Optimization of passively Q-switched lasers

In optimizing passively Q-switched lasers, there is a unique choice of output coupler and unsaturated absorber transmission which maximizes the laser output energy and efficiency for each three-way combination of laser gain medium, absorber medium, and pump intensity (i.e, inversion density). In the present paper, we generalize and solve the three coupled differential equations which describe the passively Q-switched laser to obtain closed form solutions for key laser parameters such as the output energy and pulsewidth. We then apply the Lagrange multiplier technique to determine the optimum mirror reflectivities and unsaturated absorber transmissions as a function of two dimensionless variables. The first variable, z, corresponds to the ratio of the logarithmic round-trip small signal gain to the round-trip dissipative (nonuseful) optical loss and is identical to that which was used in previous treatments to optimize the rapidly Q-switched laser. The second variable, /spl alpha/, is unique to the passively Q-switched laser and is equal to the saturation energy density of the amplifying medium divided by the saturation energy density of the absorber. It is largely determined by the ration of the absorber to stimulated emission cross sections, but also depends on the speed of relaxation mechanisms in the amplifying and absorbing media relative to the resonator photon decay time. Several design curves, valid for all four level amplifying and absorbing media, are then generated. These permit the design of an optimum passively Q-switched laser and an estimate of its key performance parameters to be obtained quickly with the aid of a simple hand calculator. In the limit of large /spl alpha/ (>10), the design curves are virtually indistinguishable from the rapidly Q-switched case. The curves can also be used to perform rapid tradeoff studies of different absorbing materials. The theory can also be applied to CW-pumped, repetitively Q-switched systems through a simple multiplicative factor for the laser gain. The theory is applied to the analysis of a passively Q-switched Nd:YAG laser previously reported in the literature and shown to give excellent agreement with the experimental results.< >