  The ever-increasing demand for high speed and large bandwidth has made
photonic systems a leading candidate for the next generation of
telecommunication and radar technologies. The photonic platform enables high
performance while maintaining a small footprint and provides a natural
interface with fiber optics for signal transmission. However, producing sharp,
narrow-band filters that are competitive with RF components has remained
challenging. In this paper, we demonstrate all-silicon RF-photonic multi-pole
filters with $\sim100\times$ higher spectral resolution than previously
possible in silicon photonics. This enhanced performance is achieved utilizing
engineered Brillouin interactions to access long-lived phonons, greatly
extending the available coherence times in silicon. This Brillouin-based
optomechanical system enables ultra-narrow (3.5 MHz) multi-pole response that
can be tuned over a wide ($\sim10$ GHz) spectral band. We accomplish this in an
all-silicon optomechanical waveguide system, using CMOS compatible fabrication
techniques. In addition to bringing greatly enhanced performance to silicon
photonics, we demonstrate reliability and robustness, necessary to transition
silicon-based optomechanical technologies from the scientific bench-top to
high-impact field-deployable technologies.
