On validity of paraxial theory for super-Gaussian laser beams propagating in a plasma

In the present paper, we have investigated a situation where a high intensity laser beam passes through a gas and ionizes this gas by tunnel ionization. Here the electric field of the laser provides a sufficient velocity to the electrons to surpass the Coulomb barrier of the atom. Owing to the ionization the plasma density enhances which affects the laser beam propagation. The use of paraxial ray approximation theory for the present case of super-Gaussian lasers reveals the self-focusing of the beams and frequency upshifting. The predicted self-focusing of the laser beams is contrary to the expected outcome of defocusing of these beams in the plasma, indicating that the paraxial theory may not be valid for the case of super-Gaussian lasers even for the inclusion of most of the near axis region in the theory.