Solution to causality paradox upon total reflection

Abstract

A dispute about the existence of an additional time (named as the Goos-Hänchen time) associated with the Goos-Hänchen shift in total reflection has recently arisen. At the same time, an inconsistency between the optical ray model and the electromagnetic theory also appears in the optical planar waveguide. By analyzing light propagation in an optical planar waveguide with both the zigzag-ray model and the electromagnetic theory, this paper shows that the Goos-Hänchen time really exists, and the total time delay upon total reflection upon an ideal nonabsorbing plasma mirror is the sum of the group-delay time and the Goos-Hänchen time. The causality paradox of total reflection of a TM wave upon an ideal nonabsorbing plasma mirror is also solved taking into consideration the negative Goos-Hänchen shift. Finally, the expression of the group velocity of the guided mode in optical planar waveguide was obtained, which clearly shows that the time delay upon total reflection is the sum of the group-delay time and the Goos-Hänchen time at given any time.