Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws

Metamaterials allow for extraordinary electromagnetic properties that are not attainable in nature(1-9). Indefinite media with hyperbolic dispersion, in particular, have found intriguing applications(10-13). The miniaturization of optical cavities increases the photon density of states and therefore enhances light-matter interactions for applications in modern optoelectronics. However, scaling down the optical cavity is limited to the diffraction limit and by the reduced quality factor. Here, we experimentally demonstrate an optical cavity made of indefinite metamaterials that confines the electromagnetic field to an extremely small space. The experiments reveal that indefinite cavities demonstrate anomalous scaling laws: cavities with different sizes can resonant at the same frequency, and a higher-order resonance mode oscillates at a lower frequency. We also demonstrate a universal fourth power law for the radiation quality factor of the wave vector. Cavities with sizes down to lambda/12 are realized with ultrahigh optical indices (up to 17.4), a feature that is critically important for many applications(14-18).