Gas-Solid Phase Transition in Laser Multiple Filamentation

Abstract

While propagating in transparent media, near-infrared multi-terawatt (TW) laser beams break up in a multitude of filaments of typically 100-200 um diameter with peak intensities as high as 10 to 100 TW/cm 2 . We observe a phase transition at incident beam intensities of 0.4 TW/cm 2 , where the interaction between filaments induce solid-like 2-dimensional crystals with a 2.7 mm lattice constant, independent of the initial beam diameter. Below 0.4 TW/cm 2 , we evidence a mixed phase state in which some filaments are closely packed in localized clusters, nucleated on inhomogeneities (seeds) in the transverse intensity profile of the beam, and other are sparse with almost no interaction with their neighbors, similar to a gas. This analogy with a thermodynamic gas-solid phase transition is confirmed by calculating the interaction Hamiltonian between neighboring filaments, which takes into account the effect of diffraction, Kerr self-focusing and plasma generation. The shape of the effective potential is close to a Morse potential with an equilibrium bond length close to the observed value.Many physical systems are well described by statistical models driven by nearest-neighbor interactions, such as spin models [1][2][3]. Recently, we showed that the formation of multiple filamentation patterns in high-power ultrashort laser pulses also belong to this category [4,5].Laser filaments are produced in high-power, ultrashort laser pulses propagating in air or other transparent media [6][7][8] by a dynamic balance between Kerr selffocusing, and defocusing by higher-order non-linear effects including the ionization of the medium and other polarization saturation terms [9,10]. At 800 nm, this balance clamps the filaments intensity to typically 50 TW/cm 2 [11,12]. Filaments cannot be considered as virtual optical fibers guiding the light within their core: they continuously interact and exchange energy with the photon bath surrounding them [13][14][15][16]. This photon bath, also known as energy reservoir [13,17,18], plays a key role in the filamentation process. In particular, the photon bath feeds the filament and balances its energy losses, allowing it to self-heal after an obstacle [14][15][16] or extend its propagation distance [19].In the case of multifilamentation, the laser energy reservoir also mediates interactions between neighboring filaments [20][21][22][23][24][25][26]. This interaction is attractive if the filaments are in phase, and repulsive if they are in antiphase [27,28], corresponding to constructive and destructive interferences in the photon bath, respectively. Previous theoretical and experimental studies have shown that the relative phase between filaments is mainly randomly driven by intensity fluctuations during the collapse [29] and is then stabilized for the filaments propagating after the collapse [30].Recently we showed that at laser powers exceeding 100 TW, this mutual interaction limits the density of filaments in the transverse beam profile [31], resulting in the * corresponding author jean-pi...

Linearity of charge measurement in laser filaments

“…We also investigated its sensitivity to the screening of the electric field by space charges, by switching from the parallel configuration [Fig. In summary, both the peak ionic current and the corresponding total collected charge are representative of the ion density in the plasma channel after 10 µs to 100 µs, except in the case of multiple filamentation, where the typical distance between filaments is in the millimeter-range [41][42][43].…”

Measurements of fluence profiles in femtosecond laser sparks and superfilaments in air

“…When the optical power of the laser pulse is many times the critical power for self-focusing, the transverse modulation instability partitions the laser beam into multiple filaments [9], which are individually regularized through the mechanism discussed above and, under certain conditions, interact with each other. The filament interaction may result in the rogue-wave phenomena [10], phase transitions in multi-filamentation [11], and the coalescence of multiple filaments, individually formed on the way towards the focal plane of the optical system, into a structure termed the superfilament [12]. It has been argued that for superfilamentation to occur, the laser beam, carrying peak power many times the critical power for self-focusing, has to be relatively tightly focused with an external focusing optic.…”