Spatio-temporal dynamics of single-cycle optical pulses and nonlinear frequency conversion

We model propagation of initially single-cycle wave packet exhibiting paraxial spatial diffraction in a homogeneous isotropic dielectric medium with normal group velocity dispersion and instantaneous cubic nonlinearity. We show that for higher input intensity, the number of field oscillations is increased and the temporal spectrum shifts to shorter wavelengths in the axial beam part and to longer wavelengths at the periphery of the beam, and this is accompanied by the formation of closed surfaces of equal phase. We find that at tripled frequencies a minimum of spectral density forms at low spatial frequencies, which is characteristic for single-cycle pulses. At higher spatial frequencies, the maximum of the spectral density shifts to quadruple temporal frequencies