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 quasi-periodic 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.