Generation of on-axis optical filaments by means of Dammann lenses

The generation of filaments with ultrashort laser pulses is based on the sustained balance between self-focusing (Kerr effect) and ionization. When the peak power of the laser pulse is close to a critical self-focusing power value (P
cr
) a single filament develops. If the beam power exceeds about more than 10 times P
cr
, modulation instability can cause several co-propagating filaments formed from a single laser beam spontaneously, thus entering into the multiple filaments (MFs) regime. To avoid the random space-time localization of MFs, the initial beam is modified by methods that include, among others, changes in its ellipticity or wavefront shaping. However, although the generation of controlled off-axis MFs has been extensively studied, less attention has been paid to the generation of sequential on-axis MFs. This is the key point of this work.