Rayleigh Wavelength Research Articles

Multilayer dielectric substrate for improved Raman spectroscopy

To enhance Raman scattering, we propose a multi-layer substrate which behaves similar to a magnetic mirror or what is also known as high-impedance surface (HIS). Due to this property, the electric field of the illuminating light is increased by a factor of two. This field enhancement doubles the amplitude of the Raman signal generated by the molecules residing on this multi-layer structure. On the other hand, the introduced multi-layer structure is designed to operate as a filter for the scattered field at the Rayleigh wavelength, so that the wave transmitted through this structure mainly contains the Raman signal with 45 dB rejection of the Rayleigh wavelength. The designed substrate reduces the complexity of the conventional Raman setup and helps to realize a more compact setup.

Relationship between morphology and transparency in glass-ceramic materials: comment

Borrelli et al. [J. Opt. Soc. Am. B35, 1725 (2018)JOBPDE0740-322410.1364/JOSAB.35.001725] applied the approach of Debye and Bueche in a discussion of light scattering in glass-ceramics. We show that this approach leads to equations that are qualitatively different from those presented by Borrelli et al. We also demonstrate that the experimental example of Rayleigh wavelength dependence of turbidity of glass-ceramic presented by Borrelli et al. seems to be not convincing.

Focus on lasers, imaging, and microscopy

Focus on lasers, imaging, and microscopy

Shape optimized inclined single and double wall wave barriers for ground vibration mitigation

Stiff wave barriers are capable of reducing the transmission of ground vibrations. Most designs consist of a single vertical wall, although double walls are also being considered. This paper investigates the shape optimization (position, inclination, length and thickness) of these topologies in a two-dimensional setting, for a point source and a point receiver placed symmetrically with respect to the design domain. Three types of sources are studied: a single-frequency source, a broadband source and a harmonic source within a given frequency range. An economical constraint on the maximum material use is considered. A multi-region BEM methodology is used for evaluating the objective function and its gradient. Analytical expressions are presented for the sensitivities, providing a very effective simulation tool for this type of problem. It is found that significant improvement can be achieved by repositioning and inclining the walls when compared to the reference cases. It is also found that optimized double wall barriers outperform single wall barriers. The improvement is insignificant for sources which generate Rayleigh wavelengths similar to the design domain depth, but it greatly increases as frequency increases and the penetration depth decreases.

MHD natural convection flow enclosure in a corrugated cavity filled with a porous medium

In this article, a complete structure of corrugated surface is established for heat transfer effects in the presence of uniform magnetic field. A natural convection phenomenon is presented for MHD flow filled in a porous corrugated cavity at various wavelengths and partially heated domain. The governing partial differential equations consist of continuity, momentum and energy equations along with the corrugated conditions at the surface. This system is properly nondimensionalized and then solved via finite element method (FEM). In order to obtain the high resolution near the surface of corrugation, mesh generation is improved at the various portions of the cavity. The flow patterns and temperature distribution within the entire domain of the cavity can be visualized through streamlines and isotherms, respectively. Computational experiment is performed for various values of wavelength number (0⩽n⩽15), Rayleigh number (104⩽Ra⩽106), Darcy number (10-5⩽Da⩽10-3), and Hartmann number (10⩽Ha⩽103) to illustrate the effects on streamlines, isotherms, velocities and heat transfer rate. Heat transfer rate is increased due to increase in Rayleigh number and wavelength parameter. Darcy and Hartmann number does not have significant effects on the temperature distribution.

Horizontal resolution of multichannel analysis of surface waves

The multichannel analysis of surface wave (MASW) method has been effectively and widely used to determine near-surface shear-wave velocity. Horizontal resolution of the MASW method represents the minimum horizontal length of recognizable geologic anomalous bodies on a pseudo-2D S-wave velocity [Formula: see text] section. Accurately assessing the achievable lateral resolution is one of the main issues in lateral variation reconstruction using the MASW method. It is difficult to quantitatively estimate the horizontal resolution of the MASW method because of the many influencing factors, such as parameters of the observation system, the depth of an anomalous body, and the velocity contrast between the anomalous body and the surrounding rocks. We first analyzed the horizontal resolution of the MASW method based on numerical simulation experiments. According to different influencing factors of the horizontal resolution, we established different laterally heterogeneous models and observation systems and then simulated several synthetic multichannel records with a finite-difference method along a linear survey line using the roll-along acquisition mode. After the extraction of dispersion curves of Rayleigh waves and inversion for S-wave velocity profiles for each synthetic shot gather, a pseudo-2D S-wave velocity section can be generated by aligning the 1D S-wave velocity models. Ultimately, we evaluated the horizontal resolution capability of the MASW method on pseudo-2D [Formula: see text] maps. Our numerical investigation results and field data analysis indicate that [Formula: see text] values on the maps are not the same as the true [Formula: see text] values for structures whose lateral dimension is shorter than a receiver spread length and that anomalous bodies, which are larger and have high velocity contrast, are easier to distinguish on [Formula: see text] maps with a shorter receiver spread length. The horizontal resolution decreases with the increasing depth and is approximately one-half of the shortest Rayleigh wavelength that can penetrate to the depth.

Properties of mixed metal–dielectric nanogratings for application in resonant absorption, sensing, and display

We treat fundamental resonance effects in hybridized metal–dielectric elements that may find applications in absorption, sensing, and displays. The hybrid structures support guided-mode resonance (GMR) and surface plasmon resonance (SPR) operating independently or in unison. Numerical simulations of periodic resonant films coated in gold that effectively combine principles of both resonance effects show viability of absorbers with equalized spectra and hybrid waveguides. The experimentally measured spectra show qualitative agreement with theoretical models. We introduce a hybrid GMR/SPR refractive-index sensor consisting of a thin aluminum film integrated with a subwavelength silicon-dioxide grating. The sensor operates between the Rayleigh wavelengths of the cover and the substrate. A GMR is excited by TE-polarized light and is subsequently attenuated by the Rayleigh anomaly as the cover index increases. In transverse-magnetic-polarized light, it operates as a Rayleigh sensor with sharp spectral features that would be easily monitored with a spectrum analyzer. As a final device example, we present simulation results pertaining to a one-dimensional color filter utilizing SPR, GMR, and the Rayleigh anomaly and convert it into a polarization insensitive two-dimensional device. With dual periods along orthogonal directions, two resonant peaks are induced within the visible spectrum for unpolarized input light rendering a color-mixing effect. The output color of the dual pixel is tunable with the input polarization state.

Fractal and spinodal-decomposed turbidities of nanoporous glass: fluctuation picture in turbid and transparent Vycor.

The light propagation and scattering in monolithic transparent nanoporous materials such as Vycor glasses exhibit two optical turbidities, both of which are slightly deviated from the λ-4 Rayleigh wavelength dependence in the visible region: one is a transient white turbidity τf, characterized by the convex-upward dependence on the inverse fourth power of wavelength, and the other is turbidity τsp inherent to the structural inhomogeneity, characterized by the convex-downward dependence. The former is attributed to a fractal-like percolation network of imbibed or drained pores as a consequence of transient imbibition or drainage of wetting fluid into or from the pore space. The latter is attributed to the structural inhomogeneities inherent to the original dry porous glass, which are produced by spinodal decomposition. In this paper, we develop a general scheme to estimate the transmittance spectra of Vycor through the turbidities τf and τsp in the visible region on the basis of the theory of dielectric constant fluctuations. We show the applicability and its limitation of the turbidity analysis of the photospectroscopically measured data as a method to study the correlation functions that characterize the pore space and the structural features of isotropic transparent nanoporous media, on the presupposition that there exists no light attenuation other than the scattering.

Double wall barriers for the reduction of ground vibration transmission

Stiff wall barriers can be effective in reducing the transmission of environmental ground vibration. Up to now, single wall barriers have mostly been studied. In building acoustics, however, double walls are used in order to realize a high level of sound insulation. In this paper, the potential of using double walls in reducing ground vibration transmission is investigated by means of numerical simulations. Two cases are studied: jet-grout walls and concrete walls in a homogeneous soil with elastic properties representative of a sandy soil. For both cases, the three-dimensional free field response due to a point load is computed using a 2.5D finite element methodology. Subsequently, the free field response is computed for a simplified train load. Double jet-grout wall barriers are found to be slightly more effective than single wall barriers, in particular when the thickness of the walls and the intermediate soil matches a quarter Rayleigh wavelength. The largest increase in vibration reduction is found for the area closest to the vibration source, where the vibration levels have the highest values. The performance of concrete wall barriers, however, is mainly determined by the stiffness of the walls, and almost no difference in performance is found for single and double walls.

Double wall barriers as mitigation measures for ground vibration transmission

Stiff wall barriers can be effective in reducing the transmission of environmental ground vibration. Up to now, single wall barriers have mostly been studied. In building acoustics, however, double walls are used in order to realize a high level of sound insulation. In this paper, the potential of using double jet-grout walls in reducing ground vibration transmission is investigated. The three-dimensional free field response due to a point load and a simplified train load is computed using a two-and-a-half dimensional finite element methodology. Double jet-grout wall barriers are found to be slightly more effective than single wall barriers, in particular when the thickness of the walls and the intermediate soil matches a quarter Rayleigh wavelength. The largest increase in vibration reduction is found for the area closest to the vibration source, where the vibration levels have the highest values.

Numerical investigation on vibration isolation by softer in-filled trench barriers

This paper deals with a 2-D finite element study in PLAXIS 2D on isolation of steady-state surface vibrations by softer backfilled trenches in an elastic, isotropic, and homogeneous half-space. Effects of barrier geometric features and infill material characteristics on reducing vertical and horizontal components of surface displacements are investigated. This study adopts a non-dimensional approach where the geometric parameters are normalized against the Rayleigh wavelength of vibration in half-space and backfill shear wave velocity is expressed as a ratio of that of parent soil. Softer barriers of shear wave velocity ratios less than unity are considered as they are found significantly effective than stiffer barriers. Effects of the parameters participating on wave isolation are extensively discussed and some guidelines are framed regarding their optimal selection. Non-dimensional charts are developed which would provide a sound basis for designing such barriers in actual engineering practice. The design charts are validated with some documented results and close agreement is obtained.

Diffraction of Rayleigh wave by simple surface irregularity using boundary element method

The topographic amplification effect is studied in this paper in the case of a semi-circular canyon under incident Rayleigh wave. Time-frequency domain boundary element method has been applied to investigate the wave diffraction phenomena. The model consists of a semi-circular canyon cut from an isotropic elastic half plane. The total response is decomposed into free field motion and scattered wave field. The former can be constructed analytically by superposing on incident and reflected Rayleigh waves in the half plane and the later by using boundary element method with linear elements. The analyses are performed in the frequency domain and then converted into time domain using fast Fourier transform (FFT) algorithm. It is shown that the weak and strong singularities in the governing integral equations for linear elements can be removed by analytical approaches. Different ranges of Rayleigh wavelengths from low to high are considered. The results are presented versus dimensionless frequency and distance. A limiting value for Rayleigh wavelength can be recognized beyond which the canyon has no important effects on scattering of harmonic incident waves. Furthermore, a parametric study has been performed for different values of Poisson’s ratios. The published works in the effects of this parameter are somewhat few and limited to specific values of Poisson’s ratio. Finally, the spatial variations of surface displacements for the Rayleigh wave impulse of Ricker wavelet type are obtained. The spatial distribution shows the generation of backward-scattered Rayleigh wave which its intensity depends on predominant frequency of the input impulse as well as Poisson’s ratio of the medium. Dynamic responses of the points just located at the edges of the semi-circular canyon are compared to each other which accounts for the isolation efficiency of the canyon.

Photospectroscopically observed pore-space correlations of a wetting fluid during the drying process in nanoporous Vycor glass.

We use light scattering to study spatial correlations in the pore space of Vycor glass upon draining a wetting fluid. We analyze the transmission spectrum of forward-scattered light on the basis of the theory of dielectric constant fluctuation, whereas conventional light scattering analyzes the scattered light at small angles of monochromatic incident light. Assuming that the drained pores, which are surrounded by filled pores, exhibit long-range correlations of a fractal dimension of 2.5, we analytically derive the corresponding turbidity. The slight deviation from the λ(-4) Rayleigh wavelength dependence directly provides the correlation length of the interconnected network of drained pores. The estimated length, ranging from 0.5 to 18 nm at most, is almost the same order as that indirectly estimated from our previous simple effective Rayleigh scatterer model.

Analysis and design of open trench barriers in screening steady-state surface vibrations

The problem of vibration isolation by rectangular open trenches in a plane strain context is numerically studied using a finite element code, PLAXIS. The soil media is assumed to be linear elastic, isotropic, and homogeneous subjected to a vertical harmonic load producing steady-state vibration. The present model is validated by comparing it with previously published works. The key geometrical features of a trench, i.e., its depth, width, and distance from the source of excitation, are normalized with respect to the Rayleigh wavelength. The attenuation of vertical and horizontal components of vibration is studied for various trench dimensions against trench locations varied from an active to a passive case. Results are depicted in non-dimensional forms and conclusions are drawn regarding the effects of geometrical parameters in attenuating vertical and horizontal vibration components. The screening efficiency is primarily governed by the normalized depth of the barrier. The effect of width has little significance except in some specific cases. Simplified regression models are developed to estimate average amplitude reduction factors. The models applicable to vertical vibration cases are found to be in excellent agreement with previously published results.

Numerical study on screening of surface waves using a pair of softer backfilled trenches

Vibration screening effectiveness of a pair of in-filled trenches is numerically studied under conditions of plane strain using PLAXIS 2D in a linear elastic, isotropic, and homogeneous half-space acted upon by a steady-state vertical excitation. Barrier efficiency is analyzed in terms of reduction of vertical and horizontal vibration components with respect to the variations in barrier geometry and in-fill material parameters. The geometric features are normalized with respect to Rayleigh wavelength of vibration in soil. The in-fill trench material is considered to be softer and accordingly assigned lower shear wave velocities than the half-space. Non-dimensional design charts are developed and the key parameters participating in wave screening process are identified. Some recommendations are made regarding the optimal selection of these parameters. Comparison with a few published results shows close agreement. Such an isolation scheme may be advantageous in circumstances where a single trench requires unrealistic depth.

The influence of source–receiver interaction on the numerical prediction of railway induced vibrations

Abstract The numerical prediction of vibrations in buildings due to railway traffic is a complicated problem where wave propagation in the soil couples the source (railway tunnel or track) and the receiver (building). This through–soil coupling is often neglected in state-of-the-art numerical models in order to reduce the computational cost. In this paper, the effect of this simplifying assumption on the accuracy of numerical predictions is investigated. A coupled finite element–boundary element methodology is employed to analyze the interaction between a building and a railway tunnel at depth or a ballasted track at the surface of a homogeneous halfspace, respectively. Three different soil types are considered. It is demonstrated that the dynamic axle loads can be calculated with reasonable accuracy using an uncoupled strategy in which through–soil coupling is disregarded. If the transfer functions from source to receiver are considered, however, large local variations in terms of vibration insertion gain are induced by source–receiver interaction, reaching up to 10 dB and higher, although the overall wave field is only moderately affected. A global quantification of the significance of through–soil coupling is made, based on the mean vibrational energy entering a building. This approach allows assessing the common assumption in seismic engineering that source–receiver interaction can be neglected if the distance between source and receiver is sufficiently large compared to the wavelength of waves in the soil. It is observed that the interaction between a source at depth and a receiver mainly affects the power flow distribution if the distance between source and receiver is smaller than the dilatational wavelength in the soil. Interaction effects for a railway track at grade are observed if the source–receiver distance is smaller than six Rayleigh wavelengths. A similar trend is revealed if the passage of a freight train is considered. The overall influence of dynamic through–soil coupling in terms of power flow remains limited to 2 dB, but the insertion gain at particular locations can easily reach 10 dB. This is of the same order of magnitude as other sources of uncertainty in the numerical prediction of railway induced vibrations; this should hence be accounted for when performing vibration predictions.

A Numerical Study of the Screening Effectiveness of Open Trenches for High-Speed Train-Induced Vibration

This study used the 2D boundary element method in time domain to examine the screening effectiveness of open trenches on reducing vibration generated by a high-speed train. The parameters included configurations of the trench, train speed, the distance between the source and the trench, and the Poisson’s ratio of the soil. A reducing displacement level (in dB scale) was defined and used to evaluate the screening effectiveness of a wave barrier. The maximal reducing displacement level reached 25 dB when an open trench was used as a wave barrier. The depth of an open trench is a main influential parameter of screening effectiveness. The cutoff frequency of the displacement spectrum increases with decreasing trench depth. The maximal screening effectiveness occurs when the depth is 0.3-0.4 Rayleigh wavelength. Using an open trench as a wave barrier can reduce 10–25 dB of vibration amplitude at frequencies between 30 and 70 Hz. A considerable increase in screening effectiveness of the open trench was observed from 30 to 70 Hz, which matches the main frequencies of vibration induced by Taiwan High Speed Rail. The influence of trench width on screening effectiveness is nonsignificant except for frequencies from 30 to 40 Hz. Poisson’s ratio has various effects on the reduction of vibration at frequencies higher than 30 Hz.

Accurate Analysis of Light Scattering and Absorption by an Infinite Flat Grating of Thin Silver Nanostrips in Free Space Using the Method of Analytical Regularization

We study the plane wave scattering and absorption by a flat grating of thin silver nanostrips located in free space, in the visible-light range. The formulation involves generalized boundary conditions imposed on the strip median lines. We use an accurate numerical solution to this problem based on the dual-series equations and the method of analytical regularization. This guarantees fast convergence and controlled accuracy of computations. Reflectance, transmittance, and absorbance as a function of the wavelength and the grating parameters are analyzed. In addition to well-known surface-plasmon resonances, sharp resonances are revealed in the H-polarized scattering near but not equal to the Rayleigh wavelengths of nonzero diffraction orders; in the E-polarized scattering these resonances are not visible. Asymptotic formulas for the frequencies and natural fields of the grating resonances are presented.

Subgrade stiffening next to the track as a wave impeding barrier for railway induced vibrations

This paper studies the efficiency of subgrade stiffening next to the track as a mitigation measure for railway induced vibrations by means of a two-and-a-half-dimensional coupled finite element–boundary element methodology. An analysis in the frequency–wavenumber domain for a homogeneous halfspace reveals that the block of stiffened soil next to the track can act as a wave impeding barrier. It is demonstrated that the wave impeding effect depends on the relation between the Rayleigh wavelength in the soil and the free bending wavelength in the block of stiffened soil, as the transmission of plane waves in the soil with a longitudinal wavelength smaller than the bending wavelength is hindered. This leads to a critical frequency from which this mitigation measure starts to be effective, depending on the stiffness contrast between the soil and the block of stiffened soil. The existence of a critical angle delimiting an area where vibration levels are reduced in case of harmonic excitation on the rail is also demonstrated. Two applications involving a layered halfspace are finally discussed to demonstrate that the performance of this mitigation measure critically depends on the soil characteristics.

Periodicity-induced effects in the scattering and absorption of light by infinite and finite gratings of circular silver nanowires

We study numerically the effect of periodicity on the plasmon-assisted scattering and absorption of visible light by infinite and finite gratings of circular silver nanowires. The infinite grating is a convenient object of analysis because of the possibility to reduce the scattering problem to one period. We use the well-established method of partial separation of variables however make an important improvement by casting the resulting matrix equation to the Fredholm second-kind type, which guarantees convergence. If the silver wires have sub-wavelength radii, then two types of resonances co-exist and may lead to enhanced reflection and absorption: the plasmon-type and the grating-type. Each type is caused by different complex poles of the field function. The low-Q plasmon poles cluster near the wavelength where dielectric function equals -1. The grating-type poles make multiplets located in close proximity of Rayleigh wavelengths, tending to them if the wires get thinner. They have high Q-factors and, if excited, display intensive near-field patterns. A similar interplay between the two types of resonances takes place for finite gratings of silver wires, the sharpness of the grating-type peak getting greater for longer gratings. By tuning carefully the grating period, one can bring together two resonances and enhance the resonant scattering of light per wire by several times.