Theory of multicolor soliton microcombs

We present a general theory of multicolor soliton microcombs. These frequency combs require specially engineered dispersion and have an optical spectrum consisting of multiple spectral windows, centered at distinct frequencies. Our theory is based on a multiple-scale approach applied to the Lugiato-Lefever equation, and provides a framework to investigate different pumping configurations. For multi-frequency pumping, we predict a progressively lower pumping threshold as the number of spectral windows increases due to an enhancement of the effective nonlinear parameter. However, multi-frequency pumping is not a prerequisite for the formation of these combs and can emerge even with a single driving field. Our theoretical predictions are in excellent agreement with numerical simulations.