Theory of multicolor soliton microcombs

We present a general theory of multicolor soliton microcombs. These frequency combs require engineered dispersion and have an optical spectrum consisting of multiple spectral windows. Our theory is based on a multiple-scale approach applied to the Lugiato-Lefever equation (LLE) and provides a framework to investigate different pumping configurations. For multi-frequency pumping, we predict a decreasing pumping threshold as the number of spectral windows increases due to an enhanced effective nonlinear parameter. However, comb formation does not require multi-frequency pumping and can emerge even with a single driving field.