V.R. Velasco

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.

Thomas–Fermi–Dirac theory of the hole gas of a double p-type δ-doped GaAs quantum wells

We present the hole subband structure of two coupled p-type d-doped GaAs quantum wells as a function of the impurity concentration and the distance l between them, including exchange effects. We present an analytical expression for the Hartree–Fock potential as a function of these two magnitudes, by using the Thomas–Fermi–Dirac approximation. The numerical results for a double Be-d-doped GaAs quantum well show that many body effects are important when the concentration is low and the energy levels are degenerate for l P 100 � and an impurity concentration of 5 · 10 12 cm � 2 , while without exchange effects the energy levels are degenerated for l P 150 � and the same impurity concentration. We present an expression for the relative electronic mobility, that is, we calculate the ratio of the electronic mobility of a double d-doped quantum well and that of a simple d-doped quantum well. The theoretical results agree quite well with the experimental data available. � 2003 Elsevier Science B.V. All rights reserved.

Surface and interface shear horizontal acoustic waves in piezoelectric superlattices

The propagation of acoustic waves of shear horizontal polarization in infinite and semi-infinite superlattices made of two piezoelectric media is studied within a Green’s function method. Localized modes induced by a free surface of the superlattice or a superlattice/substrate interface are investigated theoretically. These modes appear as well-defined peaks of the total density of states inside the minigaps of the superlattice. The spatial localization of the different modes is studied by means of the local density of states. The surface of the superlattice and the superlattice/substrate interface are considered to be either metallized or nonmetallized. We show the possibility of the existence of interface modes, which are without analogue in the case of the interface between two homogeneous media (the so-called Maerfeld–Tournois modes). We also generalize to piezoelectric superlattices a rule about the existence and number of surface states, namely when one considers two semi-infinite superlattices toge...

Dynamics of surfaces with overlayers

Abstract Waves, in two interfaces (A-B-C) systems are analysed in terms of elastic Green functions mainly in the case of very thin medium B. The theory is applied to study a thin overlayer on a semi-infinite substrate where the dispersion relations of the localized eigenmodes are obtained in closed form. The effects of the overlayer on the substrate atoms mean square displacements and on the energy of interaction of point defects with surfaces are derived in closed form. The long wavelength limit of an atomic model is also studied. Identification of the results obtained for the overlayers by the two, elastic and atomic, approaches yields some simple relations between their parameters.

Omnidirectional phononic reflection and selective transmission in one-dimensional acoustic layered structures

Abstract We report the theoretical evidence for the occurrence of omnidirectional reflection in one-dimensional phononic crystal structures, namely, a layered periodic structure that may exhibit total reflection of waves for all incident angles and polarizations in a given frequency range “the omnidirectional band gap”. By introducing a defect layer in the finite-size layered structure, selective waves falling within this omnidirectional band gap may be transmitted through the structure. Such acoustic materials could be used for designing high-quality acoustic mirrors and filters in many frequency ranges of interest.

Optical properties of (001) GaN/AlN quantum wells

Abstract The absorption coefficient and the photoluminescence of (001) GaN/AlN quantum wells are calculated for several values of the well width, with and without the excitonic effect corrections, in the usual monoelectronic approach and as a many-body problem. The calculation was performed considering separate isolated bands for electrons, heavy and light holes. The monoelectronic approach to the optical properties was performed by assuming infinite well walls and finite well walls, respectively. The calculation including the excitonic effect as a many-body problem was performed within a recent approach designed for low-dimensional systems. The different wells studied here present many localized states and a complicated absorption spectrum. The monoelectronic approach in the infinite quantum well approximation reproduces quite well the spectrum of the wide wells due to the fact that the ground states of electrons and holes are well fixed by this model of quantum well.

Application of the phase time and transmission coefficients to the study of transverse elastic waves in quasiperiodic systems with planar defects

Abstract We study the transverse elastic waves in quasiperiodic structures by means of the transmission/reflection phase times and the corresponding transmission/reflection coefficients. We see that these concepts are powerful tools to study multilayer systems, besides the frequency spectrum. We study how the presence of planar defects in quasiperiodic Fibonacci and Rudin–Shapiro sequences strongly modify the phase times and transmission coefficient, and not only the frequency spectrum of the systems.

Interface-phonon-limited two-dimensional mobility in AlGaN∕GaN heterostructures

The room temperature polar-optical-phonon-limited two-dimensional electron mobility in AlxGa1−xN∕GaN heterostructures is calculated taking into account the interaction of conduction electrons and interface-phonon modes. The polar optical oscillations are described via the uniaxial dielectric continuum model. Electron–polar-optical-phonon scattering rates are evaluated from a general expression that is always valid as long as the interaction Hamiltonian matrix elements depend only on the magnitude of the phonon wave vector. Values for the 300K low-field mobility (μ) of a few hundreds cm2∕Vs are obtained within a simplified relaxation time scheme involving electron-phonon absorption scattering rates. It is found that the way of describing the electronic states in the conduction band strongly affects the calculation of μ. The typical triangular well model gives the poorest results compared with a previously proposed analytical approximation of the conduction band potential profile. We present a discussion on...

Electronic Properties of Fibonacci Quasi‐Periodic Heterostructures

We study the electronic states of GaAs-AlAs Fibonacci heterostructures grown along the (001) direction. We employ an empirical tight-binding Hamiltonian including spin-orbit coupling together with the surface Greens function matching method. We present results for the L point of the finite eighth Fibonacci generation. We compare these results with those of the constituent quantum wells. No Fibonacci spectrum is found in the energy regions studied, but broad bands with different spatial localization in different energy ranges.

Electromagnetic wave propagation in quasi-periodic photonic circuits

We study theoretically and experimentally the properties of quasiperiodic one-dimensional serial loop structures made of segments and loops arranged according to a Fibonacci sequence (FS). Two systems are considered. (i) By inserting the FS horizontally between two waveguides, we give experimental evidence of the scaling behaviour of the amplitude and the phase of the transmission coefficient. (ii) By grafting the FS vertically along a guide, we obtain from the maxima of the transmission coefficient the eigenmodes of the finite structure (assuming the vanishing of the magnetic field at the boundaries of the FS). We show that these two systems (i) and (ii) exhibit the property of self-similarity of order three at certain frequencies where the quasiperiodicity is most effective. In addition, because of the different boundary conditions imposed on the ends of the FS, we show that horizontal and vertical structures give different information on the localization of the different modes inside the FS. Finally, we show that the eigenmodes of the finite FS coincide exactly with the surface modes of two semi-infinite superlattices obtained by the cleavage of an infinite superlattice formed by a periodic repetition of a given FS.