Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses

Abstract

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...

Ultrafast supercontinuum generation in bulk condensed media

“…Therefore all subsequent features of the filament propagation in the regime of normal GVD, i.e. pulse splitting, conical emission and any nonlinear interactions, may be interpreted assuming the pulses as spontaneously occurring nonlinear X-waves [99]. Consequently, the formation and propagation features of spatiotemporal light bullets in the regime of anomalous GVD may be interpreted in terms of nonlinear O-waves [83].…”

Collapse Arrest in Instantaneous Kerr Media via Parametric Interactions

“…The stabilization mechanism is given by higher order cascaded nonlinearities in normal dispersion. Notably, collapse-free propagation in a nonlinear Kerr material with normal dispersion also allows the generation of X waves [20,35,36], optical pulses with a characteristic X shape in the space-time or angle-wavelength domain. Although the study of X waves is beyond the scope of this Letter, the interpretation of the nonlinear phase exchange among the components in terms of higher order defocusing nonlinearity opens up new perspectives for understanding such waves.…”

Gas-Solid Phase Transition in Laser Multiple Filamentation

“…Further modelling should include realistic intensity flux [44,45] and intensity shapes [46], and advanced phase profile such as the recently studied spatio-temporal optical vortices [30]. Such features will expectedly improve the description of inter-filament interactions.…”