Modelling light wave propagation and interaction and dynamical regimes analysis using the Lyapunov exponents method in ring fibre cavities

The ‘Cabaret’ finite differences method allows the performance of fast and conclusive modelling of the microcavity temporal dynamics with group velocity dispersion, cross- and self- phase modulation included. The proposed scheme and model allow us to study the dynamics of a cavity with two counter-propagating pulses, second order dispersion, modulation instability, Rayleigh scattering and other effects along the cavity roundtrips number up to 10 6…7 . The possibility of Lyapunov exponents mapping for the Raman and SBS fibre lasers and cavities is discussed.