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

High-finesse Fabry-Perot cavities with bidimensional Si$_3$N$_4$ photonic-crystal slabs