Fabry-P\'erot Metacavities with Single-Layered Dielectric Metamirrors
The Fabry-P\'{e}rot resonator is a cornerstone of photonics and wave physics, providing a universal mechanism for spectral confinement and resonant enhancement of wave-matter interactions. In this work, we establish an analytically tractable class of Fabry-P\'{e}rot metacavities in which the reflecting elements are realized by single-layer periodic arrays of circular dielectric cylinders acting as metamirrors. Both the reflection efficiency and reflection phase of such metamirrors are obtained in closed form and shown to be widely and independently tunable, encompassing ideal electric and magnetic mirror limits with unit reflectivity. Building on these results, we derive explicit analytical expressions that fully describe the optical responses of Fabry-P\'{e}rot cavities composed of two such parallel metamirrors. Our combined analytical and numerical investigations reveal that these metamirrors provide exceptional flexibility for tailoring Fabry-P\'{e}rot resonances across a broad spectral range, enabling precise control over resonance positions and quality factors. In particular, the framework naturally predicts the emergence of Fabry-P\'{e}rot bound states in the continuum with formally infinite Q-factors. These results establish dielectric-metamirror-based Fabry-P\'{e}rot cavities as a versatile and fundamentally transparent platform for engineering high-Q optical resonances.