We propose a detailed stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering gallery mode resonators pumped in the normal dispersion regime. We analyze the spatial bifurcation structure of the stationary states depending on two parameters that are experimentally tunable, namely the pump power and the cavity detuning. Our study demonstrates that the non-trivial equilibria play an important role in this bifurcation map, as their associated eigenvalues undergo critical bifurcations that are foreshadowing the existence of localized spatial structures. In particular, we show that in the normal dispersion regime, dark cavity solitons can emerge in the system, and thereby generate a Kerr comb. We also show how these solitons can coexist in the resonator as long as they do not interact with each other. The Kerr combs created by these (sets of) dark solitons are also analyzed, and their stability is discussed as well.

We investigate the formation of cavity solitons in crystalline whispering-gallerymode disk resonators that are pumped in different dispersion regimes. In the Fourier domain, these dissipative structures correspond to specific types of mode-locked Kerr optical frequency combs. Depending on the sign of the second-order chromatic dispersion and on the pumping conditions, we show that either bright or dark cavity solitons can emerge, and we show that these two regimes are associated with characteristic spectral signatures that can be discriminated experimentally. We use the Lugiato-Lefever spatiotemporal formalism to investigate the temporal dynamics leading to the formation of these azimuthal solitons, as well as the emergence of Turing patterns. The theoretical results are in excellent agreement with experimental measurements that are obtained using calcium and magnesium fluoride disk resonators pumped near 1550 nm.

Optical Kerr frequency combs are known to be effective coherent multiwavelength sources for ultrahigh capacity fiber communications. These combs are the frequency-domain counterparts of a wide variety of spatiotemporal dissipative structures, such as cavity solitons, chaos, or Turing patterns (rolls). In this Letter, we demonstrate that Turing patterns, which correspond to the so-called primary combs in the spectral domain, are optimally coherent in the sense that for the same pump power they provide the most robust carriers for coherent data transmission in fiber communications using advanced modulation formats. Our model is based on a stochastic Lugiato-Lefever equation which accounts for laser pump frequency jitter and amplified spontaneous emission noise induced by the erbium-doped fiber amplifier. Using crystalline whispering-gallery-mode resonators with quality factor Q∼10^{9} for the comb generation, we show that when the noise is accounted for, the coherence of a primary comb is significantly higher than the coherence of their solitonic or chaotic counterparts for the same pump power. In order to confirm this theoretical finding, we perform an optical fiber transmission experiment using advanced modulation formats, and we show that the coherence of the primary comb is high enough to enable data transmission of up to 144  Gbit/s per comb line, the highest value achieved with a Kerr comb so far. This performance evidences that compact crystalline photonic systems have the potential to play a key role in a new generation of coherent fiber communication networks, alongside fully integrated systems.