Direction-dependent elastic properties and phononic behavior of PMMA/BaTiO3 nanocomposite thin films.

Determination of the anisotropic mechanical properties of nanostructured hybrid films is of great importance to improve fabrication and to enable reliable utility. Here, we employ spontaneous Brillouin light spectroscopy to record the phononic dispersion relation along the two symmetry directions in a supported PMMA (poly(methylmethacrylate))-BaTiO3 hybrid superlattice (SL) with a lattice constant of about 140 nm. Several dispersive elastic modes are resolved for in-plane wave propagation, whereas along the periodicity direction the SL opens a wide propagation stop band for hypersonic phonons and near UV photons both centered at about 280 nm. A thorough theoretical analysis based on the finite element method quantitatively captures the band diagrams along the two main symmetry directions, helps identify the large density mismatch effect on the unexpectedly low sound phase velocity, and reveals significant anisotropy of the SL elastic tensor. Phonon propagation is a sensitive index of the structure, density, and the mechanical moduli of nanocomposite films.

Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs.

We discuss the simultaneous existence of phononic and photonic band gaps in a periodic array of holes drilled in a Si membrane. We investigate in detail both the centered square lattice and the boron nitride (BN) lattice with two atoms per unit cell which include the simple square, triangular and honeycomb lattices as particular cases. We show that complete phononic and photonic band gaps can be obtained from the honeycomb lattice as well as BN lattices close to honeycomb. Otherwise, all investigated structures present the possibility of a complete phononic gap together with a photonic band gap of a given symmetry, odd or even, depending on the geometrical parameters.

Surface acoustic waves in one-dimensional piezoelectric-metallic phononic crystal: Effect of a cap layer.

We study the propagation of transverse acoustic waves associated with the surface of a semi-infinite superlattice (SL) composed of piezoelectric-metallic layers and capped with a piezoelectric layer. We present closed-form expressions for localized surface waves, the so-called Bleustein-Gulyaev (BG) waves depending on whether the cap layer is open-circuited or short-circuited. These expressions are obtained by means of the Green's function method which enables to deduce also the densities of states. These theoretical results are illustrated by a few numerical applications to SLs made of piezoelectric layers of hexagonal symmetry belonging to the 6 mm class such as PZT4 and ZnO in contact with metallic layers such as Fe, Al, Au, Cu and boron-doped-diamond. We demonstrate a rule about the existence of surface modes when considering two complementary semi-infinite SLs obtained by the cleavage of an infinite SL along a plane parallel to the piezoelectric layers. Indeed, when the surface layers are open-circuited, one obtains one surface mode per gap, this mode is associated with one of the two complementary SLs. However, when the surface layers are short-circuited, this rule is not fulfilled and one can obtain 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. We show that in addition to the BG surface waves localized at the surface of the cap layer, there may exist true guided waves and pseudo-guided waves (i.e. leaky waves) induced by the cap layer either inside the gaps or inside the bands of the SL respectively. Also, we highlight the possibility of existence of interface modes between the SL and a cap layer as well as an interaction between these modes and the BG surface mode when both modes fall in the same band gaps of the SL. The strength of the interaction depends on the width of the cap layer. Finally, we show that the electromechanical coupling coefficient (ECC) is very sensitive to the cap layer thickness, in particular we calculate and discuss the behavior of the ECC as a function of the adlayer thickness for the low velocity surface modes of the SL which exhibit the highest ECC values. The effect of the nature of the metallic layers inside the SL on the ECC is also investigated. The different surface modes discussed in this work should have applications in sensing applications.

Two types of modes in finite size one-dimensional coaxial photonic crystals: general rules and experimental evidence.

We demonstrate analytically and experimentally the existence and behavior of two types of modes in finite size one-dimensional coaxial photonic crystals 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 by gap associated to either one or the other of the two surfaces surrounding the structure. The latter modes are independent of N . These results generalize our previous findings on the existence of surface modes in two semi-infinite superlattices obtained from the cleavage of an infinite superlattice between two cells. 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.

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.

Propagation and localization of electromagnetic waves in quasiperiodic serial loop structures.

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.

Bulk and surface acoustic waves in solid-fluid Fibonacci layered materials.

We study theoretically the propagation and localization of acoustic waves in quasi-periodic structures made of solid and fluid layers arranged according to a Fibonacci sequence. We consider two types of structures: either a given Fibonacci sequence or a periodic repetition of a given sequence called Fibonacci superlattice. Various properties of these systems such as: the scaling law and the self-similarity of the transmission spectra or the power law behavior of the measure of the energy spectrum have been highlighted for waves of sagittal polarization in normal and oblique incidence. In addition to the allowed modes which propagate along the system, we study surface modes induced by the surface of the Fibonacci superlattice. In comparison with solid-solid layered structures, the solid-fluid systems exhibit transmission zeros which can break the self-similarity behavior in the transmission spectra for a given sequence or induce additional gaps other than Bragg gaps in a periodic structure.

Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials.

We theoretically investigate the photonic band structure of one-dimensional superlattices composed of alternating layers of right-handed and left-handed materials (RHM and LHM). The dispersion curves are mainly studied by assuming that the dielectric permittivity and magnetic permeability are constant in each layer. It is shown that such structures can exhibit new types of electromagnetic modes and dispersion curves that do not exist in usual superlattices composed only of RHM. In particular, we emphasize the possibility of bands that originate from the interface modes localized at the boundary between a LHM and RHM or from confined modes in one type of layers. These waves are evanescent in both or in one constituent of the superlattice. One of the pass bands may lie below the light lines of the constituting material and go down to the static limit of a vanishing frequency omega, even at a value of the wave vector k(//) (parallel to the layers) that is different from zero. For a given value of the wave vector k(//), the dispersion curves omega versus k(z) (where k(z) is the Bloch wave vector of the periodic system along the axis of the superlattice) may exist only in a limited part of the superlattice Brillouin zone and exhibit a zigzag behavior instead of a monotonic behavior as in usual superlattices. With an appropriate choice of the parameters, we show that it is possible to realize an absolute (or omnidirectional) band gap for either transverse electric (TE) or transverse magnetic (TM) polarization of the electromagnetic waves. A combination of two multilayer structures composed of RHM and LHM is proposed to realize, in a certain range of frequency, an omnidirectional reflector of light for both polarizations.