Abstract

The effects of material dispersion on a femtosecond pulse undergoing self-focusing have been shown to drastically modify the temporal envelope of the pulse.^1-4 In a material with an index of refraction that increases with intensity (n = n_o + n₂I, where n₂ > 0), a steady-state analysis predicts that a laser beam will self-focus if the power P in the beam is greater than the critical power P_cr = π(0.61λ)²/8n_on₂. For sufficiently long interaction lengths and P > P_cr, a singularity results that corresponds to catastrophic self-focusing. For femtosecond pulses, numerical simulations of the nonlinear Schrödinger equation (NLSE) in the positive group-velocity dispersion (GVD) regime have shown that dispersion can suppress catastrophic self-focusing and can lead to temporal splitting of the pulse. The predicted pulse spectra from these simulations also support the hypothesis that supercontinuum generation (SCG) occurs at the pulse splitting threshold and is a result of the interplay between self-focusing, self-phase modulation, and GVD.

© 1997 Optical Society of America