Nearly Vertical Hopf Bifurcation for a Passively Q-Switched Microchip Laser

Passively Q-switched microchip lasers generate strongly pulsating intensity oscillations that emerge from a Hopf bifurcation point. We show that this bifurcation is nearly vertical and explain why strongly pulsating oscillations are immediately observed as we pass the Hopf bifurcation point. The laser dynamical problem is mathematically a singular perturbation problem which we investigate. The leading order problem is conservative and corresponds to Lotka–Volterra equations.