  When a photo-diode is illuminated by a pulse train from a femtosecond laser,
it generates microwaves components at the harmonics of the repetition rate
within its bandwidth. The phase of these components (relative to the optical
pulse train) is known to be dependent on the optical energy per pulse. We
present an experimental study of this dependence in InGaAs pin photo-diodes
illuminated with ultra-short pulses generated by an Erbium-doped fiber based
femtosecond laser. The energy to phase dependence is measured over a large
range of impinging pulse energies near and above saturation for two typical
detectors, commonly used in optical frequency metrology with femtosecond laser
based optical frequency combs. When scanning the optical pulse energy, the
coefficient which relates phase variations to energy variations is found to
alternate between positive and negative values, with many (for high harmonics
of the repetition rate) vanishing points. By operating the system near one of
these vanishing points, the typical amplitude noise level of commercial-core
fiber-based femtosecond lasers is sufficiently low to generate state-of-the-art
ultra-low phase noise microwave signals, virtually immune to amplitude to phase
conversion related noise.
