Generalized Theory of Multicolor Microcombs

Kerr ring microresonator-based optical frequency combs have attracted significant interest due to their suitability for on-chip integration and their wide-ranging applications in telecommunications, sensing, and spectroscopy [1]. Two main challenges in microcomb development are stabilizing the comb offset frequency and generating broadband combs [1], [2]. A promising approach to address both is the generation of multicolor soliton microcombs [3]. These emerge in systems with an engineered dispersion profile consisting of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$J$</tex> equally spaced regions of anomalous dispersion (orange curves in Fig. 1(a) and (c) for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$J=3$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$J=5$</tex> respectively). Multicolor microcombs feature spectra spanning multiple distinct spectral windows, each centered at a different frequency (blue curves in Fig. 1(a) and (c)). In the time domain, they consist of a rapidly oscillating carrier and a meta-envelope which has the hyperbolic secant shape characteristic of single-color solitons (see Fig. 1(b)-(d)). Despite purely numerical investigations on the two-color case <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(J=2)$</tex> [3], [4], a general theory that elucidates the physical properties of these states has yet to be published.