Finite Lateral Width Research Articles

A Recursive Legendre Polynomial Analytical Integral Method for the Fast and Efficient Modelling Guided Wave Propagation in Rectangular Section Bars of Orthotropic Materials

Ultrasonic guided waves are widely used in non-destructive testing (NDT), and complete guided wave dispersion, including propagating and evanescent modes in a given waveguide, is essential for NDT. Compared with an infinite plate, the finite lateral width of a rectangular bar introduces a greater density of modes, and the dispersion solutions become more complicated. In this study, a recursive Legendre polynomial analytical integral (RLPAI) method is presented to calculate the dispersion behaviours of guided waves in rectangular bars of orthotropic materials. The existing polynomial method involves a large number of numerical integration steps, and it is often computationally costly to compute these integrals. The presented RLPAI method uses analytical integration instead of numerical integration, thus leading to a significant improvement in the computational speed. The results are compared with those published previously to validate our method, and the computational efficiency is discussed. The full three-dimensional dispersion curves are plotted. The dispersion characteristics of propagating and evanescent waves are investigated in various rectangular bars. The influences of different width-to-thickness ratios on the dispersion curves of four types of low-order modes for a rectangular bar of an orthotropic composite are illustrated.

Spoof surface plasmon analysis based on Marcatili’s method

Motivated by surface plasmon polariton waveguides in the optical regime, spoof surface plasmon (SSP) waveguides have received a lot of attention in terahertz and millimeter wave frequencies. Most research on these kinds of waveguides is numerical. However, some limited analytical work can be seen in the literature. In this paper, one type of SSP waveguide that is composed of a rectangular corrugation with finite lateral width on the ground is considered, and an analytical method, which is inspired by Marcatili’s method, is proposed in order to calculate the dispersion curve of the first mode. The results of this analytical method and a numerical commercial eigenmode solver are compared. The accuracy of this method by varying different geometrical parameters is shown. Finally, it is shown that this method works well in predicting the electromagnetic fields of the first mode.

Selective generation of ultrasonic guided waves for damage detection in rectangular bars

Ultrasonic guided waves are used in non-destructive testing and structural health monitoring solutions for long-range inspection, in applications ranging from Civil Engineering to Aerospace. In order to ease the inspection process, it is generally preferable to generate a carefully selected single mode. Although single mode Lamb wave generation is not difficult to achieve in infinite plate-like structures, with carefully polarized or sized piezoceramic elements, for example, such selective generation is much more difficult in a rectangular bar. In this article, we consider the propagation along a thin plate of finite rectangular cross section, which corresponds to a rectangular bar. The finite lateral width leads to a greater density of modes compared to an infinite plate. The authors have previously addressed this matter and developed a methodology for the selective generation of modes in the harmonic regime. This article extends this methodology to selective mode generation for finite time excitation, such as bursts. Results are presented for single mode generation of A0,0 and A0,1 in an aluminum bar instrumented with eight piezoelectric transducers. The waveguide modal basis is calculated with the two-dimensional semi-analytical finite element method, and measurements are conducted using a three-dimensional laser-Doppler vibrometer. To illustrate the potential of the method for structural health monitoring purposes, the detection of a defect simulated by a pair of magnets placed at various positions over the bar width is demonstrated.

Evolution of topological superconductivity by orbital-selective confinement in oxide nanowires

We determine the optimal conditions to achieve topological superconducting phases having spin-singlet pairing for a planar nanowire with finite lateral width in the presence of an in-plane external magnetic field. We employ a microscopic description that is based on a three-band electronic model including both the atomic spin-orbit coupling and the inversion asymmetric potential at the interface between oxide band-gap insulators. We consider amplitudes of the pairing gap, spin-orbit interactions and electronic parameters that are directly applicable to nanowires of LaAlO$_3$-SrTiO$_3$. The lateral confinement introduces a splitting of the $d$-orbitals that alters the orbital energy hierarchy and significantly affects the electron filling dependence of the topological phase diagram. Due to the orbital directionality of the $t_{2g}$-states, we find that in the regime of strong confinement the onset of topological phases is pinned at electron filling where the quasi flat heavy bands start to get populated. The increase of the nanowire thickness leads to a changeover from sparse-to-dense distribution of topologically non-trivial domains which occurs at the cross-over associated to the orbital population inversion. These findings are corroborated by a detailed analysis of the most favorable topological superconducting phases in the electron doping-magnetic field plane highlighting the role of orbital selective confinement.

Quantum confinement of exciton-polaritons in a structured (Al,Ga)As microcavity

The realization of quantum functionalities with polaritons in an all-semiconductor platform requires the control of the energy and spatial overlap of the wave functions of single polaritons trapped in potentials with precisely controlled shape and size. In this study, we reach the confinement of microcavity polaritons in traps with an effective potential width down to 1 um, produced by patterning the active region of the (Al,Ga)As microcavity between two molecular beam epitaxy growth runs. We correlate spectroscopic and structural data to show that the smooth surface relief of the patterned traps translates into a graded confinement-potential characterized by lateral interfaces with a finite lateral-width. We show that the structuring method is suitable for the fabrication of arrays of proximal traps, supporting hybridization between adjacent lattice sites.

Design of a hybrid spoof plasmonic sub-terahertz waveguide with low bending loss in a broad frequency band.

The effect of dielectric cladding on the waveguiding characteristics of an array of metallic pillars on a metal plane in the sub-terahertz band is explored. Firstly, a 2D structure made up of a metallic grating of infinite lateral width with various dielectric overlays is analytically studied to get more insight into the problem. Then the ideas inferred from the 2D structure are applied to the realistic 3D structure that has a finite lateral width. It is shown that by proper design of the dielectric medium surrounding the metallic structure the modal field confinement can be enhanced in a broad frequency band resulting in a low bending loss. Especially, by integrating the pillars into a silicon channel of finite size and evacuating the spaces between them a highly confined spoof surface plasmon is supported and a considerable reduction in the bending loss over a broad bandwidth is observed. Due to small cross-sectional size, low bending loss and ease of fabrication, the proposed waveguide is a promising choice for millimeter-wave and terahertz integrated circuits; particularly those based on the silicon technology.

Magnetic noise around metallic microstructures

We compute the local spectrum of the magnetic field near a metallic microstructure at finite temperature. Our main focus is on deviations from a plane-layered geometry for which we review the main properties. Arbitrary geometries are handled with the help of numerical calculations based on surface integral equations. The magnetic noise shows a significant polarization anisotropy above flat wires with finite lateral width, in stark contrast to an infinitely wide wire. Within the limits of a two-dimensional setting, our results provide accurate estimates for loss and dephasing rates in so-called “atom chip traps” based on metallic wires. A simple approximation based on the incoherent summation of local current elements gives qualitative agreement with the numerics, but fails to describe current correlations among neighboring objects.

Second harmonic generations in aperiodic optical superlattices with finite width and in one-dimensional defective photonic crystals made of nonlinear optical materials

The characteristics of the second harmonic generations (SHGs) in homogeneous and inhomogeneous systems are investigated. We consider two kinds of structures: one is aperiodic optical superlattices (AOSs) with homogeneous linear susceptibility and the modulated second-order nonlinear susceptibility; the second is linear and nonlinear susceptibilities both the system with inhomogeneous. We derive a general solution of SHG for the AOS with finite lateral width and of SHG in considering the depletion of the pump light power. We carry out the design of AOSs by using simulation annealing (SA) algorithm and show that the constructed AOSs can implement multiple wavelength SHGs with identical effective nonlinear coefficient at the preassigned wavelengths of incident light. We observe great enhancement of SHGs in the one-dimensional photonic crystals (PCs) with defects consisting of multiple photonic quantum wells made of nonlinear material when the frequency of fundamental wave aims at one of the defect states. We also propose an effective design approach of aperiodically stacked layers of nonlinear material and air in terms of the SA method. The constructed structure can achieve multiple-wavelength SHGs at the preas-signed wavelengths.

Electron spin precession in semiconductor quantum wires with Rashba spin-orbit coupling

The influence of the Rashba spin-orbit coupling on the electron spin dynamics is investigated for a ballistic semiconductor quantum wire with a finite width. We monitor the spin evolution using the time-dependent Schr\"odinger equation. The pure spin precession characteristic of the 1D limit is lost in a 2D wire with a finite lateral width. In general, the time evolution in the latter case is characterized by several frequencies and a nonrigid spin motion.

Coupled third harmonic generations and multiple mode effects in aperiodic optical superlattices with a finite lateral width

We study the coupled third harmonic generations (CTHGs) from quasi-one-dimensional aperiodic optical superlattices (AOSs) with a finite lateral width. We design the special AOS that can implement multiple wavelength CTHG with identical effective nonlinear coefficient at the preassigned wavelengths of incident light with the use of simulated annealing method. We reveal the effects of mode-mode coupling and the lateral width of the AOSs on the CTHG for the two cases: One case corresponds to the incident light beam of a plane wave profile and other case to the incident light beam of Gaussian profile. The results show that the characteristics of the CTHG from the AOSs are closely related to the profiles of the incident fundamental frequency light beam. For the incidental plane wave beam, the dependence of the effective nonlinear coefficient on the width of the AOS is quite weak. On the contrary, for the incident Gaussian profile beam, this dependence exhibits a rapid decrease at the beginning and then tends to a constant. We also display the variation of the effective nonlinear coefficients with the optical wave propagating distance from the impinging surface of incident light beam in the sample illuminating by the plane wave light beam and find that this variation exhibits basically increasing behavior. This clearly infers that the contribution of every individual block to optical CTHG process is a constructive addition. When increasing the number of the modes, the effective nonlinear coefficient of CTHG is rapidly decreased at the beginning and it then tends to a saturation value for the incident plane wave light beam. However, for the incident light beam of Gaussian profile, similar behavior is observed only when the lateral width of the AOS is smaller than that of the Gaussian profile beam; in contrast, the Nc dependence of the effective nonlinear coefficient of the CTHG is quite weak.

Second-harmonic generation and multiple mode effects in aperiodic opticalsuperlattices with finite lateral width

We have studied second-harmonic generation (SHG) from quasi-one-dimensionalaperiodic optical superlattices (AOSs) of finite lateral width by inverting poledferroelectric domains. The search for optimal AOS structures corresponds withsolving a difficult inverse source problem. We describe the design principle inreal-space representation and undertake model designs. The numerical simulationsshow that the constructed AOSs can implement multiple-wavelength SHG withidentical effective nonlinear coefficients at the pre-assigned wavelengths of theincident light. We investigate the effects of mode–mode coupling and thelateral width of the superlattice on the SHG for two cases: incident lightbeams of plane-wave and Gaussian profiles. When the number of modesincreases, the effective nonlinear coefficient decreases in an oscillatoryfashion at the beginning and then tends to a constant. For an incidentplane-wave beam, the dependence of the effective nonlinear coefficient onthe width of the sample is quite weak, while for an incident Gaussianbeam this dependence exhibits a rapid decrease at the beginning and thentends to a constant. We display the variation in the effective nonlinearcoefficients with the distance of propagation of the optical wave from where theincident light beam impinges on the sample surface and find that thisvariation exhibits monotonically increasing behaviour. This clearly infersthat the contribution of every block to the optical SHG process takesthe form of constructive addition. It is expected that this new designmethod may provide an effective and useful technique for constructingnonlinear optical material to match various practical applications.

Flexural waves on narrow plates.

Flexural wave speeds on beams or plates depend upon the bending stiffnesses which differ by the well-known factor (1 - nu2). A quantitative analysis of a plate of finite lateral width displays the plate-to-beam transition, and permits asymptotic analysis that shows the leading order dependence on the width. Orthotropic plates are analyzed using both the Kirchhoff and Kirchhoff-Rayleigh theories, and isotropic plates are considered for Mindlin's theory with and without rotational inertia. A frequency-dependent Young's modulus for beams or strips of finite width is suggested, although the form of the correction to the modulus is not unique and depends on the theory used. The sign of the correction for the Kirchhoff theory is opposite to that for the Mindlin theory. These results indicate that the different plate and beam theories can produce quite distinct behavior. This divergence in predictions is further illustrated by comparison of the speeds for antisymmetric flexural, or torsional, modes on narrow plates. The four classical theories predict limiting wave speeds as the plate width vanishes, but the values are different in each case. The deviations can be understood in terms of torsional waves and how each theory succeeds, or fails, in approximating the effect of torsion. Dispersion equations are also derived, some for the first time, for the flexural edge wave in each of the four "engineering" theories.

Initiation of a doubly diffusive convection in a stable halocline

A vertically stable density stratification with temperature gradient T z < 0, salinity gradient S z < 0, and with density compensating horizontal T/S gradients is unstable to lateral intrusions because the molecular heat diffusivity is much larger than the salt diffusivity. Previous marginal instability theory is extended to the supercritical regime. The fastest growing vertical wavelength (δ z ) is obtained in a model of a T/S front with finite lateral width (L * ) and lateral salinity variation (ΔS). The value of δ z ΔS/|S z | varies only slightly with the parameters, and this result is applied to the smallest step size observed in the main thermocline of the Weddell Sea. Nonlinear considerations show that the laterally divergent heat/salt flux produced by the instability forces a mean vertical circulation which enhances the compensating lateral T/S gradients, thereby accelerating the intrusive instability, and eventually producing local density ratios sufficient to initiate strong vertical convection. This suggests that weak isopycnal T/S gradients are necessary to initiate the steps which subsequently merge into larger layers.

Observation and analysis of quantum wire structures by high-resolution X-ray diffraction

We report on the double-crystal X-ray diffraction analysis of AlGaAs/GaAs quantum wire structures. We show that X-ray scattering is very sensitive to the modulation of structural parameters parallel to the crystal surface under certain diffraction conditions. The experimental diffraction patterns exhibit quantum wire satellite peaks which allow us to determine the quantum wire period and the quantum wire width. Furthermore, we found that due to the finite lateral width of the quantum wires a partial asymmetric strain relaxation of the unit cell occurs resulting in an orthorhombic lattice deformation.

Design of Dielectric Grating Antennas for Millimeter-Wave Applications

At theoretical procedure well suited for generating design data on dielectric grating antennas for the millimeter-wave region is presented. The procedure utilizes the effective dielectric constant (EDC) method to determine the phase constant of the leaky modes supported by the antenna structure of finite lateral width. The radiation or leakage constant of these modes is obtained from the relatively simple boundary value problem of dielectric grating antennas of infinite width. For single-beam radiation, the practicably interesting case, the phase and leakage constants completely determine the field distribution in the antenna aperture, from which the directivity gain and radiation pattern are then calculated. The dependence of the antenna characteristics on the dimensions of the radiating structure is presented and discussed for epsilon = 12, the dielectric constant of typical millimeter-wave materials, such as silicon and GaAs.

Shading effects of finite width overhang on windows facing toward the equator

Analytical methods are presented for calculating either monthly average or clear-day insolation on a vertical surface facing the equator with overhang shading of finite lateral width. The technique is an extension of that presented by Jones[1] for overhangs of infinite lateral extent.

Energy Transformations and Meridional Circulations associated with simple Baroclinic Waves in a two-level, Quasi-geostrophic Model

The changes in geostrophic kinetic energy predicted by the “2 – ½ dimensional” quasi-geostrophic vorticity equations without friction are shown to be compatible with the mechanical energy equation. The second-order effects on a zonal current due to the presence of very simple unstable baroclinic waves are then analysed, using a two-level model of finite lateral width without friction or heat sources. In addition to the poleward transport of sensible heat and the creation of kinetic energy by these waves, it is shown that they are accompanied in this model by a weak meridional circulation. This circulation consists of an indirect cell in middle latitudes with direct cells to the north and south. The possible importance of this mechanism in providing appropriately distributed sources and sinks of relative zonal momentum (and therefore in prescribing the distribution with latitude of the surface zonal winds) is demonstrated with the aid of Widger's observations of the horizontal momentum transfer by eddies during January 1946. Finally it is shown that about 95 per cent of the perturbation energy in the unstable waves of this type comes from the “potential energy” of the basic current, the small remainder coming from the kinetic energy of that current.