Photonic Wannier-Stark Ladder from Coupled Electromagnetic Cavities

Abstract

We have investigated the photonic Wannier-Stark ladder in the system of coupled electromagnetic cavities, which consists of a stack of metallic plates structured with subwavelength apertures and where the tilted potential effect is mimicked by imposing the gradient variation of refractive index. Making an analogy to its quantum counterpart and assuming the translational property of its solutions, we have shown the photonic ladder has the eigenenergies, that is, frequencies, in a geometrical series. Within the approximation of small gradient, the ladder states manifest the equidistant frequency spacing in the spectrum. By both analytical derivation and numerical simulation, we have illustrated the geometrically progressed energies of the photonic Wannier-Stark ladder.