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