Succinct formulas for decomposition of complex refraction angle

When a plane wave is incident on an interface between two different media, reflection and refraction will occur. For dissipative media, the refraction angle will be complex, which means that the constant-phase plane will depart from the constant-amplitude plane. This article gives an explicit physical illustration, and presents a more succinct formulas of aspect angle of constant-phase plane compared with the existed results. For the case of a total reflection, this article also shows how to decompose the complex angle and analyzes the influence of the loss in medium.