 figures ; accepted for publication in Phys. Rev. Fluid
Time-Reversal Generation of Rogue Waves
The formation of extreme localizations in nonlinear dispersive media can be
explained and described within the framework of nonlinear evolution equations,
such as the nonlinear Schr\"odinger equation (NLS). Within the class of exact
NLS breather solutions on finite background, which describe the modulational
instability of monochromatic wave trains, the hierarchy of both in time and
space localized rational solutions are considered to be appropriate prototypes
to model rogue wave dynamics. Here, we use the time-reversal invariance of the
NLS to propose and experimentally demonstrate a new approach to construct
strongly nonlinear localized waves focused both in time and space. The
potential areas of applications of this time-reversal approach range from
remote sensing to motivated analogous experimental analysis in other nonlinear
dispersive media, such as optics, Bose-Einstein condensates and plasma, where
the wave motion dynamics is governed by the NLS
Elastic Time Reversal Mirror Experiment in a Mesoscopic Natural Medium at the Low Noise Underground Laboratory of Rustrel, France
A seismic time reversal experiment based on Time Reversal Mirror (TRM)
technique was conducted in the mesoscopically scaled medium at the LSBB
Laboratory, France. Two sets of 50 Hz geophones were distributed at one meter
intervals in two horizontal and parallel galleries 100 m apart, buried 250 m
below the surface. The shot source used was a 4 kg sledgehammer. Analysis shows
that elastic seismic energy is refocused in space and time to the shot
locations with good accuracy. The refocusing ability of seismic energy to the
shot locations is roughly achieved for the direct field, and with excellent
quality, for the early and later coda. Hyper-focussing is achieved at the shot
points as a consequence of the fine scale randomly heterogeneous medium between
the galleries. TRM experiment is sensitive to the roughness of the mirror used.
Roughness induces a slight experimental discrepancy between recording and
re-emitting directions degrading the quality of the reversal process.Comment: 7 pages, 7 figures - This paper aimed at describing time reversal
mirror method applied at mesoscopic scale to a natural medium in the frame of
an active seismic experiment. The results confirm the hyper-focusing process
in an anelastic medium and the efficiency of scattered waves within the coda
to refocus at the source using the time reversal mirro
Enhanced nonlinear imaging through scattering media using transmission matrix based wavefront shaping
Despite the tremendous progresses in wavefront control through or inside
complex scattering media, several limitations prevent reaching practical
feasibility for nonlinear imaging in biological tissues. While the optimization
of nonlinear signals might suffer from low signal to noise conditions and from
possible artifacts at large penetration depths, it has nevertheless been
largely used in the multiple scattering regime since it provides a guide star
mechanism as well as an intrinsic compensation for spatiotemporal distortions.
Here, we demonstrate the benefit of Transmission Matrix (TM) based approaches
under broadband illumination conditions, to perform nonlinear imaging. Using
ultrashort pulse illumination with spectral bandwidth comparable but still
lower than the spectral width of the scattering medium, we show strong
nonlinear enhancements of several orders of magnitude, through thicknesses of a
few transport mean free paths, which corresponds to millimeters in biological
tissues. Linear TM refocusing is moreover compatible with fast scanning
nonlinear imaging and potentially with acoustic based methods, which paves the
way for nonlinear microscopy deep inside scattering media
Tailoring Instantaneous Time Mirrors for Time Reversal Focusing in Absorbing Media
The time reversal symmetry of the wave equation allows wave refocusing back
at the source. However, this symmetry does not hold in lossy media. We present
a new strategy to compensate wave amplitude losses due to attenuation. The
strategy leverages the instantaneous time mirror (ITM) which generates reversed
waves by a sudden disruption of the medium properties. We create a
heterogeneous ITM whose disruption is unequal throughout the space to create
waves of different amplitude. The time-reversed waves can then cope with
different attenuation paths as typically seen in heterogeneous and lossy
environments. We consider an environment with biological tissues and apply the
strategy to a two-dimensional digital human phantom from the abdomen. A
stronger disruption is introduced where the forward waves suffer a history of
higher attenuation, with a weaker disruption elsewhere. Computer simulations
show heterogeneous ITM is a promising technique to improve time reversal
refocusing in heterogeneous, lossy, and dispersive spaces.Comment: 11 pages, 11 figure
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