We perform the first theoretical modeling of the full spectral-temporal dynamics of octave-spanning parametric microresonator comb generation through use of the Lugiato-Lefever model extended to include higher-order dispersion and self-steepening. We show that three distinct stages are necessary to achieve single-pulse modelocking and discuss the dispersion characteristics required for ultrabroadband, stabilized comb generation. Our simulations agree well with previous experimental demonstrations and predict many of the observed features, including multipulse generation, dispersive wave generation, modelocking, and comb stabilization.
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