Magic Cancellation Point for Vibration Resilient Ultrastable Microwave Signal

Photonically-synthesized microwave signals have demonstrated the ability to surpass the phase-noise performance achievable by traditional means of RF signal generation. However, in order for microwave-photonic oscillators to truly replace their RF counterparts, this phase noise advantage must also be realizable when operating outside of a laboratory. Oscillators in general are known to be notoriously vibration sensitive, with both traditional RF and optical oscillators degrading sharply in phase noise in all but the most stationary of environments. We demonstrate here a powerful technique that makes use of a precise frequency difference between two optical signals, termed the "magic cancellation point", to enable the cancellation of vibration-induced noise upon optical frequency division to the RF. Beyond simply mitigating the effects of vibration, this technique also preserves the excellent phase noise that would ordinarily be characteristic of signals obtained from a frequency division process. At a center frequency of 10 GHz, our divided down oscillator achieves -42 dBc/Hz, -72 dBc/Hz, -102 dBc/Hz, and -139 dBc/Hz at 1 Hz, 10 Hz, 100 Hz, and 10 kHz offset frequencies, respectively. In addition, from optical to RF, we showcase the cancellation of vibration-induced phase noise by 22.6 dB, reaching an acceleration sensitivity of $1.5 \times 10^{-10}$ g$^{-1}$. This technique applies widely to optical carriers of any center wavelength and derived from an arbitrary resonator geometry.