A note on Snell laws for electromagnetic plane waves in lossy media

Based on Maxwell's equations and Ohm's law, we rederived the Snell laws for reflection and transmission of harmonic inhomogeneous plane electromagnetic (EM) waves propagating through planar lossy interfaces. The present results are new, simple and exact and they recover the ordinary Snell laws in the case of lossless media. Besides, these results show that the wave propagation direction strongly depends on the polarization state of the EM wave and the lossy media can behave as a polarizing device. Moreover, we verify that in low frequency regime these traveling waves do not exhibit total internal reflection at interfaces between two adjacent lossy media.