  We report the synthesis and measurement of an ultra-precise and extremely
stable optical frequency in the telecommunications window around 1543 nm. Using
a fibre-based femtosecond frequency comb we have phase-stabilised a fibre laser
at 194 THz to an optical frequency standard at 344 THz, thus transferring the
properties of the optical frequency standard to another spectral region.
Relative to the optical frequency standard, the synthesised frequency at 194
THz is determined to within 1 mHz and its fractional frequency instability is
measured to be less than 2*10^{-15} at 1 s, reaching 5*10^{-18} after 8000 s.
We also measured the synthesised frequency against a caesium fountain clock:
here the frequency comparison itself contributes less than 4 mHz (2*10^{-17})
to the uncertainty. Our results confirm the suitability of fibre based
frequency comb technology for precision measurements and frequency synthesis,
and enable long-distance comparison of optical clocks by using optical fibres
to transmit the frequency information.
