Extreme events in resonant radiation from three-dimensional light bullets

Abstract

We report measurements that show extreme events in the statistics of resonant radiation emitted from spatiotemporal light bullets. We trace the origin of these extreme events back to instabilities leading to steep gradients in the temporal profile of the intense light bullet that occur during the initial collapse dynamics. Numerical simulations reproduce the extreme valued statistics of the resonant radiation which are found to be intrinsically linked to the simultaneous occurrence of both temporal and spatial self-focusing dynamics. Small fluctuations in both the input energy and in the spatial phase curvature explain the observed extreme behaviour.The first direct measurement of extreme or rogue wave in the ocean [1] has triggered a large number of studies and renewed interest in what used to be believed as a "sailor's tale". Extreme events have since been observed in many other systems illustrating the wide range of underlying dynamics that can lead to their appearance [2,3]. In an optical context, the recent observation that solitons with extreme spectral red-shifts can emerge from an incoherent fibre supercontinuum [4] has attracted considerable attention and subsequent studies have highlighted the role of nonlinear noise amplification in the spontaneous emergence of highly localised structures [5,6] and the role of collisions in observing long tail statistics [7][8][9].While most rogue waves studies in optics have focussed on the 1+1D fibre case (one spatial dimension and one temporal dimension), the emergence of extreme events during full 3D propagation of light pulses with nonlinear spatio-temporal dynamics has been much less studied [11][12][13][14]. In the normal group velocity dispersion (GVD) regime, the combined action of spatial and temporal selffocusing leads to the formation of a dynamically stable filament characterised by an intense, localised peak surrounded by a weaker reservoir that continuously refuels the central core region [10]. In this regime, long tail statistics in the fluctuations at the spectral edge of a single filament similar to that of an incoherent fibre supercontinuum have been observed [11,12,14]. More recently, extreme events in the multi-filament regime where localized structures emerge from filaments merging have been measured experimentally [13].Strictly speaking, 3D stable solitons do not exist and the physical structure closest to a soliton is the 2D Townes spatial profile [15,16] which is unstable and leads to self-similar collapse of the laser beam in the normal GVD regime when the beam power exceeds the critical power for self-focusing [17]. On the other hand, in the anomalous GVD all three dimensions contribute to the spatio-temporal collapse with formation of light bullets [18]. Although such light bullets lend themselves to a tempting analogy with 1D fundamental solitons, recent work has shown that in fact 3D light bullets correspond to a form of polychromatic (weakly localised) Bessel beam that emerges spontaneously during the collapse phase of an initially Gauss...

Resonant radiation in synchronously pumped passive Kerr cavities

“…The generation of resonant dispersive waves (DWs) is a central process in nonlinear optics [1,2], with important implications for fiber supercontinuum generation [3][4][5], nonlinear dynamics [6][7][8], mode-locked lasers [9][10][11], and microresonator frequency combs [12][13][14]. It describes the transfer of energy from a strong pump to a weak linear wave, and occurs when the dispersion of the nonlinear medium permits phase-matching between the interacting fields.…”

Regularizing Aperiodic Cycles of Resonant Radiation in Filament Light Bullets

“…It is used for the investigation of, e.g., supercontinuum [5], high harmonic [6], or terahertz generation [7], few-cycle pulse generation [8], or complex nonlinear dynamics as self-organization [9]. Analogies to other areas of physics as artificial event horizons [10] or the ubiquitous rogue wave formation [11][12][13] have been shown, providing a useful test for the investigation Hawking radiation [14] or the predictability of extreme events [15].…”

Super-resonant radiation stimulated by high-harmonics

“…Introduction -The process of resonant radiation emission in nonlinear media is extremely general and has been studied in a plethora of different systems, like solitons in fibers and bulk media [1][2][3][4][5][6], three dimensional light bullets [7][8][9], dispersive shock waves [10], passive resonators [11][12][13][14][15], and even more complex scenarios combining a mixture of the above [16]. The shedding of this light is dictated by a nonlinear momentum conservation, i.e.…”