12 - Serial Loop Structures: Photonic Bandgaps, Confined, Cavity, and Surface Modes
Résumé
In this chapter, we investigate the electromagnetic band structure, transmission, phase time, as well as confined and surface modes in a one-dimensional photonic structure made of loops pasted together with segments of finite length. In this serial loop structure, the loops and segments are constituted of dielectric monomode materials. Analytic expressions are reported for the band structure for a large number N of loops and for transmission coefficients and phase times with and without defect for any value of N. Experimental and numerical results show the existence of large gaps in these homogeneous structures. These gaps originate both from the periodicity of the system and the loop resonant states. The gap widths depend on the finite segment lengths and the loop diameters. Defect modes may occur in these bandgaps by introducing defective segments in these structures. The localized states appear as very narrow peaks both in the transmission spectrum and in the transmission phase time of finite serial loop structure (SLS). The localized state behavior is analyzed in terms of the length and position of the defect segment. The transmission phase measurements enable us to derive the density of states in these structures depending on whether the SLS exhibits or not transmission zeros. In addition, we demonstrate analytically and experimentally the existence and behavior of two types of modes in finite size SLS made of N cells with vanishing magnetic field on both sides. We highlight the existence of N-1 confined modes in each band and one mode per gap associated to either one or the other of the two surfaces surrounding the structure. The latter modes are independent of N. For such structures, N confined loop modes exist also, when their wavelength is commensurable with the two loop lengths defined by the loop connections. These modes form a flat band. When the above condition is not fulfilled, these N modes become usually one almost-flat band. There exist also two degenerate modes of zero frequency: ground state and invariant by translation state. The analytical results are obtained by means of the Green's function method, whereas the experiments are carried out using coaxial cables in the radio-frequency regime.