Abstract
It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we present a general analysis of the regions of existence and stability of cavity solitons and patterns in the Lugiato-Lefever equation, a mean-field model that finds applications in many different nonlinear optical cavities. We demonstrate that the rich dynamics and coexistence of multiple solutions in the Lugiato-Lefever equation are of key importance to understanding frequency comb generation. A detailed map of how and where to target stable Kerr frequency combs in the parameter space defined by the frequency detuning and the pump power is provided. Moreover, the work presented also includes the organization of various dynamical regimes in terms of bifurcation points of higher codimension in regions of parameter space that were previously unexplored in the Lugiato-Lefever equation. We discuss different dynamical instabilities such as oscillations and chaotic regimes.
Highlights
Optical frequency combs can be used to measure light frequencies and time intervals more and precisely than ever before [1], opening a large avenue for applications
We aim to realize two goals: (i) to interpret how various coherent structures in microresonators, such as patterns and solitons, are intimately related to different types of Kerr frequency combs; (ii) to expand the study of the Lugiato-Lefever equation (LLE) to operating regimes that will prove to be of key importance for frequency comb generation, but so far have not been much explored
This study provides us with essential information about the location in parameter space where stable cavity solitons (CSs) and frequency combs can be found
Summary
Optical frequency combs can be used to measure light frequencies and time intervals more and precisely than ever before [1], opening a large avenue for applications. A new generation of comb sources has been demonstrated in compact high-Q optical microresonators with a Kerr nonlinearity pumped by continuous-wave laser light [2]. 1(a) and 1(b), a spatially localized bright light spot embedded in a homogeneous background of light has been shown to exist at the output of the resonator [10] Such structures, localized in space, are known as spatial cavity solitons (CSs). Recent experimental observations of 1D temporal CSs in fiber resonators [7] have renewed the interest in the LLE This interest was further strengthened when it was demonstrated that the LLE can be used to efficiently model Kerr frequency combs and that these were found, in some conditions, to be closely related to temporal CSs present inside the cavity [4,5,6].
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