High-power femtosecond filaments—laser-light beams capable of kilometer-long propagation—attract interest of nonlinear-optics community due to their numerous applications in remote sensing, lightning protection, virtual antennas, and waveguiding. Specific arrangements of filaments, into waveguides or hyperbolic metamaterials, allow for efficient control and guiding of electromagnetic radiation, radar-beam manipulation, and resolution enhancement. These applications require spatially uniform distribution of densely packed filaments.
In order to address this challenge, we investigate the dynamic properties of large rectangular filament arrays propagating in air depending on four parameters: the phase difference between the neighboring beams, the size of the array, separation between the beams, and excitation power. We demonstrate that, as a result of the mutual interaction between the filaments, the arrays where the nearest neighbor beams are out-of-phase are more robust than the arrays with all the beams in phase.
Our analysis of the array stability reveals that there exist certain trade-offs between the stability of a single filament and the stability of the entire array. We show that in the design of the experiment, the input parameters have to be chosen in such a way that they ensure a sufficiently high filling fraction, but caution has to be used in order not to compromise the overall array stability.
In addition, we show the possibility of filament formation by combining multiple beams with energies below the filamentation threshold. This approach offers additional control over filament formation and allows one to avoid the surface damage of external optics used for filamentation.