E H El Boudouti

Propagation and localization of acoustic waves in Fibonacci phononic circuits

A theoretical investigation is made of acoustic wave propagation in one-dimensional 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 diameter-modulated 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 diameter-modulated 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.

Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides

The photonic band structures and transmission spectra of serial loop structures (SLSs), made of loops pasted together with segments of finite length, are investigated experimentally and theoretically. These monomode structures, composed of one-dimensional dielectric materials, may exhibit large stop bands where the propagation of electromagnetic waves is forbidden. The width of these band gaps depends on the geometrical and compositional parameters of the structure and may be drastically increased in a tandem geometry made up of several successive SLSs which differ in their physical characteristics. These SLSs may have potential applications as ultrawide-band filters.

Large omnidirectional band gaps and selective transmission in one-dimensional multilayer photonic structures

It has been shown that a one-dimensional periodic structure such as a superlattice can exhibit the property of omnidirectional reflection, which means that any incident wave launched from the vacuum (or from a substrate) will undergo a total reflection at the superlattice boundary, whatever the incident angle or the polarization of light is. In this communication, we show that large omnidirectional band gaps can be obtained by associating two or several superlattices in tandem. We discuss the existence conditions for these gaps as compared to the usual case of a binary superlattice. By introducing a defect layer in the finite layered structure, one can obtain localized modes inside these omnidirectional band gaps, giving rise to the selective transmission through the structure. These modes appear as peaks in the transmission spectrum with a very high quality factor, and therefore may have useful applications in the frame of photonic band-gap materials.

Localized and resonant acoustic modes in semi-infinite superlattices

Abstract We investigate the existence of localized and resonant acoustic modes associated with the surface of a semi- infinite superlattice or its interface with a substrate, considering the case of shear horizontal vibrations. These modes appear as well-defined peaks of the density of states, either inside the minigaps or inside the bulk bands of the superlattice. The density of states, which are calculated as functions of the frequency ω and the wave vector k ∥ (parallel to the interfaces), are obtained from an analytic determination of the Green function for a semi-infinite superlattice with or without a cap layer, as well as for a superlattice in contact with a substrate. Besides, we show that the creation from the infinite superlattice of a free surface or of the substrate-superlattice interface gives rise to δ peaks of weight 1 4 in the density of states, at the edges of the superlattice bulk bands. Finally it will be emphasized that the same calculations can be transposed to the study of the electronic structure of superlattices in the Kronig-Penney model, or to the propagation of polaritons.

Surface states in one-dimensional photonic band gap structures

We study, both theoretically and experimentally, the existence and behavior of surface localized modes in a one-dimensional (1D) comblike photonic band gap structure. The structure is composed of a waveguide, along which dangling side branches are grafted periodically. We demonstrate a theoretical rule about the existence of surface states in such 1D periodic structures; namely, when one considers together two semi-infinite structures obtained by cutting an infinite one along a plane perpendicular to the axis of the structure, one always has as many localized surface states as minigaps. We propose an original method to observe the surface modes, namely, by measuring the transmission through a guide along which a finite comb is attached vertically. The surface modes of the comb are obtained as maxima or minima of the transmission spectrum. The experiments are performed by using coaxial cables in the frequency range of a few hundred MHz.

Guided acoustic waves of an adlayer deposited on a superlattice

We show that the degree of localization of guided acoustic modes associated with an adlayer can be increased if the substrate is a superlattice instead of being a homogeneous medium. This is due to the existence of minigaps, and also of two types of polarization for the minibands, which may prohibit the propagation of these modes into the superlattice. As a consequence, the experimental observation of the pseudo-guided modes induced by the adlayer can become possible, or at least facilitated. To demonstrate theoretically this new idea, we study the localized and resonant modes of an adlayer deposited on a superlattice which are obtained as well-defined peaks of the total and local density of states, calculated by means of a Greens function method.

Electronic surface states in GaAs/Ga1 − xAlxAs superlattice: effect of surface location

Abstract Two Green function techniques (the direct matching formalism and the interface response theory) are used to investigate the electronic structure of a semi-infinite GaAs/Ga1 − xAlxAs superlattice being in contact with a Ga1 − yAlyAs substrate. The effect of the superlattice termination on the formation of a surface state as well as on the density-of-states distributions is studied in a systematic way by varying the position of the superlattice surface (i.e. substrate/superlattice interface) within a superlattice period. It has been found that the occurrence, the position and the localization properties of surface states are very sensitive to the way the superlattice is terminated—they occur in particular mini-gaps only for some ranges of the outermost layer thickness. When this thickness is close to the value at which surface states merge into the mini-bands, the density-of-states distributions exhibit the most pronounced modifications.

Sharp resonant phonons in two adsorbed slabs

The existence of sharp resonant phonons in a slab separated from its semi-infinite substrate by a buffer layer is reported here. These resonant phonons appear as well-defined peaks in the phonon density of states. Such sharp resonant phonons are obtained here by a Greens function method both in the continuum elastic and in atomic approaches.

The influence of capping layers on surface phonon polaritons in superlattices

The influence of capping layers on surface phonon polaritons in two-layer superlattices is investigated here theoretically. General analytical expressions are given. A few illustrative applications are presented afterwards, for p-polarized non-retarded polaritons within GaAs-InAs superlattices with or without an InP capping layer. A few dispersion curves for such polaritons are drawn. The variation of the frequencies of these polaritons with the thickness of the capping layer is given.

Resonant guided elastic waves in an adsorbed slab: theoretical analysis of the density of states

An isolated elastic slab presents an infinite number of guided vibrational modes. Upon its adsorption on a semi-infinite substrate some of them become resonant with the bulk modes of the substrate. Such resonances were initially studied by Brillouin and by inelastic helium-atom scattering. We present here an exact method for obtaining the total vibrational density of states of the adsorbed slab. This method is then applied to isotropic elastic media and gives a semi-analytical expression for the vibrational density of states. Detailed analysis for an Al slab on a W substrate and vice versa shows that the resonant modes appear in general as well defined peaks in the total density of states. The position of these peaks enables us to study the speed of the resonant modes as a function of the thickness of the slab or of the propagation vector parallel to the surface.