Numerical treatment of UV-pumped, white-light-seeded single-pass noncollinear parametric amplifiers

A technique for numerically simulating second-order nonlinear interactions of light waves modulated spatially and temporally in both amplitude and phase in a uniaxial medium with arbitrary polarization and propagation directions is presented. A three-dimensional grid technique that automatically adapts grid parameters to the evolving sampled amplitudes by means of an analytical fit function is described. By means of spatiotemporal split-step fast-Fourier-transform propagation, diffraction and group-velocity dispersion can be included. We employ this technique for femtosecond noncollinear white-light-seeded parametric amplification in experimental designs presented earlier [Opt. Lett.22, 1494 (1997); Opt. Lett.23, 1283 (1998)]. The dependence of phase mismatch on signal wavelength provides a quantitative measure of the achromaticity of phase matching. Our results indicate that the pump pulse characteristics and not phase mismatching limit the amplification and the bandwidth of the parametric amplifier.