Elastic wave propagation in smooth and wrinkled stratified polymer films.

Periodic materials with sub-micrometer characteristic length scale can provide means for control of propagation of hypersonic phonons. In addition to propagation stopbands for the acoustic phonons, distinct dispersive modes can reveal specific thermal and mechanical behavior under confinement. Here, we employ both experimental and theoretical methods to characterize the phonon dispersion relation (frequency versus wave vector). We employed Brillouin light scattering (BLS) spectroscopy to record the phonon dispersion in stratified multilayer polymer films. These films consist of 4-128 alternate polycarbonate (PC) and poly (methyl methacrylate) (PMMA) layers along and normal to the periodicity direction. The distinct direction-dependent phonon propagation was theoretically accounted for, by considering the polarization, frequency and intensity of the observed modes in the BLS spectra. Layer-guiding was also supported by the glass transition temperatures of the PC and PMMA layers. The number of phonon dispersion branches increased with the number of layers but only a few branches were observable by BLS. Introduction of an additional in-plane periodicity, through a permanent wrinkling of the smooth PC/PMMA films, had only subtle consequences in the phonon propagation. Using the frequencies of the periodicity induced modes and momentum conservation equation we were able to precisely back calculate the wrinkle periodicity. However, a wrinkling-induced acoustic stopband utilizing flexible layered materials is still a challenge.

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.

Monolithic phononic crystals with a surface acoustic band gap from surface phonon-polariton coupling.

We theoretically and experimentally demonstrate the existence of complete surface acoustic wave band gaps in surface phonon-polariton phononic crystals, in a completely monolithic structure formed from a two-dimensional honeycomb array of hexagonal shape domain-inverted inclusions in single crystal piezoelectric Z-cut lithium niobate. The band gaps appear at a frequency of about twice the Bragg band gap at the center of the Brillouin zone, formed through phonon-polariton coupling. The structure is mechanically, electromagnetically, and topographically homogeneous, without any physical alteration of the surface, offering an ideal platform for many acoustic wave applications for photonics, phononics, and microfluidics.

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.

Anisotropic propagation and confinement of high frequency phonons in nanocomposites.

We show that self-ordered anodic aluminum oxide containing hexagonal arrays of cylindrical nanopores with submicron periodicity is a versatile model system for the exploration of rich phononic phenomena at gigahertz frequencies, which are intimately linked to fluids located in the nanopores and their interactions with the pore walls. Using high-resolution Brillouin spectroscopy we report the first realization of directional flow of elastic energy parallel and perpendicular to the pore axes, phonon localization, and tunability of the phononic band structure.

Low-power phonon lasing through position-modulated Kerr-type nonlinearity.

We demonstrate low-power amplification process in cavity optomechanics (COM). This operation is based on the nonlinear position-modulated self-Kerr interaction. Owing to this nonlinear term, the effective coupling highly scales with the photon number, resulting in a giant enhancement of the cooperativity. Even for small nonlinearity, the system reaches the amplification threshold for weak driving strength, leading to low-power phonon lasing. This amplifier can be phase-preserving and provides a practical advantage related to the power consumption issues. This work opens up new avenues to perform low-power and efficient amplifiers in optomechanics and related fields.

Robustness of elastic properties in polymer nanocomposite films examined over the full volume fraction range.

Polymers with nanoparticle inclusions are attractive materials because physical properties can be tuned by varying size and volume fraction range. However, elastic behavior can degrade at higher inclusion fractions when particle-particle contacts become important, and sophisticated measurement techniques are required to study this crossover. Here, we report on the mechanical properties of materials with BaTiO3 nanoparticles (diameters < 10 nm) in a polymer (poly(methyl methacrylate)) matrix, deposited as films in different thickness ranges. Two well-known techniques, time and frequency domain Brillouin light scattering, were employed to probe the composition dependence of their elastic modulus. The time domain experiment revealed the biphasic state of the system at the highest particle volume fraction, whereas frequency domain Brillouin scattering provided comprehensive information on ancillary variables such as refractive index and directionality. Both techniques prove complementary, and can in particular be used to probe the susceptibility of elastic properties in polymer nanocomposites to aging.

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.

Numerical emulation of Thru-Reflection-Line calibration for the de-embedding of Surface Acoustic Wave devices.

In this contribution, a rigorous numerical calibration is proposed to characterize the excitation of propagating mechanical waves by interdigitated transducers (IDTs). The transition from IDT terminals to phonon waveguides is modeled by means of a general circuit representation that makes use of Scattering Matrix (SM) formalism. In particular, the three-step calibration approach called the Thru-Reflection-Line (TRL), that is a well-established technique in microwave engineering, has been successfully applied to emulate typical experimental conditions. The proposed procedure is suitable for the synthesis/optimization of surface-acoustic-wave (SAW) based devices: the TRL calibration allows to extract/de-embed the acoustic component, namely resonator or filter, from the outer IDT structure, regardless of complexity and size of the letter. We report, as a result, the hybrid scattering parameters of the IDT transition to a mechanical waveguide formed by a phononic crystal patterned on a piezoelectric AlN membrane, where the effect of a discontinuity from periodic to uniform mechanical waveguide is also characterized. In addition, to ensure the correctness of our numerical calculations, the proposed method has been validated by independent calculations.

Multicoaxial cylindrical inclusions in locally resonant phononic crystals.

It is known that the transmission spectrum of the so-called locally resonant phononic crystal can exhibit absolute sharp dips in the sonic frequency range due to the resonance scattering of elastic waves. In this paper, we study theoretically, using a finite difference time domain method, the propagation of acoustic waves through a two-dimensional locally resonant crystal in which the matrix is a fluid (such as water) instead of being a solid as in most of the previous papers. The transmission is shown to be dependent upon the fluid or solid nature of the matrix as well as upon the nature of the coating material in contact with the matrix. The other main purpose of this paper is to consider inclusions constituted by coaxial cylindrical multilayers consisting of several alternate shells of a soft material (such as a soft rubber) and a hard material (such as steel). With respect to the usual case of a hard core coated with a soft rubber, the transmission spectrum can exhibit in the same frequency range several peaks instead of one. If two or more phononic crystals are associated together, we find that the structure displays all the zeros of transmission resulting from each individual crystal. Moreover, we show that it is possible to overlap the dips by an appropriate combination of phononic crystals and create a larger acoustic stop band.

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.

Directional elastic wave propagation in high-aspect-ratio photoresist gratings: liquid infiltration and aging.

Determination of the mechanical properties of nanostructured soft materials and their composites in a quantitative manner is of great importance to improve the fidelity in their fabrication and to enable the subsequent reliable utility. Here, we report on the characterization of the elastic and photoelastic parameters of a periodic array of nanowalls (grating) by the non-invasive Brillouin light scattering technique and finite element calculations. The resolved elastic vibrational modes in high and low aspect ratio nanowalls reveal quantitative and qualitative differences related to the two-beam interference lithography fabrication and subsequent aging under ambient conditions. The phononic properties, namely the dispersion relations, can be drastically altered by changing the surrounding material of the nanowalls. Here we demonstrate that liquid infiltration turns the phononic function from a single-direction phonon-guiding to an anisotropic propagation along the two orthogonal directions. The susceptibility of the phononic behavior to the infiltrating liquid can be of unusual benefits, such as sensing and alteration of the materials under confinement.

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.

Omnidirectional elastic band gap in finite lamellar structures.

This paper presents a comprehensive theoretical analysis of the occurrence of omnidirectional reflection in one-dimensional phononic crystal structures. We discuss the conditions for a one-dimensional layered structure, made of elastic materials, to exhibit total reflection of acoustic incident waves in a given frequency range, for all incident angles and all polarizations. The property of omnidirectional reflection can be fulfilled with a simple finite superlattice if the substrate from which the incident waves are launched is made of a material with high acoustic velocities (this is very similar to the case of omnidirectional optical mirror where the incident light is generated in vacuum). However, if the substrate is made of a material with low acoustic velocities, we propose two solutions to obtain an omnidirectional band gap, namely, the cladding of a superlattice with a layer of high acoustic velocities, which acts like a barrier for the propagation of phonons, or the association in tandem of two different superlattices in such a way that the superposition of their band structures exhibits an absolute acoustic band gap. We discuss the appropriate choices of the material and geometrical properties to realize such structures. The behavior of the transmission coefficients are discussed in relation with the dispersion curves of the finite structure embedded between two substrates. Both transmission coefficients and densities of states (from which we derive the dispersion curves) are calculated in the framework of a Green's function method.

Guided elastic waves along a rod defect of a two-dimensional phononic crystal.

It was shown that elastic waves propagating out-of-plane in a two-dimensional phononic crystal can experience full-band-gaps for nonzero values of the wave-vector component parallel to the rods. By further inserting a rod defect, it is demonstrated that modes propagating along the rod defect can be localized within the band-gaps of the phononic crystal. Such waveguide modes are exhibited for a tungsten/epoxy composite containing an aluminum nitride rod as the rod defect. It is expected that guided modes of such a structure can be excited and detected electrically owing to the piezoelectric effect.

Out-of-plane propagation of elastic waves in two-dimensional phononic band-gap materials.

We have used a plane-wave-expansion model to study the out-of-plane propagation of elastic waves in a two-dimensional phononic band-gap material. The case of quartz rods embedded in an epoxy matrix has been computed. Band gaps for nonzero values of the wave-vector component parallel to the rods are shown to exist and are investigated. For wavelengths smaller than the period of the structure, modes are found that are localized in the epoxy intersites, and propagate perpendicularly to the plane of the structure.

Tunable filtering and demultiplexing in phononic crystals with hollow cylinders.

Acoustic band gap (ABG) materials constituted of steel hollow cylinders immersed in water can exhibit a tunable narrow pass band (NPB) located inside their gap. We theoretically investigate, using the finite difference time domain (FDTD) method, the properties of waveguides composed of a row of hollow cylinders in a two-dimensional (2D) phononic crystal made of filled steel cylinders. These waveguides exhibit NPB's at frequencies slightly higher than their infinite periodic ABG counterpart. The frequency of the waveguide's NPB can be selected by adjusting the inner radius of the hollow cylinders or by changing the nature of the fluid that fills them. We show that a waveguide constituted of a row of hollow cylinders with different inner radii can transport waves at two different frequencies. By selectively filling the cylinders with water or mercury we have created an active device that permits the transmission of waves at one, both, or neither of these frequencies. Finally, we examine the multiplexing and demultiplexing capabilities of Y shaped waveguides constituted of hollow cylinders.

Stopping of acoustic waves by sonic polymer-fluid composites.

A two-dimensional periodic array of air cylinders in water is known to have giant acoustic stop bands [M.S. Kushwaha and B. Djafari-Rouhani, J. Appl. Phys. 84 (1998) 4677]. It is shown in the present paper that hollow cylinders made of an elastically-soft polymer containing air inside and arranged on a square lattice in water can still give rise to large acoustic band gaps. Similar properties can also be obtained with a close-packed array of tubes containing water when arranged on a honeycomb lattice in air. The transmission coefficient of films made of such polymer-fluid composites has been calculated by finite difference time domain method. With film thickness not exceeding 75 mm, a deep sonic attenuation band was found with, in the best cases, a lower limit below 1 kHz and an upper limit above 10 kHz.