Abstract
A nonlinear theory of intense laser-plasma interactions is developed and used to describe relativistic optical guiding, coherent harmonic radiation production, and nonlinear plasma wakefield generation. Relativistic optical guiding is found to be ineffective in preventing the leading portion (\ensuremath{\le} a plasma wavelength) of a laser pulse from diffracting. Coherent harmonic generation is found to be most efficient for short laser pulses. Optical guiding and harmonic generation may be enhanced by the presence of large amplitude plasma wakefields. These phenomena may be important in laser-driven plasma accelerators, x-ray sources, and fusion schemes.
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