  We propose a new approach to supercontinuum generation and
carrier-envelope-offset detection based on saturated second-order nonlinear
interactions in dispersion-engineered nanowaveguides. The technique developed
here broadens the interacting harmonics by forming stable bifurcations of the
pulse envelopes due to an interplay between phase-mismatch and pump depletion.
We first present an intuitive heuristic model for spectral broadening by
second-harmonic generation of femtosecond pulses, and show that this model
agrees well with experiments. Then, having established strong agreement between
theory and experiment, we develop scaling laws that determine the energy
required to generate an octave of bandwidth as a function of input pulse
duration, device length, and input pulse chirp. These scaling laws suggest that
future realization based on this approach could enable supercontinuum
generation with orders of magnitude less energy than current state-of-the-art
devices.
