Nonlinear Electromagnetic X Waves

Conti, Claudio; Trillo, Stefano; Trapani, P. Di; Valiulis, G.; Piskarskas, A.; Jedrkiewicz, O.; Trull, J.

doi:10.1103/physrevlett.90.170406

Cited by 232 publications

(142 citation statements)

References 25 publications

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confidence: 99%

“…Independently from this work, a second approach has been proposed [16] sharing with the first the genuine idea of filaments as non-soliton, but conical waves. The important difference is that here the Authors have outlined the key role of chromatic dispersion, fully neglected in previous case, thus interpreting the filament on the basis the dynamics of non-linear X waves [17,18,19].The major problem concerning the experimental characterization of the wave packet dynamics is that most of the measurements have been limited either to the pure temporal domain, by on-axis auto or cross correlation technique, or to the pure spatial one, by time integrated CCD-based detection. An example of ST experimental characterization has been that reported in Ref [20].…”

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Nonlinear space–time dynamics of ultrashort wave packets in water

et al. 2004

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We have monitored the space-time transformation of 150-fs pulse, undergoing self-focusing and filamentation in water, by means of the nonlinear gating technique. We have observed that pulse splitting and subsequent recombination apply to axial temporal intensity only, whereas space-integrated pulse profile preserves its original shape. PACS numbers: 190.5530, 190.5940, 260.5950, 320.7100 Spatial and temporal transformations of wave packets which undergo self-focusing in transparent media with Kerr nonlinearity attract a great deal of interest from the point of view both of fundamental and applied science. Self-focusing of ultrashort light pulses with power well exceeding that for continuous-wave (CW) beam collapse gives rise to a variety of spatial, temporal and interrelated (spatio-temporal, ST) effects and has been a topic of intense theoretical and experimental research [1,2,3,4,5,6,7,8]. Discovery of a long range propagation (filamentation) of ultrashort laser pulses in air boosted an interest in ST transformation through filamentation dynamics in gasses [9,10], solids [11] and liquids [12, 13].Numerical models of different complexity have been elaborated to study temporal, and, more generally, ST dynamics. Propagation of intense light pulses in media with rather distinct optical properties (amount of normal GVD, nonlinearity, etc; namely gasses, solids and liquids) under various initial conditions (pulse duration, beam width, power, wavelength) has been examined. In spite of different regimes, temporal pulse splitting emerged as a common feature resulting from the interplay between self-focusing, self-phase-modulation and normal dispersion. The open question is then what happens after the pulse splitting occurs. A scenario leading to subsequent multiple splitting has been predicted, but not observed directly (see the discussion in Ref [14] and references therein). In Ref.[7] pulse recombination after splitting has been observed and attributed to possible underlined multiple splitting.More recently, two interpretations have been proposed for understanding filament formation in condensed matter. Some of the present Authors, after having experimentally demonstrated that filaments cannot be treated as a self guided beams, have outlined the key role plaid by non-linear losses in ruling a spontaneous transformation from gaussian to conical (Bessel-like) wave, in the frame of a CW model [15]. In this context, the conical wave provides the beam with a large (and not absorbed) power reservoir that keeps "refuelling" the hot central spot and so ensures stationarity, even in presence of nonlinear losses. Independently from this work, a second approach has been proposed [16] sharing with the first the genuine idea of filaments as non-soliton, but conical waves. The important difference is that here the Authors have outlined the key role of chromatic dispersion, fully neglected in previous case, thus interpreting the filament on the basis the dynamics of non-linear X waves [17,18,19].The major problem concerning the ...

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Nonlinear space–time dynamics of ultrashort wave packets in water

et al. 2004

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“…In contrast to linear X waves, which require complex beam shaping, nonlinear X waves spontaneously reshape from the initial Gaussian wave packet. In the second-harmonic generation experiment (in birefringent crystals possessing quadratic nonlinearity), the spontaneous reshaping was shown to be driven by mutual balance between selffocusing nonlinearity arising from phase-mismatched interaction and dispersive contribution, which resembles an effective anomalous group velocity dispersion through the angular dispersion [35,36]. Although the initial experiment on strong space-time localization has indicated an apparent axial compression of the wave packet in both (spatial and temporal) dimensions [37], intrinsic spatiotemporal structure of the X wave suggests that considerable amount of energy should be stored out of axis, in slowly decaying tails.…”

Section: Nonlinear X-waves -Conical Light Bulletsmentioning

confidence: 99%

Nonlinear localization of light

Dubietis¹

2006

Lithuanian J. Phys.

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We briefly overview historical, fundamental, and practical aspects of light wave propagation, where strong multidimensional localization and precise control of ultrashort signals is demanded. The main topic is focused on the state of art of recently discovered nonlinear conical waves, or so-called X-shaped light bullets, which have been demonstrated to appear spontaneously in many different, frequently encountered operating regimes in transparent gaseous, liquid, and solid media. Owing to unique features of white-light frequency spectrum, strong localization, deep-field stationarity, and hot-spot regeneration property, nonlinear conical waves have great potential in all applications requiring energy transfer to matter over very limited transverse areas in thick media, which thus suffer the short focal depth of conventional laser beams. Practical applications that cover many different areas ranging from nano-science to high-field physics are discussed.

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“…For example, it arises in plasma physics [53] and in normally dispersive optical waveguide arrays modeling [14,39]. In the context of water waves the HypNLS equation is the leading order model of the wave envelope evolution.…”

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Some special solutions to the Hyperbolic NLS equation

Vuillon

Dutykh

Fedele

2018

Communications in Nonlinear Science and Numerical Simulation

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Abstract. The Hyperbolic Nonlinear Schrödinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrow-band deep water gravity waves. In this study, the symmetries and conservation laws of this equation are computed. The Petviashvili method is then exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly accurate Fourier solver.

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Nonlinear Electromagnetic X Waves

Cited by 232 publications

References 25 publications

Nonlinear space–time dynamics of ultrashort wave packets in water

Nonlinear space–time dynamics of ultrashort wave packets in water

Nonlinear localization of light

Some special solutions to the Hyperbolic NLS equation

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