Abstract

Since first demonstrated in 2007, the generation of frequency combs in microresonators has attracted significant interest. A small footprint, high power efficiency and on-chip potential make them attractive substitutes for commercially existing comb sources [1]. Extensive experimental research on such Kerr combs has followed, but theoretical analyses are comparatively scarce. This deficiency can be linked to the intractable computational complexity of the existing models [2]. Here we report that octave-spanning Kerr frequency combs can be realistically and efficiently modeled with a generalized Lugiato-Lefever (LL) equation [3], which has been extensively used in the past to model macroscopic optical fiber resonators. Steady-state Kerr comb solutions in good agreement with reported experiments can be obtained by solving this equation with a Newton-Rhapson root-finding algorithm, a method which is orders-of-magnitude faster than any other technique, even when including more modes than ever before. Additionally, using split-step Fourier integration of the LL model, dynamical instabilities of Kerr frequency combs can be studied in a similarly fast fashion. Our results reveal characteristic spectral signatures of such instabilities.

© 2013 IEEE