  We investigate the optical properties of microcavities with suspended
subwavelength structured mirrors, such as high-contrast gratings or
two-dimensional photonic crystals slabs, and focus in particular on the regime
in which the microcavity free-spectral range is larger than the width of a Fano
resonance of the highly reflecting structured mirror. In this unusual regime,
the transmission spectrum of the microcavity essentially consists in a single
mode, whose linewidth can be significantly narrower than both the Fano
resonance linewidth and the linewidth of an equally short cavity without
structured mirror. This generic interference effect---occuring in any
Fabry-Perot resonator with a strongly wavelength-dependent mirror---can be
exploited for realizing small modevolume and high quality factor microcavities
and, if high mechanical quality suspended structured thin films are used, for
optomechanics and optical sensing applications.
