  We have realized a suspended, high-reflectivity focusing metamirror
($f\approx 10$ cm, $\mathcal{R} \approx 99\%$) by non-periodic photonic crystal
patterning of a Si$_3$N$_4$ membrane. The design enables construction of a
stable, short ($L$ = 30 $\mu$m), high-finesse ($\mathcal{F}>600$) membrane
cavity optomechanical system using a single plano dielectric end-mirror. We
present the metamirror design, fabrication process, and characterization of its
reflectivity using both free space and cavity-based transmission measurements.
The mirror's effective radius of curvature is inferred from the transverse mode
spectrum of the cavity. In combination with phononic engineering and
metallization, focusing membrane mirrors offer a route towards
high-cooperativity, vertically-integrated cavity optomechanical systems with
applications ranging from precision force sensing to hybrid quantum
transduction.
