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This paper presents a closed-form analysis of saturable absorber mode locking of a homogeneously broadened laser. A solution is obtained for the case of a short relaxation time of the saturable absorber. This pulse is a hyperbolic secant as a function of time. For each choice of parameters two pulse widths are found. A stability analysis shows that the solution of greater width is stable. The requirements for achieving mode locking with a fast saturable absorber are stated. The effect of a time-varying laser medium gain is investigated analytically.
H. A. Haus (1975) studied this question.