  We predict and observe the appearance of an excess noise factor due to the
non-Hermiticity of the modes of two actively harmonically mode-locked lasers.
The non uniform distribution of gain and losses in the ring cavities of these
lasers causes a non-orthogonality of the longitudinal modes, which is
responsible for an increase of the rate of spontaneous emission falling in the
lasing pulsed mode. This leads to an increase of the phase noise of the pulse
train generated by these lasers by more than 20 dB at some offset frequencies.
This degradation can be prohibitive for the use of these lasers for several
applications such as the generation of high spectral purity RF and low jitter
clock signals.
