Self-guiding and stability of intense optical beams in gases undergoing ionization

The propagation of intense optical beams in gases undergoing ionization is analyzed. Two types of optical beam modes are considered: a fundamental Gaussian and a higher-order radially polarized beam. The propagation dynamics include the effects of diffraction, nonlinear self-focusing, and ionization. For sufficiently intense optical beams the neutral gas undergoes ionization, generating a plasma which tends to defocus the beam. An envelope equation governing the spot size for both types of beams is derived, analyzed, and solved numerically. Self-guided solutions, which result from a balancing of diffraction, plasma defocusing, and nonlinear self-focusing, are analyzed for both types of beams. These equilibrium solutions are found to be unstable due to an ionization-modulation instability for which asymptotic growth rates are obtained. A self-guided inverse Cherenkov accelerator based on the higher-order radially polarized mode is proposed and analyzed. In addition, the depletion of the optical field due to collision and ionization losses is analyzed and the attenuation length is derived.