Two-dimensional nonlinear modes and frequency combs in bottle microresonators

We theoretically investigate frequency comb generation in a bottle microresonator accounting for the azimuthal and axial degrees of freedom. We first identify a discrete set of the axial nonlinear modes of a bottle microresonator that appear as tilted resonances bifurcating from the spectrum of linear axial modes. We then study azimuthal modulational instability of these modes and show that families of two-dimensional (2D) soliton states localized both azimuthally and axially bifurcate from them at critical pump frequencies. Depending on detuning, 2D solitons can be stable, form persistent breathers or chaotic spatio-temporal patterns, or exhibit collapse-like evolution.