  We give a solution to the fundamental problem of restoring optical resonances
in deep subwavelength structures by resorting to indefinite metamaterials. We
prove that a nanometric thick hyperbolic slab with very small permittivities
exhibits etalon resonances and provides high-contrast optical angular
filtering. This is possible since the hyperbolic dispersion allows the vacuum
radiation to couple with medium plane waves with longitudinal wavenumbers large
enough to yield optical standing waves within the nanometric slab thickness.
Our findings can form the basis of a novel way for shrinking optical devices
down to the deep subwavelength scale.
