Propagation of electromagnetic waves in periodic and Fibonacci photonic loop structures

We investigate theoretically and experimentally the propagation of electromagnetic waves in one-dimensional periodic and quasi-periodic photonic band gap structures made of serial loop structures separated by segments. The quasi-periodic structures are ordered according to a Fibonacci sequence constituted of two blocks A and B where each block is composed of a loop attached to a segment. It is demonstrated that the general trend of the transmission spectrum of the Fibonacci structure may be considered as an intermediate spectrum between those corresponding to the periodic structures composed of only blocks A or only blocks B. In particular, besides the existence of extended and forbidden modes, some narrow frequency bands appear in the transmission spectra inside the gaps as defect modes. These modes are shown to be localized only within one of the two blocks constituting the structure. A numerical analysis of the transmission phase time enables us to derive the group velocity as well as the density of states in these structures. In particular, the localized modes may give rise to a strong normal dispersion in the gap, giving rise to a slow group velocity below the normal propagation speed in the coaxial cables. The dependence of the band gap structure on the lengths of the finite segment and the loop diameter is presented. The experimental results are obtained using coaxial cables in the frequency range of few hundreds of MHz. These results are in very good agreement with theoretical prediction using Green's function method. The scaling property has been checked theoretically in the case where the absorption in the cables is neglected.