  Light scattering by a two-dimensional photonic crystal slab (PCS) can result
in dramatic interference effects associated with Fano resonances. Such devices
offer appealing alternatives to distributed Bragg reflectors or filters for
various applications such as optical wavelength and polarization filters,
reflectors, semiconductor lasers, photodetectors, bio-sensors, or non-linear
optical components. Suspended PCSs also find natural applications in the field
of optomechanics, where the mechanical modes of a suspended slab interact via
radiation pressure with the optical field of a high finesse cavity. The
reflectivity and transmission properties of a defect-free suspended PCS around
normal incidence can be used to couple out-of-plane mechanical modes to an
optical field by integrating it in a free space cavity. Here, we demonstrate
the successful implementation of a PCS reflector on a high-tensile stress
Si$_3$N$_4$ nanomembrane. We illustrate the physical process underlying the
high reflectivity by measuring the photonic crystal band diagram. Moreover, we
introduce a clear theoretical description of the membrane scattering properties
in the presence of optical losses. By embedding the PCS inside a high-finesse
cavity, we fully characterize its optical properties. The spectrally, angular,
and polarization resolved measurements demonstrate the wide tunability of the
membrane's reflectivity, from nearly 0 to 99.9470~$\pm$ 0.0025 \%, and show
that material absorption is not the main source of optical loss. Moreover, the
cavity storage time demonstrated in this work exceeds the mechanical period of
low-order mechanical drum modes. This so-called resolved sideband condition is
a prerequisite to achieve quantum control of the mechanical resonator with
light.
