Laser mode competition and stability analysis in intensity-time plane

It is numerically analyzed the mode competition in a laser with three modes that are oscillating over their threshold, solving the coupled mode equations and following the semiclassical formalism of Lamb. The analysis is started from the stability conditions in different situations of coupling between modes: the weak coupling approximation, the single-mode and two-mode operating and the strong coupling approximation. We plot the trajectories for the coupled oscillators versus time. In our work we assumed homogeneous broadening of the gain medium. This implies that the results apply to a solid-state or a dye laser. For a gas laser, we have to include Doppler broadening and the analysis in this case will be more complicated. The conclusions are that the dynamics of the system can become multistabile and/or unstabile and highly sensitive to the initial conditions and the coupling matrix.