Coherent Reflection Coefficients Research Articles

Generalized statistical dynamical theory of x-ray diffraction by imperfect multilayer crystal structures with defects

The generalized statistical dynamical theory of x-ray scattering by imperfect single crystals with randomly distributed Coulomb-type defects has been extended to characterize structure imperfections in the real multilayers of arbitrary thickness in Bragg diffraction geometry. The recurrence relations for the coherent amplitude reflection and transmission coefficients of such multilayers, which consist of any number of layers with constant strain and randomly distributed defects in each one, have been derived within the concept of the dynamical wave field, i.e., the so-called Ewald-Bethe-Laue approach, with rigorous accounting for boundary conditions at layer interfaces. The analytical expression for the differential dynamical diffuse component of the reflection coefficient of an imperfect multilayer system has been obtained as well. This expression establishes direct connection between the distribution of the diffuse scattering intensity in a momentum space and statistical characteristics of defects in each layer. In addition, the integrals from differential diffuse scattering intensity over the Ewald sphere and over vertical divergence have been found, which correspond to diffuse components in measurements of rocking curves and reciprocal space maps, respectively. The developed theory provides the dynamical description for the one- and two-dimensional angular distributions of the mutually consistent coherent and diffuse components of x-ray scattering intensities, which are measured by the high-resolution double- and triple-crystal diffractometers, respectively, from imperfect films, multilayer structures, superlattices, etc. Examples of simulated rocking curves for the imperfect superlattice with defects of several types and reciprocal space map for the ion-implanted sample of yttrium iron garnet film with defects are given and discussed.

Optical properties of structures composed of periodic, quasi-periodic, and aperiodic sequences of particulate monolayers

The spectra of the coherent transmission and reflection coefficients of multilayers consisting of the periodic, Fibonacci (quasi-periodic), and Thue–Morse (aperiodic) sequences of plane-parallel monolayers of monodisperse spherical alumina and silica particles are investigated using the quasi-crystalline approximation (QCA) and the transfer matrix method (TMM). The additional opportunities for the transmission and reflection spectra manipulation in comparison with the periodic sequence of monolayers are demonstrated. Photonic band gaps in the spectra of the particulate structures are shifted to the short-wavelength range in comparison with those for systems of homogeneous layers. The shift is larger for the Thue–Morse sequence. The widths of the photonic band gaps for particulate systems are narrower than the ones for multilayers consisting of homogeneous layers of an equivalent volume of matter. The results can be used to create optical, optoelectronics, and photonics devices—for example, multispectral filters, light emitting diodes, solar cells, displays.

Periodic structures with spherical alumina particles: Transmission and reflection spectra

Coherent transmission and reflection coefficients of individual monolayers of spherical alumina particles in the wavelength range from 0.3 to 1.0 μm and multilayers consisting of a set of such monolayers are computed. Quasi-crystalline approximation of the theory for multiple scattering of waves and the transfer matrix method are used. Three types of coherent transmittance minima inherent to close-packed regular disperse systems are singled out and described. Spectra of a glass plate with one-sided and double-sided coating with alumina particles are analyzed. Systems for creating antireflection coatings, diffuse light scattering structures, selective and nonselective filters of transmitted and reflected light are considered.

Layered periodic disperse structures of spherical alumina particles: Coherent transmittance and reflectance spectra

Coherent transmittance and reflectance spectra of multilayers consisting of plane-parallel monolayers of spherical monodisperse alumina particles are investigated. In the quasicrystalline approximation (QCA) of the statistical theory of multiple scattering of waves the coherent transmission and reflection coefficients of constituent monolayers are computed. Using the coefficients obtained, the transmittance and reflectance of the multilayers are calculated using the transfer matrix method (TMM) within the wavelength range of 0.3–2.0μm. Multilayers consisting of close-to-regularly-packed monolayers (planar photonic crystals with nonideal lattice) and partially-ordered monolayers of particles are investigated. Three types of coherent transmittance minima caused by the wave interference are singled out. The spectral positions and values of these minima are determined by optical constants, size, concentration, and the arrangement of particles in a monolayer, as well as by the spacing between the monolayer and their thicknesses. The results are in good agreement with the known theoretical and experimental data. They can be used to solve the problem of a lattice quality control in photonic crystals. Coherent transmittance and reflectance spectra of a system consisting of a glass plate coated with monolayers of spherical alumina particles are analyzed. Monolayer parameters for creating antireflection coatings, diffuse light scattering structures, and filters of transmitted and reflected light are considered. The approach developed can be applied to disperse structures of isotropic particles of other materials.

Phonon Conductance of Potassium- and Sodium-Doped Transpolyacetylene Chain

A theoretical approach for the study of phonon dynamics and scattering properties of doped transpolyacetylene chain is presented. The coherent reflection and transmission scattering cross-sections for phonons incident on the doped unit cell boundary are calculated in accordance with the Landauer-Buttiker electron scattering description, using the matching procedure with the nearest and next nearest neighbor elastic force constants. This is done for two different dopants, namely, the potassium and sodium atoms. Our numerical results yield an understanding of the transpolyacetylene chain dynamical properties and the effects on phonon conductance due to phonon incident on the doped unit cell boundary. The coherent reflection and transmission coefficients show characteristic spectral features, depending on the cutoff frequencies for the propagating phonons and on the nature of the dopants. They illustrate the occurrence of Fano resonances in the scattering spectra that result from the interactions of propagating elastic waves of the undoped transpolyacetylene chain with the localized modes due to the breakdown of the translation symmetry in the x direction.

Multiple-scattering model for the coherent reflection and transmission of light from a disordered monolayer of particles

Using a multiple-scattering formalism, we derive closed-form expressions for the coherent reflection and transmission coefficients of monochromatic electromagnetic plane waves incident upon a two-dimensional array of randomly located spherical particles. The calculation is performed within the quasi-crystalline approximation, and the statistical correlation among the particles is assumed to be given simply by a correlation hole. In the resulting model, the size of the spheres and the angle of incidence are both unrestricted. The final formulas are relatively simple, making the model suitable for a straightforward interpretation of optical-sensing measurements.

Coherent transmission and reflection of a two-dimensional planar photonic crystal

A method for modeling the radial distribution function for particles of a two-dimensional planar photonic crystal in the form of a monolayer of spatially ordered monodisperse spherical particles is proposed. The coherent transmission and reflection coefficients for layers under normal illumination are calculated in the quasi-crystalline approximation of the multiple wave scattering theory. The dependence of the coherent transmission and reflection of the layer on the degree of ordering of the spherical particles is investigated. The influence of the long-range order on the coherent transmission and reflection coefficients for layers with triangular, square, and hexagonal lattices is estimated. Monolayers of weakly absorbing dielectric and strongly absorbing metallic particles are considered.

Reprint of: Two-dimensional planar photonic crystals: Calculation of coherent transmittance and reflectance at normal illumination under the quasicrystalline approximation

The technique to calculate coherent transmission and reflection coefficients of two-dimensional (2D) planar photonic crystal (PC) at the normal to layer plane illumination is proposed. It is based on the quasicrystalline approximation of the theory of multiple scattering of waves. At this approximation spatial particle correlations are characterized by the radial distribution function. We propose the method of the 2D planar PC radial distribution function simulation. It consists in the calculation of coordination circles of ideal crystal lattice and following blurring them into the “rings” with fuzzy edges to describe the crystal lattice of an actual crystal. The width of the “rings” depends on the distance from coordinate origin. The blurring technique is proposed and discussed. The method allows simulation of the PCs lattices with various ordering degrees and spatial particle correlations. The results of numerical calculations of coherent transmittance and reflectance of monolayers with different orderings and refractive indices of spherical monodisperse particles are displayed.

Two-dimensional planar photonic crystals: Calculation of coherent transmittance and reflectance at normal illumination under the quasicrystalline approximation

The technique to calculate coherent transmission and reflection coefficients of two-dimensional (2D) planar photonic crystal (PC) at the normal to layer plane illumination is proposed. It is based on the quasicrystalline approximation of the theory of multiple scattering of waves. At this approximation spatial particle correlations are characterized by the radial distribution function. We propose the method of the 2D planar PC radial distribution function simulation. It consists in the calculation of coordination circles of ideal crystal lattice and following blurring them into the “rings” with fuzzy edges to describe the crystal lattice of an actual crystal. The width of the “rings” depends on the distance from coordinate origin. The blurring technique is proposed and discussed. The method allows simulation of the PCs lattices with various ordering degrees and spatial particle correlations. The results of numerical calculations of coherent transmittance and reflectance of monolayers with different orderings and refractive indices of spherical monodisperse particles are displayed.

On the Effective Low-Grazing Reflection Coefficient of Random Terrain Roughness for Modeling Near-Earth Radiowave Propagation

An investigation on the effects of terrain roughness on near-ground radiowave propagation is featured. In spite of the fact that a variety of analytical and numerical routines have been proposed by many workers for the general treatment of the scattering properties of rough surfaces, much disagreement remains in the solution of the problem for near-grazing scenarios. In striving to analytically describe the near-grazing propagation of signals from 2D and 3D radiators, an existing volumetric polarization current-based perturbation approach is exploited in this work to formulate closed-form expressions for the coherent rough surface reflection coefficients. Although the perturbation approach was originally intended for analyzing the scattering coefficients of a ground with scale of roughness much smaller than the wavelength, it is shown through Monte Carlo simulations that the effective reflection coefficients reported herein are applicable for near-ground path-loss prediction even when the surface variation (rms height) is on the order of a wavelength or more.

Light propagation through a monolayer of discrete scatterers: analysis of coherent transmission and reflection coefficients

An investigation of the coherent transmission and reflection coefficients of a monolayer of spherical scatterers as a function of their size, optical constants, and concentration is carried out. An analysis is performed of the quasi-crystalline approximation of the multiple-wave scattering theory and on the single-scattering approximation (SSA). The results permit determining the limits of applicability of the SSA to the layers with the partial ordering of spherical scatterers in analyzing the phases of the transmitted and the reflected waves. The phase of the transmitted and the reflected waves is investigated in the conditions of the quenching effect. It is shown that in such a case small changes in the refractive index of particles can cause dramatic phase changes. This effect can be used to modulate the light-wave phase, e.g., by electrically controlled composite liquid-crystals films.

Acoustic wave reflection from a rough seabed with a continuously varying sediment layer overlying an elastic basement

Acoustic plane wave interactions with a rough seabed with a continuously varying density and sound speed in a fluid-like sediment layer overlying an elastic basement is considered in this paper. The sediment layer possesses a generalized exponential type of variation in density and one of the three classes of sound speed profiles, which are constant, k 2-linear, or inverse-square variations. Analytical solutions for the Helmholtz equation in the sediment layer, combined with a formulation based upon boundary perturbation theory, facilitate numerical implementation for the solution of coherent field. The coherent reflection coefficients corresponding to the aforementioned density and sound speed profiles for various frequencies, roughness parameters, basement stiffness, are numerically generated and analyzed. Physical interpretations are provided for various results. The proposed model characterizes three important features of a realistic sea floor, including seabed roughness, sediment inhomogeneities, and basement shear property, therefore, provides a canonical environmental model for the study of seabed acoustics.

Coherent reflection of acoustic plane wave from a rough seabed, with a random sediment layer overlying an elastic basement

The problem of coherent reflection of an acoustic plane wave from a rough seabed with a randomly inhomogeneous sediment layer overlying a uniform elastic basement is considered in this analysis. The randomness of the sound field is attributable to the roughness of the seabed and the sound-speed perturbation in the sediment layer, resulting in a joint rough surface and volume scattering problem. An approach based upon perturbation theory, combined with a derived Green's function for a slab bounded above and below by a fluid and an elastic half-space, respectively, is employed to obtain an analytic solution for the coherent field in the sediment layer. Furthermore, a boundary perturbation theory developed by Kuperman and Schmidt (1989) is applied to treat the problem of rough surface scattering. A linear system is then established to facilitate the computation of the coherent reflection field. The coherent reflection coefficients for various surface roughness, sediment randomness, frequency, sediment thickness, and basement elasticity have been generated numerically and analyzed. It was found that the higher/larger size of surface and/or medium randomness, frequency, thickness, and shear-wave speed, the lower the coherent reflection. Physical interpretations of the various results are provided.

ACOUSTIC PLANE WAVE INTERACTION WITH A RANDOMLY INHOMOGENEOUS SLAB BOUNDED BY ROUGH SURFACES

Acoustic plane wave incident upon a fluid slab bounded by rough surfaces, within which the sound-speed distribution is subject to random perturbation, is considered. A theory based upon a boundary perturbation method in conjunction with a formulation derived from Green's function for the coherent field in the random medium has been applied to a typical oceanic environment, to study the coherent reflection from and transmission through the rough-and-random slab. Under the assumption of independence between the randomness of rough surface and that of sound-speed perturbation, the coherent fields may be obtained straightforwardly using formulations compatible with those employed in the existing literature. The reflection and transmission coefficients are then numerically generated for various cases to analyze the effects of surface roughness and medium inhomogeneities. The results have shown that both mechanisms reduce the coherent reflection and transmission coefficients, because of the generation of incoherent scattered fields which in effect are to disperse coherent energy. It is also interesting to note that the variation of the reflection coefficient near the critical angle presents distinctive characteristics for different scattering mechanisms, potentially allowing to identify the dominant one for a particular problem under consideration.

Coherent Reflection from a Rough Interface Over an Inhomogeneous Transition Fluid Layer

This paper considers plane-wave reflection from a rough interface over a transition layer within which the density and the sound speed vary simultaneously and continuously. By applying the Kuperman and Schmidt's formulation based upon the first-order boundary perturbation method, the coherent component of the reflection field may be conveniently solved by replacing the boundary conditions for the smooth interface with a set of effective boundary conditions. In contrast to the traditional analysis that the medium is generally discretized into a number of layers, the present study treats the transition layer as a whole by properly choosing the variations of the acoustic properties within the layer. The results for the coherent reflection coefficients in relation to various relevant parameters are generated and analyzed. It was found that the coherent reflection coefficient decreases as frequency increases. Also, it was shown that the root-mean-square roughness is the dominant factor in determining the coherent reflection coefficient, while the spatial correlation of the rough surface can have only a minor effect.

COHERENT REFLECTION FROM A ROUGH INTERFACE OVER AN INHOMOGENEOUS TRANSITION FLUID LAYER

This paper considers plane-wave reflection from a rough interface over a transition layer within which the density and the sound speed vary simultaneously and continuously. By applying the Kuperman and Schmidt's formulation based upon the first-order boundary perturbation method, the coherent component of the reflection field may be conveniently solved by replacing the boundary conditions for the smooth interface with a set of effective boundary conditions. In contrast to the traditional analysis that the medium is generally discretized into a number of layers, the present study treats the transition layer as a whole by properly choosing the variations of the acoustic properties within the layer. The results for the coherent reflection coefficients in relation to various relevant parameters are generated and analyzed. It was found that the coherent reflection coefficient decreases as frequency increases. Also, it was shown that the root-mean-square roughness is the dominant factor in determining the coherent reflection coefficient, while the spatial correlation of the rough surface can have only a minor effect.

SEABOTTOM BACKSCATTER STUDIES IN THE WESTERN CONTINENTAL SHELF OF INDIA

In this paper, a study is initiated to observe the interaction effect of the sound signal with three different sediment bottoms in the shelf area between Cochin and Mangalore in the western continental shelf of India. An echo signal acquisition system has been designed and interfaced with the 12 kHz echosounder installed onboard ORV Sagar Kanya. The reflection coefficients including attenuation at the seawater/bottom interface are computed in the three different sediment areas based on the sediment mean grain size. The experimental coherent reflection coefficients are calculated using the attenuation corrected reflection coefficients and the normalized cross-correlation between successive backscatter echo signal waveforms in those areas. Further, analyses conducted by determining the echo peak Probability Density Function (PDF) and matching them with the experimental echo peak histograms provide root mean square (rms) roughness amplitude in the three different survey areas. The rms roughness values are used to compute the coherent reflection coefficients. An attempt to establish concurrence between the coherent reflection coefficients based upon the rms roughness amplitude and the experimental coherent reflection coefficients using the backscatter echo signals, reveals the importance of seawater/bottom interface roughness in the coarse grained sediment bottoms like sand and silty sand. The existence of microtopographic features are responsible for the seawater/bottom interface roughness. However, in the fine grained sediment area, the bottom does not contain any such feature.

Acoustic wave scattering from a randomly rough surface

Acoustic wave scattering from a randomly rough surface is studied using a multiple scattering analysis. Assuming the surface asperities to be small, approximate boundary conditions are used to derive a pair of coupled integral equations for the velocity potentials. The Dyson equation is next derived on introducing symbolic operators. Using the bilocal approximation the Dyson equation is solved, thereby obtaining explicit expressions for the coherent reflection and transmission coefficients. The analysis is similarly carried on further to compute the incoherent intensity by using the ladder approximation, and hence an expression for the scattering coefficient is obtained.

Coherent Transmission and Reflection by a monolayer of discrete scatterers

AbstractCoherent transmission and reflection of a plane wave through a monolayer of discrete particles are considered on the basis of simple and physically transparent formulae for the single scattering approximation (SSA) corrected by introducing a multiple scattering permittivity factor. This factor allows for multiple scattering of Waves between monolayer particles, opposite to the SSA. The multiple scattering permittivity factor is considered on the basis of the quasi‐crystalline approximation (QCA) via Ť matrix formalism. The multiple scattering permittivity factor and parameters for obtaining coherent transmission and reflection coefficients (the effective extinction coefficient and the transmission and reflection coefficients due to rescattering) are calculated within the scope of QCA and plotted for comparison with SSA results. The expressions for these values are simplified for small Rayleigh particles to simple analytical formulae.

Mean dyadic Green's function of a randomly rough surface

The problem of wave propagation and scattering over a randomly rough surface is considered from a multiple-scattering point of view. Assuming that the magnitude of irregularities are small an approximate boundary condition is specified. This enables us to derive an integral equation for the dyadic Green's function (DGF) in terms of the known unperturbed DGF. Successive iteration of this integral equation yields the Neumann series. On averaging this and using a diagram method the Dyson equation is derived. Bilocal approximation to the mass operator leads to an integral equation whose kernel is of the convolution type. This is then readily solved and the results are presented in a simplified and useful form. It is observed that the coherent reflection coefficients involve infinite series of multiple scattering. Two special cases are considered the results of which are in agreement with our expectations.