We study theoretically and experimentally the existence and behavior of the localized surface modes in one-dimensional ͑1D͒ quasiperiodic photonic band gap structures. These structures are made of segments and loops arranged according to a Fibonacci sequence. The experiments are carried out by using coaxial cables in the frequency region of a few tens of MHz. We consider 1D periodic structures ͑superlattice͒ where each cell is a well-defined Fibonacci generation. In these structures, we generalize a theoretical rule on the surface modes, namely when one considers two semi-infinite superlattices obtained by the cleavage of an infinite superlattice, it exists exactly one surface mode in each gap. This mode is localized on the surface either of one or the other semi-infinite superlattice. We discuss the existence of various types of surface modes and their spatial localization. The experimental observation of these modes is carried out by measuring the transmission through a guide along which a finite superlattice ͑i.e., constituted of a finite number of quasiperiodic cells͒ is grafted vertically. The surface modes appear as maxima of the transmission spectrum. These experiments are in good agreement with the theoretical model based on the formalism of the Green function.

A theoretical investigation is made of acoustic wave propagation in onedimensional phononic bandgap structures made of slender tube loops pasted together with slender tubes of finite length according to a Fibonacci sequence. The band structure and transmission spectrum is studied for two particular cases. (i) Symmetric loop structures, which are shown to be equivalent to diametermodulated slender tubes. In this case, it is found that besides the existence of extended and forbidden modes, some narrow frequency bands appear in the transmission spectra inside the gaps as defect modes. The spatial localization of the modes lying in the middle of the bands and at their edges is examined by means of the local density of states. The dependence of the bandgap structure on the slender tube diameters is presented. An 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 stop bands (localized modes) may give rise to unusual (strong normal) dispersion in the gaps, yielding fast (slow) group velocities above (below) the speed of sound. (ii) Asymmetric tube loop structures, where the loops play the role of resonators that may introduce transmission zeros and hence new gaps unnoticed in the case of simple diametermodulated slender tubes. The Fibonacci scaling property has been checked for both cases (i) and (ii), and it holds for a periodicity of three or six depending on the nature of the substrates surrounding the structure.

We study the propagation of electromagnetic waves in one-dimensional quasiperiodic photonic band gap structures made of serial loop structures separated by segments. Different quasiperiodic structures such as Fibonacci, Thue-Morse, Rudin-Shapiro, and double period are investigated with special focus on the Fibonacci structure. Depending on the lengths of the two arms constituting the loops, one can distinguish two particular cases. (i) There are symmetric loop structures, which are shown to be equivalent to impedance-modulated mediums. In this case, it is found that besides the existence of extended and forbidden modes, some narrow frequency bands appear as defect modes in the transmission spectrum inside the gaps. These modes are shown to be localized within only one of the two types of blocks constituting the structure. An 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 stop bands (localized modes) may give rise to unusual (strong normal) dispersion in the gaps, yielding fast (slow) group velocities above (below) the velocity of light. (ii) There are also asymmetric loop structures, where the loops play the role of resonators that may introduce transmission zeros and hence additional gaps unnoticed in the case of simple impedance-modulated mediums. A comparison of the transmission amplitude and phase time of Fibonacci systems with those of other quasiperiodic systems is also outlined. In particular, it was shown that these structures present similar behaviors in the transmission spectra inside the regions of extended modes, whereas they present different localized modes inside the gaps. Experiments and numerical calculations are in very good agreement.

Using a Green's function method, we present a comprehensive theoretical analysis of the propagation of sagittal acoustic waves in superlattices ͑SLs͒ made of alternating elastic solid and ideal fluid layers. This structure may exhibit very narrow pass bands separated by large stop bands. In comparison with solid-solid SLs, we show that the band gaps originate both from the periodicity of the system ͑Bragg-type gaps͒ and the transmission zeros induced by the presence of the solid layers immersed in the fluid. The width of the band gaps strongly depends on the thickness and the contrast between the elastic parameters of the two constituting layers. In addition to the usual crossing of subsequent bands, solid-fluid SLs may present a closing of the bands, giving rise to large gaps separated by flat bands for which the group velocity vanishes. Also, we give an analytical expression that relates the density of states and the transmission and reflection group delay times in finite-size systems embedded between two fluids. In particular, we show that the transmission zeros may give rise to a phase drop of in the transmission phase, and therefore, a negative delta peak in the delay time when the absorption is taken into account in the system. A rule on the confined and surface modes in a finite SL made of N cells with free surfaces is demonstrated, namely, there are always N-1 modes in the allowed bands, whereas there is one and only one mode corresponding to each band gap. Finally, we present a theoretical analysis of the occurrence of omnidirectional reflection in a layered media made of alternating solid and fluid layers. We discuss the conditions for such a structure to exhibit total reflection of acoustic incident waves in a given frequency range for all incident angles. Also, we show how this structure can be used as an acoustic filter that may transmit selectively certain frequencies within the omnidirectional gaps. In particular, we show the possibility of filtering assisted either by cavity modes ͑in particular sharp Fano resonances͒ or by interface resonances.

We study the propagation of acoustic waves associated with the surface of a semi-infinite superlattice ͑SL͒ consisting of alternating elastic solid and ideal fluid layers or its interface with a semi-infinite fluid. We present closed-form expressions for localized surface and interface waves depending on whether the SL is terminated with a fluid layer or a solid layer. We also calculate the corresponding Green's function and densities of states. These general results are illustrated by a few applications to periodic Plexiglas-water and Al-water SLs. In the case of a fluid layer termination, we generalize a rule obtained previously about the existence and behavior of surface waves in the case of pure transverse or longitudinal waves in solid-solid SLs, namely ͑i͒ the creation from the infinite SL of a free surface gives rise to ␦ peaks of weight ͑−1/4͒ in the density of states, at the edges of the SL bulk bands, ͑ii͒ by considering together the two complementary semi-infinite SLs obtained by the cleavage of an infinite SL along a plane lying within the fluid layer and parallel to the interfaces, one always has as many localized surface modes as minigaps, for any value of the wave vector k ʈ ͑parallel to the interfaces͒. However, this rule is not fulfilled when the cleavage is carried out inside the solid layer. Indeed, in this case, the dispersion curves may present zero, one, or two modes inside each gap of the two complementary SLs depending on the position of the plane where the cleavage is produced. Finally, we investigate the localized and resonant modes associated with the presence of a fluid cap layer made of mercury, with finite or semi-infinite extent, on top of the above-mentioned SLs. Different guided modes induced by the adsorbed fluid layer are obtained and their properties are investigated.