A Time-Domain Analysis of Enhanced Total Internal Reflection Using the FDTD Method

There is a long-standing debate surrounding whether or not enhanced total internal reflection (ETIR) is possible. ETIR implies that the magnitude of the reflection coefficient is greater than unity and is conjectured to be possible when a field is incident from a lossless material to a gainy material beyond the critical angle. In this letter, we examine this problem through finite-difference time-domain (FDTD) modeling. The two-dimensional simulations employ a Gaussian incident beam and make no a priori assumptions about the reflection coefficient. We consider illumination of gainy, lossless, and lossy materials. The Poynting vector is used to examine the flow of energy. For a gainy material, the magnitude of the reflection coefficient is found to be greater than unity, but there is a delay between when energy enters the gainy material and when the "excess" energy is reflected from the interface. Thus, given the Goos-Hanchen shift associated with total internal reflection, where the reflected beam is shifted relative to the incident beam (so that fields must travel in the gainy material before being reflected), the existence of ETIR appears not only to be plausible, but to be inevitable.