Analytical model for the design of external-cavity passively Q-switched fiber lasers

An analytical model has been developed to minimize the effective mode area in a saturable absorber for an external-cavity passively Q-switched fiber laser. Under the condition of minimum effective mode size inside the saturable absorber, the analytical expressions for two key parameters of an optimum system have been derived. One parameter is the optimum focal position that is analytically derived to be a function of the thickness and initial transmission of the saturable absorber. The other parameter is the optimum magnification of the re-imaging optics that is analytically derived to be in terms of the numerical aperture and core radius of the laser fiber as well as the thickness and initial transmission of the saturable absorber. The present model provides a straightforward procedure to adopt a focusing system for the output performance. A diode-pumped ytterbium-doped fiber lasers with a Cr:YAG crystal as a saturable absorber is considered to illustrate the utility of the present model.