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Analytical theory of gain-switched laser pulses: From Lotka-Volterra slow-fast dynamics to passive Q switching.

Gain switching is a simple technique for generating short pulses through direct modulation of optical gain in lasers. Its mathematical description requires the connection between a slowly varying, low intensity solution and a short, high intensity solution. Previous studies constructed a complete pulse by patching these two partial solutions at an arbitrary point in the phase plane. Here, we develop an asymptotic theory in which slow and fast solutions are matched together through a third intermediate solution. The mathematical analysis of the laser problem benefits from a preliminary study of the Lotka-Volterra equations when the two competing populations exhibit different timescales. Since this particular limit has never been explored, we first analyze the Lotka-Volterra equations before applying the theory to the more complex laser equations. We show a significant effect of the transition layer on the pulse intensity. Last, we discuss the case of sustained laser pulses generated through the Q-switching technique and show how their description may benefit from our theory.