Effects of losses on the transmission and reflection of electromagnetic waves at the interface of metamaterial with zero real part of permittivity

Abstract

Electromagnetic wave refraction and reflection at the interface between vacuum and lossy metamaterial with zero real part of permittivity are analytically described by macroscopic classical electrodynamics. The analytical model is based on exact solutions of electromagnetic boundary problems. We have good reason to believe that in lossy metamaterial with zero real part of permittivity, the values of the magnetic field and energy flow are nonzero due to the crucial role of losses in epsilon-near-zero metamaterials. It is shown that the significant transmission of waves occurs for almost all incident angles. Moreover, the transmission coefficient increases with increasing loss for TE and TM wave polarizations. Numerical results are presented to show that the optical characteristics of waves at the interface of the metamaterial are highly sensitive to the losses and polarization of waves. The effect of the losses is most pronounced for transverse electric waves. The main contribution of this article is the characterization of the role of losses in the optical properties of epsilon-near-zero metamaterials that differs from some analogs known in the literature.