Discussion of the Epsilon-Near-Zero Effect of Graphene in a Horizontal Slot Waveguide

Horizontal slot waveguides based on graphene have been considered an attractive structure for optical waveguide modulators for transverse magnetic (TM) modes. Graphene is embedded in the slot region of a horizontal slot waveguide. If graphene were treated as an isotropic material and its dielectric constant were made close to zero by adjusting its Fermi level, the surface-normal electric field component of the fundamental TM mode of a horizontal slot waveguide might be highly enhanced in graphene. This could cause a large increase in the attenuation coefficient of the mode. This is called the epsilon-near-zero (ENZ) effect. This paper discusses that graphene needs to be treated as an anisotropic material that has an almost real surface-normal dielectric constant component. Then, the ENZ effect does not exist. Approximate analytic expressions and numerical simulation are used for the discussion, and they demonstrate that horizontal slot waveguides are not appropriate for graphene-based modulators for TM modes.