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