Abstract
By using perturbation theory we derive an expression for the electrical field of a Gaussian laser beam propagating in a gas medium. This expression is used as a trial solution in a variational method to get quasi-analytical solutions for the width, intensity, and self-focusing distance. The approximation gives a better agreement with results of numerical simulations for a broad range of values of the input power than previous analytical results available in the literature. The results apply in the case of ultrashort pulses too.
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