We present an extended approach towards analysis of controlled mode coupling in multi-waveguide systems based on tunable hyperbolic metamaterials (THMMs), derived from generalized reciprocity relation, suitable for lossy reciprocal anisotropic media. The expressions for overlap integrals and coupling coefficients for various waveguide systems with Type I and Type II HMM media are provided as functions of an external bias. For the first time, the application of coupled mode theory is illustrated for HMMs by example of a perturbed waveguide as well as a directional coupler, where coupling between modes and waveguides is controlled with an external voltage.
In this work we present a generalized coupled mode formulation dedicated to waveguides based on double-negative (DNG) as well as single-negative (SNG) metamaterials. Our approach is derived from generalized reciprocity relation, instead of polarization perturbation, which extends its applicability to lossy reciprocal media, including SNG materials. The coupled mode equations are established for various SNG/DNG multi-waveguide configurations and illustrated for two coupled systems based on SNG medium.