Dynamics in a tightly-focused end-pumped solid-state laser near degenerate cavity configurations

We numerically study the dynamics of a tightly-focused end-pumped solid-state laser near the degenerate cavity configurations by using the Collins integral together with a rate equation. We find that the field and gain adjust their distributions to exhibit the temporal rather than spatiotemporal instabilities in spite of the coupling of many transverse modes. These instabilities are attributed to the frequency locking but phase unlocking of the degenerate Laguerre-Gaussian modes. The phase portrait is plotted in the three dimensional space with gain, real part, and imaginary part of the field because of similar dynamics for every transverse point. Both of the portrait and the Poincare map show the peculiar features. Moreover, the route to chaos is the mixed effect of period-doubling and quasi-period as the cavity length is tuned.