Plane waves in regular arrays of dipole scatterers and effective-medium modeling

A simple analytical theory for finding eigensolutions for plane electromagnetic waves propagating along an axis in infinite regular arrays of small dipole particles is presented. The spacing between dipoles in every plane is assumed to be smaller than the wavelength; separation between the planes is arbitrary. The influence of evanescent modes is taken into account. This theory gives a model for an effective propagation constant that can be applied in a wide frequency range from the quasi-static regime to the Bragg reflection (photonic bandgap) region.     

Ultrashort pulsed bessel beams and spatially induced group-velocity dispersion.

We find a new family of solutions of the nonparaxial wave equation that represents ultrashort pulsed light beam propagation in free space. The spatial and temporal parts of these pulsed beams are separable; the spatial transverse part is described by a Bessel function and remains unchanged during propagation, but the temporal profile can be arbitrary. Therefore the pulsed beam exhibits diffraction-free behavior with no transverse spreading, but the temporal part changes as if in a dispensive medium; the change is dominated by what we call spatially induced group-velocity dispersion. The analytical and numerical investigations show that the even- and odd-order spatially induced dispersions partially compensate for each other so as to give rise to pulse spreading, weakening, asymmetry, and center shift.     

Elastic Gaussian wave packets in isotropic media

Summary The theory of Gaussian wave packet (GWP) propagation in elastic materials is developed. The GWP solutions are in the form of localized disturbances with Gaussian spatial envelopes at any instant in time. The method is explicitly time dependent, but is conceptually no more difficult than time harmonic ray theory. The equations of propagation and evolution are very similar to those of standard, elastodynamic ray theory, but include an extra degree of freedom not considered previously: the temporal width of the pulse. The theory is valid if the carrier wavelength is short in comparison with typical length scales in the medium. Interfaces of discontinuity in material properties give rise to reflected and transmitted GWPs. Explicit expressions are presented that relate the incident GWP to the reflected and transmitted GWPs. These results are illustrated by numerical simulations of a pulse incident upon a spherical interface.With 5 Figures     

Theoretical Analysis of Pulsed Photoacoustic Effect in Solids

This article presents a one-dimensional theory of a photoacoustic cell, working in the pulse regime. A four-layer system with elements of finite thickness has been assumed to represent consecutive parts of the photoacoustic cell. A parabolic heat equation with an instantaneous, bulk heat source has been solved using the Fourier transform of spatial coordinates. The theory allows one to assume that a heat source is existing in every part of the system and that an arbitrary time profile of the initial pulse is applied. Consequently, the system can be treated as an arbitrary photothermic or photoacoustic one-dimensional system. As a result, one obtains temperature profiles in the entire system at any time instant after its excitation with a light pulse. The gas-pressure evolution is dependent on the thermal and optical properties of the sample, the cell geometry, and duration and shape of the initial pulse.     

Defect-Mediated Growth of Crystallographic Shear Plane

As representative extended planar defects, crystallographic shear (CS) planes, namely Wadsley defects, play an important role in modifying the physical and chemical properties of metal oxides. Although these special structures have been intensively investigated for high-rate anode materials and catalysts, it is still experimentally unclear how the CS planes form and propagate at the atomic scale. Here, the CS plane evolution in monoclinic WO₃ is directly imaged via in situ scanning transmission electron microscope. It is found that the CS planes nucleate preferentially at the edge step defects and proceed by the cooperative migration of WO₆ octahedrons along particular crystallographic orientations, passing through a series of intermediate states. The local reconstruction of atomic columns tends to form (102) CS planes featured with four edge-sharing octahedrons in preference to the (103) planes, which matches well with the theoretical calculations. Associated with the structure evolution, the sample undergoes a semiconductor-to-metal transition. In addition, the controlled growth of CS planes and V-shaped CS structures can be achieved by artificial defects for the first time. These findings enable an atomic-scale understanding of CS structure evolution dynamics.     

Preliminary Report: Heat Pulse Propagation in Solid 4He up to 56 bar Between 40 and 500 mK

Heat pulse propagation in the solid ⁴He has been studied between 40 and 500 mK. Response to heat pulses are detected by a titanium film superconducting transition edge bolometer. Crossover behavior from second sound in normal solid above 500 mK to ballistic propagation below 200 mK is observed. Detailed study is made to search for possible modification of this propagation behavior by the appearance of supersolidity. It is found, that the ballistic phonon propagation velocity remains constant, within 0.3% scatter of data, below 100 mK at all pressures measured between 25 and 56 bar. The temporal evolution of the detected pulse shape has not revealed any anomaly below 200 mK.     

Joint Spatial and Temporal Characterization of the Wideband Wireless Communication Channel

We present a novel approach for the joint study of the spatial and temporal correlations of the wideband random microwave propagation in a disordered environment. We specifically address the issue of the time dependence of small-scale spatial variations in the transmitted field resulting from pulse propagation. Using Fourier transform techniques performed on the field spectra measured in indoor environment over an area of several square wavelengths, λ2, in steps of λ/10 we obtain very fine maps of the spatial variations of pulse responses in different moments of time with a one-ns resolution. A transition from a well-defined wavefront at the time of first arrivals to a complex interference pattern of waves coming from multiple directions shortly thereafter can be clearly seen.     

A k-space method for large-scale models of wave propagation in tissue

Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for “slow” (c(x)⩽c₀) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed     

Kurtosis parameter K of arbitrary electromagnetic beams propagating through non-Kolmogorov turbulence

General analytical formulae for the kurtosis parameters K (K parameters) of the arbitrary electromagnetic (AE) beams propagating through non-Kolmogorov turbulence are derived, and according to the unified theory of polarization and coherence, the effect of degree of polarization (DOP) of an electromagnetic beam on the K parameter is studied. The analytical formulae can be given by the second-order moments and fourth-order moments of the Wigner distribution function for AE beams at source plane, the two turbulence quantities relating to the spatial power spectrum, and the propagation distance. Our results can also be extended to the arbitrary beams and the arbitrary spatial power spectra of Kolmogorov turbulence or non-Kolmogorov turbulence. Taking the stochastic electromagnetic Gaussian Schell-model (SEGSM) beam as an example, the numerical examples indicate that the K parameters of a SEGSM beam in non-Kolmogorov turbulence depend on propagation distance, the beam parameters and turbulence parameters. The K parameter of a SEGM beam is more sensitive to effect of turbulence with smaller inner scale and generalized exponent parameter. A non-polarized light has the strongest ability of resisting turbulence (ART), however, a fully polarized SEGSM beam has the poorest ART.     

Propagation of optical pulses with spatial and temporal dependence

A convenient approximate formula is proposed for the study of free-space propagation of spatial and temporal pulses with an identifiable carrier frequency. It does not contain a time derivative operation on the pulse's temporal envelope explicitly. It is shown that once a short (for example, picosecond or subpicosecond) pulse is created with a spatial and a temporal structure, it does not last forever. The approximation discussed is valid over a certain distance as dictated by the wave equation. Beyond this distance, the spatial and temporal characteristics begin to influence each other significantly. Two examples are presented. The first example is that of a pulse with a factored form of a spatial envelope times a temporal envelope. The second example is that of a clear aperture with a grating, by which pulse stretching or temporal distortion is examined and the result is in agreement with that found in the literature.     

A SIMPLE THEORY FOR LOW CYCLE MULTIAXIAL FATIGUE

Abstract— A theoretical development based on a simple physical model is proposed to help the designer predict high strain multi-axial fatigue behaviour. This approach hypothesises that the maximum shear strain γ*, on planes driving the crack through the thickness, controls the fatigue crack propagation rate and hence the life. The direct strain δ*_n acting normal to the plane of γ* can exert a secondary modifying influence. Experimental results from several research laboratories have been analysed in this manner with some success.     

Scattering from cylinders using the two-dimensional vector plane wave spectrum

The two-dimensional vector plane wave spectrum (VPWS) is scattered from parallel circular cylinders using a boundary value solution with the T-matrix formalism. The VPWS allows us to define the incident, two-dimensional electromagnetic field with an arbitrary distribution and polarization, including both radiative and evanescent components. Using the fast Fourier transform, we can quickly compute the multiple scattering of fields that have any particular functional or numerical form. We perform numerical simulations to investigate a grating of cylinders that is capable of converting an evanescent field into a set of propagating beams. The direction of propagation of each beam is directly related to a spatial frequency component of the incident evanescent field.     

Dislocation modeling of quasi-static crack propagation in an elasto-plastic medium

A dislocation model for simulating two-dimensional quasi-static crack propagation is presented. The crack and plastic flow along slip planes are described using dislocation dipoles. A stationary crack can be modeled as well as a propagating crack along a straight line inclined at an arbitrary angle to a free surface of a semi-infinite medium. Cracks are also allowed to kink. A superdipole algorithm is introduced to save simulation time without loosing important information and necessary geometric details. It reduces the number of dislocation dipoles on slip planes in the plastic wake. The paper gives results on crack shapes for stationary and advancing cracks as well as it describes how the size of the plastic zone depends on crack inclination angles. Results on stress intensity factors (SIF) are given using two different approaches as well as kinking cracks are introduced and SIF at kinked crack tips are calculated.     

Dust particle formation in low pressure Ar/CH4 and Ar/C2H2 discharges used for thin film deposition

This paper deals with the study of the temporal and spatial evolution of the dust formation in two types of capacitively coupled discharges in Ar/C₂H₂ and Ar/CH₄ gas mixtures used for thin film deposition. To initiate the particle growth in the Ar/CH₄ discharge it is necessary either to apply transiently high power to the discharge or to inject transiently a pulse of C₂H₂. In the Ar/C₂H₂ discharge, however, the particles are formed spontaneously at constant low power. Due to the different initiation process the further temporal evolution of the dust formation is significantly different for both kind of gas mixtures. In the case of argon/acetylene the formation of dust particles shows a periodical behavior, which is not observed in the argon/methane mixture. The dust particles are detected by means of laser light scattering and by measuring the extinction of the laser after passing the discharge. The chemical nature of the particles was studied in situ by means of a multi pass FTIR-spectrometer. The thin film deposition was measured with an in situ ellipsometer.     

Knight Shift Data and Superconducting T c Modeling Based on an Effective Hole Model

The superconducting T _c of cuprates have been modeled on a linear scaling with hole concentration per CuO₂ plane and a deleterious influence of bond resonance with the apical system (effective hole formalism). In cases where distribution between various hole reservoirs is not trivial, Knight shift can provide actual hole concentrations. It is shown here that when Knight shift data are used in an effective hole algorithm, satisfactory T _c predictions can be made, corroborating the deleterious influence on T _c of apical O and earlier assumptions concerning hole distributions. For the case of stacking of more than two CuO₂ planes, the inner plane has to be treated as an infinite layer analog in the effective hole model. A separation into inner and outer planes with different dopings is indeed observed by Knight shift, with higher doping in the latter. This is explained here as being due to a tendency to equalize an effective doping degree, as the outer planes lose holes in resonance of bonding with the apical system.     

Knight Shift Data and Superconducting Tc Modeling Based on an Effective Hole Model

The superconducting T _c of cuprates have been modeled on a linear scaling with hole concentration per CuO₂ plane and a deleterious influence of bond resonance with the apical system (effective hole formalism). In cases where distribution between various hole reservoirs is not trivial, Knight shift can provide actual hole concentrations. It is shown here that when Knight shift data are used in an effective hole algorithm, satisfactory T _c predictions can be made, corroborating the deleterious influence on T _c of apical O and earlier assumptions concerning hole distributions. For the case of stacking of more than two CuO₂ planes, the inner plane has to be treated as an infinite layer analog in the effective hole model. A separation into inner and outer planes with different dopings is indeed observed by Knight shift, with higher doping in the latter. This is explained here as being due to a tendency to equalize an effective doping degree, as the outer planes lose holes in resonance of bonding with the apical system.     

On the crack propagation with variable velocity

The plane problem of propagation of a straight crack in an elastic medium under arbitrary variable loading is considered. The locations of the edges of the crack are specified as arbitrary smooth functions of time under the only restriction that crack speed at any instant of time is less than the velocity of Rayleigh wave. Solution for the distribution of plane stress components near the crack tip is obtained. In particular, expressions for stress intensity factors at the crack are given, which thus makes it possible to deduce the crack motion under given loading conditions.     

EBSD investigation of the microstructure and microtexture evolution of 1050 aluminum cross deformed from ECAP to plane strain compression

Electron backscattered diffraction (EBSD) was used to document the microstructure and texture developed due to cross deformation of commercial purity 1050 aluminum alloy. The materials are first deformed in equal channel angular pressing die (ECAP) to different number of passes; 1,4, 8, 12, and 16 passes, via route B_C and then deformed in plane strain compression (PSC) to two axial true plastic strain values of 0.5 and 1.0. Deformation path change was proven to be a very effective tool for manipulating the evolution of microstructure and microtexture. The study provides a documentation of the evolution of microstructure parameters namely cell size, misorientation angle, fraction of submicron grain size, and fraction of high angle grain boundaries. These microstructure parameters were investigated on two planes; the plane normal to the loading direction in PSC (RD–TD) and that plane normal to the transverse direction (RD–ND). These microstructure parameters are compared to those achieved due to the ECAP process only. The ideal rolling texture orientations are depicted and crystal orientation maps were generated. The spatial distribution of grains having these orientations is revealed through these maps. The fraction of the main texture components for a 10° spread around the specified orientations is experimentally calculated and a quantitative idea on the evolution of microtexture is also presented.     

Propagation of terahertz pulses in random media

We describe measurements of single-cycle terahertz pulse propagation in a random medium. The unique capabilities of terahertz time-domain spectroscopy permit the characterization of a multiply scattered field with unprecedented spatial and temporal resolution. With these results, we can develop a framework for understanding the statistics of broadband laser speckle. Also, the ability to extract information on the phase of the field opens up new possibilities for characterizing multiply scattered waves. We illustrate this with a simple example, which involves computing a time-windowed temporal correlation between fields measured at different spatial locations. This enables the identification of individual scattering events, and could lead to a new method for imaging in random media.     

A diffraction model of direction multiplexing method for hiding multiple images

Spherical surface (or cylinder) is considered to be regarded as the observing plane in an optical system. Several original images are placed at different directions on a sphere (or cylinder). The diffraction model between two slant planes is proposed to construct the propagation relation equation of the light field expressed by two images. The interference of two optical beams is used for hiding a secret pattern into two phase-only masks. The geometric parameters of the system (orientation and distance) can serve as an additional key for enhancing security. The numerical simulation results are made in order to validate the performance of the multiple encryption schemes.