Tunable optical frequency division method for ultra-stable microwave generation

In this Letter, we present a novel, to the best of our knowledge, optical frequency division (OFD) scheme to directly synthesize fine-tunable ultra-stable microwave from optical references by utilizing an optical frequency comb (OFC) as a transfer oscillator. By providing a tunable and theoretically unbiased division ratio, this scheme fully decouples the OFD from specific OFC parameters and enables high transfer fidelity. Using cavity-stabilized lasers as references, we demonstrated the generation of a 1.21 GHz ultra-stable microwave signal with a frequency instability of 1.0 × 10^-15 at 1 s and a residual instability of 1.1 × 10^-15<i>τ</i>^-1/2. Furthermore, 10 MHz signals with a residual instability of 3.0 × 10^-15 at 1 s and 1.6 × 10^-17 at 10,000 s were synthesized, representing the most stable result reported to date. This method is particularly advantageous for OFCs without tight-locking capabilities and facilitates the simultaneous downconversion of multiple optical references via a single OFC, which is attracting for optical atomic clock applications, as for absolute frequency measurement and time scale generation.