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 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.
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.
We show that, in the high wave-vector-mismatch (cascading) limit, the well-known paraxial description of parametric frequency conversion in quadratic media entails effective lensing effects, which can have a self-focusing or a self-defocusing nature, critically depending on the mismatch sign, the selected wave, and the launching condition (second-harmonic generation or downconversion). Numerical and experimental evidence of this behavior is reported. (C) 2002 Optical Society of America
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