Transmission properties in lossy single-negative materials

We theoretically investigate the transmission properties at an interface between a dielectric and a lossy single-negative (SNG) material. The transmission property is specifically investigated in the refractive angle calculated by the inhomogeneous wave theory. With the existence of a loss in an SNG material, the calculated refractive angle can be negative. That is, the negative refraction phenomenon, which is an important consequence in a double-negative (DNG) material, can also be found in an SNG material. We analyze the refractive angle as functions of the angle of incidence, the wave frequency, and the loss. For the epsilon-permittivity SNG material, the frequency-dependent negative refractive angle is shown to possess a critical frequency at which the absolute value in the negative refractive angle attains a maximum.