Three-dimensional nanometer-scale optical cavities of indefinite medium

Miniaturization of optical cavities has numerous advantages for enhancing light - matter interaction in quantum optical devices, low-threshold lasers with minimal power consumption, and efficient integration of optoelectronic devices at large scale. However, the realization of a truly nanometer-scale optical cavity is hindered by the diffraction limit of the nature materials. In addition, the scaling of the photon life time with the cavity size significantly reduces the quality factor of small cavities. Here we theoretically present an approach to achieve ultrasmall optical cavities using indefinite medium with hyperbolic dispersion, which allows propagation of electromagnetic waves with wave vectors much larger than those in vacuum enabling extremely small 3D cavity down to (λ/20) ³. These cavities exhibit size-independent resonance frequencies and anomalous scaling of quality factors in contrast to the conventional cavities, resulting in nanocavities with both high Q/V _m ratio and broad bandwidth.