Optical resonances and angular filtering functionality of subwavelength hyperbolic etalons

We show that a slab of subwavelength thickness can exhibit etalon resonances and can provide angular filtering functionality at optical wavelengths if it is filled by an anisotropic medium whose principal permittivities have different signs (hyperbolic medium) and have amplitudes smaller than one. This is possible since extraordinary plane waves hyperbolic dispersion allows the vacuum radiation to couple with medium plane waves whose longitudinal wavenumbers are sufficiently large to allow the settlement of standing waves within the nanometric slab thickness. We consider a mixture of metal nanoparticles dispersed within a liquid crystal matrix and we show that it can be designed to exhibit the considered unusual optical response.