Spatial frequency modulation of \(q\)-gaussian laser beams in a collisional plasma exhibiting an axial density ramp

This study investigates the phenomenon of spatial frequency chirping in q-Gaussian laser beams interacting nonlinearly with plasmas exhibiting an axial density ramp. The chirping, also known as phase anomaly, arises from the inherent uncertainty between a photon's position and momentum.The non-uniform intensity distribution of the laser beam leads to uneven heating of plasma electrons, causing a redistribution of charged particles due to which self focusing of laser beam takes place. The reduction in transverse dimensions subsequently spreads the transverse momentum of photons, modifying the axial phase of the laser beam. Employing variational theory, equations governing the evolution of the laser beam's radius and spatial frequency (axial phase) were derived and solved numerically. This allowed for analysis of how various laser and plasma parameters influence the changes in the laser beam's spatial frequency (axial phase).