A Time-Delayed Renewal Model for Kerr Frequency Combs

The main workhorses of analysis and numerical simulations of Kerr optical frequency combs have been the Ikeda map (IM), as well as its mean-field approximation, the Lugiato-Lefever equation (LLE) [1], [2]. Each approach has its limitations: e.g., the solutions of the IM do not necessarily verify the continuity of the field, and it has been so far difficult to perform bifurcation analysis of the IM using numerical path-continuation methods. Similarly, even if the LLE is suitable for bifurcation analysis, it does not take into account multiple modes of cavity, although an alternative strategy was proposed in [3]. Furthermore, and contrary to the IM, the mean-field approximation in the LLE precludes the appearance of Kelly sidebands which are an experimental reality [4].