Partial Band Gaps Research Articles

Achieving directional propagation of elastic waves via topology optimization

This paper presents a study on topology optimization of novel material microstructural configurations to achieve directional elastic wave propagation through maximization of partial band gaps. A waveguide incorporating a periodic-microstructure material may exhibit different propagation properties for the plane elastic waves incident from different inlets. A topology optimization problem is formulated to enhance such a property with a gradient-based mathematical programming algorithm. For alleviating the issue of local optimum traps, the random morphology description functions (RMDFs) are introduced to generate random initial designs for the optimization process. The optimized designs finally converge to the orderly material distribution and numerical validation shows improved directional propagation property as expected. The utilization of linear two-dimension phononic crystal with efficient partial band gap is suitable for directional propagation with a broad frequency range.

Observation of trampoline phenomena in 3D-printed metamaterial plates

Two dimensional phononic metamaterials, consisting of plates with resonant cylinders have been shown to attenuate waves much larger than their characteristic unit cell size by opening subwavelength band gaps. However the bandwidth of the gap correlates strongly with the resonator mass, which limits metamaterials functionality in mass sensitive applications. Trampoline phenomena have theoretically been shown to broaden the width of the first partial band gap by up to a factor 4 of the linear, resonant band gap. In this work, we provide an experimental demonstration of the trampoline phenomena in 3D-printed plates, consisting of pillars and holes, composed of a single material. We observe the opening of significant locally resonant band gaps, ≈ 30% normalized width, without adding any significant mass to the homogeneous plate. We show numerically and experimentally that trampoline plates increase both partial and full band gaps width, while reducing the base-plate’s mass by ≈30% in the studied configurations.

Spin-filtered time-of-flight k-space microscopy of Ir – Towards the “complete” photoemission experiment

The combination of momentum microscopy (high resolution imaging of the Fourier plane) with an imaging spin filter has recently set a benchmark in k-resolution and spin-detection efficiency. Here we show that the degree of parallelization can be further increased by time-of-flight energy recording. On the quest towards maximum information (in earlier work termed “complete” photoemission experiment) we have studied the prototypical high-Z fcc metal iridium. Large partial bandgaps and strong spin-orbit interaction lead to a sequence of spin-polarized surface resonances. Soft X-rays give access to the 4D spectral density function ρ (EB,kx,ky,kz) weighted by the photoemission cross section. The Fermi surface and all other energy isosurfaces, Fermi velocity distribution vF(kF), electron or hole conductivity, effective mass and inner potential can be obtained from the multi-dimensional array ρ by simple algorithms. Polarized light reveals the linear and circular dichroism texture in a simple manner and an imaging spin filter exposes the spin texture. One-step photoemission calculations are in fair agreement with experiment. Comparison of the Bloch spectral function with photoemission calculations uncovers that the observed high spin polarization of photoelectrons from bulk bands originates from the photoemission step and is not present in the initial state.

Non-Hermiticity-induced flat band

We demonstrate the emergence of an entire flat band embedded in dispersive bands at the exceptional point of a PT symmetric photonic lattice. For this to occur, the gain and loss parameter effectively alters the size of the partial flat band windows and band gap of the photonic lattice simultaneously. The mode associated with the entire flat band is robust against changes in the system size and survives even at the edge of the lattice. Our proposal offers a route for controllable localization of light in non-Hermitian systems and a technique for measuring non-Hermiticity via localization.

Sound transmission loss characteristics of sandwich panels with a truss lattice core.

Sandwich panels are extensively used in constructional, naval, and aerospace structures due to the high stiffness and strength-to-weight ratios. In contrast, the sound transmission properties are adversely influenced by the low effective mass. Phase velocity matching of structural waves propagating within the panel and the incident pressure waves from the fluid medium leads to coincidence effects resulting in reduced impedance and high sound transmission. Truss-like lattice cores with porous microarchitecture and reduced inter panel connectivity offer the potential to satisfy the conflicting structural and vibroacoustic response requirements. This study combines Bloch-wave analysis and the finite element method to understand wave propagation and hence sound transmission in sandwich panels with a truss lattice core. Three dimensional coupled fluid-structure finite element simulations are conducted to compare the performance of a representative set of lattice core topologies. Potential advantages of sandwich structures with a lattice core are identified. The significance of partial band gaps is evident in the sound transmission loss characteristics of the panels studied. This work demonstrates that, even without optimization, significant enhancements in sound transmission loss performance can be achieved in truss lattice core sandwich panels compared to a traditional sandwich panel employing a honeycomb core under constant mass constraint.

On acoustic wave beaming in two-dimensional structural lattices

We discuss directional energy flow, often referred to as wave beaming, in two-dimensional periodic truss lattices under infinitesimal harmonic excitation. While the phenomenon of directional wave guiding is well-known and commonly treated in the context of dispersion relations, the theoretical and computational tools to predict beaming are limited, which is why a fundamental understanding for complex lattices is incomplete. Here, we present a new strategy to identify partial band gaps and wave beaming in a simple fashion, covering wide frequency ranges and distinguishing in-plane and out-of-plane vibrational modes in lattices composed of linear elastic Euler-Bernoulli beams. By calculating group velocities that provide insight into the frequency-dependent directional energy flow, we show that dispersion surfaces overlap in frequency and beaming direction, elucidating the need to consider multiple surfaces when predicting global system response – in contrast to many prior approaches that focused on the lowest surface(s) individually. These concepts are demonstrated for three examples of two-dimensional structural lattices (of rectangular, sheared, and hexagonal architecture), for each of which we study the influence of geometry on wave dispersion. Direct numerical simulations validate directional energy flow predictions, demonstrate directional frequency dispersion, and highlight conventional dispersion analysis limitations.

Photonic hyperuniform networks obtained by silicon double inversion of polymer templates

Hyperuniform disordered networks belong to a peculiar class of structured materials predicted to possess partial and complete photonic bandgaps for relatively moderate refractive index contrasts. The practical realization of such photonic designer materials is challenging however, as it requires control over a multi-step fabcrication process on optical length scales. Here we report the direct-laser writing of hyperuniform polymeric templates followed by a silicon double inversion procedure leading to high quality network structures made of polycrystalline silicon. We observe a pronounced gap in the shortwave infrared centered at a wavelength of $\lambda_{\text{Gap}}\simeq $ 2.5 $\mu$m, in nearly quantitative agreement with numerical simulations. In the experiments the typical structural length scale of the seed pattern can be varied between 2 $\mu$m and 1.54 $\mu$m leading to a blue-shift of the gap accompanied by an increase of the silicon volume filling fraction.

Wave control through soft microstructural curling: bandgap shifting, reconfigurable anisotropy and switchable chirality

In this work, we discuss and numerically validate a strategy to attain reversible macroscopic changes in the wave propagation characteristics of cellular metamaterials with soft microstructures. The proposed cellular architecture is characterized by unit cells featuring auxiliary populations of symmetrically-distributed smart cantilevers stemming from the nodal locations. Through an external stimulus (the application of an electric field), we induce extreme, localized, reversible curling deformation of the cantilevers—a shape modification which does not affect the overall shape, stiffness and load bearing capability of the structure. By carefully engineering the spatial pattern of straight (non activated) and curled (activated) cantilevers, we can induce several profound modifications of the phononic characteristics of the structure: generation and/or shifting of total and partial bandgaps, cell symmetry relaxation (which implies reconfigurable wave beaming), and chirality switching. While in this work we discuss the specific case of composite cantilevers with a PDMS core and active layers of electrostrictive terpolymer P(VDF-TrFE-CTFE), the strategy can be extended to other smart materials (such as dielectric elastomers or shape-memory polymers).

Vibrational band structure of nanoscale phononic crystals

AbstractThe vibrational properties of two‐dimensional phononic crystals are studied with large‐scale molecular dynamics simulations and finite element method calculation. The vibrational band structure derived from the molecular dynamics simulations shows the existence of partial acoustic band gaps along the –M direction. The band structure is in excellent agreement with the results from the finite element model, proving that molecular dynamics simulations can be used to study the vibrational properties of such complex systems. An analysis of the structure of the vibrational modes reveals how the acoustic modes deviate from the homogeneous bulk behavior for shorter wavelengths and hints toward a decoupling of vibrations in the phononic crystal.

Optimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materials

The elastic wave propagation is investigated in a beam lattice material characterized by a square periodic cell with anti-tetrachiral microstructure. With reference to the Floquet-Bloch spectrum, focus is made on the band structure enrichments and modifications which can be achieved by equipping the cellular microstructure with tunable local resonators. By virtue of its composite mechanical nature, the so-built inertial meta-material gains enhanced capacities of passive frequency-band filtering. Indeed the number, placement and properties of the inertial resonators can be designed to open, shift and enlarge the band gaps between one or more pairs of consecutive branches in the frequency spectrum. In order to improve the meta-material performance, several nonlinear optimization problems are formulated. The largest among the band gap amplitudes in the low-frequency range is selected as suited objective function. Proper inequality constraints are introduced to restrict the admissible solutions within a compact set of mechanical and geometric parameters, including only physically realistic properties of both the lattice and the resonators. The optimization problems related to full and partial band gaps are solved by using a globally convergent version of the numerical method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique. The optimal solutions are numerically computed, discussed and compared from the qualitative and quantitative viewpoints, bringing to light the limits and potential of the meta-material performance. The clearest trends emerging from the numerical analyses are pointed out and interpreted from the physical viewpoint. Finally, some specific recommendations about the microstructural design of the meta-material are synthesized.

Complete band gaps including non-local effects occur only in the relaxed micromorphic model

In this paper, we substantiate the claim implicitly made in previous works that the relaxed micromorphic model is the only linear, isotropic, reversibly elastic, nonlocal generalized continuum model able to describe complete band-gaps on a phenomenological level. To this end, we recapitulate the response of the standard Mindlin–Eringen micromorphic model with the full micro-distortion gradient ∇P, the relaxed micromorphic model depending only on the CurlP of the micro-distortion P, and a variant of the standard micromorphic model, in which the curvature depends only on the divergence DivP of the micro distortion. The Div-model has size-effects, but the dispersion analysis for plane waves shows the incapability of that model to even produce a partial band gap. Combining the curvature to depend quadratically on DivP and CurlP shows that such a model is similar to the standard Mindlin–Eringen model, which can eventually show only a partial band gap.

Waveform-preserved unidirectional acoustic transmission based on impedance-matched acoustic metasurface and phononic crystal

The waveform distortion happens in most of the unidirectional acoustic transmission (UAT) devices proposed before. In this paper, a novel type of waveform-preserved UAT device composed of an impedance-matched acoustic metasurface (AMS) and a phononic crystal (PC) structure is proposed and numerically investigated. The acoustic pressure field distributions and transmittance are calculated by using the finite element method. The subwavelength AMS that can modulate the wavefront of the transmitted wave at will is designed and the band structure of the PC structure is calculated and analyzed. The sound pressure field distributions demonstrate that the unidirectional acoustic transmission can be realized by the proposed UAT device without changing the waveforms of the output waves, which is the distinctive feature compared with the previous UAT devices. The physical mechanism of the unidirectional acoustic transmission is discussed by analyzing the refraction angle changes and partial band gap map. The calculated transmission spectra show that the UAT device is valid within a relatively broad frequency range. The simulation results agree well with the theoretical predictions. The proposed UAT device provides a good reference for designing waveform-preserved UAT devices and has potential applications in many fields, such as medical ultrasound, acoustic rectifiers, and noise insulation.

Analysis of magneto-optical properties for three-dimensional photonic crystals in high-symmetry arrangement doped by metamaterials and uniaxial materials

Abstract In this paper, we use a modified plane wave expansion (PWE) method to investigate the properties of photonic band gaps (PBGs) for the extraordinary mode in the three-dimensional (3D) photonic crystals (PCs) which are composed of the anisotropic dielectric (the uniaxial materials) spheres immersed in the homogeneous metamaterials (epsilon-negative materials) background with high-symmetry (body-centered-cubic) lattices, as the magneto-optical Voigt effects are considered. The equations for calculating the PBGs in the first irreducible Brillouin zone are theoretically derived. It is numerically illustrated that the anisotropic PBGs and two flattened band regions can be achieved. The influences of the ordinary-refractive index, extraordinary-refractive index, filling factor of dielectric spheres, electronic plasma frequency and cyclotron frequency on the magneto-optical properties of such 3D PCs also are studied in detail, respectively, and some corresponding physical explanations are given. The numerical results demonstrate that the anisotropy can open partial band gaps in the proposed PCs, and the complete PBGs can be obtained compared with the conventional PCs only containing the isotropic material with similar structures. The bandwidths of PBGs can be tuned by introducing the epsilon-negative materials into such PCs containing the uniaxial materials. The anisotropic PBGs can be manipulated by the parameters as mentioned above. As the proposed PCs with high-symmetry lattices, the complete PBGs can be obtained by introducing the uniaxial materials.

Wave propagation in 3D viscoelastic auxetic and textile materials by homogenized continuum micropolar models

We analyze in this contribution the impact of wave damping on the dispersion features of 3D viscoelastic periodic structures, which are modeled as Kelvin–Voigt viscoelastic beam-lattices. The band diagram structure and damping ratio are computed for different repetitive structures, based on the micropolar viscoelastic response of the effective medium obtained by the homogenization of the initially discrete lattice architecture. The employed methodology is herewith exemplified for the cases of the 3D hexagon structure, which shows negative Poisson’s ratio for reentrant configurations, and the 2D plain weave textile structure. The dispersion relations and damping ratio are obtained by inserting an harmonic plane waves Ansatz into the dynamical equations of motion of the obtained effective viscoelastic anisotropic continuum. The 3D reentrant hexagon is an auxetic metamaterial showing excellent wave absorption capabilities, as reflected by the high incidence of partial band gaps. The textile plain weave structure shows a complete band gap for low frequencies. Comparing the frequency band structure of the effective continuum with that obtained by Floquet–Bloch analysis extended to a 3D context shows that the wave propagation characteristics can be directly obtained from the homogenized continuum at low frequencies.

Evidence of near-infrared partial photonic bandgap in polymeric rod-connected diamond structures.

We present the simulation, fabrication, and optical characterization of low-index polymeric rod-connected diamond (RCD) structures. Such complex three-dimensional photonic crystal structures are created via direct laser writing by two-photon polymerization. To our knowledge, this is the first measurement at near-infrared wavelengths, showing partial photonic bandgaps for this structure. We characterize structures in transmission and reflection using angular resolved Fourier image spectroscopy to visualize the band structure. Comparison of the numerical simulations of such structures with the experimentally measured data show good agreement for both P- and S-polarizations.

Wave propagation in periodically undulated beams and plates

This paper investigates the effects of periodic geometric undulations on the dispersion properties of 1D and 2D elastic structures. Periodic undulations result from the spatial modulation of the curvature of beams and plates, which leads to the coupling of transverse and in-plane motion. Such coupling affects the modal structure, and leads to interactions that produce complete, modal and partial frequency bandgaps along with directional wave motion. The effects of relevant geometrical parameters defining the undulation, such as spatial period and undulation amplitude, are investigated through the application of the Plane Wave Expansion Method and a Finite Element-based analysis of dispersion. Experimental illustration of the bandgap behavior of undulated beams, and numerical simulations of wave motion in plates serve as partial validations of the analytical predictions, and as demonstrations of the potential application of the concept for the design of structural components and elastic waveguides with tailored bandgap and directional properties.

Anomalous d-like surface resonances on Mo(110) analyzed by time-of-flight momentum microscopy

The electronic surface states on Mo(110) have been investigated using time-of-flight momentum microscopy with synchrotron radiation (hν=35eV). This novel angle-resolved photoemission approach yields a simultaneous acquisition of the E-vs-k spectral function in the full surface Brillouin zone and several eV energy interval. (kx,ky,EB)-maps with 3.4Å−1 diameter reveal a rich structure of d-like surface resonances in the spin–orbit induced partial band gap. Calculations using the one-step model in its density matrix formulation predict an anomalous state with Dirac-like signature and Rashba spin texture crossing the bandgap at Γ¯ and EB=1.2eV. The experiment shows that the linear dispersion persists away from the Γ¯-point in an extended energy- and k∥-range. Analogously to a similar state previously found on W(110) the dispersion is linear along H¯−Γ¯−H¯ and almost zero along N¯−Γ¯−N¯. The similarity is surprising since the spin–orbit interaction is 5 times smaller in Mo. A second point with unusual topology is found midway between Γ¯ and N¯. Band symmetries are probed by linear dichroism.

Photonic band structure of two-dimensional metal/dielectric photonic crystals

An improved plane wave expansion method for the numerical calculation of photonic bands of metal/dielectric photonic crystal (PC) are presented. This method is applied to two-dimensional PCs with frequency-dependent dielectric constants. We obtained the photonic band structure of three kinds of structures: sawtooth, cylinder and hole PCs. The results show that the lowest band-1 is relatively flat, and does not approach zero. Also, there is no complete band-gap that extends throughout the first Brillouin zone for these three structures. However, there are partial band-gaps in different directions in the first Brillouin zone. For the complementary cylinder and hole PCs, their photonic bands are similar except for the lowest three bands; the hole PC’s lowest frequency of band-1 is larger than that of cylinder PC for the configuration R/d = 0.2.

Negative refractions by triangular lattice sonic crystals in partial band gaps**Project supported by the Inonu Universty Scientific Research Projects Coordination Unit (Grant Nos. 2012/29 and 2013/56).

This study numerically demonstrates the effects of partial band gaps on the negative refraction properties of sonic crystal. The partial band gap appearing at the second band edge leads to the efficient transmissions of scattered wave envelopes in the transverse directions inside triangular lattice sonic crystal, and therefore enhances the refraction property of sonic crystal. Numerical simulation results indicate a diagonal guidance of coupled scattered wave envelopes inside crystal structure at the partial band gap frequencies and then output waves are restored in the vicinity of the output interface of sonic crystal by combining phase coherent scattered waves according to Huygens’ principles. This mechanism leads to two operations for wavefront engineering: one is spatial wavefront shifting operation and the other is convex–concave wavefront inversion operation. The effects of this mechanism on the negative refraction and wave focalization are investigated by using the finite difference time domain (FDTD) simulations. This study contributes to a better understanding of negative refraction and wave focusing mechanisms at the band edge frequencies, and shows the applications of the slab corner beam splitting and SC-air multilayer acoustic system.

Application of a Helmholtz structure for low frequency noise reduction

In this work, we numerically investigate the existence of low-frequency band gaps in the Helmholtz resonance structure. Finite element method is utilized to calculate the band structure and transmission spectrum. Three band gaps and two neighboring partial band gaps are found from 0 to 4000 Hz. Geometrical parameters which may affect the band gap width or positions such as the inlet width and length are analyzed. Results indicate that the first band gap will become wider and higher with the increase of the inlet width of the resonators. However, variation trend of the first band gap is completely opposite when inlet length becomes longer. Calculated transmission spectrum validates the band structure well. This designed and calculated structure has potential application in the low-frequency noise reduction.