Abstract:Microresonator combs exploit parametric oscillation and nonlinear mixing in an ultrahigh-Q cavity. This new comb generator offers unique potential for chip integration and access to high repetition rates. However, time-domain studies reveal an intricate spectral coherence behavior in this type of platform. In particular, coherent, partially coherent or incoherent combs have been observed using the same microresonator under different pumping conditions. In this work, we provide a numerical analysis of the coherence dynamics that supports the above experimental findings and verify particular design rules to achieve spectrally coherent microresonator combs. A particular emphasis is placed in understanding the differences between so-called Type I and Type II combs. and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000). 3. T. W. Hänsch, "Nobel Lecture: Passion for precision," Rev. Mod. Phys. 78, 1297-1309(2006. 4. N. R. Newbury, "Searching for applications with a fine-tooth comb," Nature Photon. 5, 186-188 (2011). 5. V. Torres-Company and A. M. Weiner, "Optical frequency comb technology for ultra-broadband radio-frequency photonics," Laser and Photon. Rev. (in press, 2013). DOI 10.1002/lpor201300126. 6. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, "Microresonator-based optical frequency combs," Science 332, 555-559 (2011). 145-152 (2014). 43. F. Leo, S. Coen, P. Kockaert, S. P. Goza, P. Emplit, and M. Haelterman, "Temporal cavity solitons in onedimensional Kerr media as bits in an all-optical buffer," Nat. Photonics 4, 471-476 (2010). 44. H. Lajunen, V. Torres-Company, J. Lancis, E. Silvestre, and P. Andres, "Pulse-by-pulse method to characterize partially coherent pulse propagation in instantaneous nonlinear media," Opt. Express 18, 14979-14991 (2010). 45. M. Erkintalo and S. Coen, "Coherence properties of Kerr frequency combs," Opt. Lett. 39, 283-286 (2014). 46. M. Haelterman, S. Trillo, and S. Wabnitz, "Additive-modulation-instability ring laser in the normal dispersion regime of a fiber," Opt. Lett. 17, 745-747 (1992). 47. I. V. Barashenkov and Y. S. Smirnov, "Existence and stability chart for the ac-driven, damped nonlinear Schrodinger solitons," Phys. Rev. E 54, 5707-5725 (1996)