Propagation of plane waves and of waveguide modes in quasiperiodic dielectric heterostructures

We study the propagation of electromagnetic waves in one-dimensional quasiperiodic systems and its dispersion relation for plane waves and for waveguide structures. In the photonic band gaps, periodic, Fibonacci, and Thue-Morse multilayer systems can be described by a complex effective wave vector. Its negative imaginary part causes an exponential decay of the transmission coefficient due to a distributed quasitotal reflection. Its real part is independent of frequency, so that the phase time becomes independent of the system size. This time alternates between two distinct values and approximately equals the Büttiker-Landauer tunneling time. Superluminal group velocities are obtained for the propagation of narrow frequency band wave packets. The effective complex wave vector results from multiple reflections of oscillating propagating waves. For both the plane wave and the waveguide dispersion the most ordered structures exhibit the most effective coherent interference and thus the deepest gaps in the transmission spectra as well as the smallest decay length. The Thue-Morse sequence is less ordered than the Fibonacci one, which in turn is less ordered than the periodic system. Increasing disorder enhances the phase time, the Büttiker-Landauer time, and the density of states in the gap regions. The group velocity becomes smaller, but still remains superluminal. The spectra of λ/4 systems are similar for both the plane-wave and the waveguide dispersion. The Fibonacci scaling relation has been checked. It holds for a periodicity of 6, whereas the claimed periodicity of 3 has found to be not valid in general.