Parameter ranges for CW passive mode locking

CW passive mode locking of a homogeneously broadened laser is considered. In the coordinate plane, whose abscissa is proportional to the small-signal saturable absorber loading, and whose ordinate is proportional to the small-signal gain, the following regimes are laid out: 1) steady-state single-pulse mode-locking solutions; 2) stability against relaxation oscillations; 3) self-starting of mode locking. The assumption is made that CW mode locking can be obtained only for a choice of parameters for which all three regimes overlap. We require further that the overlap regime be reached by a monotonic increase of small-signal gain (pumping), without passing outside regime 2). Under these conditions one may state requirements on the system parameters for the obtainment of single-pulse mode locking by a saturable absorber. The analysis explains why it has been impossible to mode lock passively the CW Nd:YAG laser, but passive mode locking of the CW dye-laser system is possible.