We discover long-lived (microsecond-scale) optical waveguiding in the wake of atmospheric laser filaments. We also observe the formation and then outward propagation of the consequent sound wave. These effects may be used for remote induction of atmospheric long-lived optical structures from afar which could serve for a variety of applications.* These authors contributed equally to this work.
2Propagation of self-guided laser filaments through air and other gases results in a rich variety of phenomena and applications [1][2][3]. A laser filament is formed when a femtosecond pulse, with peak intensity above the critical power for collapse (3 GW in air at an optical wavelength of 800 nm), is propagating in a transparent medium [1]. In air, the diameter of a filament is approximately 100 μm and it can propagate over distances much longer than the Rayleigh length, from 10 cm up to the kilo-meter range [4][5][6][7]. A filament is formed due to a dynamic balance between the linear diffractive and dispersive properties of the medium and its nonlinear features such as self-focusing optical Kerr effect and defocusing due to the free electrons which are released from molecules through multi-photon ionization. In the atmosphere, filaments can be initiated at predefined remote distances [4,5] and propagate through fog, clouds and turbulence [8,9]. Thus, filaments are attractive for atmospheric applications such as remote spectroscopy This mechanism was used for guiding properly delayed picosecond pulses [21,22], but at times larger than several nanosecond after the filamenting pulse, even this process does not leave behind any waveguiding effects. In fact, all processes resulting from plasma or molecular alignment in the wake of atmospheric laser filaments are limited to the first few nanoseconds period. Consequently, it was generally believed that ten nanoseconds after the filament, the medium does not exhibit any waveguiding effect. In contrast to that, it was recently discovered that 0.1-1 milliseconds after the filament, there is a circular negative index change that acts as an antiguide by defocusing a probe beam [23]. This effect was attributed to reduction in the air density at the center of the filament 4 as a result of heating. Altogether, to the best of our knowledge, thus far all experiments and theories on laser filamentation in the atmosphere concluded that there is no longlived (>10 nanosecond) waveguiding effect left behind the femtosecond filamenting pulse. This severely limits any CW application of laser filamentation, because the repetition rate of any high power laser used for creating the filament is low, hence for most of the time between pulses light would not be guided. Likewise, any other potential application would have to "live" on a picosecond scale, because at later times, waveguiding by the filament was thought to be nonexistent.Here, we show the exact opposite: we demonstrate theoretically and experimentally that the filament induces a transient positive index change which lasts for approximate...