Transition from linear- to nonlinear-focusing regime in filamentation

Laser filamentation in gases is often carried out in the laboratory with focusing optics to better stabilize the filament, whereas real-world applications of filaments frequently involve collimated or near-collimated beams. It is well documented that geometrical focusing can alter the properties of laser filaments and, consequently, a transition between a collimated and a strongly focused filament is expected. Nevertheless, this transition point has not been identified. Here, we propose an analytical method to determine the transition, and show that it corresponds to an actual shift in the balance of physical mechanisms governing filamentation. In high-NA conditions, filamentation is primarily governed by geometrical focusing and plasma effects, while the Kerr nonlinearity plays a more significant role as NA decreases. We find the transition between the two regimes to be relatively insensitive to the intrinsic laser parameters, and our analysis agrees well with a wide range of parameters found in published literature

Free-Space Nonlinear Beam Combining for High Intensity Projection

Abstract The controlled interaction of two high intensity beams opens new degrees of freedom for manipulating electromagnetic waves in air. The growing number of applications for laser filaments requires fine control of their formation and propagation. We demonstrate, experimentally and theoretically, that the attraction and fusion of two parallel ultrashort beams with initial powers below the critical value (70% P critical), in the regime where the non-linear optical characteristics of the medium become dominant, enable the eventual formation of a filament downstream. Filament formation is delayed to a predetermined distance in space, defined by the initial separation between the centroids, while still enabling filaments with controllable properties as if formed from a single above-critical power beam. This is confirmed by experimental and theoretical evidence of filament formation such as the individual beam profiles and the supercontinuum emission spectra associated with this interaction