Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references

We use femtosecond laser frequency combs to convert optical frequency references to the microwave domain, where we demonstrate the synthesis of $10\text{-}\mathrm{GHz}$ signals having a fractional frequency instability of $⩽\le 3.5\times {10}^{-15}$ at a $1\text{-}\mathrm{s}$ averaging time, limited by the optical reference. The residual instability and phase noise of the femtosecond-laser-based frequency synthesizers are $6.5\times {10}^{-16}$ at $1\mathrm{s}$ and $-98\mathrm{dBc}∕\mathrm{Hz}$ at a $1\text{-}\mathrm{Hz}$ offset from the $10\text{-}\mathrm{GHz}$ carrier, respectively. The timing jitter of the microwave signals is $3.3\mathrm{fs}$.