  As a basic building block, optical resonant cavities (ORCs) are widely used
in light manipulation; they can confine electromagnetic waves and improve the
interaction between light and matter, which also plays an important role in
cavity quantum electrodynamics, nonlinear optics and quantum optics. Especially
in recent years, the rise of metamaterials, artificial materials composed of
subwavelength unit cells, greatly enriches the design and function of ORCs.
Here, we review zero-index and hyperbolic metamaterials for constructing the
novel ORCs. Firstly, this paper introduces the classification and
implementation of zero-index and hyperbolic metamaterials. Secondly, the
distinctive properties of zero-index and hyperbolic cavities are summarized,
including the geometry-invariance, homogeneous/inhomogeneous field
distribution, and the topological protection (anomalous scaling law, size
independence, continuum of high-order modes, and dispersionless modes) for the
zero-index (hyperbolic) metacavities. Finally, the paper introduces some
typical applications of zero-index and hyperbolic metacavities, and prospects
the research of metacavities.
