  Repeatedly alternating the sign of dispersion along a waveguide substantially
increases the bandwidth to input peak power efficiency of supercontinuum
generation (SCG). Here, we explore, theoretically and numerically, how to
optimize sign-alternating dispersion waveguides for nonlinear pulse
compression, so that the compression ratio is maximized. By exploring a
previously unknown SCG phase effect, we find emergent phase effects unique to
these structures where the spectral phase converges to a parabolic profile
independent of uncompensated higher-order dispersion. The combination of an
easy to compress phase spectrum, with low input power requirements, then makes
sign-alternating dispersion a scheme for high-quality nonlinear pulse
compression that removes the need for high powered lasers. Also, we show a new
scheme for the design of practical waveguide segments that can compress SCG
pulses to near transform-limited durations, which is integral for the design of
these alternated waveguides and in general, for nonlinear pulse compression
experiments. We conclude by showing how compression can be maximized for
alternating dispersion waveguides within the integrated photonics platform,
showing compression to two optical cycles.
