Femtosecond optical pulse amplification in saturated media

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Abstract
The generalized form of a nonlinear equation modeling the evolution of femtosecond pulses in a wide range of laser media is derived. Together with auxiliary equations, it describes both amplitude and phase changes owing to a variety of linear and nonlinear effects. These effects include gain saturation, more than one kind of self-phase modulation, and both gain and phase dispersions. The model is applied to previous experiments of ultrashort-pulse amplification in a dye-laser amplifier and is found to describe quantitatively the observed strong spectral changes. We show that the spectral changes are due both to gain dispersion and to the interplay of various dispersive and nonlinear effects.