Properties of optical resonator with a layered metamaterial

The properties of longitudinal and transverse modes of an open optical resonator containing layers of a metamaterial with negative refractive index are studied. Due to the presence of these layers, the metaresonator acquires unique properties compared to a conventional open resonator. Eigenmodes of the metaresonator are studied in which the properties depend on the average dispersion and the average diffraction, which may be either positive, negative, or zero. The conditions of the existence and profiles of the waveguiding modes are obtained. The resonator with zero average diffraction is of particular interest. It is shown that, in this case, the waveguiding mode may have an arbitrary amplitude profile. Under these conditions, the discrete set of the transverse modes becomes continuous, and the eigenfrequencies become independent of the transverse amplitude profile. The resonator’s stability conditions are derived based on the ray-matrix method and diffraction theory. It is shown that insertion of a metamaterial into the resonator substantially affects the region of stability and existence of the waveguiding modes. In particular, the unstable empty resonator can thus be rendered stable.