Standing Wave Profile Research Articles

Numerical spectral analysis of standing waves in quantum hydrodynamics with viscosity

<abstract><p>We study the spectrum of the linearization around standing wave profiles for two quantum hydrodynamics systems with linear and nonlinear viscosity. The essential spectrum for such profiles is stable; we investigate the point spectrum using an Evans function technique. For both systems we show numerically that there exists a real unstable eigenvalue, thus providing numerical evidence for spectral instability.</p></abstract>

Acoustofluidics in an equilateral triangular channel

Acoustofluidics is of great interest in many fields, such as physics, biology, chemistry, medicine, and manufacturing. Numerous research has been conducted on the basic physics of acoustofluidics in common (e.g., rectangular and circular) fluid channels. Recently, it has been reported that the resonant acoustic field in a triangular channel can be applied for rapid acoustofluidic sedimentation of microparticles. In this paper, we examine in detail the fundamentals of acoustofluidics in triangular channels and show their potential for ultrasonic particle manipulation. The variations of acoustofluidic fields, including acoustic resonances, acoustic radiation force, and outer acoustic streaming, in an equilateral triangular channel are investigated both experimentally and numerically. We develop a generalized limiting velocity solution for predicting the outer acoustic streaming fields in triangular channels of arbitrary shape. We show that it can generate both symmetric and antisymmetric acoustic resonances in triangular channels, which lead to outer acoustic streaming fields that are similar or distinct to those seen in common fluid channels. Boundary vibration-dependent asymmetric standing wave profiles can typically be excited, where spatial separation of acoustic pressure and streaming patterns is observed, which is consistent with the recent prediction of acoustofluidics in asymmetric acoustic resonances. The results demonstrate the richness of acoustic resonances and boundary-driven acoustic streaming patterns that arise in standing acoustic wave fields and open perspectives for acoustomicrofluidic applications such as heat and mass transfer enhancement and dynamic manipulation of micro- and nanoparticles.

Geometric Nanophotonics: Light Management in Single Nanowires through Morphology.

Comprehensive control of light-matter interactions at the nanoscale is increasingly important for the development of miniaturized light-based technologies that have applications ranging from information processing to sensing. Control of light in nanoscale structures-the realm of nanophotonics-requires precise control of geometry on a few-nanometer length scale. From a chemist's perspective, bottom-up growth of nanoscale materials from chemical precursors offers a unique opportunity to design structures atom-by-atom that exhibit desired properties. In this Account, we describe our efforts to create chemically and morphologically precise Si nanowires (NWs) with designed nanophotonic properties using a vapor-liquid-solid (VLS) growth process. A synthetic technique termed "Encoded Nanowire Growth and Appearance through VLS and Etching" (ENGRAVE) combines optimized VLS growth, dopant modulation, and dopant-dependent wet-chemical etching to produce NWs with precisely designed diameter modulations, yielding lithographic-like morphological control that can vary from sinusoids to fractals. The ENGRAVE NWs thus provide a versatile playground for coupling, trapping, and directing light in a nanoscale geometry. Previously, the nanophotonic functionality of NWs primarily relied on uniform-diameter structures that exhibit Mie scattering resonances and longitudinally oriented guided modes, two key photonic properties that typically cannot be utilized simultaneously due to their orthogonality. However, when the NW diameter is controllably modulated along the longitudinal axis on a scale comparable to the wavelength of light-a geometry we term a geometric superlattice (GSL)-we found that NWs can exhibit a much richer and tunable set of nanophotonic properties, as described herein. To understand these unique properties, we first summarize the basic optical properties of uniform-diameter NWs using Mie scattering theory and dispersion relations, and we describe both conventional and relatively new microscopy methods that experimentally probe the optical properties of single NWs. Next, delving into the properties of NW GSLs, we summarize their ability to couple a Mie resonance with a guided mode at a select wavevector (or wavelength) dictated by their geometric pitch. The coupling forms a bound guided state (BGS) with a standing wave profile, which allows a NW GSL to serve as a spectrally selective light coupler and to act as optical switch or sensor. We also summarize the capacity of a GSL to trap light by serving as an ultrahigh (theoretically infinite) quality factor optical cavity with an optical bound state in the continuum (BIC), in which destructive interference prevents coupling to and from the far field. Finally, we discuss a future research outlook for using ENGRAVE NWs for nanoscale light control. For instance, we highlight research avenues that could yield light-emitting devices by interfacing a NW-based BIC with emissive materials such as quantum dots, 2D materials, and hybrid perovskite. We also discuss the design of photonic band gaps, generation of high-harmonics with quasi-BIC structures, and the possibility for undiscovered nanophotonic properties and phenomena through more complex ENGRAVE geometric designs.

Nonlinear Spherical Standing Waves in an Acoustically Excited Liquid Drop

Nonlinear evolution of a standing acoustic wave in a spherical resonator with a perfectly soft surface is analyzed. Quadratic approximation of nonlinear acoustics is used to analyze oscillations in the resonator by the slowly varying amplitude method for the standing wave harmonics and slowly varying profile method for the standing wave profile. It is demonstrated that nonlinear effects may lead to considerable increase in peak pressure at the center of the resonator. The proposed theoretical model is used to analyze the acoustic field in liquid drops of an acoustic fountain. It is shown that, as a result of nonlinear evolution, the peak negative pressure may exceed the mechanical strength of the liquid, which may account for the explosive instability of drops observed in experiments.

3D printed components with ultrasonically arranged microscale structure

This paper shows the first application of in situ manipulation of discontinuous fibrous structure mid-print, within a 3D printed polymeric composite architecture. Currently, rapid prototyping methods (fused filament fabrication, stereolithography) are gaining increasing popularity within the engineering commnity to build structural components. Unfortunately, the full potential of these components is limited by the mechanical properties of the materials used. The aim of this study is to create and demonstrate a novel method to instantaneously orient micro-scale glass fibres within a selectively cured photocurable resin system, using ultrasonic forces to align the fibres in the desired 3D architecture. To achieve this we have mounted a switchable, focused laser module on the carriage of a three-axis 3D printing stage, above an in-house ultrasonic alignment rig containing a mixture of photocurable resin and discontinuous 14 μm diameter glass fibre reinforcement(50 μm length). In our study, a suitable print speed of 20 mm s−1 was used, which is comparable to conventional additive layer techniques. We show the ability to construct in-plane orthogonally aligned sections printed side by side, where the precise orientation of the configurations is controlled by switching the ultrasonic standing wave profile mid-print. This approach permits the realisation of complex fibrous architectures within a 3D printed landscape. The versatile nature of the ultrasonic manipulation technique also permits a wide range of particle types (diameters, aspect ratios and functions) and architectures (in-plane, and out-plane) to be patterned, leading to the creation of a new generation of fibrous reinforced composites for 3D printing.

MEMS-Based Tuning of InGaAs/GaAs Quantum Dot-VCSOA

The wavelength tuning mechanism for quantum dot vertical cavity semiconductor optical amplifiers (QD-VCSOAs) is investigated theoretically. It is shown that the narrow optical gain bandwidth of QD-VCSOA cannot be extended considerably by reduction of the mirror reflectivity. Gain spectra of the MEMS tunable QD-VCSOA is calculated by including the effect of bias voltage on the air-gap thickness, effective mirror reflectivity, gain enhancement factor, and resonance wavelength of the cavity. The MEMS tuning scheme is evaluated for a semiconductor-coupled cavity design and operation in reflection mode under electrical pumping. The standing wave profile in the cavity is calculated by transmission matrix method to consider possible displacement of the standing wave peaks from each QD stack due to changes in the resonance wavelength of the cavity. It is found that such a system enables the cavity-limited gain spectra to be dynamically swept over a range effectively extending the usable gain bandwidth of the amplifier.

Metamaterial mirrors in optoelectronic devices

The phase reversal that occurs when light is reflected from a metallic mirror produces a standing wave with reduced intensity near the reflective surface. This effect is highly undesirable in optoelectronic devices that use metal films as both electrical contacts and optical mirrors, because it dictates a minimum spacing between the metal and the underlying active semiconductor layers, therefore posing a fundamental limit to the overall thickness of the device. Here, we show that this challenge can be circumvented by using a metamaterial mirror whose reflection phase is tunable from that of a perfect electric mirror (φ=π) to that of a perfect magnetic mirror (φ=0). This tunability in reflection phase can also be exploited to optimize the standing wave profile in planar devices to maximize light-matter interaction. Specifically, we show that light absorption and photocurrent generation in a sub-100nm active semiconductor layer of a model solar cell can be enhanced by ∼20% over a broad spectral band.

Momentum-resolved electronic structure at a buried interface from soft X-ray standing-wave angle-resolved photoemission

Angle-resolved photoemission spectroscopy (ARPES) is a powerful technique for the study of electronic structure, but it lacks a direct ability to study buried interfaces between two materials. We address this limitation by combining ARPES with soft X-ray standing-wave (SW) excitation (SWARPES), in which the SW profile is scanned through the depth of the sample. We have studied the buried interface in a prototypical magnetic tunnel junction La0.7Sr0.3MnO3/SrTiO3. Depth-and momentum-resolved maps of Mn 3d eg and t2g states from the central, bulk-like and interface-like regions of La0.7Sr0.3MnO3 exhibit distinctly different behavior consistent with a change in the Mn bonding at the interface. We compare the experimental results to state-of-the-art density-functional and one-step photoemission theory, with encouraging agreement that suggests wide future applications of this technique.

Control of Electrical Alternans in Canine Cardiac Purkinje Fibers

Alternation in the duration of consecutive cardiac action potentials (electrical alternans) may precipitate conduction block and the onset of arrhythmias. Consequently, suppression of alternans using properly timed premature stimuli may be antiarrhythmic. To determine the extent to which alternans control can be achieved in cardiac tissue, isolated canine Purkinje fibers were paced from one end using a feedback control method. Spatially uniform control of alternans was possible when alternans amplitude was small. However, control became attenuated spatially as alternans amplitude increased. The amplitude variation along the cable was well described by a theoretically expected standing wave profile that corresponds to the first quantized mode of the one-dimensional Helmholtz equation. These results confirm the wavelike nature of alternans and may have important implications for their control using electrical stimuli.

Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation

We make a detailed numerical study of the spectrum of two Schrödinger operators L± arising from the linearization of the supercritical nonlinear Schrödinger equation (NLS) about the standing wave, in three dimensions. This study was motivated by a recent result of the second author on the conditional asymptotic stability of solitary waves in the case of a cubic nonlinearity. Underlying the validity of this result is a spectral condition on the operators L±, namely that they have no eigenvalues nor resonances in the gap (a region of the positive real axis between zero and the continuous spectrum), which we call the gap property. The present numerical study verifies this spectral condition and shows further that the gap property holds for NLS exponents of the form 2 β + 1, as long as β* < β ⩽ 1, where Our strategy consists of rewriting the original eigenvalue problem via the Birman–Schwinger method. From a numerical analysis viewpoint, our main contribution is an efficient quadrature rule for the kernel 1/|x − y| in , i.e. proved spectrally accurate. As a result, we are able to give similar accuracy estimates for all our eigenvalue computations. We also propose an improvement in Petviashvili's iteration for the computation of standing wave profiles which automatically chooses the radial solution.All our numerical experiments are reproducible. The Matlab code can be downloaded from http://www.acm.caltech.edu/~demanet/NLS/.

Element-selective vertical height determination for an organic monolayer by a scanned-energy photoelectron-yield soft x-ray standing wave technique

A photoelectron-yield soft x-ray standing wave (SW) technique with the scanned-energy mode has been applied to the vertical height determination of the atoms of specific elements involved in an organic monolayer prepared by the Langmuir–Blodgett method on a W∕C superlattice substrate (d=30.9Å) that serves as a SW generator. The vertical positions of two different-element atoms were determined from the SW profiles. This kind of information is complementary to the molecular-orientation estimation by the polarized x-ray absorption spectroscopy and the combination of these techniques will be a powerful tool to understand the structures of organic monolayers.

Generation, propagation, and annihilation of metastable patterns

We study the full-time dynamics of the initial value problem, for u ε = u ε ( x , t ) , u t ε = ε 2 u xx ε - F ′ ( u ε ) , x ∈ R , t > 0 , u ε ( x , 0 ) = u 0 ( x ) , x ∈ R , where 0 < ε ⪡ 1 and F ( u ) has global minimum 0 at u = ± 1 . We assume that u 0 ( · ) is bounded, continuous and independent of ε , changes sign finitely many times, and lim inf | x | → ∞ | u 0 ( x ) | > 0 . There are four stages in the dynamics. The first, phase separation of O ( | ln ε | ) long, develops phase regions where u ε ≈ ± 1 . The second, generation of metastable patterns of O ( ε - 1 ) long, allows u ε to enter an O ( e - ℓ / ε ) neighborhood of a standing wave profile near each interface x = z i where ℓ = min i { F ″ ( ± 1 ) ( z i + 1 - z i ) } is the shortest weighted length of phase regions. The third, super-slow motion of interfaces of O ( e ℓ / ε ) long, displays the O ( e - ℓ / ε ) speed interface motion governed by an approximate ode system. The fourth stage, annihilation of interfaces of O ( 1 ) long, interlaces with the third stage. Interfaces annihilate when they are close enough, and after every annihilation, new metastable patterns are developed to restore the super-slow motions of remaining interfaces. Eventually u ε approaches a stable equilibrium which has only one or none interface. The first and third stages have been studied. Here, we provide rigorous analysis for the second and fourth stages. To be self-contained, we also provide simplified analysis for the first and third stages, thereby completing the analytic treatment for the full-time behavior of the dynamics.

Stable single-mode operation of distributed feedback lasers with wirelike active regions

A stable single-mode operation mechanism in distributed feedback (DFB) lasers with wirelike active regions was theoretically investigated by taking into account matching between standing wave profiles of each resonant mode and periodic active regions. As a result, it was clarified that the resonant modes at the longer wavelength side of the stopband have higher modal gain than those at the shorter wavelength side and that the oscillation takes place at the longer wavelength side resonant mode nearest to the stopband. The influence of the cleaved facet with respect to the grating phase was also analyzed. The measured spectral properties of buried heterostructure GaInAsP/InP DFB lasers consisting of wirelike active regions, such as a subthreshold gain spectrum and the lasing wavelength with respect to the stop band, agreed well with theoretical results. Finally, it was confirmed that a stable single-mode operation was preserved even after a room temperature continuous wave aging of 7300 h at bias current of around 10/spl times/ the threshold.

X-ray standing wave studies of strained InxGa1−xAs/InP short-period superlattices

We report an x-ray standing wave (XSW) study on a set of structurally well-characterized InxGa1−xAs/InP short-period superlattices grown by metal–organic chemical vapor deposition and chemical-beam epitaxy techniques. It was possible to model the x-ray standing wave profiles only once the superlattice period has been assumed to be constituted by four layers of well-defined chemical composition [barrier (InP), first interface (InAs0.7P0.3), well (In0.53Ga0.47As), and second interface (In0.53Ga0.47As0.7P0.3)], and of variable thickness. The thickness of the four layers have been obtained by fitting the high resolution x-ray diffraction profiles of the heterostructures. The presence of partially disordered interface layers, as evidenced by a transmission electron microscopy study, causes a significant reduction of the coherent fraction, F, of both Ga and As atoms. The difference in F values among measured samples illustrates how the XSW can provide important information on the quality of semiconductor superlattices. Comparison with a “long period (160 Å)” In0.53Ga0.47As/InP superlattice, where the role played by InAs0.7P0.3 and In0.53Ga0.47As0.7P0.3 interface layers is negligible, confirms this picture. The coherent fraction of both As and Ga correlates well with the average perpendicular lattice misfit 〈Δa⊥/a〉 determined by x-ray diffraction.

Nonlinear standing waves in a layer excited by the periodic motion of its boundary

A new analytical approach is developed for the description of standing waves caused by arbitrary periodic vibration of a boundary. The approach is based on the nonlinear evolution equation written for an auxiliary function. This equation offers the possibility to study not only the steady-state acoustic field, but also its evolution in time. One can take into account the dissipative properties of the medium and the difference between one of the resonant frequencies and the fundamental frequency of the driving motion of the wall. An exact nonsteady-state solution is derived corresponding to the sawtooth-like periodic vibration of the boundary. The maximal “amplitude” values of the particle velocity and the energy of a standing wave are calculated. The temporal profiles of standing waves at different points of the layer are presented. A new possibility of pumping a high acoustic energy into a resonator is indicated for the case of a special type of the wall motion having the form of an “inverse saw.” Theoretically, such a vibration leads to an “explosive instability” and an unlimited growth of the standing wave. For a harmonic excitation, the exact non-steady-state solution is derived as well. The standing wave profiles are described by Mathieu functions, and the energy characteristics by their eigenvalues.

High-performance 1.55-μm wavelength GaInAsP-InP distributed-feedback lasers with wirelike active regions

High-performance 1.55-/spl mu/m wavelength GaInAsP-InP strongly index-coupled and gain-matched distributed-feedback (DFB) lasers with periodic wirelike active regions mere fabricated by electron beam lithography, CH/sub 4//H/sub 2/-reactive ion etching, and organometallic vapor-phase epitaxial regrowth, whose index-coupling coefficient was more than 300 cm/sup -1/. In order to design lasers for low threshold current operation, threshold current dependences on the number of quantum wells and the wire width mere investigated both theoretically and experimentally. A record low threshold current density of 94 A/cm/sup 2/ among 1.55-/spl mu/m DFB lasers was successfully obtained for a stripe width of 19.5 /spl mu/m and a cavity length of 600 /spl mu/m. Moreover, a record low threshold current of 0.7 mA was also realized at room temperature under CW condition for a 2.3-/spl mu/m-wide buried heterostructure with a 200-/spl mu/m-long cavity. Finally, we confirmed stable single-mode operation due to a gain-matching effect between the standing-wave profile and the wirelike active region.

X-ray standing wave study of wet-etch sulphur-treated InP(100) surfaces

Normal incidence X-ray standing wave (NIXSW) measurements are presented for sulphur terminated InP(100) surfaces, prepared by wet-etch in (NH 4) 2S solution followed by UHV anneal. Standing wave profiles for sulphur 1s photoyield in three planes (220, 311 and 31 1 ) indicate that sulphur is close to the phosphorus site. Coherent positions and fractions are compared with the predictions of a number of models of the surface, including novel 2×2 structures. The experimental data can be reproduced by a general two-dimer model, but it is more likely that the data are reflecting significant disorder.

Microwave experiment on a costas-array reflecting screen

A novel technique to examine thinned-array reflecting screens by means of a microwave interferometer operating at a 8.8 mm wavelength is suggested. The screen is modeled with a 6×6 Costas array, and the standing wave profiles are analyzed for the near-field region of the screen. The results of the experiment show an increase in the fractal dimension of the screen accompanied by a decrease in field strength near the first antinode and by rearrangement of the standing wave profile.

Surface structure of [formula omitted] determined by back-reflection X-ray standing-wave method

The surface structure of S Ni(111) -(√3 × √3) R30° has been studied by means of the back-reflection X-ray standing wave (SW) method. The SW profiles of the surface S atoms were measured for the (111) and (11 1 ̄ ) reflections by monitoring the S-K fluorescence yield. The results of the (111) reflection in combination with previous SEXAFS results have revealed that the surface Ni layer is vertically relaxed outward by 0.12 ± 0.05 A ̊ . The (11 1 ̄ ) data have clarified that 80 ± 5% of the S adsorb on fcc hollow sites which are directly above the third-layer Ni atom, while the rest (20 ± 5%) occupy the hcp hollow sites above the second-layer Ni atom. These results are discussed in comparison with several previous investigations.

Long time evolution of standing gravity waves in deep water

A numerical study of the long time evolution of standing gravity waves with a breaking model is presented. We propose two simple and heuristic breaking models. The models simulate numerically the frequency downshift phenomenon which Lake et al. (1977) have reported experimentally. Our results show a new recurrence after the frequency downshift. A new method to obtain a standing wave profile is also proposed.