Analytical solution of the transient temperature profile in gain medium of passively Q-switched microchip laser

The transient temperature evolution in the gain medium of a continuous wave (CW) end-pumped passively Q-switched microchip (PQSM) laser is analyzed. By approximating the time-dependent population inversion density as a sawtooth function of time and treating the time-dependent pump absorption of a CW end-pumped PQSM laser as the superposition of an infinite series of short pumping pulses, the analytical expressions of transient temperature evolution and distribution in the gain medium for four- and three-level laser systems, respectively, are given. These analytical solutions are applied to evaluate the transient temperature evolution and distribution in the gain medium of CW end-pumped PQSM Nd:YAG and Yb:YAG lasers.