Radio Frequency from Optical with Instabilities below $10^{-15}$- Generation and Measurement

This paper presents a frequency synthesis that achieves exceptional stability by transferring optical signals to the radio frequency (RF) domain at 100 MHz. We describe and characterize two synthesis chains composed of a cryogenic silicon cavity-stabilized laser at 1542 nm and an ultra-low expansion (ULE) glass cavity at 1157 nm, both converted to 10 GHz signals via Ti:Sapphire and Er/Yb:glass optical frequency combs (OFCs). The 10 GHz microwave outputs are further divided down to 100 MHz using a commercial microwave prescaler, which exhibits a residual frequency instability of $\sigma_y(1~\text{s})<10^{-15}$ and low $10^{-18}$ level at a few thousand seconds. Measurements are performed using a newly developed custom ultra-low-noise digital measurement system and are compared to the carrier-suppression technique. The new system enables high-sensitivity evaluation across the entire synthesis chain, from the optical and microwave heterodynes as well as the direct RF signals. Results show an absolute instability of $\sigma_y(1~\text{s})~\approx~4.7\times10^{-16}$ at 100 MHz. This represents the first demonstration of such low instability at 100 MHz, corresponding to a phase noise of -140 dBc/Hz at a 1 Hz offset and significantly surpassing earlier systems. These advancements open new opportunities for precision metrology and timing systems.