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We stabilise a microwave oscillator at 9.6 GHz to an optical clock laser at344 THz by using a fibre-based femtosecond laser frequency comb as a transferoscillator. With a second frequency comb we measure independently theinstability of the microwave source with respect to another optical clock laserfrequency at 456 THz. The total fractional frequency instability of thisoptic-to-microwave and microwave-to-optic conversion resulted in an Allandeviation sigma_y, of sigma_y=1.2E-14 at 1 s averaging time (band width 50kHz). The residual phase noise density is -97 dBc/Hz at 10 Hz offset from the9.6 GHz carrier. Replacing the existing quartz-based interrogation oscillatorof the PTB caesium fountain CSF1 with this optically stabilised microwavesource will reduce the instability contribution due to the Dick effect from the1E-13-level at 1s averaging time to an insignificant level at the currentstatus of CSF1. Therefore this new microwave source can be an alternative tocryogenic sapphire-loaded cavity oscillators in order to overcome thelimitations of state-of-the-art quartz oscillators.

The stability of an optical clock laser transferred to the interrogation oscillator for a Cs fountain