Reverse wavefront engineering for remote generation of a near-infrared femtosecond Bessel beam filament in air

Precise control of the filamentation of an ultrashort and intense near-infrared laser pulse in air is crucial for many applications but remains challenging. By combining inverse design for shaping of a pulse at the output of a laser with simulation of the nonlinear propagation of the pulse in air, we numerically investigate the way to simultaneously control the length and position of a plasma filament at an arbitrary remote distance for the first time. An intermediate state, with a Bessel-Gauss beam profile, is introduced between the laser output and the filament. Through forward and backward propagations of the intermediate state, an end-to-end design of the initial laser pulse is achieved to match the desired filament characteristics. Our calculations show that a properly engineered torus pulse can project such a Bessel-Gauss beam at remote distance and generate a long plasma filament without requiring any feedback loop. We also proposed an experimental arrangement to project such an intermediate state and generate the corresponding filament remotely. The method can be further extended to other types of filaments or targets that may be reached from different intermediate states.