Non-reciprocal and non-Newtonian mechanical metamaterials.

Non-Newtonian liquids are characterized by stress and velocity-dependent dynamical response. In elasticity, and in particular, in the field of phononics, reciprocity in the equations acts against obtaining a directional response for passive media. Active stimuli-responsive materials have been conceived to overcome it. Significantly, Milton and Willis have shown theoretically in 2007 that quasi-rigid bodies containing masses at resonance can display a very rich dynamical behavior, hence opening a route toward the design of non-reciprocal and non-Newtonian metamaterials. In this paper, we design a solid structure that displays unidirectional shock resistance, thus going beyond Newton's second law in analogy to non-Newtonian fluids. We design the mechanical metamaterial with finite element analysis and fabricate it using three-dimensional printing at the centimetric scale (with fused deposition modeling) and at the micrometric scale (with two-photon lithography). The non-Newtonian elastic response is measured via dynamical velocity-dependent experiments. Reversing the direction of the impact, we further highlight the intrinsic non-reciprocal response.

Micro-Scale Mechanical Metamaterial with a Controllable Transition in the Poisson's Ratio and Band Gap Formation.

The ability to significantly change the mechanical and wave propagation properties of a structure without rebuilding it is currently one of the main challenges in the field of mechanical metamaterials. This stems from the enormous appeal that such tunable behavior may offer from the perspective of applications ranging from biomedical to protective devices, particularly in the case of micro-scale systems. In this work, a novel micro-scale mechanical metamaterial is proposed that can undergo a transition from one type of configuration to another, with one configuration having a very negative Poisson's ratio, corresponding to strong auxeticity, and the other having a highly positive Poisson's ratio. The formation of phononic band gaps can also be controlled concurrently which can be very useful for the design of vibration dampers and sensors. Finally, it is experimentally shown that the reconfiguration process can be induced and controlled remotely through application of a magnetic field by using appropriately distributed magnetic inclusions.

3D Auxetic Metamaterials with Elastically-Stable Continuous Phase Transition.

In solid state physics, phase transitions can influence material functionality and alter their properties. In mechanical metamaterials, structural-phase transitions can be achieved through instability or buckling of certain structural elements. However, these fast transitions in one mechanical parameter typically affect significantly the remaining parameters, hence, limiting their applications. Here, this limitation is addressed by designing a novel 3D mechanical metamaterial that is capable of undergoing a phase transition from positive to negative Poisson's ratio under compression, without significant degradation of Young's modulus (i.e. the phase transition is elastically-stable). The metamaterial is fabricated by two-photon lithography at the micro-scale and its mechanical behavior is assessed experimentally. For another choice of structural parameters, it is then shown that the auxetic behavior of the considered 3D metamaterial class can be maintained over a wide range of applied compressive strain.

Brillouin Light Scattering Characterisation of Gray Tone 3D Printed Isotropic Materials.

Three-dimensional direct laser writing technology enables one to print polymer microstructures whose size varies from a few hundred nanometers to a few millimeters. It has been shown that, by tuning the laser power during writing, one can adjust continuously the optical and elastic properties with the same base material. This process is referred to as gray-tone lithography. In this paper, we characterize by Brillouin light scattering the complex elastic constant C11 of different reticulated isotropic polymers, at longitudinal phonon frequencies of the order of 16 GHz. We estimate the real part of the C11 constant to vary from 7 to 11 GPa as a function of laser power, whereas its imaginary part varies between 0.25 and 0.6 GPa. The linear elastic properties are further measured at a fixed laser power as a function of temperature, from 20∘C to 80∘C. Overall, we show that our 3D printed samples have a good elastic quality with high Q factors only ten times smaller than fused silica at hypersonic frequencies.

Single-Step-Lithography Micro-Stepper Based on Frictional Contact and Chiral Metamaterial.

Stepper motors and actuators are among the main constituents of control motion devices. They are complex multibody systems with rather large overall volume due to their multifunctional parts and elaborate technological assembly processes. Miniaturization of individual parts is still posing assembly problems. In this paper, a single-step lithography process to fabricate a micro-stepper engine with an accurate micrometric rotation axis and an overall sub-millimeter size is demonstrated. The device is based on the frictional contacts and chiral metamaterials to get rid of the dependence on the accuracy of parts. The functional aspects of fabricated samples are discussed for many rotation cycles and for different frictional surfaces.

Experimental observation of roton-like dispersion relations in metamaterials.

Previously, rotons were observed in correlated quantum systems at low temperatures, including superfluid helium and Bose-Einstein condensates. Here, following a recent theoretical proposal, we report the direct experimental observation of roton-like dispersion relations in two different three-dimensional metamaterials under ambient conditions. One experiment uses transverse elastic waves in microscale metamaterials at ultrasound frequencies. The other experiment uses longitudinal air-pressure waves in macroscopic channel­based metamaterials at audible frequencies. In both experiments, we identify the roton-like minimum in the dispersion relation that is associated to a triplet of waves at a given frequency. Our work shows that designed interactions in metamaterials beyond the nearest neighbors open unprecedented experimental opportunities to tailor the lowest dispersion branch­while most previous metamaterial studies have concentrated on shaping higher dispersion branches.

Dipole states and coherent interaction in surface-acoustic-wave coupled phononic resonators.

Manipulation of mechanical motion at the micro-scale has been attracting continuous attention, leading to the successful implementation of various strategies with potential impact on classical and quantum information processing. We propose an approach based on the interplay between a pair of localised mechanical resonators and travelling surface acoustic waves (SAW). We demonstrate the existence of a two-sided interaction, allowing the use of SAW to trigger and control the resonator oscillation, and to manipulate the elastic energy distribution on the substrate through resonator coupling. Observation of the vectorial structure of the resonator motion reveals the existence of two coupling regimes, a dipole-dipole-like interaction at small separation distance versus a surface-mediated mechanical coupling at larger separation. These results illustrate the potential of this platform for coherent control of mechanical vibration at a resonator level, and reciprocally for manipulating SAW propagation using sub-wavelength elements.

Generation of coherent acoustic beams in solids by mixing of counterpropagating, detuned optical beams [Invited].

We model the generation of coherent acoustic beams in a homogeneous solid from the interference of two oppositely propagating, detuned optical laser beams. This configuration is reciprocal to Brillouin light scattering in the backward interaction arrangement. Generation of a confined ultrasound beam is predicted, close to the Brillouin frequency. Optoacoustic gain spectra and beam shapes are obtained numerically using a finite element model. The acoustic spectra are non-symmetrical, i.e., non-Lorentzian, and result from excitation of the continuum of bulk elastic waves. The acoustic beam width correspondingly varies with detuning frequency and optical beam waist.

A differential optical interferometer for measuring short pulses of surface acoustic waves.

The measurement of the displacements caused by the propagation of a short pulse of surface acoustic waves on a solid substrate is investigated. A stabilized time-domain differential interferometer is proposed, with the surface acoustic wave (SAW) sample placed outside the interferometer. Experiments are conducted with surface acoustic waves excited by a chirped interdigital transducer on a piezoelectric lithium niobate substrate having an operational bandwidth covering the 200-400MHz frequency range and producing 10-ns pulses with 36nm maximum out-of-plane displacement. The interferometric response is compared with a direct electrical measurement obtained with a receiving wide bandwidth interdigital transducer and good correspondence is observed. The effects of varying the path difference of the interferometer and the measurement position on the surface are discussed. Pulse compression along the chirped interdigital transducer is observed experimentally.

Surface Brillouin scattering in photonic crystal fibers.

We report, to the best of our knowledge, the first experimental observation of surface Brillouin scattering in silica-based photonic crystal fibers, arising from the interaction between guided light and surface acoustic waves. This was achieved using small-core and high air-filling fraction microstructured fibers that enable a strong opto-acoustic coupling near the air holes while mitigating the acoustic leakages in the microstructured cladding. It is further shown that this new type of light scattering is highly sensitive to the fiber air-hole microstructure, thus providing a passive and efficient way to control it. Our observations are confirmed through numerical simulations of the elastodynamics equation.

Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre.

Brillouin scattering in optical fibres is a fundamental interaction between light and sound with important implications ranging from optical sensors to slow and fast light. In usual optical fibres, light both excites and feels shear and longitudinal bulk elastic waves, giving rise to forward-guided acoustic wave Brillouin scattering and backward-stimulated Brillouin scattering. In a subwavelength-diameter optical fibre, the situation changes dramatically, as we here report with the first experimental observation of Brillouin light scattering from surface acoustic waves. These Rayleigh-type surface waves travel the wire surface at a specific velocity of 3,400 m s(-1) and backscatter the light with a Doppler shift of about 6 GHz. As these acoustic resonances are sensitive to surface defects or features, surface acoustic wave Brillouin scattering opens new opportunities for various sensing applications, but also in other domains such as microwave photonics and nonlinear plasmonics.

Simultaneous bandgaps in LiNbO3 phoxonic crystal slab.

We study simultaneous photonic and phononic crystal slabs created in Z-cut lithium niobate membranes. Bandgaps for guided waves are identified using the three-dimensional finite element method (FEM). Three lattices are considered: the square, the hexagonal, and the honeycomb lattices. We investigate the evolution of band gaps as a function of geometrical parameters such as hole radius and membrane thickness. We show the existence of dual photonic and phononic bandgaps in the triangular lattice for suitable geometrical parameters and specific modal symmetries for both the elastic and the electromagnetic fields.

Reduction and control of stimulated Brillouin scattering in polymer-coated chalcogenide optical microwires.

We investigate the onset of nonlinear effects in hybrid polymer-chalcogenide optical microwires and show that they provide an enhanced Kerr nonlinearity while simultaneously mitigating stimulated Brillouin scattering as compared to both chalcogenide and silica optical fibers. It is shown in particular that the polymer cladding surrounding the microwire significantly broadens the Brillouin linewidth and increases the threshold, thus enabling Kerr nonlinear applications. We also study the influence of the wire diameter on the Brillouin dynamics and demonstrate that the Brillouin frequency shift can be finely tuned over a wide radio-frequency range.

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.

Computation of plate wave dispersion diagrams and surface wave velocities without explicit boundary conditions.

We discuss the computation of the band structure of plate waves using the plane wave expansion (PWE) method. This method is generally used to formulate eigenvalue problems to compute dispersion diagrams for solid-solid phononic crystals. We show how the free surface boundary condition can be included implicitly in the form of the PWE solution, thus leading to an efficient eigenvalue problem. This generic method for wave dispersion is non-iterative and does not require an initial guess for the solution. Furthermore, surface acoustic wave velocities can be estimated from the slowest wave for large wave vectors. Examples for a single plate and a multilayer plate are given, and extension to piezoelectric materials is discussed.

Prediction and measurement of boundary waves at the interface between LiNbO3 and silicon.

Interface acoustic waves (IAWs) propagate along the boundary between two perfectly bonded solids. For a leakage- free IAW, all displacement fields must be evanescent along the normal to the boundary inside both solids, but leaky IAWs may also exist depending on the selected combination of materials. When at least one of the bonded solids is a piezoelectric material, the IAW can be excited by an interdigital transducer (IDT) located at the interface, provided one can fabricate the transducer and access the electrical contacts. We discuss here the fabrication and characterization of IAW resonators made by indirect bonding of lithium niobate onto silicon via an organic layer. In our fabrication process, IDTs are first patterned over the surface of a Y-cut lithium niobate wafer. A thin layer of SU-8 photo-resist is then spun over the IDTs and lithium niobate to a thickness below one micrometer. The SU-8-covered lithium niobate wafer then is bonded to a silicon wafer. The stack is subsequently cured and baked to enhance the acoustic properties of the interfacial resist. Measurements of resonators are presented, emphasizing the dependence of propagation losses on the resist properties. Comparison with theoretical computations based on periodic finite element/boundary element analysis allows for explanation of the actual operation of the device.

3-D electrostatic hybrid element model for SAW interdigital transducers.

In this work, the singular behavior of charges at corners and edges on the metallized areas in SAW transducers are investigated. In particular, it is demonstrated that a tensor product of the commonly used Tchebychev bases overestimates the singularities at corners, and, hence, it cannot be used in a proper boundary element method formulation. On the other hand, it is shown that a simple finite element method-like approach is impractical due to the enormous number of unknowns required to model the electrode's large length-to-width ratio. These considerations are then used for defining a hybrid element model, which combines Tchebychev and linear polynomials over differently meshed domains. Such an approach is shown to suitably account for charge singularities while greatly reducing the number of unknowns. Results are obtained for isotropic and anisotropic substrates for non-periodic configurations.

High-frequency surface acoustic waves excited on thin-oriented LiNbO3 single-crystal layers transferred onto silicon.

The need for high-frequency, wide-band filters has instigated many developments based on combining thin piezoelectric films and high acoustic velocity materials (sapphire, diamond-like carbon, silicon, etc.) to ease the manufacture of devices operating above 2 GHz. In the present work, a technological process has been developed to achieve thin-oriented, single-crystal lithium niobate (LiNbO3) layers deposited on (100) silicon wafers for the fabrication of radio-frequency (RF) surface acoustic wave (SAW) devices. The use of such oriented thin films is expected to favor large coupling coefficients together with a good control of the layer properties, enabling one to chose the best combination of layer orientation to optimize the device. A theoretical analysis of the elastic wave assumed to propagate on such a combination of material is first exposed. Technological aspects then are described briefly. Experimental results are presented and compared to the state of art.

Guided acoustic wave Brillouin scattering in photonic crystal fibers.

We experimentally investigate guided acoustic wave Brillouin scattering in several photonic crystal fibers by use of the so-called fiber loop mirror technique and show a completely different dynamics with respect to standard all-silica fibers. In addition to the suppression of most acoustic phonons, we show that forward Brillouin scattering in photonic crystal fibers is substantially enhanced only for the fundamental acoustic phonon because of efficient transverse acousto-optic field overlap. The results of our numerical simulations reveal that this high-frequency phonon is indeed trapped within the fiber core by the air-hole microstructure, in good agreement with experimental measurements.

Waveguiding inside the complete band gap of a phononic crystal slab.

The propagation of acoustic waves in a square-lattice phononic crystal slab consisting of a single layer of spherical steel beads in a solid epoxy matrix is studied experimentally. Waves are excited by an ultrasonic transducer and fully characterized on the slab surface by laser interferometry. A complete band gap is found to extend around 300 kHz, in good agreement with theoretical predictions. The transmission attenuation caused by absorption and band gap effects is obtained as a function of frequency and propagation distance. Well confined acoustic wave propagation inside a line-defect waveguide is further observed experimentally.