Frequency comb generation in SNAP bottle resonators

We develop a theory of optical frequency comb generation in ultra-compact surface nanoscale axial photonic (SNAP) bottle microresonators, employing the nonlinear interaction of whispering gallery modes which are confined along an optical fiber with nanoscale radius variation. We predict that a SNAP microresonator with a radius of a few micrometers can generate a frequency comb with an ultra-fine sub-gigahertz spectral spacing, which would require traditional ring resonators of centimeter radius. We identify regimes of stable or quasiperiodic comb dynamics due to soliton excitation, and show that special engineering of the SNAP radius profile can be used to compensate for nonlinearity-induced dispersion.