In-plane Wave Research Articles

Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers

We report on the experimental observation of non-equilibrium longitudinal (LO) and interface transverse-like (IF-TO) optical phonons populations associated with electron transport in resonant-phonon THz quantum-cascade lasers. The measured LO-phonon occupation numbers are in excellent agreement with the result of Monte Carlo simulations at a phonon in-plane wave number q = 4.2 × 10+4 cm−1, and they remain about 40% larger than the IF-TO ones.

Simulating the Manufacturing Process and Subsequent Structural Stiffness of Composite Wind Turbine Blades with and without Defects

Traditional ply-based and zone-based models are limited in their ability to account for the fiber directions resulting from the forming of fabric-reinforced composite wind turbine blades. Compounding the problem is the presence of defects such as resin-rich pockets of the polymer matrix due to out-of-plane and in-plane waves resulting from the manufacturing process. As a result, blades are typically overdesigned, unnecessarily increasing weight and material costs. In the current research, a methodology is presented for simulating the manufacturing process for fabric-reinforced composite wind turbine blades using ABAQUS/Explicit. The methodology captures the evolution of the yarn directions during the forming process thereby allowing for a map of the fiber orientations throughout the blade. A hybrid approach using conventional beam and shell elements is used to model the various fabric layers. Using experimental shear, tensile, bending, and friction data to characterize the mechanical behavior of the fabric layers, the model captures in-plane yarn waviness and changes in the in-plane yarn orientations as they conform to the shape of the mold, as well as out-of-plane wave defects as a result of the manufacturing process. Subsequently, after the fabric layers have been laid into the mold and the final yarn orientations are known, the structural stiffness of the blade resulting from the resin-infused fabrics can be calculated. The methodology can thereby link the resulting bending and torsional stiffnesses of the blade back to the manufacturing process. This paper discusses the methodology for determining the material properties of the beam and shell elements in their final orientations in the cured composite to predict the structural stiffness of a wind turbine blade.

Band structures and localization properties of aperiodic layered phononic crystals

The band structures and localization properties of in-plane elastic waves with coupling of longitudinal and transverse modes oblique propagating in aperiodic phononic crystals based on Thue–Morse and Rudin–Shapiro sequences are studied. Using transfer matrix method, the concept of the localization factor is introduced and the correctness is testified through the Rytov dispersion relation. For comparison, the perfect periodic structure and the quasi-periodic Fibonacci system are also considered. In addition, the influences of the random disorder, local resonance, translational and/or mirror symmetries on the band structures of the aperiodic phononic crystals are analyzed in this paper.

Resonance Quenching and Guided Modes Arising from the Coupling of Surface Plasmons with a Molecular Resonance

In this paper, we describe experimental and modeling results that illucidate the nature of coupling between surface plasmon polaritons in a thin silver film with the molecular resonance of a zinc phthalocyanine dye film. This coupling leads to several phenomena not generally observed when plasmons are coupled to transparent materials. The increased absorption coefficient near a molecular resonance leads to a discontinuity in the refractive index, which causes branching of the plasmon resonance condition and the appearance of two peaks in the p-polarized reflectance spectrum. A gap exists between these peaks in the region of the spectrum associated with the molecular resonance and reflects quenching of the plasmon wave due to violation of the resonance condition. A second observation is the appearance of a peak in the s-polarized reflection spectra. The initial position of this peak corresponds to where the refractive index of the adsorbate achieves its largest value, which occurs at wavelengths just slightly larger than the maximum in the molecular resonance. Although this peak initially appears to be nondispersive, both experimental data and optical modeling indicate that increasing the film thickness shifts the peak position to longer wavelengths, which implies that this peak is not associated with the molecular resonance but, rather, is dispersive in nature. Indeed, modeling shows that this peak is due to a guided mode in the film, which appears in these conditions due to the abnormally high refractive index of the film near the absorbance maximum. Results also show that, with increasing film thickness, numerous additional guided modes appear and move throughout the visible spectrum for both s- and p-polarized light. Notably, these guided modes are also quenched near the location of the molecular resonance. The quenching of both the plasmon resonance and the guided modes can be explained by a large decrease in the in-plane wave propagation length that occurs near the molecular resonance, which is a direct result of the film's large absorption coefficient.

Wave localization in two-dimensional porous phononic crystals with one-dimensional aperiodicity

The localization properties of in-plane elastic waves propagating in two-dimensional porous phononic crystals with one-dimensional aperiodicity are initially analyzed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method in this paper. The band structures characterized by using localization factors are calculated for different phononic crystals by altering matrix material properties and geometric structure parameters. Numerical results show that the effect of matrix material properties on wave localization can be ignored, while the effect of geometric structure parameters is obvious. For comparison, the periodic porous system and Fibonacci system with rigid inclusion are also analyzed. It is found that the band gaps are easily formed in aperiodic porous system, but hard for periodic porous system. Moreover, compared with aperiodic system with rigid inclusion, the wider low-frequency band gaps appear in the aperiodic porous system.

Ultrawide phononic band gap for combined in-plane and out-of-plane waves

We consider two-dimensional phononic crystals formed from silicon and voids, and present optimized unit-cell designs for (1) out-of-plane, (2) in-plane, and (3) combined out-of-plane and in-plane elastic wave propagation. To feasibly search through an excessively large design space (~10(40) possible realizations) we develop a specialized genetic algorithm and utilize it in conjunction with the reduced Bloch mode expansion method for fast band-structure calculations. Focusing on high-symmetry plain-strain square lattices, we report unit-cell designs exhibiting record values of normalized band-gap size for all three categories. For the case of combined polarizations, we reveal a design with a normalized band-gap size exceeding 60%.

Density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multilayer configurations: Exact treatment of exchange interactions

We study the in-plane and out-of-plane density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multilayer configurations. We locate the soft modes by evaluating linear response functions within the conserving time-dependent Hartree-Fock (TDHF) approximation. The short-range exchange effects are taken into account by solving the Bethe-Salpeter integral equation numerically. An instability phase diagram is calculated for both single-layer and multilayer systems and the unstable wave vector is indicated. In all cases, the in-plane density wave instability is found to precede the out-of-plane instability. The unstable wave vector is found to be approximately twice the Fermi wave vector of one of the subbands at a time and can change discontinuously as a function of density and dipolar interaction strength. In multilayer configurations, we find a large enhancement of density-wave instability driven by dilute quasiparticles in the first excited subband. Finally, we provide a simple qualitative description of the phase diagrams using an RPA-like approach. Compared to previous works done within the RPA approximation, we find that inclusion of exchange interactions stabilize the normal liquid phase further and increase the critical dipolar interaction strength corresponding to the onset of density-wave instability by over a factor of two.

Interactions of Diffraction Modes Contributed From Surface Photonic Crystals and Nanoholes in a GaN-Based Light-Emitting Diode

Photonic crystals (PhCs) were typically fabricated on the mesa surface of an LED to improve light extraction, which is regarded as the weak coupling between the laterally propagated light in the epilayers and the surface nanostructure. Here, we report GaN-based LEDs with the PhC structure on the mesa surface and nanohole reflectors surrounding the light-emitting mesa. The output power of the new LED structure is higher than that of the device with only surface PhCs due to the enhanced diffraction of low-order modes propagated in the lateral direction, in addition to the higher order mode light diffraction from the surface PhCs. From the relative angular spectra, the interaction of in-plane optical wave with the nanoholes (which are etched through multiple quantum wells) is much stronger than that with surface PhCs, suggesting an efficient light diffraction to the surface normal by nanoholes.

Spin-related phenomena in InAs/GaSb quantum wells

We have studied theoretically the influence of symmetry breaking mechanisms: structural inversion asymmetry, bulk inversion asymmetry, relativistic and non-relativistic interface Hamiltonian and warping on spin split of levels Delta E and optical absorption of linearly polarized light in asymmetrical quantum wells made from zincblende materials grown on [001] direction. The AlSb/InAs/GaSb/AlSb broken-gap quantum wells with hybridized electron-hole states sandwiched by the AlSb barriers have been considered. We have obtained substantial contributions of these effects into the absolute values of spin split of electron and hole states and spinflip optical transitions for the initial state in-plane wave vectors along low symmetry directions such as [12].

DNA Concentration Modulation on Supported Lipid Bilayers Switched by Surface Acoustic Waves

Spatially addressable arrays of molecules embedded in or anchored to supported lipid bilayers are important for on-chip screening and binding assays; however, methods to sort or accumulate components in a fluid membrane on demand are still limited. Here we apply in-plane surface acoustic shear waves (SAWs) to laterally accumulate double-stranded DNA segments electrostatically bound to a cationic supported lipid bilayer. The fluorescently labeled DNA segments are found to segregate into stripe patterns with a spatial frequency corresponding to the periodicity of the standing SAW wave (~10 μm). The DNA molecules are accumulated 10-fold in the regions of SAW antinodes. The superposition of two orthogonal sets of SAW sources creates checkerboard like arrays of DNA demonstrating the potential to generate arrayed fields dynamically. The pattern relaxation time of 0.58 s, which is independent of the segment length, indicates a sorting and relaxation mechanism dominated by lipid diffusion rather than DNA self-diffusion.

Broadband Energy Conversion Between Off-Plane Gaussian Lightwave and In-Plane Surface Plasmon Waves

We report on highly efficient energy conversion between off-plane Gaussian beam and in-plane surface plasmon waves (SPWs). The finite-difference time-domain method was used to analyze the conversion efficiency. In contrast to the single plasmonic rib structure, coupled ribs provide broadband and highly efficient SPW-conversion due to enlarged coupling zone. The simulation shows that Gaussian beam-to-SPWs conversion efficiency can be higher than 50% for the wavelength range from 750 to 950 nm. Compared to in-plane excitation, the present structure is superior in terms of the critical dimension of fabrication, showing promise as an efficient SPW generator in plasmonic nano-circuritry.

First-principles study of ballistic transport properties in Co2MnSi/X/Co2MnSi(001) (X=Ag, Au, Al, V, Cr) trilayers

We investigate and discuss the origin of interface resistance in magnetic trilayers with the half-metallic Co${}_{2}$MnSi by performing first-principles electronic-structure and ballistic transport calculations for Co${}_{2}$MnSi/$X/$Co${}_{2}$MnSi(001) ($X=$ Ag, Au, Al, V, Cr). We found that the matching of the Fermi surface projected to the two-dimensional Brillouin zone of in-plane wave vector (${k}_{\ensuremath{\parallel}}$) is a main contributing factor for the spacer ($X$) dependence of the interfacial resistance. Furthermore, the MnSi-terminated interface shows low resistance compared with the Co-terminated interface because the Co-terminated interface has a larger $d$ component in the local density of states at the Fermi level than that of the MnSi-terminated interface. We conclude that Ag, Au, and Al spacers with MnSi termination of CMS$/X/$CMS trilayers will provide the large interfacial spin-asymmetry coefficient because of the small interface resistance in parallel magnetization.

Highly Anisotropic Anomaly in the Dispersion of the Copper-Oxygen Bond-Bending Phonon in SuperconductingYBa2Cu3O7from Inelastic Neutron Scattering

Motivated by predictions of a substantial contribution of the "buckling" vibration of the CuO(2) layers to d-wave superconductivity in the cuprates, we have performed an inelastic neutron scattering study of this phonon in an array of untwinned crystals of YBa(2)Cu(3)O(7). The data reveal a pronounced softening of the phonon at the in-plane wave vector q=(0,0.3) upon cooling below ~105 K, but no corresponding anomaly at q=(0.3,0). Based on the observed in-plane anisotropy, we argue that the electron-phonon interaction responsible for this anomaly supports an electronic instability associated with a uniaxial charge-density modulation and does not mediate d-wave superconductivity.

Magnetic and energetic properties of low-index Cr surfaces and Fe/Cr interfaces: A first-principles study

Density functional theory calculations are performed to investigate the impact of magnetism on the energetics of low-index Cr surfaces and Fe/Cr interfaces, that is, Cr(100), Cr(110), Fe/Cr(100), and Fe/Cr(110). We have also determined the stability of various Cr magnetic structures, particularly the spin-density waves, in the presence of these surfaces and interfaces. We show that the most stable structure of the spin-density wave is mainly dictated by the subtle balance between bulk and surface/interface influences, and strongly dependent on the surface/interface orientation. Regarding the Cr surfaces, we confirm the role of magnetism to lower the surface energy of Cr(100) with respect to Cr(110). Among all the possible orientations of the wave vector, only the out-of-plane wave is found to be stable near Cr(100) surfaces with the high-moment sites located at the surface layer. At variance, the in-plane wave is shown to be the most stable one, consistent with experimental data for very thin Cr(110) films. Concerning the Fe/Cr interfaces, magnetic frustrations are identified to be responsible for a higher formation energy of Fe/Cr(110) compared to that of Fe/Cr(100). This unusual anisotropy of interface energies is clearly different from the corresponding interfaces between Cr and a nonmagnetic element, Cu. Two ways are suggested to relax partially the magnetic frustrations at the (110) interface and to lower its formation energy. Noncollinear magnetic configurations can be developed where local moments of Fe and Cr atoms are perpendicular to each other. Also, in order to preserve phase coherence, in-plane spin-density waves show a very stable magnetic structure with the nodes at the interface layer. The presence of low-moment sites at Fe/Cr(110) offer another way to relax the magnetic frustrations and lower the interfacial energy.

The wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges

In this paper, wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach. The dynamic responses, active and reactive power flow in the finite plate are calculated by the Mindlin plate theory (MPT) and classic plate theory (CPT). To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate, the near-field and far-field waves are entirely contained in the wave approach. The in-plane longitudinal and shear waves are also considered. The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies. The influence of the plate thickness on the vibrational power flow is investigated. From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies. Furthermore, the effects of structural damping on the active and reactive power flow at the junction are also analyzed.

Retarded long-range interaction in split-ring-resonator square arrays

We systematically investigate the optical extinction spectra of planar gold split-ring-resonator square arrays operating at $\ensuremath{\sim}$200-THz frequency versus the lattice constant and versus angle of incidence. We find a strong dependence of the resonance damping on the in-plane wave vector, namely, the resonance damping increases (decreases) versus the in-plane wave vector for small lattice constants (large lattice constants). By comparison with two simple one-dimensional models as well as with more complete numerical calculations, this behavior is interpreted in terms of a long-range retarded interaction among the split-ring resonators. In contrast, the assumptions of only nearest-neighbor interaction and/or of an instantaneous interaction lead to a striking disagreement with the overall experimental facts.

Elastic properties of porous low-k dielectric nano-films

Low-k dielectrics have predominantly replaced silicon dioxide as the interlayer dielectric for interconnects in state of the art integrated circuits. In order to further reduce interconnect RC delays, additional reductions in k for these low-k materials are being pursued via the introduction of controlled levels of porosity. The main challenge for such dielectrics is the substantial reduction in elastic properties that accompanies the increased pore volume. We report on Brillouin light scattering measurements used to determine the elastic properties of these films at thicknesses well below 200 nm, which are pertinent to their introduction into present ultralarge scale integrated technology. The observation of longitudinal and transverse standing wave acoustic resonances and their transformation into traveling waves with finite in-plane wave vectors provides for a direct non-destructive measure of the principal elastic constants that characterize the elastic properties of these porous nano-scale films. The mode dispersion further confirms that for porosity levels of up to 25%, the reduction in the dielectric constant does not result in severe degradation in the Young’s modulus and Poisson’s ratio of the films.

The propagation of in-plane P-SV waves in a layered elastic plate with periodic interface cracks: exact versus spring boundary conditions

The propagation of in-plane (P-SV) waves in a symmetrically three-layered thick plate with a periodic array of interface cracks is investigated. The exact dispersion relation is derived based on an integral equation approach and Floquet's theorem. The interface cracks can be a model for interface damage, but a much simpler model is a recently developed spring boundary condition. This boundary condition is used for the thick plate and also in the derivation of plate equations with the help of power series expansions in the thickness coordinate. For low frequencies (cracks small compared to the wavelength) the three approaches give more or less coinciding dispersion curves, and this is a confirmation that the spring boundary condition is a reasonable approximation at low frequencies.

In-plane plasmonic modes of negative group velocity in perforated waveguides

Eigenmodes in a typical perforated metal-insulator-metal waveguide structure have been analyzed. It is shown that the lowest eigenmode originates from a plasmonic waveguide mode between metallic layers and has net negative group velocity on the lower branch under TM polarization. The negative group velocity is directly derived from the dispersion curve in the plane of in-plane wave number and photon energy, and is responsible for the negative refraction effect reported in fishnet metamaterials.

Seismic Response Analysis of Transmission Tower-Line System on a Heterogeneous Site to Multi-Component Spatial Ground Motions

This paper studies the nonlinear responses of a coupled transmission towerline system on a heterogeneous site subjected to multi-component spatially varying ground motions. The three-dimensional finite element model of the transmission tower-line system is established with consideration of the geometric nonlinearity of the transmission lines. The spatial variation of ground motions associated with the wave passage, coherency loss and local site effects are considered. The spatial ground motions on ground surface are derived by modelling the base rock motion propagating through the local soil sites. The base rock motions are assumed consisting of out-of-plane and in-plane waves and are simulated stochastically based on an empirical coherency loss function and the filtered Tajimi-Kanai power spectral density function. The effects of multi-component, spatial variations of ground motions and varying site conditions at multiple tower foundations on seismic response of the transmission tower-line system are analysed. The study reveals that for a reliable seismic response analysis and safe and economic seismic resistance design of transmission tower-line systems, the multi-support and multi-component earthquake excitations with consideration of the effects of local site conditions on ground motion spatial variations should be considered.