143 research outputs found
Akhmediev Breathers and Peregrine Solitary Waves in a Quadratic Medium
We investigate the formation of optical localized nonlinear structures,
evolving upon a non-zero background plane wave, in a dispersive quadratic
medium. We show the existence of quadratic Akhmediev breathers and Peregrine
solitary waves, in the regime of cascading second-harmonic generation. This
finding opens a novel path for the excitation of extreme rogue waves and for
the description of modulation instability in quadratic nonlinear optics
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
Parametric Frequency Conversion of Short Optical Pulses Controlled by a CW Background
We predict that parametric sum-frequency generation of an ultra-short pulse
may result from the mixing of an ultra-short optical pulse with a
quasi-continuous wave control. We analytically show that the intensity, time
duration and group velocity of the generated idler pulse may be controlled in a
stable manner by adjusting the intensity level of the background pump
Extreme high-intensity and ultrabroadband interactions in anisotropic β-BaB_2O_4 crystals
International audienceWe derive unidirectional pulse propagation equations to describe extreme high-intensity and ultra-broadband optical interactions in uniaxial crystals, showing both second-and third-order nonlinear optical susceptivities. We focus our attention on the anisotropic nature of the quadratic and cubic nonlinear response of β−BaB 2 O 4 (BBO) crystals. Two nonlinearly coupled first order (in the propagation coordinate) equations describe the dynamics and interactions of the ordinary and extraordinary field polarizations, and are valid for arbitrarily wide pulse bandwidth. We exploit this model to predict harmonic and supercontinuum generation in BBO crystals under strong and competing influence of quadratic and cubic susceptivities
Optical Kerr spatiotemporal dark extreme waves
We study the existence and propagation of multidimensional dark
non-diffractive and non-dispersive spatiotemporal optical wave-packets in
nonlinear Kerr media. We report analytically and confirm numerically the
properties of spatiotemporal dark lines, X solitary waves and lump solutions of
the (2 + 1)D nonlinear Schrodinger equation (NLSE). Dark lines, X waves and
lumps represent holes of light on a continuous wave background. These solitary
waves are derived by exploiting the connection between the (2 + 1)D NLSE and a
well-known equation of hydrodynamics, namely the (2+1)D Kadomtsev-Petviashvili
(KP) equation. This finding opens a novel path for the excitation and control
of spatiotemporal optical solitary and rogue waves, of hydrodynamic nature.Comment: arXiv admin note: text overlap with arXiv:1608.08771,
arXiv:1602.0846
Nonlinear envelope equation for broadband optical pulses in quadratic media
We derive a nonlinear envelope equation to describe the propagation of
broadband optical pulses in second order nonlinear materials. The equation is
first order in the propagation coordinate and is valid for arbitrarily wide
pulse bandwidth. Our approach goes beyond the usual coupled wave description of
phenomena and provides an accurate modelling of the evolution of
ultra-broadband pulses also when the separation into different coupled
frequency components is not possible or not profitable
Broadband parametric processes in χ^(2) nonlinear photonic crystals
International audienceWe develop a general model, based on a (2+1)D unidirectional pulse propagation equation, for describing broadband noncollinear parametric interactions in two-dimensional quadratic lattices. We apply it to the analysis of twin-beam optical parametric generation in hexagonally poled LiTaO 3 , gaining further insights into experimental observations
Resonant radiation emitted by solitary waves via cascading in quadratic media
We present a systematic investigation of the resonant radiation emitted by localized soliton-like wave-packets supported by second-harmonic generation in the cascading regime. We emphasize a general mechanism which allows for the resonant radiation to grow without the need for higher-order dispersion, primarily driven by the second-harmonic component, while radiation is also shed around the fundamental-frequency component through parametric down-conversion processes. The ubiquity of such a mechanism is revealed with reference to different localized waves such as bright solitons (both fundamental and second-order), Akhmediev breathers, and dark solitons. A simple phase matching condition is put forward to account for the frequencies radiated around such solitons, which agrees well with numerical simulations performed against changes of material parameters (say, phase mismatch, dispersion ratio). The results provide explicit understanding of the mechanism of soliton radiation in quadratic nonlinear media
Roadmap on optical rogue waves and extreme events
The pioneering paper 'Optical rogue waves' by Solli et al (2007 Nature 450 1054) started the new subfield in optics. This work launched a great deal of activity on this novel subject. As a result, the initial concept has expanded and has been enriched by new ideas. Various approaches have been suggested since then. A fresh look at the older results and new discoveries has been undertaken, stimulated by the concept of 'optical rogue waves'. Presently, there may not by a unique view on how this new scientific term should be used and developed. There is nothing surprising when the opinion of the experts diverge in any new field of research. After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation. We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems. Theorists, in turn, have suggested many other situations when rogue waves may be observed. The strict definition of a rogue wave is still an open question. For example, it has been suggested that it is defined as 'an optical pulse whose amplitude or intensity is much higher than that of the surrounding pulses'. This definition (as suggested by a peer reviewer) is clear at the intuitive level and can be easily extended to the case of spatial beams although additional clarifications are still needed. An extended definition has been presented earlier by N Akhmediev and E Pelinovsky (2010 Eur. Phys. J. Spec. Top. 185 1-4). Discussions along these lines are always useful and all new approaches stimulate research and encourage discoveries of new phenomena. Despite the potentially existing disagreements, the scientific terms 'optical rogue waves' and 'extreme events' do exist. Therefore coordination of our efforts in either unifying the concept or in introducing alternative definitions must be continued. From this point of view, a number of the scientists who work in this area of research have come together to present their research in a single review article that will greatly benefit all interested parties of this research direction. Whether the authors of this 'roadmap' have similar views or different from the original concept, the potential reader of the review will enrich their knowledge by encountering most of the existing views on the subject. Previously, a special issue on optical rogue waves (2013 J. Opt. 15 060201) was successful in achieving this goal but over two years have passed and more material has been published in this quickly emerging subject. Thus, it is time for a roadmap that may stimulate and encourage further research.Peer ReviewedPostprint (author's final draft
Baseband modulation instability as the origin of rogue waves
We study the existence and properties of rogue wave solutions in different
nonlinear wave evolution models that are commonly used in optics and
hydrodynamics. In particular, we consider Fokas-Lenells equation, the
defocusing vector nolinear Schr\"odinger equation, and the long-wave-short-wave
resonance equation. We show that rogue wave solutions in all of these models
exist in the subset of parameters where modulation instability is present, if
and only if the unstable sideband spectrum also contains cw or zero-frequency
perturbations as a limiting case (baseband instability). We numerically confirm
that rogue waves may only be excited from a weakly perturbed cw whenever the
baseband instability is present. Conversely, modulation instability leads to
nonlinear periodic oscillations
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