A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity

In this paper, the research related to the formation of optical dissipative structures in Kerr-nonlinear whispering-gallery mode resonators pumped with continuous-wave lasers is reviewed. Pattern formation in these systems can be analysed using the paradigmatic Lugiato-Lefever model, which is a partial differential equation ruling the dynamics of the intra-cavity laser field. Various dissipative structures such as Turing rolls, solitons, breathers and spatio-temporal chaos can emerge in the resonator depending on the laser power and frequency. The bifurcation analysis enables a classification of these patterns, and also permits identification of their basins of attraction. This article is part of the theme issue `Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.