Diffraction Of Plane Research Articles

Diffraction of plane P waves by a circular unlined tunnel in an unsaturated poroelastic half-space

Diffraction of plane P waves by a circular unlined tunnel in an unsaturated poroelastic half-space

Diffraction of plane P waves by a circular-arc canyon in an unsaturated poroelastic half-space

Based on the theory of unsaturated porous elastic medium, the diffraction around the circular-arc canyon in unsaturated half-space under the incidence of plane P wave is studied by using the Fourier-Bessel series expansion method of wave function. Through numerical examples, the influence of parameters such as incident wave frequency, incident angle, arc depth-width ratio and saturation on the surface displacement amplitude in unsaturated half-space circular-arc canyon is analyzed. The results show that the saturation has a significant effect on the variation of surface displacement amplitude, and the influence law of saturated and unsaturated site soils on the variation of surface displacement amplitude is very different under different depth-to-width ratio and incident frequency. In the case of different depth-width ratios of unsaturated half-space circular-arc canyon, the displacement amplitude change of semi-circular canyon (h/a = 1) is more sensitive to the change of saturation than that of shallow circular canyon (h/a = 0.5). When the incident frequency is low, the maximum displacement amplitude of the half-space circular-arc-canyon in both saturated and unsaturated cases increases with the increase of the incident angle. It is worth noting that when the saturation Sr = 0.99, i.e., when the soil is close to saturation, the maximum surface displacement amplitude caused by unsaturated depressed terrain (Sr = 0.8) is greater than that caused by the saturated soil case as the incidence angle increases.

Breaking Boundaries in LED Technology: Exploring the Revolutionary Diode Characteristics of Screen Printed (TiO2)1−x (CuO)x Thick Films

A thick TiO2-CuO composite film is deposited on a Si substrate by a low-cost screen printing method. Both anatase and CuO-doped TiO2 are characterized for diode applications. X-ray Diffraction (XRD) confirms that the composite film exists as an anatase phase of TiO2 and a monoclinic phase of CuO with a maximum diffraction of (101) plane. SEM images depict the less severe agglomeration of particles for the doped TiO2 as compared to the anatase TiO2. The UV–visible spectra reveal a direct band gap shift of 3.35 eV (pure TiO2) to 3.26 eV (doped TiO2). From the PL study, the blue shaded emission is perfectly derived for anatase TiO2 while the color is seen to change to the white zone supporting TiO2-CuO composite formation as depicted by the CIE diagram. The diode parameters such as ideality factor (n) and barrier height (Φb) are calculated with the help of I–V characteristics. This only reported novel effort on screen-printed TiO2-CuO thick film may help in manufacturing possible LEDs for optoelectronic applications.

Growth of TiO2–CdO coated films: A brief study for optoelectronic applications

Current work reports the deposition of pure and TiO2 doped CdO printed films on glass substrate via cost-effective screen-printing method and then sintered at 550 °C for 10 min. The pure TiO2, CdO and TiO2–CdO coated films were used to investigate the structural, morphological and opto-electrical properties by different analytical techniques. X-ray diffraction pattern of polycrystalline doped analogue confirms the existence of TiO2 anatase phase and cubic phase of CdO with a maximum diffraction of (101) plane. Surface morphology is derived from scanning electron microscopy finding out porous images along with EDS results to confirm the desired composition. The spectra of UV–Vis diffused reflectance spectroscopy and photoluminescence absorbance peaks show a red shift due to change in reflectance. IR transmittance spectra recorded in 4000-400 cm−1 region exhibits the stretching modes of O–Ti–O and Cd–O groups present in these samples. The current vs. voltage (IV) characteristics and direct current conductivity measurement shows p-n junction diode behaviour. All the parameters were calculated and described in-depth, including structural, optical and electrical properties. The obtained results suggest that TiO2–CdO thick film could be used in optoelectronic applications due to the shift in optical radiation absorption to visible region, reduction in recombination rate of charge carriers and increase in electrical conductivity.

Fabrication and improved response of ZnO-CdO composite films under different laser irradiation dose

Promising Zinc Oxide (ZnO) and Cadmium Oxide (CdO) alloy (ZnO-CdO) films were fabricated on glass substrates by screen printing route for optoelectronic applications. The Nd:YAG green diode laser of wavelength 532 nm and laser fluence of 1.8 J/cm2 was used to irradiate the fabricated films at room temperature. The characterization of these films were systematically studied by means of X-ray diffraction (XRD), UV–vis, photoluminescence (PL), Raman spectroscopy and two probe method for conductivity measurement. The XRD pattern shows that all the films were well crystallized with maximum diffraction of (101) plane and mixed phases of ZnO and CdO were detected. The structure, space group and other crystal related parameters were confirmed from Rietveld refinement of XRD data. The basic optical parameters (band gap, refractive index and extinction coefficient) have been estimated using absorbance spectra. The PL spectrum of ZnO-CdO composite films exhibits red shift and blue- green emissions shift upon laser irradiation were confirmed from CIE 1931 diagram. The Raman spectroscopy indicates that the quality of the ZnO-CdO films was increased while their structure defects were increased. DC conductivity measurement confirms semiconductor behaviour. All the parameters such as particle size, optical constants, colour emission and activation energy have been significantly improved upon laser irradiations dose of 1.8 J/cm2 for different durations of time. This study could be appropriate for optoelectronic applications.

Microstructure and orientation evolution of microinjection molded β‐nucleated isotactic polypropylene/poly(ethylene terephthalate) blends

AbstractThe influence of different shear stresses induced by changing injection molding speeds on molecular chain orientation and lamellar branching of β‐nucleated iPP/poly(ethylene terephthalate) (PET) microparts was investigated using two‐dimensional wide‐angle X‐ray diffraction and 2D‐small‐angle X‐ray scattering. Results indicated that the prevailing shear stress can promote the formation of parent–daughter α‐crystal structure and twisted shish–kebab structure in subsequent microparts. The diffraction of (300) plane of β‐crystals was also observed at varying injection speeds. Increasing injection speeds can significantly enhance the content of β‐crystals from 24 to 41% for β‐nucleated iPP microparts. Additionally, the content of β‐crystals was further enhanced in β‐nucleated iPP/PET microparts with in situ formation of PET microfibrils under intensive shearing conditions. The addition of both PET and β‐nucleation agents coupling with high shearing conditions exerts a synergetic effect on the development of β‐crystals. However, the orientation degree of crystal lattice decreased with increasing injection speeds for both β‐nucleated iPP and iPP/PET microparts.

高山-峡谷复合地形对入射平面P-SV波的散射

As a common composite site, the hill-canyon topography has complex coherence effects on seismic wave scattering. However, the publications of related research are still very limited. Therefore, a multi-domain indirect boundary element method was proposed to solve the scattering of in-plane elastic waves, and the scattering and diffraction of plane P-SV waves by hill-canyon topography were studied. The method takes advantages of both full-space Green’s function and half-space Green’s function to construct the scattered field in the independent closed region and the half-space open region, respectively. Combined with the auxiliary function method, dynamic wavefield solutions for the hill-canyon site were given, with the calculation accuracy ensured and the solution efficiency improved. The proposed method was verified through comparison of the results with published ones, and numerical calculations were performed in the frequency domain and time domain in the case of a Gaussian hill-canyon site. Results show that, the distribution of the surface displacement amplitude is very complex. There is significant dynamic interaction between the hill and the canyon, and the frequency-domain response depends on the frequency and angle of the incident wave. The presence of hills has an inhibition effect on the canyon for vertically incident waves, which significantly changes the peak acceleration and spectrum characteristics inside the canyon. Different height-to-width ratios of hills will cause changes in the seismic effect, and the presence of bedrock will also obviously amplify the seismic effect of the overall terrain.

Analytical and numerical methods for efficient calculation of edge diffraction by an arbitrary incident signal.

In the present study, diffraction of plane and spherically spreading signals by half-planes is considered. An existing analytical impulse response is investigated, which is exact for plane and approximate for spherical incident signals. It is shown that all its primitive functions with respect to time exist and have an explicit form involving elementary functions. The primitive functions are employed to (i) prove that the convolution of the impulse response with any bounded signal is also bounded for all times, (ii) obtain analytically the diffraction response as a combination of elementary functions for any incident signal approximated piecewise by fitting polynomials, (iii) improve the performance of the numerical convolution by orders of magnitude, and (iv) handle the convolution of very coarsely sampled incident signals. An impulse response is presented for finite-length edges, which, unlike the traditional integration formulas along the edge, is an explicit form of time. Because it is based on the impulse response for infinite edges, it inherits all aforementioned benefits associated with its primitive functions. Furthermore, it offers a substantial computational benefit compared to traditional integration formulas along the edge. Finally, the requirements for the direct application of the presented results to other impulse responses are discussed.

Theory of Sound Barriers: Diffraction of Plane, Cylindrical and Spherical Waves on a “Hard-Soft” Half Plane

When designing sound barriers, it is important to clarify the following problems: feasibility of partial or full coverage of the barrier surface with absorbent material or formation of barriers using sound-scattering surfaces. The study of the indicated applied problems for plane barriers leads to the necessity of formulating and solving the problems of diffraction of sound waves on a half-plane with boundary conditions of different type (various) on the half-plane sides. The solution of such problems by traditional methods is significantly complicated in comparison with the consideration of similar problems under the boundary conditions of the same type on the entire boundary of the scattering body and often leads to hardly determinable results. Simple methods for solving problems on diffraction of acoustic waves on a half-plane with Neumann boundary conditions on the one side of the half-plane and Dirichlet boundary conditions on another side are presented in the present article. For plane incident waves, the proposed method is based on the usage of the method of separation of variables with the subsequent summation of the Fourier — Bessel series. In the case of cylindrical and spherical waves, the method for obtaining solution consists in utilizing the results found for plane waves in combination with the Keller’s geometrical theory of diffraction. New analytical solutions of the diffraction problems for plane, cylindrical, and spherical waves on a hard-soft half-plane are obtained. These solutions are valid in the far-field diffraction region (that is, at large distances from the barrier edge and have the same “simplicity” as the solutions corresponding for the boundary conditions of the same type. This circumstance makes them convenient for comparative analysis in applications of sound barriers.

Scattering of Plane and Cylindrical SH Waves by a Horseshoe Shaped Cavity

An analytical solution for diffraction of both plane and cylindrical SH waves induced by a horseshoe shaped cavity with an inverted arch is presented in this paper. The geometry of the cavity is assumed to be composed of two circular arcs. By introducing an auxiliary boundary, the whole physical region is divided into two computational regions. The scattered wavefield in the open region and the standing wavefield in the enclosed region are presented by means of the wave function expansion method. Both of the wavefields are given in terms of the wave function series with unknown coefficients. By applying the Graf’s addition formula, two systems of equations for seeking the unknowns are derived by taking advantage of the boundary conditions based on the region-matching strategy. The problem of wave scattering is finally solved after seeking the solutions of the two systems of equations through standard matrix techniques. Then the effects of the excitation frequency, the cavity embedment depth and cavity geometry are discussed. The differences in terms of ground motions under different excitations and the influence of source location under cylindrical waves are also examined.

The scattering of SH waves by a finite crack with a superposition-based diffraction technique

The problem of diffraction of cylindrical and plane horizontally polarized shear waves (SH waves) by a finite crack embedded in a plane bidimensional elastic full-space is revisited. Particularly, we construct an approximate solution by the addition of independent diffracted terms. In our method the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of a generalized wedge is first considered. This result is then used as a building block to compute the diffraction of the main incident waves. The interaction between the opposite edges of the crack is later considered in terms of a series, one term at a time until a desired tolerance is reached. Moreover, we propose a procedure to determine the number of required interactions as a function of frequency. The solution derived with the superposition technique is shown to be effective at low and high frequencies and as shown by comparisons with a direct boundary element method software, highly accurate solutions are obtained after retaining just a few terms of the infinite series.

Scattering of a plane electromagnetic wave by a perfectly conducting cylinder in a spherically symmetric radially inhomogeneous absorbing plasma formation

The problem of diffraction of a plane electromagnetic wave by an ideally conducting cylinder of a finite dimensions is solved by the edge wave method. The cylinder is situated in an absorbing radially inhomogeneous plasma formation. The edge wave method is applied for bodies situated in an inhomogeneous medium. Analytic expressions for determination of the dependence of the effective radar cross section of a cylinder that depend on the irradiation angle are obtained, and the corresponding graphical dependences are calculated on the basis of these dependences.

Diffraction of plane and cylindrical waves by a cylindrical metamaterial shell with a negative refractive index

The problems of scattering of plane and cylindrical waves by a cylindrical metamaterial shell are solved rigorously. The influence of the geometric dimension of the shell, the value of the negative refractive index of the metamaterial medium, and the location of the cylindrical wave source on the near (far) field structure is investigated. It is shown that, in the quasi-opticl region, a caustic with one cusp is formed inside an electrically thick shell and whispering-gallery waves or standing waves are formed in between the facets of an electrically thin shell. It is found that, in the resonance region, reactive (surface) fields with substantial amplitudes are observed near the boundaries of a thin shell.

Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors

A detailed model of diffraction of plane and Gaussian beams on plane uniform phase Bragg gratings based on a Kogelnik’s theory of coupled waves is presented. The model describes reflecting gratings (Bragg mirrors) with arbitrary orientation in a plane-parallel plate having no material losses. It takes into account spectral width and angular

Diffraction of plane and cylindrical waves by a metamaterial cylinder

Rigorous solution of the problem of plane- and cylindrical-wave scattering by a circular cylinder made from a metamaterial is presented. It is shown that, inside a metamaterial cylinder, a symmetric caustic of refracted geometrical-optics rays with one cuspidal point is formed. The influence of the position of a cylindrical-wave source and the absolute value of the refractive index of the metamaterial both on the scattering pattern and the near field structure is studied.

An Analytic Solution for the Diffraction of Plane P Waves by a Cylindrical Inclusion in Half Space

This paper presents an analytic solution for the diffraction of plane P waves by a cylindrical inclusion in half space by Fourier-Bessel wave function expansion method, in which the flat surface of half space is approximated by a large curved surface. The equation can be constructed by the continue boundary and the free surface condition. Based on parametric analysis, the impact of the inclusion on surface displacement amplitude is discussed. It is illustrated that there is large difference of the diffraction characteristics between the hard inclusion and soft inclusion. The displacement response depends strongly on the incident angle and frequency. The diffraction effect can be ignored with large embedded depth of the inclusion.

Investigation of yellow luminescence intensity of N-polar unintentionally doped GaN**

This paper reports that the yellow luminescence intensity of N-polar GaN Epi-layers is much lower than that of Ga-polar ones due to the inverse polarity, and reduces drastically in the N-polar unintentionally-doped GaN after etching in KOH solution. The ratio of yellow luminescence intensity to band-edge emission intensity decreases sharply with the etching time. The full width at half maximum of x-ray diffraction of (10–12) plane falls sharply after etching, and the surface morphology characterized by scanning electron microscope shows a rough surface that changes with the etching time. The mechanism for the generation of the yellow luminescence are explained in details.

Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green’s functions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of fictitious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through numerical examples.

Дифракция сдвиговой плоской электроупругой волны на полубесконечном электроде в пьезоэлектрическом пространстве с щелью.

Дифракция сдвиговой плоской электроупругой волны на полубесконечном электроде в пьезоэлектрическом пространстве с щелью.

Diffraction of plane electromagnetic waves by a wedge with perfect mixed anisotropic conductivity sides in a chiral medium

The Sommerfeld–Malyuzhinets integral method is used to solve the problem of the diffraction of plane circlepolarized electromagnetic waves normally incident on the edge of a wedge with the sides possessing perfect mixed anisotropic conductivity, which is immersed in an isotropic chiral medium.