# Imaginary part of Poynting vector

When I am studying the total reflection phenomenon, I calculated the Poynting vector of the transmitted wave, which can be written as $S_t=A(k_{x}\hat{x}+i\alpha\hat{z})$ A is some constant. I choosed $z=0$ as the interface, light incident from the region $z>0$, If total reflection occurs, the z-component become imaginary, for some reference the imaginary part is regarded as "reactive power" like in AC circuit.

In Hecht's text, stated that the energy is circulating across the interface. But how can I see it from mathematical expressions?

• It is common practice to use complex amplitudes for power in the discussion of stationary sinusoidal oscillations in electrical networks. The imaginary part stands for the oscillation between capacitive and inductive energy. The natural generalization to complex Poynting vectors for sinusoidal electromagnetic waves is the oscillating energy density between the E- and the H-field (as energy density per time). If I remember right it is something like $j\omega$ times maximal stored energy density maybe times some factor $\frac12$ (field does not matter since energy oscillates between the fields). Jan 15, 2014 at 8:34