We show that a laser with a saturable absorber, described by the Yamada mod
el, displays excitability just below threshold. A small perturbation, for e
xample, a small input pulse, can trigger a single high output pulse, after
which the system relaxes back to the off state. In order to study possible
applications, such as pulse reshaping and clock recovery, approximate expre
ssions are given for the excitability threshold and the delay between input
and output pulses. Under the influence of optical noise, the system displa
ys coherence resonance: below threshold the laser produces pulse trains wit
h minimal jitter for a particular optimal noise level. This all-optical coh
erence resonance allows direct experimental verification. [S1063-651X(99)02
712-9].