We investigate the dynamical behavior of a self-pulsing laser under the influence of stimulated Brillouin scattering (SBS), a system which has previously been shown to favor extreme statistics. Using a laser model coupling a multi-Stokes Brillouin scattering process with the population inversion formalism for the gain and taking into account saturable absorption effects, we demonstrate that different statistical distribution types arise as the nonlinear interactions between the laser and higher-order SBS waves lead to the occurrence of high intensity short pulses. By taking into account up to five Stokes orders, we show that highly skewed statistics and pulses with extreme peak intensities can be obtained, allowing us to describe more accurately the experimental observations and to better apprehend the underlying physics. We also unexpectedly demonstrate that the acoustic noise does not affect the emergence of such extreme events.

• Received 16 May 2019

DOI:https://doi.org/10.1103/PhysRevA.100.013809