Ultrafast nonlinear dynamics of whispering-gallery mode micro-cavity lasers

We explore the ultrafast spatio-temporal dynamics of whispering-gallery micro-cavity lasers. To model the dynamics of the nonlinear whispering-gallery modes we develop a three-dimensional Finite-Difference Time-Domain modelling framework based on the spin and therefore optical polarisation resolved Maxwell-Bloch equations. The numerical algorithm brings together a real value form of the optical Bloch equations with the curl part of Maxwell's equations. The Hamiltonian of the two-level system contains either linear or circular polarised transitions. In cylindrical micro-cavity lasers the coherent, nonlinear emission process leads to ultrafast fan-like rotational phase dynamics of the degenerate whispering-gallery modes. This rotation is shown to be arrested in gear-shaped micro-cavity lasers followed by an over-damped relaxation oscillation.