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.

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M. Kieliszczyk, B. Janaszek, A. Tyszka-Zawadzka, and P. Szczepański, "Mode coupling in graphene-based hyperbolic metamaterial waveguides," Proc. SPIE 10719, Metamaterials, Metadevices, and Metasystems 2018, 107192L (Presented at SPIE Nanoscience + Engineering: August 23, 2018; Published: 27 September 2018); https://doi.org/10.1117/12.2321015.