Optical resonant cavities play an important role in electromagnetic wave control; they can confine electromagnetic waves and improve the interaction between light and matter. However, because of the limitations of the standing-wave formation conditions for Fabry-Perot-type resonance, the miniaturization of optical resonant cavities formed using traditional materials is difficult. Recently, the miniaturization of three-dimensional optical resonant cavities has been demonstrated based on electric hyperbolic metamaterials (HMMs); their isofrequency contour takes the form of an open hyperboloid because the principal components of the permittivity tensor have opposite signs. Here, based on the permeability tensor, we propose theoretically and verify experimentally a planar magnetic hyperbolic cavity with a subwavelength scale, $(\lambda /12)\times (\lambda /17)$, using a circuit-based HMM in the microwave regime. Furthermore, the anomalous scaling laws in the circuit-based magnetic hyperbolic cavities are studied. As the frequency increases, the mode order decreases, which is markedly different from traditional cavities. It is also possible to realize size-independent cavity modes based on the HMMs by design. In addition, by considering a composite structure that contains two hyperbolic cavities, the coupling of two hyperbolic cavity modes in the near-field regime is demonstrated. The circuit-based hyperbolic cavities not only extend previous research work on hyperbolic cavities to magnetic HMMs, but they also have a planar structure that is easier to integrate and has a smaller loss. Finally, the hyperbolic cavities may enable their use in some microwave-related applications, such as in high-sensitivity sensors, resonance imaging, and miniaturized narrowband filters.

• Received 15 January 2020
• Revised 4 March 2020
• Accepted 24 March 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.044024