Externally refuelled optical filaments

Plasma channels produced in air through femtosecond laser filamentation1–4 hold great promise for a number of applications, including remote sensing5, attosecond physics6,7 and spectroscopy8, channelling microwaves9–12 and lightning protection13. In such settings, extended filaments are desirable, yet their longitudinal span is limited by dissipative processes. Although various techniques aiming to prolong this process have been explored, the substantial extension of optical filaments remains a challenge14–21. Here, we experimentally demonstrate that the natural range of a plasma column can be enhanced by at least an order of magnitude when the filament is prudently accompanied by an auxiliary beam. In this arrangement, the secondary low-intensity ‘dressing’ beam propagates linearly and acts as a distributed energy reservoir22, continuously refuelling the optical filament. Our approach offers an efficient and viable route towards the generation of extended light strings in air without inducing premature wave collapse or an undesirable beam break-up into multiple filaments2. Since the first experimental observation of self-channelling intense femtosecond laser pulses in air by Braun and colleagues1, optical filamentation has been a topic of intense investigation23–27. In general, this process results from the dynamic balance between beam self-focusing effects and the defocusing action of free electrons produced through the photoionization of air molecules. When the energy of an intense laser pulse exceeds a certain threshold, the transverse profile of the beam eventually reshapes into an intense 100 mm filament core and a surrounding wider, but much less intense, background (photon bath). Remarkably, in this setting, the photon bath continuously feeds energy to the filament, so this self-organized phenomenon can persist over many diffraction lengths4,28. Ultimately, however, the finite energy contained in this arrangement is dissipated and the filament vanishes. In other words, only a small fraction of energy is utilized to support the filament core. This represents a fundamental limitation in potential applications such as remote sensing and microwave channelling where long-ranged filaments are often required. Methods to prolong these light strings have been pursued in previous work, and approximately twofold elongations have been reported17,18. However, substantially extending the longevity of such entities remains a problem. In this Letter, we report an order of magnitude extension of an optical filament in air. This is accomplished by appropriately employing a surrounding auxiliary dressing beam, which continuously supplies energy to the filament in a way that considerably protracts its longevity. Our experiments demonstrate that this lowintensity dress acts like an artificial photon bath, the sole purpose of which is to continuously refuel the light string ‘in flight’. Rather than concentrating all the available laser energy into a single beam, which can cause either a premature burnout because of ionization losses or chaotic multi-filamentation29, our scheme provides a versatile route by which to appropriately economize this power consumption to achieve maximum propagation distance. This mode of operation closely resembles that encountered in other dissipative systems associated with a finite amount of combustible material; maximum performance can be achieved by expending this energy at an optimal, gradual rate instead of igniting it all at once. As indicated in our study, such dressed beam configurations are in principle scalable and can thus be used in establishing long-range filaments. The basic idea behind the proposed method is illustrated in Fig. 1. Figure 1a presents the dynamics of an unaided Gaussian pulsed filament in air. As is clearly shown, this filament can only propagate for a while until dissipation effects deplete its energy after a characteristic length L1. Beyond this point, the beam irreversibly diffracts. On the other hand, as shown in Fig. 1b, this dynamic balance can be considerably extended, up to a distance of L2, when this same filament beam is initially surrounded by a low-intensity annular dress. What makes this possible is the fact that the dress wave is radially distributed over a much broader region so as to prevent it from triggering any nonlinear effects. In this scenario,