Abstract: The electromagnetic wave after refraction can change its phase propagation direction as well as its amplitude in lossy media. Conventional textbooks usually treat the problem in terms of complex refractive angles or complex wave vectors. However, these complex concepts lack geometrical or physical significance, and the intrinsic relationship between these two treatments is less discussed. In this paper, based on the study of isotropic media，the two methods are discussed in detail and their equivalence is proved from the perspective of refraction angle and Fresnel coefficient. Numerical simulation by the finite-difference time-domain method verifies the reliability of the theoretical analysis. More interestingly, the electromagnetic wave may not change its propagation direction after oblique incidence into a lossy medium. These analyses not only provides a clear understanding of the laws of electromagnetic wave propagation in lossy media, but also helpful on the teaching of electromagnetism.

Key words: loss medium, Snell's law, complex refraction angle, complex wave vector