  We have used injection locking to multiply the repetition rate of a passively
mode-locked femtosecond fiber laser from 40 MHz to 1 GHz while preserving
optical phase coherence between the master laser and the slave output. The
system is implemented almost completely in fiber and incorporates gain and
passive saturable absorption. The slave repetition rate is set to a rational
harmonic of the master repetition rate, inducing pulse formation at the least
common multiple of the master and slave repetition rates.
