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 (IFC) takes the form of an open hyperboloid because the principal components of the permittivity tensor have opposite signs. In this work, based on the permeability tensor we proposed theoretically and verified 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 were studied. As the frequency increased, the mode order decreased, which is markedly different from traditional cavities. It was also possible to realize size-independent cavity modes based on the HMMs by design. In addition, by considering a composite structure that contained two hyperbolic cavities, the coupling of two hyperbolic cavity modes in the near-field regime was demonstrated. The circuit-based hyperbolic cavities not only extended 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.

中文翻译：

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基于电路的磁双曲腔

光学谐振腔在电磁波控制中起着重要作用。它们可以限制电磁波并改善光与物质之间的相互作用。然而，由于法布里-珀罗（Fabry-Perot）型共振的驻波形成条件的限制，使用传统材料形成的光学共振腔的小型化是困难的。最近，基于电双曲线超材料（HMM）证明了三维光学谐振腔的小型化。它们的等频轮廓（IFC）采用开放双曲面的形式，因为介电常数张量的主要成分具有相反的符号。在这项工作中，我们基于磁导率张量在理论上提出并通过实验验证了具有亚波长尺度的平面双曲磁腔$（\lambda /12）\times （\lambda /17）$在微波状态下使用基于电路的HMM。此外，研究了基于电路的磁双曲腔中的反常缩放定律。随着频率增加，模式阶数减小，这与传统腔明显不同。通过设计，还可以基于HMM实现尺寸无关的腔模。另外，通过考虑包含两个双曲腔的复合结构，证明了在近场状态下两个双曲腔模式的耦合。基于电路的双曲腔不仅将先前关于双曲腔的研究扩展到磁性HMM，而且它们还具有易于集成且损耗较小的平面结构。最后，双曲腔可以使其在某些与微波相关的应用中使用，