Showing papers on "Plane wave published in 1992"
TL;DR: It is found that when ∈(r) is sharply peaked, photonic levels become almost degenerate throughout the Brillouin zone, corresponding to standing waves.
Abstract: The problems associated with the poor convergence of the Fourier transform of the hard-sphere dielectric function are discussed. A significant band gap between the eighth and ninth levels has been found for air spheres in fcc. We also consider a periodic array of Gaussian spheres, which converges well and allows a consistent and reliable determination of the general features of photonic bands. It is found that when \ensuremath{\epsilon}(r) is sharply peaked, photonic levels become almost degenerate throughout the Brillouin zone, corresponding to standing waves.
408 citations
TL;DR: In this paper, the recursive convolution approach is extended to media with dispersions described by multiple second-order poles, and the significant change from the first-order implementation is that the single backstore variable for each secondorder pole is complex.
Abstract: Previously, a method for applying the finite-difference time domain (FDTD) method to dispersive media with complex permittivity described by a function with a single first-order pole was presented. This method involved the recursive evaluation of a discrete convolution, and was therefore relatively efficient. In this work, the recursive convolution approach is extended to media with dispersions described by multiple second-order poles. The significant change from the first-order implementation is that the single backstore variable for each second-order pole is complex. The approach is demonstrated for a pulsed plane wave incident on a medium with a complex permittivity described by two second-order poles, and excellent agreement is obtained with the exact solution. >
389 citations
TL;DR: In this paper, the horizontal field generated by return strokes over the finitely conducting ground can be obtained to a high accuracy by using the expression for the surface impedance of the Earth.
Abstract: Horizontal fields generated by return strokes play an important role in the interaction of lightning-generated electromagnetic fields with overhead power lines. In many of the recent investigations on the interaction of lightning electromagnetic fields with power lines, the horizontal field was calculated by employing the expression for the tilt of the electric field of a plane wave propagating over the finitely conducting Earth. In this paper we show that the horizontal field generated by return strokes over the finitely conducting ground can be obtained to a high accuracy by using the expression for the surface impedance of the finitely conducting Earth. The method is suitable to calculate horizontal fields generated by return strokes at distances as close as 200 m. At these close ranges the use of the wave tilt expression can cause large errors.
198 citations
TL;DR: In this paper, the ZnSe axicon is used to efficiently generate approximations to diffraction-free Bessel function beams at λ = 10.6 μm.
Abstract: ZnSe axicon is used to efficiently generate approximations to diffraction-free Bessel function beams at λ = 10.6 μm. The central spot radius of ~ 170 μm generated when the axicon is illuminated by a plane wave is maintained for distances of up to 11 cm with sufficient laser power to allow drilling of plexiglass to be demonstrated.
183 citations
TL;DR: In this article, surface impedance boundary conditions (SIBC) are introduced into the FDTD method to reduce the solution space and produce significant computational savings, and an efficient implementation of this FDTD-SIBC based on the recursive properties of convolution with exponentials is presented.
Abstract: Surface impedance concepts are introduced into the finite-difference time-domain (FDTD) method. Lossy conductors are replaced by surface impedance boundary conditions (SIBC), reducing the solution space and producing significant computational savings. Specifically, a SIBC is developed to replace a lossy dielectric half-space. An efficient implementation of this FDTD-SIBC based on the recursive properties of convolution with exponentials is presented. Finally, three problems are studied to illustrate the accuracy of the FDTD-SIBC formulation: a plane wave incident on a lossy dielectric half-space, a line current over a lossy dielectric half-space, and wave propagation in a parallel-plate waveguide with lossy walls. >
154 citations
TL;DR: In this paper, the plane wave propagation in two kinds of Faraday chiral media, where Faraday rotation is combined with optical activity, is studied to examine methods of controlling chirality.
Abstract: Plane wave propagation in two kinds of Faraday chiral media, where Faraday rotation is combined with optical activity, is studied to examine methods of controlling chirality. The two types of media studied are magnetically biased chiroplasmas and chiroferrites. For propagation along the biasing magnetic field, four wavenumbers and two wave impedances are found which are dependent on the strength of the biasing field. Dispersion diagrams for the chiroplasma case are plotted. Propagation at the plasma frequency of the chiroplasma is also investigated. >
151 citations
TL;DR: In this article, the scattering of an incident plane wave from an array of parallel circular dielectric and/or conducting cylinders is derived rigorously using a boundary value approach using both transverse electric (TE) and transverse magnetic (TM) polarized incident plane waves.
Abstract: The scattering of an incident plane wave from an array of parallel circular dielectric and/or conducting cylinders is derived rigorously using a boundary value approach. Both transverse electric (TE) and transverse magnetic (TM) polarized incident plane waves are considered. The validity and accuracy of the method are verified by comparing the numerical results with those based on other available methods. The advantage of the proposed analysis is the simplicity and efficiency in computation. The modeling of two-dimensional objects of arbitrary cross section and composite material is outlined and sample numerical results are presented to illustrate the versatility of the method. >
148 citations
TL;DR: The first quasicrystal observed in a fluid dynamical system was reported in this paper, where ordered capillary wave states generated by three and four standing plane waves were observed at aspect ratios above 45 and for amplitudes below the amplitude at which a square-symmetric state is formed.
Abstract: We report the observation of ordered capillary-wave states generated by three and four standing plane waves. The pattern produced by the four standing plane waves forms the first quasicrystal observed in a fluid dynamical system. The states are observed at aspect ratios above 45, and for amplitudes below the amplitude at which a square-symmetric state is formed. We also report the observation of a capillary-wave state generated by three radial waves.
142 citations
15 Mar 1992
TL;DR: In this article, a modal analysis of lamellar grating in conical mountings is presented, which is an extension of the analysis of Botten et al. which considered non-conical grating.
Abstract: A rigorous modal analysis of lamellar grating, i.e., gratings having rectangular grooves, in conical mountings is presented. It is an extension of the analysis of Botten et al. which considered non-conical mountings. A key step in the extension is a decomposition of the electromagnetic field in the grating region into two orthogonal components. A computer program implementing this extended modal analysis is capable of dealing with plane wave diffraction by dielectric and metallic gratings with deep grooves, at arbitrary angles of incidence, and having arbitrary incident polarizations. Some numerical examples are included.
140 citations
TL;DR: In this article, the finite element method was used to predict the power absorbed and the resulting temperalure rise in samples of square and circular cross-section of long rods of lossy dielectric materials.
Abstract: Transient temperature profiles for long rods of lossy dielectric materials with thermally-dependent dielectric properties exposed to uniform plane waves are obtained. Maxwell's equations and the heal equation are simultaneously solved using the finite element method to predict the power absorbed and the resulting temperalure rise in samples of square and circular cross-section. Following the method introduced recently, we derive an exact radiation boundary condition which is independent of the rod cross-section
138 citations
TL;DR: In this paper, the linear theory for waves impinging obliquely on a vertical thin barrier is examined, and the theoretical solutions are obtained by an eigenfunction expansion method for the transmission and reflection coefficients.
TL;DR: In this article, a scaled dimensionless form of the Schrodinger equation is derived, so that the parameters of any optimized potential obtained for a particular collision energy and mass combination may be readily converted to apply to a new set of masses and energies.
Abstract: In this paper, the reflection and transmission of plane waves are examined from a complex potential. Such potentials have the property of absorbing wave packets incident on them and are used widely in time‐dependent quantum scattering theory. The purpose of the study is to determine the optimal form of potential to be used for absorbing wave packets near the edges of finite grids in coordinate space. The best potentials for such purposes lead to the minimum possible transmission and reflection of the incident wave packet. The Jeffreys–Wentzel–Kramers–Brillouin (JWKB) theory is used to address this problem and a new form for the optimal complex potential is proposed. A scaled dimensionless form of the Schrodinger equation is also derived, so that the parameters of any optimized potential obtained for a particular collision energy and mass combination may be readily converted to apply to a new set of masses and energies.
TL;DR: In this article, a multidimensional Fresnel integral is proposed for the case of near-grazing incidence, where the angle of incidence with respect to the plane containing the edges is small and each edge is in the transition region of the previous edge.
Abstract: Multiple forward diffraction past an array of many absorbing half-screens whose separation is large compared to wavelength is examined. Starting with the physical optics approximation for half-planes that are equally spaced and of equal height, the field incident on successive edges is represented by a multidimensional Fresnel integral, which is then expanded into a series of functions studied by Boersma (1978). When the angle of incidence with respect to the plane containing the edges is small, each edge is in the transition region of the previous edge, which precludes the use of the geometrical theory of diffraction and related asymptotic theories. The solution obtained applies for incidence either from above or below the plane containing the edges, and is especially suited to the case of near-grazing incidence. This method of solution allows for numerical evaluation of a large number of half-screens and shows how the multiple diffracted fields are influenced by the physical parameters. Both incident plane waves and incident cylindrical waves can be treated. >
Proceedings Article•
10 May 1992TL;DR: It is shown that photorefractive media can support a new type of spatial soliton, in which the diffraction is balanced by the self-scattering (two-wave mixing) of the beam spatial frequency components.
Abstract: We present a new type of spatial soliton, generated by the photorefractive (PR) effect of the medium. The shape of the soliton modulates the refractive index via the PR effect, which results in an exact compensation for the effects of diffraction, and causes the light beam to propagate the unvarying profile. This index modulation is represented in the formalism as a distribution of index gratings, each one of them induced by the interference between two spatial (frequency) plane wave components of the light beam. Since the efficiency of this effect is independent of absolute light intensity, these new solitons can be generated even at very moderate light intensities. Moreover, a given soliton waveform can propagate unchanged in the medium, at very high or very low light intensities (and at all levels in between).
TL;DR: It is shown how the ESPRIT (estimation of signal parameters via rotational invariance techniques) algorithm may be used with a square array of crossed dipoles to estimate both the two-dimensional arrival angles and the polarization of incoming narrowband signals.
Abstract: It is shown how the ESPRIT (estimation of signal parameters via rotational invariance techniques) algorithm may be used with a square array of crossed dipoles to estimate both the two-dimensional arrival angles and the polarization of incoming narrowband signals. The ESPRIT algorithm exploits the invariance properties of such an array so that both angle and polarization estimates may be computed. Some typical examples showing the use of this approach are presented. >
TL;DR: In this paper, an efficient, elegant, and systematic formulation technique which combines Fourier transform with matrix analysis methods is proposed for problems related to radiation by dipole or other sources in the presence of an arbitrarily general stratified anisotropic medium has been recently developed.
Abstract: An efficient, elegant, and systematic formulation technique which, combining Fourier transform with matrix analysis methods, is suitable for problems related to radiation by dipole or other sources in the presence of an arbitrarily general stratified anisotropic medium has been recently developed. This technique is adapted further extended to allow the presence of general bianisotropic media described by four tensors with no limitations on their elements. Two specific applications pertaining to some canonical problems of fundamental importance are included to exemplify the method and demonstrate its usefulness: radiation by an arbitrarily oriented elementary electric dipole source located in the vicinity of a general bianisotropic slab, either grounded or ungrounded, leading to the expressions of the dyadic Green's function of the structure, and reflection and transmission of an arbitrarily polarized plane wave incident upon such a slab, leading to closed-form concise expressions for the reflection and transmission coefficient matrices. >
TL;DR: In this paper, the P-SV reflection and transmission coefficients of an isotropic solid were studied and compared with the reflection coefficients of the P SVM of a solid.
Abstract: Numerous investigators have studied the P-SV reflection and transmission coefficients of an isotropic solid (Zoeppritz, 1919; Nafe, 1957; Frasier, 1970; Young and Braile, 1976; Kind, 1976; Aki and Richards, 1980).
TL;DR: In this article, a new analytical method was presented to study the effect of prominent topography on seismic ground motion, and the results showed that the hill has quite considerable effects on ground motions for both the points on the hill and its environs, these effects depend mainly on the frequency, the angle of wave incidence and the ratio of radius of hill to one-half the wave length.
Abstract: A new analytical method is presented to study the problem of scattering of plane SH waves by a semi-cylindrical hill in an otherwise homogeneous, isotropic and elastic two-dimensional half-space, using the series of wave functions and a new expansion technique. The results obtained show that (1) the hill has quite considerable effects on ground motions for both the points on the hill and its environs, (2) these effects depend mainly on the frequency, the angle of wave incidence and the ratio of radius of hill to one-half the wave length of incident waves, and (3) prominent and depression topographies having equal form and radius for the same incident waves would cause quite different mechanisms of wave propagation in both response performance and magnitude. The results, doubtless, would be useful for further deepening knowledge of the effects of prominent topography on seismic ground motion and for testing the accuracy of various approximate methods so far available.
TL;DR: In this paper, a ray-theoretical relation between the autocorrelation function of the slowness fluctuations of a random medium and the traveltime fluctuations on a profile perpendicular to the general propagation direction of an originally plane wave is established.
Abstract: SUMMARY A ray-theoretical relation is established between the autocorrelation function of the slowness fluctuations of a random medium and the autocorrelation function of the traveltime fluctuations on a profile perpendicular to the general propagation direction of an originally plane wave. Although this relation can be inverted exactly, it is preferable for applications to use the results of a forward calculation for a modified exponential autocorrelation function which represents slowness fluctuations with zero mean. The essential parameters of this autocorrelation function, standard deviation E and correlation distance a, follow by simple relations from the maximum and the zero crossing of the corresponding autocorrelation function of the traveltime fluctuations. The traveltime analysis of 2-D finite-difference seismograms shows that E and a can be reconstructed successfully, if the wavelength-tocorrelation-distance ratio is 0.5 or less. Otherwise, E is underestimated and a overestimated; however, both effects can be compensated for. The average traveltime, as determined from the finite-difference seismograms, is slightly, but systematically shorter than the traveltime according to the average slowness, i.e. the wave prefers fast paths through the medium. This is in agreement with results of Wielandt (1987) for a spherical low-velocity inclusion in a full-space and with results of Soviet authors, summarized by Petersen (1990). The velocity shift is proportional to E*, it has dispersion similar to the dispersion related to anelasticity, and it increases with the pathlength of the wave.
TL;DR: In this article, the diffraction of TE and TM-polarized plane waves by planar gratings is numerically analyzed using a combined finite element method/method ofmoments (FEM/MoM) algorithm based on the generalized network formulation.
Abstract: The diffraction of TE- and TM-polarized plane waves by planar gratings is numerically analyzed using a combined finite-element-method/method-of-moments (FEM/MoM) algorithm based on the generalized network formulation. The interior region, treated using the FEM, is truncated to a single unit cell with the introduction of an exact periodic boundary condition, which is enforced as a natural boundary condition. Using the FEM to compute the fields within the periodic structure allows gratings of arbitrary cross section and material composition to be efficiently modeled. >
TL;DR: In this paper, a nonlinear Rayleigh wave propagation in an isotropic solid is investigated theoretically and the Hamiltonian formalism is used to derive a set of coupled equations for the harmonic amplitudes.
Abstract: Nonlinear Rayleigh wave propagation in an isotropic solid is investigated theoretically. Hamiltonian formalism is used to derive a set of coupled equations for the harmonic amplitudes. Both plane and circular waves are considered. Numerical results are presented for an initially monochromatc wave that propagates in steel. It is shown that the horizontal component of the particle velocity wave forms a shock profile, while the vertical component forms a pulse. An evolution equation for the waveform is derived.
TL;DR: In this paper, the effects of various geometrical and electrical parameters on the near and far-field patterns of an eccentric multilayered, homogeneous, circular cylinder are examined.
Abstract: Electromagnetic scattering from an eccentric multilayered, homogeneous, circular cylinder is derived rigorously by using a boundary value mode-matching approach. The layers are assumed to be infinite in length and their axes are parallel to each other but their centers may have arbitrary coordinates. The composite arrangement is illuminated by a cylindrical wave from a line source of infinite extent in a direction parallel to the cylinder axis. The problem is two-dimensional and the solution to both types of polarization is presented. The effects of various geometrical and electrical parameters on the near- and far-field patterns are examined. >
TL;DR: In this article, the exact expressions for the aperture-averaging factor in the weak-turbulence regime for both plane and spherical waves were developed, which can be applied in most cases of interest with greater accuracy than previous approximations.
Abstract: Previous analyses of aperture averaging of optical scintillations in the turbulent atmosphere have generally involved either numerical integrations or approximation formulas based on asymptotic results for large apertures. Here I develop the exact expressions for the aperture-averaging factor in the weak-turbulence regime for both plane and spherical waves. For computational ease, accurate approximation or interpolation formulas that can be applied in most cases of interest with greater accuracy than previous approximations are also developed.
TL;DR: Inverse scattering for multiple conducting cylinders is investigated in this paper, where a plane wave is incident upon separate perfectly conducting cylinders of unknown shapes and the scattered field is measured outside, then, using prior knowledge of the rough positions of the scatterers, the shapes of the conducting cylinders can be reconstructed.
Abstract: Inverse scattering for multiple conducting cylinders is investigated. It is assumed that a plane wave is incident upon separate perfectly conducting cylinders of unknown shapes and the scattered field is measured outside, then, using prior knowledge of the rough positions of the scatterers, the shapes of the conducting scatterers can be reconstructed. The Newton-Kanotrovitch method is employed to solve nonlinear integral equations and the pseudoinverse technique is used to overcome the ill-posedness. Numerical examples are given to demonstrate the capability of the inversion algorithm. Good reconstruction is obtained even when the multiple scattering between two conductors is serious. The effect of noise on the reconstruction result is also investigated. >
TL;DR: In this article, the Muller-type coupled integral equations are derived for the surface electric and magnetic currents, and the power reflection coefficient is defined in terms of the scattered far fields.
Abstract: Plane wave scattering from lossy, periodic surfaces with periodicity in one direction is considered for arbitrary polarization and incidence angles The material is assumed to be homogeneous and characterized by complex values of permittivity and permeability Muller-type coupled integral equations are derived for the surface electric and magnetic currents The power reflection coefficient is defined in terms of the scattered far fields The integral equations are solved by the boundary element method (BEM) with constant elements Arbitrary surfaces are accommodated by approximating the actual profile by means of linear segments Other speed-up techniques are utilized to generate a numerically efficient solution Substantial comparison is made for special cases to verify the formulation The reflection coefficient is calculated for a variety of surface shapes A new profile shape is presented that results in a lower reflection coefficient than the commonly used triangular shape >
TL;DR: By the measurement of the variation of attenuation versus the frequency, a linear model permits the computations in a large frequency range and conclusions are carried out regarding the use of the LLW method in the inverse problem to recover elastic constants of composite materials.
Abstract: In this paper both theoretical and experimental investigations on the reflection and transmission of an incident plane wave by immersed viscoelastic orthotropic plates are presented. Taking the anisotropy of the layer into account the reflection and transmission coefficients are expressed in terms of nine complex elastic constants. In agreement with the Snell’s laws, any waves generated in the layer are bulk heterogeneous plane waves. Using a method already described in the isotropic case, the reflection and transmission coefficients are obtained as a function of the reflection and refraction coefficients of bulk heterogeneous plane waves at the two single solid/liquid interfaces, which limit the plate. In this way, these coefficients can be easily expanded in Debye’s series. In addition, for many incident and azimuthal angles, the calculations are compared with trial results on a composite made of unidirectional carbon fibers and epoxy matrix. Finally, by the measurement of the variation of attenuation versus the frequency, a linear model permits the computations in a large frequency range. Conclusions are carried out regarding the use of the LLW method in the inverse problem to recover elastic constants of composite materials.
Patent•
23 Dec 1992
TL;DR: In this paper, the phase distribution on a liquid crystal panel (6) having a spatial phase modulation function is disposed on the Fourier transform plane, thereby correcting the aberration.
Abstract: A method of and apparatus for efficiently correcting an aberration of an optical system used to record a hologram at the stage of reconstructing an image of the hologram. At the stage of reconstructing an image of a hologram (3), which contains the record of interference fringes formed by a reference plane wave and an object wave modulated by a sample, by applying a plane wave for reconstruction to the hologram (3) from a laser (1), an aberration of an optical system used to record the hologram (3) is canceled by the phase distribution on a liquid crystal panel (6) having a spatial phase modulation function, which is disposed on the Fourier transform plane, thereby correcting the aberration. The phase distribution on the liquid crystal panel (6) can be changed flexibly by a computer (9) in accordance with the aberration coefficients or degree of defocusing of the recording optical system.
TL;DR: Three-dimensional intensity information can be used to generate a set of projections from which it is possible to reconstruct the second-order statistics of the partially coherent wave field.
Abstract: The Wigner distribution of the electric fields in a quasimonochromatic light wave is equivalent, in the paraxial approximation, to the cross-spectral density function of the wave. The intensity distribution in a plane may be described as a projection across this Wigner distribution. Three-dimensional intensity information can be used to generate a set of projections from which it is possible to reconstruct the second-order statistics of the partially coherent wave field.
TL;DR: In this paper, the authors studied the scattering and diffraction of a solitary wave by a surface-piercing vertical cylinder held fixed in shallow water, and the role of the nonlinear, dispersive, and linear wave effects during the wave-structure interaction were discussed in detail.
Abstract: This is a study of the scattering and diffraction of a solitary wave by a surface-piercing vertical cylinder held fixed in shallow water. Particular interest is focused on the roles played by the nonlinear effects and the dispersive effects in this fully three-dimensional problem of strong interaction between a solitary wave and a solid structure. The theoretical model adopted here for predicting the scattering and propagation of three-dimensional long waves in shallow water is the generalized Boussinesq (gB) two-equation model, developed by Wu. Using this model, the predicted flow field, the free-surface elevations, the wave-induced forces acting on the cyiindcr during the wave impact, and the subsequent evolution of the scattered wave field are numerically evaluated. The numerical results show that the front of the scattered wave field propagates very nearly in a circular belt, which is concentric to the cylinder as an overall topographical structure. This remarkable asymptotic geometrical feature of the resulting scattered wave cannot be obtained without the basic equations being able to correctly model the three-dimensional effects, and without bias toward the direction of wave propagation. The role of the nonlinear, dispersive, and linear wave effects during the wave-structure interaction are discussed in detail.