Ultrashort laser pulse filamentation with Airy and Bessel beams

We investigate the nonlinear propagation of intense Bessel and Airy beams forming filaments in transparent media. We identify two propagation regimes separated by the relative importance of multiphoton absorption and self-focusing of the main Bessel or Airy lobe, due to the Kerr effect. We show that intense Bessel or Airy beams are reshaped into stationary nonlinear beams whose propagation is sustained by a continuous energy flux to the main lobe from its neighbors. The stationary propagation regime is obtained for Bessel cone angles exceeding a certain threshold; by focusing a Gaussian beam of sufficient power with an axicon. With respect to linear Bessel beams, stationary nonlinear Bessel beams exhibit ring compression and attenuation of contrast. For small cone angles, the nonlinear Bessel beams become unstable leading to an unsteady propagation regime. We demonstrate similar physics for intense Airy beam freely propagating in a Kerr medium: stationary nonlinear Airy beams are demonstrated in a planar geometry. These beams preserve the intensity profile and the transverse acceleration of the Airy peak. For powers in the main Airy lobe exceeding a certain threshold, this stationary propagation regime becomes unstable. In the 2-dimensional case, Airy beams with high powers in the main lobe reshape into a multifilamentary pattern induced by Kerr and multiphoton nonlinearities. The nucleation of new filaments and their interaction, affects the acceleration of the main Airy lobes.