Nonparaxial evolution of femtosecond optical pulses.

Abstract

We investigate numerically the self-focusing dynamics of femtosecond pulses in the frame of new non-paraxial amplitude equations. We find that the nonlinear regime strongly depends on the initial form of the pulses. In the case of pulse with small transverse and large longitudinal size (long pulse), the dynamics is closer to the nonlinear paraxial dynamics of a laser beam, and the difference is in the large spectral and longitudinal spatial modulation of the long pulse. We show also that non-paraxiality plays an important role on the evolution of light bullets and light disks. In regime of light bullets we observe weak self-focusing without pedestals for input power <i>P</i> valued from the critical power for collapse <i>P_cr</i> up to 16 <i>P_cr. </i>We find also nonlinear non-collapsed regime of propagation of light disks (pulses with small longitudinal and large transverse size), when the input power exceeds the critical power for collapse <i>P_cr. </i>Our results are in good agreement with the recent experiments on nonlinear propagation of femtosecond pulses. We have demonstrated for the first time that a non-paraxial model can explain such effects as spectral broadening, collapse arrest and nonlinear wave guide behavior of ultrashort optical pulses in nonlinear regime near to critical power for self-focusing.