Nonlinear losses accompanying self-focusing substantially impacts the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D+1 nonlinear Schrödinger equation which are stable against radial collapse. These are featured by linear, conical tails that continually refill the nonlinear, central spot. An experiment shows that the discovered solution behaves as strong attractor for the self-focusing dynamics in Kerr media.PACS numbers: 42.65. Re, 42.65.Tg One of the main goals of modern nonlinear wave physics is the achievement of wave localization, stationarity and stability. While in a one-dimensional geometry (e.g., in optical fibers), nonlinearity suitably balances linear wave dispersion, leading to the soliton regime, in the multidimensional case, nonlinearity drives waves either to collapse or instability. In self-focusing of optical beams, for instance, many stabilizing mechanisms, such as Kerr saturation, plasma-induced defocusing, or stimulated Raman scattering, have been explored, and are being the subject of intense debate, mainly in the context of light filamentation in air or condensed matter [1]. These mechanisms, however, are either intrinsically lossy, or, due to the huge intensities involved, are accompanied by losses, which lead ultimately to the termination of any soliton regime. Similar pictures can be traced in all phenomena commonly discussed in the context of the nonlinear Schrödinger equation (NLSE), as Bose-Einstein condensates (BEC) or Langmuir waves in plasma [2]. Nonlinear losses (NLL) arise in BEC from two-and three-body inelastic recombination, and as the natural mechanism for energy dissipation in Langmuir turbulence [3].The question then arises of whether any stationary and localized (SL) wave propagation is possible in the presence of NLL. The response, as shown in this Letter, is affirmative. These SL waves cannot be ascribed to the class of solitary waves, but are instead nonlinear conical waves (as the non-linear X waves [4]) of dissipative type, whose stationarity is sustained by a continuous refilling of the nonlinearly absorbed central spot with the energy supplied by linear, conical tails. These waves are not only robust against NLL, but find their stabilizing mechanism against perturbations in NLL themselves.Among the linear conical waves [5], the simplest one is the monochromatic Bessel beam (BB) [6], made of a superposition of plane waves whose wave vectors are evenly distributed over the surface of a cone, resulting in a nondiffracting transversal Bessel profile. Despite the ideal nature of BBs (they carry infinite power), they not only have revealed to be a paradigm for understanding wave phenomena, but also have found applications as diverse as in frequency conversion, or in atom trapping and alignment [7]. Of particular interest for us is the finding [8] that the BB is describable in terms of the interference of two conical Hankel beams [5], carrying equal amounts of energy towards and outwards the beam ...

The precise observation of the angle-frequency spectrum of light filaments in water reveals a scenario incompatible with current models of conical emission (CE). Its description in terms of linear X-wave modes leads us to understand filamentation dynamics requiring a phase-and groupmatched, Kerr-driven four-wave-mixing process that involves two highly localized pumps and two X-waves. CE and temporal splitting arise naturally as two manifestations of this process. PACS numbers: 190.5940, 320.2250 Filamentation of intense light pulses in nonlinear media has attracted much interest ever since first experimental evidences in the early '60's ([1] and references therein). Owing to the very high intensities reached during the process, several nonlinear phenomena, e.g., multiphoton absorption, plasma formation, saturable nonlinear response, stimulated Raman scattering etc., occur in addition to the optical Kerr effect. Indeed, the filament regime is enriched by peculiar phenomena like pulse splitting, self-steepening, shock-wave formation, supercontinuum generation, and conical emission (CE) [2]. In media with normal group velocity dispersion (GVD), no matter if of solid, liquid or gaseous nature, CE accompanies filamentation, producing radiation at angles that increase with increasing detuning from the carrier frequency [3,4]. In spite of the generality of the process, a clear understanding of the interplay between CE and filament dynamics is still missing. Only recently, Kolesik et al. have proposed an interpretation of filamentation dynamics in water on the basis of pulse splitting and dynamic nonlinear X waves at the far field [5], in which the double X-like structure observed in simulated anglefrequency spectra arises from the scattering of an incident field at the two main peaks of the split material response wave.Originally, CE in light filaments was interpreted in terms of the modulation instability (MI) angle-frequency gain pattern of the plane and monochromatic (PM) modes of the nonlinear Schrödinger equation (NSE) [6,7]. Measurements at large angles and detunings from the carrier frequency gave in fact results fairly compatible with this interpretation [8,9]. In the present work, owing to the use of a novel imaging spectrograph technique [3], we have been able to observe for the first time the CE in the region of small angles and detunings. The results clearly indicate a scenario not compatible with the MI analysis of PM modes. Our description by means of the spectra of the stationary linear X-waves supported by the medium, indicates that the strong localization of the self-focused field plays a crucial role in the substantial modification experienced by the MI pattern. We propose a simple picture in which the latter results from the parametric amplification of two weak X-waves by the strong, highly localized pump. Supporting this interpretation, we are able to derive, from the matching condition among the interacting waves, a simple analytical expression [Eq. (4)] that accurately determines the overall CE...

We study Bessel X waves with cone dispersion propagating in free space and dispersive media. Their propagation features find simple explanation when viewed as cylindrically symmetric versions of the so-called tilted pulses. All previously reported cases of suppression of normal material group velocity dispersion by using angular dispersion in tilted pulses, pulsed Bessel beams, and Bessel X waves are compared and presented in a unified way. We show that stationary, spatiotemporal localized Bessel X-wave transmission is also possible in the anomalous dispersion regime.

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Basic concepts of three-dimensional wave packets are applied to the description of transverse effects on the propagation of ultrashort (femtosecond) pulses. The frequency-dependent nature of diffraction acts as a kind of dispersion that modifies the pulse front surface, its group velocity, the envelope form, and the carrier frequency. If the diffracted field in the monochromatic case is known, these changes can be straightforwardly quantified. Finding the propagated pulsed beam field reduces to a well-known and simpler problem of one-dimensional pulse propagation with group velocity dispersion. The method is applied to pulsed Gaussian beams and pulsed Bessel beams. Anomalous pulse front behavior, including superluminality in pulsed Gaussian beams is found. The carrier phase at any point of space is calculated.

Excitation of unbalanced-Bessel beams by a gradual increase of nonlinearity in a water sample outlines the achievement of the first ever observed quasimonochromatic wave packet that propagates stably for hundreds of Rayleigh lengths in a focusing and dispersive Kerr medium, i.e., in the absence of spectral broadening and conical emission. A modulational instability analysis reveals the key role of nonlinear dissipation in quenching the growth of spatiotemporal unstable modes.

We show that a high-order Bessel beam propagating in a medium with nonlinear absorption is not completely absorbed, but survives in the form of a new propagation invariant vortex beam in which the beam energy and orbital angular momentum are permanently transferred to matter and at the same time refueled by spiral inward currents of energy and angular momentum. Unlike vortex solitons and dissipative vortex solitons, these vortex beams are not supported by specific dispersive nonlinearities (self-focusing or self-defocusing) and do not require gain. Propagation invariance in presence of multiple absorption of photons carrying (possibly high) orbital angular momentum makes these beams attractive for optical pumping of angular momentum over long distances.

The near-field dynamics of a femtosecond Bessel beam propagating in a Kerr nonlinear medium (fused silica) is investigated both numerically and experimentally. We demonstrate that the input Bessel beam experiences strong nonlinear reshaping. Due to the combined action of self-focusing and nonlinear losses the reshaped beam exhibits a radial compression and reduced visibility of the Bessel oscillations. Moreover, we show that the reshaping process starts from the intense central core and gradually replaces the Bessel beam profile during propagation, highlighting the conical geometry of the energy flow.