Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials

Architecture Controls Phonon Propagation in All-Solid Brush Colloid Metamaterials

Brillouin light scattering and elastodynamic theory are concurrently used to determine and interpret the hypersonic phonon dispersion relations in brush particle solids as a function of the grafting density with perspectives in optomechanics, heat management, and materials metrology. In the limit of sparse grafting density, the phonon dispersion relations bear similarity to polymer-embedded colloidal assembly structures in which phonon dispersion can be rationalized on the basis of perfect boundary conditions, i.e., isotropic stiffness transitions across the particle interface. In contrast, for dense brush assemblies, more complex dispersion characteristics are observed that imply anisotropic stiffness transition across the particle/polymer interface. This provides direct experimental validation of phonon propagation changes associated with chain conformational transitions in dense particle brush materials. A scaling relation between interface tangential stiffness and crowding of polymer tethers is derived that provides a guideline for chemists to design brush particle materials with tailored phononic dispersion characteristics. The results emphasize the role of interfaces in composite materials systems. Given the fundamental relevance of phonon dispersion to material properties such as thermal transport or mechanical properties, it is also envisioned that the results will spur the development of novel functional hybrid materials.

Tunable Hypersonic Bandgap Formation in Anisotropic Crystals of Dumbbell Nanoparticles

Phononic materials exhibit mechanical properties that alter the propagation of acoustic waves and are widely useful for metamaterials. To fabricate acoustic materials with phononic bandgaps, colloidal nanoparticles and their assemblies allow access to various crystallinities in the submicrometer scale. We fabricated anisotropic crystals with dumbbell-shaped nanoparticles via field-directed self-assembly. Brillouin light spectroscopy detected the formation of direction-dependent hypersonic phononic bandgaps that scale with the lattice parameters. In addition, the local resonances of the constituent nanoparticles enable metamaterial behavior by opening hybridization gaps in disordered structures. Unexpectedly, this bandgap frequency is robust to changes in the dumbbell aspect ratio. Overall, this study provides a structure-property relationship for designing anisotropic phononic materials with targeted phononic bandgaps.

Lifting restrictions on coherence loss when characterizing non-transparent hypersonic phononic crystals

Hypersonic phononic bandgap structures confine acoustic vibrations whose wavelength is commensurate with that of light, and have been studied using either time- or frequency-domain optical spectroscopy. Pulsed pump-probe lasers are the preferred instruments for characterizing periodic multilayer stacks from common vacuum deposition techniques, but the detection mechanism requires the injected sound wave to maintain coherence during propagation. Beyond acoustic Bragg mirrors, frequency-domain studies using a tandem Fabry–Perot interferometer (TFPI) find dispersions of two- and three-dimensional phononic crystals (PnCs) even for highly disordered samples, but with the caveat that PnCs must be transparent. Here, we demonstrate a hybrid technique for overcoming the limitations that time- and frequency-domain approaches exhibit separately. Accordingly, we inject coherent phonons into a non-transparent PnC using a pulsed laser and acquire the acoustic transmission spectrum on a TFPI, where pumped appear alongside spontaneously excited (i.e. incoherent) phonons. Choosing a metallic Bragg mirror for illustration, we determine the bandgap and compare with conventional time-domain spectroscopy, finding resolution of the hybrid approach to match that of a state-of-the-art asynchronous optical sampling setup. Thus, the hybrid pump–probe technique retains key performance features of the established one and going forward will likely be preferred for disordered samples.

Multiband Hypersound Filtering in Two-Dimensional Colloidal Crystals: Adhesion, Resonances, and Periodicity

The hypersonic phonon propagation in large-area two-dimensional colloidal crystals is probed by spontaneous micro Brillouin light scattering. The dispersion relation of thermally populated Lamb waves reveals multiband filtering due to three distinct types of acoustic band gaps. We find Bragg gaps accompanied by two types of hybridization gaps in both sub- and superwavelength regimes resulting from contact-based resonances and nanoparticle eigenmodes, respectively. The operating GHz frequencies can be tuned by particle size and depend on the adhesion at the contact interfaces. The experimental dispersion relations are well represented by a finite element method model enabling identification of observed modes. The presented approach also allows for contactless study of the contact stiffness of submicrometer particles, which reveals size effect deviating from macroscopic predictions.

Longitudinal eigenvibration of multilayer colloidal crystals and the effect of nanoscale contact bridges

Longitudinal contact-based vibrations of colloidal crystals with a controlled layer thickness are studied. These crystals consist of 390 nm diameter polystyrene spheres arranged into close packed, ordered lattices with a thickness of one to twelve layers. Using laser ultrasonics, eigenmodes of the crystals that have out-of-plane motion are excited. The particle-substrate and effective interlayer contact stiffnesses in the colloidal crystals are extracted using a discrete, coupled oscillator model. Extracted stiffnesses are correlated with scanning electron microscope images of the contacts and atomic force microscope characterization of the substrate surface topography after removal of the spheres. Solid bridges of nanometric thickness are found to drastically alter the stiffness of the contacts, and their presence is found to be dependent on the self-assembly process. Measurements of the eigenmode quality factors suggest that energy leakage into the substrate plays a role for low frequency modes but is overcome by disorder- or material-induced losses at higher frequencies. These findings help further the understanding of the contact mechanics, and the effects of disorder in three-dimensional micro- and nano-particulate systems, and open new avenues to engineer new types of micro- and nanostructured materials with wave tailoring functionalities via control of the adhesive contact properties.

Zero-frequency and slow elastic modes in phononic monolayer granular membranes

We theoretically study the dispersion properties of elastic waves in hexagonal and honeycomb monolayer granular membranes with either out-of-plane or in-plane particle motion. The particles interact predominantly via normal and transverse contact rigidities. When rotational degrees of freedom are taken into account, the bending and torsional rigidities of the intergrain contacts can control some of the phononic modes. The existence of zero-frequency modes, zero-group-velocity modes and their transformation into slow propagating phononic modes due to weak bending and torsional intergrain interactions are investigated. We also study the formation and manipulation of Dirac cones and multiple degenerated modes. This could motivate variety of potential applications in elastic waves control by manipulating the contact rigidities in granular phononic crystals.

Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves

Contact-based vibrations play an essential role in the dynamics of granular materials. Significant insights into vibrational granular dynamics have previously been obtained with reduced-dimensional systems containing macroscale particles. We study contact-based vibrations of a two-dimensional monolayer of micron-sized spheres on a solid substrate that forms a microscale granular crystal. Measurements of the resonant attenuation of laser-generated surface acoustic waves reveal three collective vibrational modes that involve displacements and rotations of the microspheres, as well as interparticle and particle-substrate interactions. To identify the modes, we tune the interparticle stiffness, which shifts the frequency of the horizontal-rotational resonances while leaving the vertical resonance unaffected. From the measured contact resonance frequencies we determine both particle-substrate and interparticle contact stiffnesses and find that the former is an order of magnitude larger than the latter. This study paves the way for investigating complex contact-based dynamics of microscale granular crystals and yields a new approach to studying micro- to nanoscale contact mechanics in multiparticle networks.

Anti-plane transverse waves propagation in nanoscale periodic layered piezoelectric structures

In this paper, anti-plane transverse wave propagation in nanoscale periodic layered piezoelectric structures is studied. The localization factor is introduced to characterize the wave propagation behavior. The transfer matrix method based on the nonlocal piezoelectricity continuum theory is used to calculate the localization factor. Additionally, the stiffness matrix method is applied to compute the wave transmission spectra. A cut-off frequency is found, beyond which the elastic waves cannot propagate through the periodic structure. The size effect or the influence of the ratio of the internal to external characteristic lengths on the cut-off frequency and the wave propagation behavior are investigated and discussed.

Coherent Acoustic Phonons in Colloidal Semiconductor Nanocrystal Superlattices

The phonon properties of films fabricated from colloidal semiconductor nanocrystals play a major role in thermal conductance and electron scattering, which govern the principles for building colloidal-based electronics and optics including thermoelectric devices with a high ZT factor. The key point in understanding the phonon properties is to obtain the strength of the elastic bonds formed by organic ligands connecting the individual nanocrystallites. In the case of very weak bonding, the ligands become the bottleneck for phonon transport between infinitively rigid nanocrystals. In the opposite case of strong bonding, the colloids cannot be considered as infinitively rigid beads and the distortion of the superlattice caused by phonons includes the distortion of the colloids themselves. We use the picosecond acoustics technique to study the acoustic coherent phonons in superlattices of nanometer crystalline CdSe colloids. We observe the quantization of phonons with frequencies up to 30 GHz. The frequencies of quantized phonons depend on the thickness of the colloidal films and possess linear phonon dispersion. The measured speed of sound and corresponding wave modulus in the colloidal films point on the strong elastic coupling provided by organic ligands between colloidal nanocrystals.

Towards GHz-THz cavity optomechanics in DBR-based semiconductor resonators

Resonators based on acoustic distributed Bragg reflectors (DBRs) were optimized to work in the GHz-THz regime, and grown by molecular beam epitaxy. We show that in structures made of GaAlAs alloys a simultaneous optimal confinement of light in the visible range and phonons in the tens of GHz range can be achieved. We report time resolved differential optical reflectivity experiments performed with fs-ps laser pulses. The experimental results are in excellent agreement with simulations based on standard transfer matrix methods. The resonant behavior of the photoelastic coefficient is discussed. The perfect optic-acoustic mode overlapping, added to a strongly enhanced coupling mechanism, implies that these DBR-based cavities could be the base of highly efficient optomechanical resonators.

Fundamentals of picosecond laser ultrasonics

The aim of this article is to provide an introduction to picosecond laser ultrasonics, a means by which gigahertz-terahertz ultrasonic waves can be generated and detected by ultrashort light pulses. This method can be used to characterize materials with nanometer spatial resolution. With reference to key experiments, we first review the theoretical background for normal-incidence optical detection of longitudinal acoustic waves in opaque single-layer isotropic thin films. The theory is extended to handle isotropic multilayer samples, and is again compared to experiment. We then review applications to anisotropic samples, including oblique-incidence optical probing, and treat the generation and detection of shear waves. Solids including metals and semiconductors are mainly discussed, although liquids are briefly mentioned.

Anisotropic hypersonic phonon propagation in films of aligned ellipsoids

A material with anisotropic elastic mechanical properties and a direction-dependent hypersonic band gap is fabricated using ac electric field-directed convective self-assembly of colloidal ellipsoids. The frequency of the gap, which is detected in the direction perpendicular to particle alignment and entirely absent parallel to alignment, and the effective sound velocities can be tuned by the particle aspect ratio. We hypothesize that the band gap originates from the primary eigenmode peak, the m-splitted (s,1,2) mode, of the particle resonating with the effective medium. These results reveal the potential for powerful control of the hypersonic phononic band diagram by combining anisotropic particles and self-assembly.

Lasing from active optomechanical resonators

Planar microcavities with distributed Bragg reflectors (DBRs) host, besides confined optical modes, also mechanical resonances due to stop bands in the phonon dispersion relation of the DBRs. These resonances have frequencies in the 10- to 100-GHz range, depending on the resonator's optical wavelength, with quality factors exceeding 1,000. The interaction of photons and phonons in such optomechanical systems can be drastically enhanced, opening a new route towards the manipulation of light. Here we implemented active semiconducting layers into the microcavity to obtain a vertical-cavity surface-emitting laser (VCSEL). Thereby, three resonant excitations--photons, phonons and electrons--can interact strongly with each other providing modulation of the VCSEL laser emission: a picosecond strain pulse injected into the VCSEL excites long-living mechanical resonances therein. As a result, modulation of the lasing intensity at frequencies up to 40 GHz is observed. From these findings, prospective applications of active optomechanical resonators integrated into nanophotonic circuits may emerge.

Transforming wave propagation in layered media via instability-induced interfacial wrinkling

The ability to control wave propagation in highly deformable layered media with elastic instability-induced wrinkling of interfacial layers is presented. The onset of a wrinkling instability in initially straight interfacial layers occurs when a critical compressive strain is achieved. Further compression beyond the critical strain leads to an increase in the wrinkle amplitude of the interfacial layer. This, in turn, gives rise to the formation of a system of periodic scatterers, which reflect and interfere with wave propagation. We demonstrate that the topology of wrinkling interfacial layers can be controlled by deformation and used to produce band gaps in wave propagation and, hence, to selectively filter frequencies. Remarkably, the mechanism of frequency filtering is effective even for composites with similar or identical densities, such as polymer-polymer composites. Since the microstructure change is reversible, the mechanism can be used for tuning and controlling wave propagation by deformation.

Sound and heat revolutions in phononics

The phonon is the physical particle representing mechanical vibration and is responsible for the transmission of everyday sound and heat. Understanding and controlling the phononic properties of materials provides opportunities to thermally insulate buildings, reduce environmental noise, transform waste heat into electricity and develop earthquake protection. Here I review recent progress and the development of new ideas and devices that make use of phononic properties to control both sound and heat. Advances in sonic and thermal diodes, optomechanical crystals, acoustic and thermal cloaking, hypersonic phononic crystals, thermoelectrics, and thermocrystals herald the next technological revolution in phononics.

Three-dimensional dielectric phoxonic crystals with network topology

We theoretically demonstrate the existence of simultaneous large complete photonic and phononic bandgaps in three-dimensional dielectric phoxonic crystals with a simple cubic lattice. These phoxonic crystals consist of dielectric spheres on the cubic lattice sites connected by thin dielectric cylinders. The simultaneous photonic and phononic bandgaps can exist over a wide range of geometry parameters. The vibration modes corresponding to the phononic bandgap edges are the local torsional resonances of the dielectric spheres and rods. Detailed discussion is presented on the variation of the photonic and phononic bandgaps with the geometry of the structure. Optimal geometry which generates large phoxonic bandgaps is suggested.

Experimental evidence of rotational elastic waves in granular phononic crystals

A generalized theory of elasticity, taking into account the rotational degrees of freedom of point bodies constituting a continuum, was proposed at the beginning of the twentieth century by the Cosserat brothers. We report the experimental observation of coupled rotational-translational modes in a noncohesive granular phononic crystal. While absent in the classical theory of elasticity, these elastic wave modes are predicted by the Cosserat theory. However the Cosserat theory fails to predict correctly the dispersion of the elastic modes in granular crystals even in the long-wavelength limit.

Ultrafast vibrations of gold nanorings

We investigate the vibrational modes of gold nanorings on a silica substrate with an ultrafast optical technique. By comparison with numerical simulations, we identify several resonances in the gigahertz range associated with axially symmetric deformations of the nanoring and substrate. We elucidate the corresponding mode shapes and find that the substrate plays an important role in determining the mode damping. This study demonstrates the need for a plasmonic nano-optics approach to understand the optical excitation and detection mechanisms for the vibrations of plasmonic nanostructures.

Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs

We demonstrate theoretically that photons and acoustic phonons can be simultaneously guided and slowed down in specially designed nanostructures. Phoxonic crystal waveguides presenting simultaneous phononic and photonic band gaps were designed in perforated silicon membranes that can be conveniently obtained using silicon-on-insulator technology. Geometrical parameters for simultaneous photonic and phononic band gaps were first chosen for optical wavelengths around 1550 nm, based on the finite element analysis of a perfect phoxonic crystal of circular holes. A plain core waveguide was then defined, and simultaneous slow light and elastic guided modes were identified for some waveguide width. Joint guidance of light and elastic waves is predicted with group velocities as low as c/25 and 180 m/s, respectively.

Collective hypersonic excitations in strongly multiple scattering colloids

Unprecedented low-dispersion high-frequency acoustic excitations are observed in dense suspensions of elastically hard colloids. The experimental phononic band structure for SiO(2) particles with different sizes and volume fractions is well represented by rigorous full-elastodynamic multiple-scattering calculations. The slow phonons, which do not relate to particle resonances, are localized in the surrounding liquid medium and stem from coherent multiple scattering that becomes strong in the close-packing regime. Such rich phonon-matter interactions in nanostructures, being still unexplored, can open new opportunities in phononics.

Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap

A fully planar two-dimensional optomechanical crystal formed in a silicon microchip is used to create a structure devoid of phonons in the GHz frequency range. A nanoscale photonic crystal cavity is placed inside the phononic bandgap crystal in order to probe the properties of the localized acoustic modes. By studying the trends in mechanical damping, mode density, and optomechanical coupling strength of the acoustic resonances over an array of structures with varying geometric properties, clear evidence of a complete phononic bandgap is shown.

Trapping and releasing light by mechanical implementation in metamaterial waveguides

We show that light trapping and releasing can be switched by a mechanic tuning effect in metamaterial waveguides. The transition mechanism between the trapping and releasing states relies on the synergetic effect of the local Bragg reflection and cavity resonance in the waveguides. As a proof-of-concept demonstration, a heterostructured metamaterial waveguide comprised of dielectric claddings and a tapered metamaterial core formed by arrays of metal slats is analytically and numerically investigated. The spatial separation of the trapped light with various frequencies and the transition between the trapping and releasing states can be predicted by a "rainbow equation." The proposed light trapping and releasing scheme based on the mechanical implementation of waveguide geometrical parameters can be exploited to develop opto-mechanical devices for slow light technology.

Dynamic self-assembly and control of microfluidic particle crystals

Engineered two-phase microfluidic systems have recently shown promise for computation, encryption, and biological processing. For many of these systems, complex control of dispersed-phase frequency and switching is enabled by nonlinearities associated with interfacial stresses. Introducing nonlinearity associated with fluid inertia has recently been identified as an easy to implement strategy to control two-phase (solid-liquid) microscale flows. By taking advantage of inertial effects we demonstrate controllable self-assembling particle systems, uncover dynamics suggesting a unique mechanism of dynamic self-assembly, and establish a framework for engineering microfluidic structures with the possibility of spatial frequency filtering. Focusing on the dynamics of the particle-particle interactions reveals a mechanism for the dynamic self-assembly process; inertial lift forces and a parabolic flow field act together to stabilize interparticle spacings that otherwise would diverge to infinity due to viscous disturbance flows. The interplay of the repulsive viscous interaction and inertial lift also allow us to design and implement microfluidic structures that irreversibly change interparticle spacing, similar to a low-pass filter. Although often not considered at the microscale, nonlinearity due to inertia can provide a platform for high-throughput passive control of particle positions in all directions, which will be useful for applications in flow cytometry, tissue engineering, and metamaterial synthesis.

Dispersion of elastic waves in three-dimensional noncohesive granular phononic crystals: properties of rotational modes

The dispersion relations of bulk modes propagating within a hexagonal close-packed structure of noncohesive monodisperse spherical elastic beads are derived. The contacts are modeled by two springs with stiffnesses given by the Hertz-Mindlin theory, one for normal interactions and one for transverse interactions. The existence of the transverse interaction requires to take into account the rotational degrees of freedom of the beads in the analysis. This leads to the prediction of translational modes and, due to the rotational degrees of freedom, of rotational modes and coupled rotational and translational modes. The study of the dispersion relations in a direction of high symmetry allows to identify the different modes and the influence of the rotational degrees of freedom on the bulk mode propagation. The evaluated dispersion relations provide guidelines for the experimental observation of rotational modes. Opportunities for controlling the dispersion laws of the modes by an external loading on the granular structure are discussed.

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.

Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs

We demonstrate planar structures that can provide simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical (or phoxonic) crystal slabs. Different phoxonic crystal (PxC) structures, composed of square, hexagonal (honeycomb), or triangular arrays of void cylindrical holes embedded in silicon (Si) slabs with a finite thickness, are investigated. Photonic band gap (PtBG) maps and the complete phononic band gap (PnBG) maps of PxC slabs with different radii of the holes and thicknesses of the slabs are calculated using a three-dimensional plane wave expansion code. Simultaneous phononic and photonic band gaps with band gap to midgap ratios of more than 10% are shown to be readily obtainable with practical geometries in both square and hexagonal lattices, but not for the triangular lattice.

Filtering of elastic waves by opal-based hypersonic crystal

We report experiments in which high quality silica opal films are used as three-dimensional hypersonic crystals in the 10 GHz range. Controlled sintering of these structures leads to well-defined elastic bonding between the submicrometer-sized silica spheres, due to which a band structure for elastic waves is formed. The sonic crystal properties are studied by injection of a broadband elastic wave packet with a femtosecond laser. Depending on the elastic bonding strength, the band structure separates long-living surface acoustic waves with frequencies in the complete band gap from bulk waves with band frequencies that propagate into the crystal leading to a fast decay.

One-dimensional hypersonic phononic crystals

We report experimental observation of a normal incidence phononic band gap in one-dimensional periodic (SiO(2)/poly(methyl methacrylate)) multilayer film at gigahertz frequencies using Brillouin spectroscopy. The band gap to midgap ratio of 0.30 occurs for elastic wave propagation along the periodicity direction, whereas for inplane propagation the system displays an effective medium behavior. The phononic properties are well captured by numerical simulations. The porosity in the silica layers presents a structural scaffold for the introduction of secondary active media for potential coupling between phonons and other excitations, such as photons and electrons.

Elastic waves in noncohesive frictionless granular crystals

An ordered structure of noncohesive spherical beads constitutes a phononic crystal. This type of media combines the properties of wave propagation in phononic crystals (dispersion due to the geometrical periodicity) with the properties of wave propagation in granular media (nonlinearities, rotational degree of freedom) and gives the opportunity to have interesting features as tunable frequency band gaps for example. In this work, the acoustic bulk modes of a hexagonal close packed (hcp) structure of beads, considered as rigid masses connected by springs, are theoretically evaluated and their associated resonance frequencies are compared to experimental results. When friction is neglected, the elastic interaction between the beads are reduced to a normal spring interaction given by the Hertz theory. According to this theory, the rigidity of the contact depends on its static loading. The theory predicts the existence of elastic transverse and longitudinal acoustical-type modes and transverse and longitudinal optical-type modes. The acoustic transfer function of a hcp crystal slab built with stainless steel beads is measured and its resonance frequencies are compared to the theoretical predictions. Despite some differences between theory and experiments, which could come for instance from the disordered character of the contact loads, the developed theory and the experimental results show relatively good agreement.

Reverse and enhanced magneto-optics of opal-garnet heterostructures

Magnetophotonic heterostructures comprising two thin opal films and a layer of bismuth-substituted yttrium iron garnet were fabricated. Such heterostructures combined properties of 1D, 2D and 3D photonic crystals. Their spectra demonstrated various optical resonances resulting in reverse and enhanced magneto-optical responses.

The "music" of core-shell spheres and hollow capsules: influence of the architecture on the mechanical properties at the nanoscale

We report on the first measurement of elastic vibrational modes in core-shell spheres (silica-poly(methyl methacrylate), SiO2-PMMA) and corresponding spherical hollow capsules (PMMA) with different particle size and shell thickness using Brillouin light scattering, supported by numerical calculations. These localized modes allow access to the mechanical moduli down to a few tens of nanometers. We observe reduced mechanical strength of the porous silica core, and for the core-shell spheres a striking increase of the moduli in both the SiO2 core and the PMMA shell. The peculiar behavior of the vibrational modes in the hollow capsules is attributed to antagonistic dependence on overall size and layer thickness in agreement with theoretical predictions.