Transmission-line matrix modeling of superluminal electromagnetic-pulse tunneling through the forbidden gap in two-dimensional photonic band structures

Abstract

The transmission-line matrix (TLM) method is shown to be an effective technique for calculating the propagation of electromagnetic waves in dielectric arrays exhibiting photonic band gaps. The simulator is particularly valuable for modeling processes whose parameters of interest are intrinsically in the time domain. To illustrate the capabilities of the technique for such temporal problems, the tunneling of electromagnetic pulses through the forbidden gap of a two-dimensional dielectric array is simulated. As researchers have recently measured in one-dimensional systems, pulses tunnel with a group velocity that exceeds the speed of light in vacuum. The TLM simulations show directly that for this superluminal tunneling process the group velocity continues to be a valid descriptor of the peak of the pulse. Furthermore, the results show that once sufficient periodicity exists to create a forbidden gap the tunneling time is constant independent of the thickness of the photonic crystal through which tunneling occurs.