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Using a 1 GW, 1 ps pump laser pulse in high-gain parametric down conversion allows us to detect sub-shot-noise spatial quantum correlation with up to 100 photoelectrons per mode by means of a high efficiency charge coupled device. The statistics is performed in single shot over independent spatial replica of the system. Evident quantum correlations were observed between symmetrical signal and idler spatial areas in the far field. In accordance with the predictions of numerical calculations, the observed transition from the quantum to the classical regime is interpreted as a consequence of the narrowing of the down-converted beams in the very high-gain regime.

We observe the formation of an intense optical wavepacket fully localized in all dimensions, i.e. both longitudinally (in time) and in the transverse plane, with an extension of a few tens of fsec and microns, respectively. Our measurements show that the self-trapped wave is a X-shaped light bullet spontaneously generated from a standard laser wavepacket via the nonlinear material response (i.e., second-harmonic generation), which extend the soliton concept to a new realm, where the main hump coexists with conical tails which reflect the symmetry of linear dispersion relationship.PACS numbers: 03.50. De,42.65.Tg,05.45.Yv,42.65.Jx Defeating the natural spreading of a wavepacket (WP) is a universal and challenging task in any physical context involving wave propagation. Ideal particle-like behavior of WPs is demanded in applications, such as microscopy, tomography, laser-induced particle acceleration, ultrasound medical diagnostics, Bose-Einstein condensation, volume optical-data storage, optical interconnects, and those encompassing long-distance or high-resolution signal transmission. The quest for light WPs that are both invariant (upon propagation) and sufficently localized in all dimensions (3D, i.e., both transversally and longitudinally or in time) against spreading "forces" exerted by diffraction and material group-velocity dispersion (GVD,) has motivated long-standing studies, which have followed different strategies in the linear [1, 2, 3, 4, 5] and nonlinear [6,7] regime, respectively.In the linear case, to counteract material (intrinsic) GVD, one can exploit the angular dispersion (i.e., dependence of propagation angle on frequency) that stems from a proper WP shape. The prototype of such WPs is the X-wave [2], a non-monochromatic, yet non-dispersive, superposition of non-diffracting cylindrically symmetric Bessel J 0 (so-called conical or Durnin [1]) beams, experimentally tested in acoustics [3], optics [4] and microwave antennae [5]. Importantly, in the relevant case of WPs with relatively narrow spectral content both temporally (around carrier frequency ω 0 ) and spatially (around propagation direction z, i.e. paraxial WPs), X-waves require normally dispersive media (k ′′ > 0). In this case, a WP with disturbance E(r, t, z) exp, has a slowly-varying envelope E = E(r, t, z) obeying the standard wave equationLaplacian, where ∇ 2 ⊥ = ∂ 2 rr + r −1 ∂ r is the transverse Laplacian, and we limit our attention to luminal WPs traveling at light group-velocity 1/k ′ = dk/dω| introducing the retarded time t = T − k ′ z in the WP barycentre frame. Propagation-invariant waves E(r, t, z) = E(r, t, z = 0) exp(iβz) can be achieved whenever their input spatio-temporal spectra E(K, Ω, z = 0) lie along the characteristics of the dispersion relationship k ′′ Ω 2 /2 − K 2 /(2k 0 ) = β, which follows from Eq. (1) in Fourier space (K, Ω) (K is the transverse wavevector related to cone angle with z-axis θ ≃ sin θ = K/k 0 , and Ω = ω − ω 0 ). In the normal GVD regime (k ′′ > 0) these curves, displayed in Fig. 1(a), refl...

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 ...

Nonlinear optical media that are normally dispersive support a new type of localized (nondiffractive and nondispersive) wave packets that are X shaped in space and time and have slower than exponential decay. High-intensity X waves, unlike linear ones, can be formed spontaneously through a trigger mechanism of conical emission, thus playing an important role in experiments.

In contrast with filamentation of ultrashort laser pulses with standard Gaussian beams in Kerr media, three different types of Bessel filaments are obtained in air or in water by focusing ultrashort laser pulses with an axicon. We thoroughly investigate the different regimes and show that the beam reshapes as a nonlinear Bessel beam which establishes a conical energy flux from the low intensity tails toward the high intensity peak. This flux efficiently sustains a high contrast long-distance propagation and easily generates a continuous plasma channel in air

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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...