The propagation of a femtosecond optical pulse in a multidimensional off-resonance two-level medium is studied. Within the quasiadiabatic following approach, the evolution of the pulse is governed by a generalized Kadomtsev-Petviashvili equation with coupling between the spatial and temporal profile. The presence of this coupling can have a dramatic influence on the dynamics of the optical pulse. Thus, one can observe effects which cannot be described within the framework of the slowly-varying envelope approximation. In particular, we show that due to the interaction between the transient diffraction and the electrodynamic absorption, stable, localized multidimensional pulses can be formed.
Mel’Nikov, I. V., Mihalache, D., & Panoiu, N. C. (2000). Localized multidimensional femtosecond optical pulses in an off-resonance two-level medium. Optics Communications, 181(4), 345–351. https://doi.org/10.1016/S0030-4018(00)00773-2