The time-dependent energy-flux pattern in total reflection of a pulsed light beam

For total reflection of a pulsed light beam at the interface between vacuum and a negative permittivity medium, the electromagnetic fields and the associated energy-flux patterns in the two media are investigated analytically and numerically. For a TE (transverse electric) polarized pulsed beam with positive Goos–Hänchen shift, energy reflection occurs not only in the second medium but also in the first medium because of interference between the incident and reflected fields. However, for TM (transverse magnetic) polarization where the Goos–Hänchen shift is negative, reflection of energy flux occurs in the first medium (or in front of the interface). At the same time, the energy flux around the interface forms time-dependent loops which absorb energy from the incoming flux in the front edge of the pulse but release energy into the outgoing flux in the later edge of the pulse to ensure energy conservation. Therefore, the so-called causality paradox in TM polarization is caused by the fact that interference between incident and reflected fields in the first medium and energy-flux loops around the interface offer a shorter path for reflection of energy flux (or photons). (paper)