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Plasmonic interpretation of bulk propagating waves in hyperbolic metamaterial optical waveguides.

Hyperbolic metamaterials (HMMs) show great promise in photonics applications because their unconventional open isofrequency surface permits enlargement of wavenumbers without limitation. Although optical behaviors in HMMs can be macroscopically described by theoretical calculations with the effective medium approximation (EMA), neglect of microscopic phenomena in each layer leads to discrepancies from exact numerical results. We clarify the origin of bulk propagating waves in HMMs and we show that they can be classified into two modes: long- and short-range surface-plasmon-based coupled modes (LRSP and SRSP, respectively). Especially, we find that the ratio of the number of LRSP and SRSP couplings dominates the property of each propagation mode. This plasmonic interpretation bridges the gap between the EMA and numerical exact solutions, thereby facilitating studies on HMM applications.