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

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Abstract
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.

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