When a photo-diode is illuminated by a pulse train from a femtosecond laser,it generates microwaves components at the harmonics of the repetition ratewithin its bandwidth. The phase of these components (relative to the opticalpulse train) is known to be dependent on the optical energy per pulse. Wepresent an experimental study of this dependence in InGaAs pin photo-diodesilluminated with ultra-short pulses generated by an Erbium-doped fiber basedfemtosecond laser. The energy to phase dependence is measured over a largerange of impinging pulse energies near and above saturation for two typicaldetectors, commonly used in optical frequency metrology with femtosecond laserbased optical frequency combs. When scanning the optical pulse energy, thecoefficient which relates phase variations to energy variations is found toalternate between positive and negative values, with many (for high harmonicsof the repetition rate) vanishing points. By operating the system near one ofthese vanishing points, the typical amplitude noise level of commercial-corefiber-based femtosecond lasers is sufficiently low to generate state-of-the-artultra-low phase noise microwave signals, virtually immune to amplitude to phaseconversion related noise.
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