Coherent Wave Propagation Research Articles

Branch-point reconstruction in laser beam projection through turbulence with finite-degree-of-freedom phase-only wave-front correction.

Wave-front sensing and deformable mirror control algorithms in adaptive optics systems are designed on the premise that a continuous phase function exists in the telescope pupil that can be conjugated with a deformable mirror for the purpose of projecting a laser beam. However, recent studies of coherent wave propagation through turbulence have shown that under conditions where scintillation is not negligible, a truly continuous phase function does not in general exist as a result of the presence of branch points in the complex optical field. Because of branch points and the associated branch cuts, least-squares wave-front reconstruction paradigms can have large errors. We study the improvement that can be obtained by implementing wave-front reconstructors that can sense the presence of branch points and reconstruct a discontinuous phase function in the context of a laser beam projection system. This study was conducted by fitting a finite-degree-of-freedom deformable mirror to branch-point and least-squares reconstructions of the phase of the beacon field, propagating the corrected field to the beacon plane, and evaluating performance in the beacon plane. We find that the value of implementing branch-point reconstructors with a finite-degree-of-freedom deformable mirror is significant for optical paths that cause saturated log-amplitude fluctuations.

Experimental Study of Wave Propagation Dynamics of Multicomponent Distillation Columns

Distillation columns with sharp separations exhibit severely nonlinear behavior, which has been known to cause difficulties in column control and design. Such a column is characterized by sharp composition and temperature variations in the column. Previously, the binary distillation case was thoroughly analyzed using a nonlinear wave theory and such an analysis was experimentally validated. For multicomponent distillation, the complicated nonlinear dynamics of the movement and interference of multiple sharp composition variations can be elucidated with a coherent-wave theory developed earlier for general countercurrent separation processes. With a ternary alcohol mixture, the present study has experimentally verified the theory by demonstrating the existence and propagation of constant-pattern coherent waves in a 50-tray stripping column in response to a step disturbance of feed composition, feed flow rate, or reboiler heat supply. The study has also tested the theory's predictions of composition profile, wave velocities, and asymmetric dynamics.

S-matrix network models for coherent waves in random media: construction and renormalization

Networks of random quantum scatterers (S-matrices) form paradigmatic models for the propagation of coherent waves in random S-matrix network models cover universal localization-delocalization properties and have some advantages over more traditional Hamiltonian models. In particular, a straightforward implementation of real space renormalization techniques is possible. Starting from a finite elementary cell of the S-matrix network, hierarchical network models can be constructed by recursion. The localization-delocalization properties are contained in the flow of the forward scattering strength ('conductance') under increasing system size. With the aid of 'small scale' numerics qualitative aspects of the localization-delocalization properties of S-matrix network models can be worked out.

S‐matrix network models for coherent waves in random media: construction and renormalization

AbstractNetworks of random quantum scatterers (S‐matrices) form paradigmatic models for the propagation of coherent waves in random media. S‐matrix network models cover universal localization‐delocalization properties and have some advantages over more traditional Hamiltonian models. In particular, a straightforward implementation of real space renormalization techniques is possible. Starting from a finite elementary cell of the S‐matrix network, hierarchical network models can be constructed by recursion. The localization‐delocalization properties are contained in the flow of the forward scattering strength (‘conductance’) under increasing system size. With the aid of ‘small scale’ numerics qualitative aspects of the localization‐delocalization properties of S‐matrix network models can be worked out.

Amorphous Silicon Three Color Detector

ABSTRACTBand gap and defect engineered amorphous silicon based nipin photo diodes with bias controlled spectral response have been fabricated successfully. The devices exhibit good linearity over a wide illumination range and linearly independent spectral response curves which are required to generate a standard RGB-signal. In the bias range from -1.5 V to 1.5 V a dynamic range exceeding 90 dB for two color sensors and 80 dB for three color sensors has been observed. The general operation principle of the multispectral photo diode is discussed using a numerical simulation program. The model describes the defect state distribution of dangling bonds according to the defect-pool model and uses coherent wave propagation in the device to calculate the profile of photo generated carriers. Additionally, an analytical model has been developed to be included into standard circuit simulation programs like SPICE (Simulation Program with Integrated Circuit Emphasis). The analytical model uses linear field approximations in both i-layers of the device.

Reformulation of the dynamical theory of coherent wave propagation by randomly distorted crystals

The coherent terms in the spherical-wave approach of the statistical dynamical theory are reformulated using rigorous boundary conditions in contrast to the intuitive boundary conditions of the original formulation by Kato [Acta Cryst. (1980), A36, 763–769, 770–778]. These boundary conditions are explained physically by a general interference effect between the forward-diffracted wave and the incident undiffracted wave (using the optical theorem) and their consequences on the total (Bragg and forward-diffracted) incoherent intensity are also discussed.

Two-period magneto-oscillations in coherent double barrier-resonant tunnelling

Applying a magnetic field B to a double-barrier resonant-tunnelling diode, perpendicular to the layer structure, introduces oscillations in current density and capacitance that are periodic in 1/B. A derivation of this periodicity is given, based on coherent wave propagation. Two magneto-periods are found, corresponding to the electron concentration in emitter and well, respectively. Numerical calculations are presented for a semiconductor model with self-consistently determined electron potential.

Coherent wave propagation in inhomogeneous materials: a comparison of theoretical models

The frequency dependent behaviour of coherent wave propagation in inhomogeneous materials is studied using several theoretical models. The predictions of a ray tracing model are compared with those of a two-dimensional finite difference model, for both isotropic and anisotropic inhomogeneous materials. The effects of frequency are studied and it is shown how the ray tracing model may be modified to incorporate the low frequency regime, in addition to the usual high frequency regime for which ray tracing approximations are valid. A further comparison is made between the ray tracing solution and an analytical solution, for electromagnetic plane waves propagating in a material with a one-dimensionally varying dielectric constant. The amplitude of the reflected wave is calculated, with good agreement between the two models over a wide range of frequencies, including low frequencies.

Correlations and fluctuations in reflection coefficients for coherent wave propagation in disordered scattering media.

The relation between the reflection coefficients and the Green's function for a coherent wave propagation in a disordered elastic-scattering medium is derived. The sum rule of the reflection and transmission coefficients corresponding to probability conservation is shown rigorously for an arbitrary scattering potential. The correlation function of the reflection coefficients is then calculated by using a Feynman-diagrammatic approach in the weak-localized multiple-scattering regime (L\ensuremath{\gg}l\ensuremath{\gg}\ensuremath{\lambda}). The result is in agreement with recent experiments on the so-called ``memory effect'' in reflection coefficients. A more general condition under which the memory effect can occur is derived. Differences between the the correlation functions for reflection and that for transmission are discussed.

Geometric scaling of the optical memory effect in coherent-wave propagation through random media.

Geometric scaling of the optical memory effect is studied for transmission and reflection. Two-dimensional momentum matching, and two-dimensional scaling of the correlation function, is obtained for smooth-surfaced samples from theory and from experiment. Very rough-surfaced samples exhibit three-dimensional scaling. Internal surface reflections are found to play an important role in determining the width of the correlation function, and are shown substantially to account for previous discrepancies between theory and experiment.

Coherent electromagnetic wave propagation through randomly distributed and oriented pair‐correlated dielectric scatterers

Coherent attenuation of electromagnetic waves by randomly distributed and oriented pair‐correlated dielectric scatterers is studied as a function of frequency and volume concentration of scatterers. Average frequency dependent dielectric properties are also studied. The results indicate that the attenuation and hence the effective properties differ considerably from those of aligned scatterers.

A Formal Representation of Abbe's Theory of Microscopic Image Formation

The theory of image generation for systems with coherent wave propagation is formally represented using the mathematical methods of Fourier optics. Abbe's theory of constructing the secondary image (the image conjugate to the object) by coherent superposition of the waves originating from the primary image (at the back focal plane of the system for plane wave illumination) is shown to be included within the general Fourier optical treatment of optical transfer systems.

Closure hypotheses from the method of smoothing for coherent wave propagation in discrete random media

A closure hypothesis is required to truncate the hierarchy of equations resulting from the conditional ensemble average of the multiple-scattering equations for coherent wave propagation in discrete random media. In this Letter the method of smoothing is used to construct a systematic sequence of closure hypotheses These include the quasi-crystalline approximation as a special case. The smoothing closure hypotheses include some of the multiple scattering neglected by the quasi-crystalline approximation. They are therefore expected to improve predictions of the attenuation coefficient of the coherent field at intermediate particle concentrations.

Effective propagation constants for coherent electromagnetic wave propagation in media embedded with dielectric scatters

In studying the multiple scattering of electromagnetic waves by random distributions of scatterers with appreciable fractional volume, the approach of quasicrystalline approximation together with the hole correction approximation has been a common method. In this paper, it is shown that such an approach will give rise to negative attenuation rate indicating a growth of the coherent wave in space which is a nonphysical solution. The result of the Percus–Yevick equation is a better representation of the pair distribution function for appreciable concentration. We use it together with the quasicrystalline approximation to study multiple scattering of electromagnetic waves by discrete spherical scatters. Waterman’s T matrix formalism is used in formulating the multiple scattering problem. Closed from solutions are obtained for the effective propagation constants in the low frequency limit and agree with Twersky’s results. Effective propagation constants at higher frequencies are calculated by numerical methods.

Coherent wave attenuation by a random distribution of particles

Coherent electromagnetic wave propagation in an infinite medium composed of a random distribution of identical, finite scatterers is studied. A self‐consistent multiple scattering theory using the T matrix of a single scatterer and a suitable averaging technique is employed. The statistical nature of the position of scatterers is accounted for by ensemble averaging. This results in a hierarchy of equations relating the different orders of correlations between the scatterers. Lax's quasi‐crystalline approximation is used to truncate the hierachy enabling passage to a homogeneous continuum whose bulk propagation characteristics such as phase velocity and coherent wave attenuation can then be studied. Three models for the pair correlation function are considered. The Matern model and the well‐stirred approximation are good only for sparse concentrations, while the Percus‐Yevick approximation is good for a wider range of concentration. The results obtained using these models are compared with the available experimental results for dielectric scatterers embedded in a host dielectric medium. Practical applications of this study include artificial dielectric (composites) and electromagnetic wave propagation through hydrometeors, dust, vegetation, etc.

A review of theories of coherent radio wave propagation through precipitation media of randomly oriented scatterers, and the role of multiple scattering

In most practical problems involving radio wave transmission through precipitation, the average, or coherent, field is one of the most important quantities. Although the classical formulation describing coherent propagation effects such as attenuation has existed for many years, it is only recently that this formulation has been extended to adequately include polarization effects. In the last 10 years, a number of theories that take into account the polarization effects caused by the random orientations of the precipitation scatterers have been developed. The similarities and differences between these theories, however, and the role of multiple scattering, are not yet well understood. This paper reviews recent work on the subject. Emphasis is placed on a clarification of (1) the similarities and differences of the various generalizations to the classical theory and (2) the role of multiple scattering in both the classical theory and these generalizations and their approximations. Some improvements to existing theories are also presented.

Coherent wave propagation through a sparse concentration of particles

The Foldy‐Twersky integral equation (FTIE) for the coherent field propagating through a sparsely populated, random, uncorrelated distribution of particles is solved to show that the average field inside any particle is a plane wave. This result is in conflict with the average single‐particle integral equation, which dictates that the average internal field cannot, in general, be a plane wave. The conflict is resolved by examining the conditions under which the average single‐particle‐scattering amplitudes resulting from the two integral equations are nearly equal. The major implications of this analysis are that (1) the classical Foldy result for the propagation constant of the coherent field follows directly from the FTIE and its implicit assumptions regardless of the electrical or physical properties of the particles and (2) the FTIE only applies to situations where the effects of multiple scattering upon the coherent field are negligible.

On the Wave Propagation in an Inhomogeneous Medium

An approximate solution of the boundary value problem for an inhomogeneous medium is shown by using the phase function method and the spectral representation of the Rayleigh diffraction formula under the condition that the spatial and temporal variation of the permittivity of medium is sufficiently smooth and small compared with that of the incident monochromatic electromagnetic waves. The formula obtained holds only in the neighborhood of the boundary plane. In the special case that the incident electromagnetic wave is plane and the variation of permittivity is induced by a monochromatic plane ultrasonic wave, the formula coincides with the Raman-Nath diffraction. Moreover, partially coherent wave propagation in an inhomogeneous medium is analyzed. The expression of van Citter-Zernike's theorem for an inhomogeneous medium is shown.

Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers

The coherent wave propagation and attenuation of electromagnetic waves in an inhomogeneous medium containing randomly distributed and randomly oriented nonspherical dielectric scatterers is studied using statistical averaging procedures and a self-consistent multiple-scattering theory. The specific geometry and orientation of the inhomogeneities are incorporated into the $T$ matrix of the scatterer thus making the formalism a convenient and computationally efficient scheme to study randomly oriented dielectric scatterers for a range of frequencies. The $T$ matrix of identical scatterers evaluated with respect to axes natural to the scatterers is then transformed to the arbitrary coordinate system by introducing rotation matrices that contain information about the orientation of individual scatterers. The rotation matrices can be integrated conveniently for random orientations of the scatterers.

Coherent electromagnetic wave propagation through randomly distributed dielectric scatterers

We present a vector multiple-scattering analysis of the coherent wave propagation through an inhomogeneous media consisting of a random distribution of identical, oriented, nonspherical, dielectric scatterers. The single-scattering aspect of the problem is dealt with through application of the transition or $T$ matrix. Configurational averaging techniques are employed to determine the hole correction integrals which are subsequently solved to yield the dispersion relations characterizing the bulk or effective properties of the medium. Closed-form solutions in the Rayleigh limit are derived for both spherical and spheroidal scatterer geometries. These solutions, together with the $T$ matrix, form the basis of our computational method for determining the coherent wave phase velocity and attenuation as a function of frequency ($\mathrm{ka}$) and scatterer concentration. Numerical results are presented for spherical and oblate spheroidal geometries over a range of $\mathrm{ka}$ values (0.05-2.0) and scatterer concentrations (0.05-0.20).