Determining energy flow propagation direction of transmitted wave at an active medium-vacuum interface

By simultaneously considering the real valued boundary conditions and Poynting theorem, time dependent Poynting flows of reflected and transmitted waves at an active medium-vacuum interface are determined uniquely. Then propagation direction of the transmitted wave is given according to its time averaged Poynting flow. Numerical simulations demonstrate that, at a high gain or loss active medium-vacuum interface, significant difference between electric and magnetic damping angle may induce energy flow propagation direction of the transmitted wave to deviate strongly away from that obtained by the usual Snell's law and to arise negative refraction generally. Our work provides a convenient way to address problems of reflection and refraction at an active media-vacuum interface.