Theory of ultrafast nonlinear refraction in semiconductor heterostructure waveguides

This study calculates the dispersion of the third-order susceptibility for a GaAs/AlAs superlattice. The calculated dispersion of Reχ⁽³⁾ below the half-bandgap is shown, illustrating the resonant enhancement at the half-bandgap. Dispersion of all eight independent χ⁽³⁾ tensor elements are addressed and the complete polarisation dependence of self-phase modulation for the usual [001]-grown waveguide orientation is obtained. There is considerable anisotropy with the effective coefficient for the TE polarization being about three times larger than for the TM polarisation around the half-bandgap due to a combination of the bulk χ⁽³⁾ anisotropy and the suppression of the heavy-hole optical matrix element for TM-polarisation.