No abstract

Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices.

Quantum emitters embedded in arbitrarily shaped epsilon-near-zero cavities can selectively excite both nonradiating and radiating modes.

Analytical and equivalent circuit models are presented to elucidate the balance of powers in scattering processes. Specifically, closed-form expressions of the associated maximal extracted, scattered, absorbed and reactive powers are formulated. The circuit model then helps to characterize in a straightforward manner these powers, to provide physical insights into the inter-relationships among this set, and thus guides the resolution of their fundamental limits. The analysis demonstrates that the absorbed power can not exceed 25% of the power extracted from the incident field (extracted power) for the lossless case and helps extricate the conditions for which the scattered and absorbed powers are equal or significantly different. A coated sphere illuminated by a plane wave under both resonant and cloaked states is selected as an illustrative example. Although the analysis and circuit models are rigorously derived for spheroidal particles, their extrapolation to arbitrary scatterers is also discussed.