We present a comprehensive analysis of the role of $\epsilon$-near-zero (ENZ) materials with realistic losses in enhanced light transmission through subwavelength channels. In this work, we utilize a bulk ENZ material consisting of heavily doped semiconductor, operating at the semiconductor's plasma frequency (in mid-infrared regime). Resonant transmission peaks for transverse magnetic polarized light have been experimentally observed when such material is used as a coupling layer and/or inside the subwavelength slit. In the process, we developed a generalized mode-matching-based approach to calculate and analyze light propagation through slits and waveguides embedded inside planar layer stacks and applied this approach to the particular case of ENZ-filled subwavelength slit. The developed formalism inherently provides the individual amplitudes of the guided modes inside the slit and their coupling efficiencies to the surrounding media. Using the calculated coupling efficiencies, we were successful in explaining the resonant transmission behavior of these structures and also were able to track the origin of enhancements. Our analysis demonstrates that in the presence of losses, the transmission efficiency is dominated by the bulk plasma resonances of the ENZ coupling layer and minimal advantage is gained by filling the slit with ENZ material. The enhancements were also observed to be dependent on the thickness of the substrate layer. Further analysis of the calculated amplitudes using the numerical algorithm developed an approximate analytical model for systems with deep subwavelength slits.

• Received 24 December 2013

DOI:https://doi.org/10.1103/PhysRevB.89.125119