Analysis of forward scattering of diffuse photon-density waves in turbid media: a diffraction tomography approach to an analytic solution

We present a model of the forward problem for diffuse photon-density waves in a turbid medium containing a spherical inhomogeneity, using diffraction tomographic (DT) methods. Recently, by use of DT methods, the forward problem was investigated [Opt. Express 1, 6 (1997); www.osa.org] assuming weak perturbations from the background medium but an arbitrary inhomogeneity structure. We apply DT concepts to a forward problem solution that permits strong perturbations but requires a spherical inhomogeneity. We show that this model is consistent with previous DT results and discuss the application of this new model.     

Diffraction of Electromagnetic Waves by an Anisotropic Cylindrical Inhomogeneity in a Planar Waveguide

We consider diffraction of electromagnetic waves by an anisotropic cylindrical inhomogeneity located in a planar waveguide with perfectly conducting walls. Anisotropy is allowed for by using the uniaxial-crystal approximation. A rigorous analytical solution is represented in the form of double sums over eigenfunctions of a planar waveguide with perfectly conducting walls and azimuthal eigenfunctions of a cylinder. Different components of the intensity of the electric field scatttered by an anisotropic inhomogeneity are numerically calculated. The influence of the anisotropy and sizes of the inhomogeneity on the scattered field is analyzed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 7, pp. 605–615, July 2005.     

Was Poisson's spot an intentional discovery?

This short historical note deals with the phenomenological aspect of diffraction patterns in obstacles having central or axial symmetry. In the special case of the circular symmetry the light spot at the centre of the shadow is called “Poisson's spot” and it is often quoted as a crucial moment in the development of the theories about light. In this paper the phenomenon is seen only as a typical case of poor knowledge of the scientific Literature and of an unattentive observation of the men involved.     

Perturbed soliton excitations in the DNA double helix

We study the nonlinear dynamics of the inhomogeneous DNA double-helical chain using the dynamic plane-base rotator model by considering angular rotation of bases in a plane normal to the helical axis. The DNA dynamics in this case is found to be governed by a perturbed sine-Gordon equation, while taking into account the interstrand hydrogen bonding energy, between bases, and the intrastrand inhomogeneous stacking energy and by making an analogy with the Heisenberg model of the Hamiltonian of an inhomogeneous anisotropic spin ladder with ferromagnetic legs and antiferromagnetic rung coupling. In the homogeneous limit the dynamics is governed by the kink-antikink soliton of the sine-Gordon equation which represents the formation of an open state configuration in the DNA double helix. The effect of inhomogeneity in the stacking energy in the form of localized and periodic variations on the formation of open states in DNA is studied under perturbation. The perturbed soliton is obtained using a multiple-scale soliton perturbation theory by solving the associated linear eigenvalue problem and by constructing the complete set of eigenfunctions. The inhomogeneity in stacking energy is found to modulate the width and speed of the soliton depending on the nature of the inhomogeneity. Also it introduces fluctuations in the form of a train of pulses or periodic oscillations in the open state configuration.     

Contrast of images of small-size objects observed through a scattering medium by the method of transmission confocal microscopy

Using the theory of vision in scattering media, we have developed a model of inhomogeneity observation in biological tissues by the method of transmission confocal microscopy. We introduce general formulas for calculating the contrast of the image of a local inhomogeneity with sinusoidal distribution of the transmission factor, which is located in a homogeneous scattering medium. The influence of observation system parameters on the maximum depth of inhomogeneity visibility is analyzed. Institute of Applied Physics, Russian Academy of Sciences, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 8, pp. 980–990, August, 1997.     

Diffraction on the wedge with an arbitrary angle

TE and TM polarized electromagnetic wave diffraction on a perfectly conductive wedge with arbitrary apex angle is numerically studied. Amathematical model for calculating the diffraction field amplitude and intensity is developed. The solution is constructed in the entire range of physical angles without restriction to the observation point remoteness. The diffraction and field interference effects near the wedge walls are studied.     

A further study of a mathematical model for a screen in open-plan offices

In order to obtain a good acoustical environment in open-plan offices, the acoustic performance of a single screen needs to be well estimated. Based on the sound pressure or the sound energy summation, the models proposed by previous investigators provided the predictions of the speech intelligibility index (SII) at the receivers behind a single screen in the open-plan offices. In the development of these models, the expression describing the diffracted field of a screen was an empirical formula and the sound diffraction is assumed to be appeared in the shadow region of the screen. In the present study, the MacDonald analytical formula is applied to describe the diffracted field of a screen, and both the diffractions in the visible region and in the shadow region are considered in the proposed model though it seems that the diffraction in the visible region is small compared with that in the shadow region. The comparison of the predicted and experimental results of the Wang and Bradley and the predicted results of the improved model shows that the improved model can provide a more accurate prediction, and further calculations indicate that the improvement is mostly due to the application of the MacDonald analytical diffraction formula.     

Thin element approximation for the analysis of blazed gratings: simplified model and validity limits

The thin element approximation is widely used to predict the diffraction efficiency of thin periodic diffractive optical elements (DOEs). However, as the period-to-wavelength ratio is reduced, the approximation becomes inaccurate. A model based on a “shadow concept” can be used to predict the diffraction efficiency with high accuracy. Hereby we extend the model to include the effect of multi-level staircase structures and non-perpendicular incident angles. We also present an error map and define regions of validity for the thin element approximation (TEA) and the shadow model.     

A comparison of the results of a numerical simulation and an approximate calculation of the statistical characteristics of radio waves in a layer with random inhomogeneities of dielectric permittivity

We consider the formation algorithm for a random inhomogeneity field of dielectric permittivity of a medium that is used in simulations of the statistical characteristics of a wave that has propagated through a randomly inhomogeneous layer. We carry out a comparison of the statistical characteristics of a geometrical-optics wave, obtained via a numerical simulation, with the results of calculations of these characteristics by approximate formulae obtained using perturbation theory. It is pointed out that the applicability limits of the perturbation method, when solving geometrical-optics equations in a randomly inhomogeneous medium, depend on the formulation (one- or two-point) of the trajectory problem. It is shown that a calculation of the spatial correlation function of the field can be carried out using the perturbation method, even in the case of relatively strong fluctuations of dielectric permittivity. This is due to the fact that, in the region where this function differs markedly from zero, the correlation function of the eikonal obtained by the perturbation method is sufficiently accurate, and amplitude fluctuations are small.     

Percus-Yevick equation for an inhomogeneous fluid: Critical region

The critical region of a locally nonuniform fluid with gaussian density inhomogeneity is investigated. Nonclassical behaviour is found; critical exponents agree very well with those obtained from the perturbation theory of liquids. The action of an external field shifts the critical region and weakens the critical behaviour. Discussed effects could be verified experimentally.     

Diffraction of sound by a rigid screen with an absorbent edge

A solution is obtained for the problem of diffraction of a plane wave sound source by a semi-infinite plane. A finite region in the vicinity of the edge has an impedance boundary condition; the remaining part of the half plane is rigid. The problem which is solved is a mathematical model for a rigid barrier with an absorbing edge. It is found that the absorbing material that comprises the edge need only be of the order of a wavelength long to have approximately the same effect on the sound attenuation in the shadow region of the barrier as a semi-infinite absorbent barrier. Also the softer the absorbent lining the greater the attenuation in the shadow of the barrier. In the illuminated region a reduction in the sound intensity level can be achieved by a suitable choice of the absorptive material of the strip and its length. It is found that the effect of the absorptive strip is lost if its length is less than two wavelengths long. For a strip length of six wavelengths or more the system is equivalent to an absorbing half plane.     

A finite difference analysis of the field present behind an acoustically impenetrable two-layer barrier

The interaction of an incident sound wave with an acoustically impenetrable two-layer barrier is considered. Of particular interest is the presence of several acoustic wave components in the shadow region of this barrier. A finite difference model capable of simulating this geometry is validated by comparison to the analytical solution for an idealized, hard-soft barrier. A panel comprising a high air-content closed cell foam backed with an elastic (metal) back plate is then examined. The insertion loss of this panel was found to exceed the dynamic range of the measurement system and was thus acoustically impenetrable. Experimental results from such a panel are shown to contain artifacts not present in the diffraction solution, when acoustic waves are incident upon the soft surface. A finite difference analysis of this experimental configuration replicates the presence of the additional field components. Furthermore, the simulated results allow the additional components to be identified as arising from the S(0) and A(0) Lamb modes traveling in the elastic plate. These Lamb mode artifacts are not found to be present in the shadow region when the acoustic waves are incident upon the elastic surface.     

Quasicollinear acoustooptical interaction in three-dimensionally optically inhomogeneous crystals

A theoretical model is given for the quasicollinear acoustooptical interaction of beams in a three-dimensionally optically inhomogeneous, anisotropic medium. Analytical solutions of the coupled wave equations are obtained for a regular linear inhomogeneity model in relation to the spatial profiles of the frequency spectrum of the diffracted field. The spatiospectral transfer functions are determined, and their selective properties are investigated for various orientations and magnitudes of the gradient of the optical inhomogeneity for both low and high diffraction efficiencies. Numerical simulation results are given.Tomsk State Academy of Control Systems and Radioelectronics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 91–104, July, 1995.     

Small perturbations in the γ-field behind a barrier

The variations in the functionals of the radiation field behind a barrier caused by a local inhomogeneity of the cavity type in the barrier are treated in the small perturbation approximation. An equation is derived for the variation which is convenient in using the statistical-test method in numerical calculations.     

Analysis of an Inhomogeneous Semitransparent Plasma by the Lines in the Emission Spectrum

Using the methods of numerical simulation, we have investigated the dependence of the intensity and parameters of the spectral line profiles in the radiation of semitransparent plasma on its optical thickness, the degree of inhomogeneity, and the parameter distribution. As a model, we used the equilibrium plasma of argon with a given temperature profile on the observation line. The calculation has been performed for the spectral lines of the argon atom characterized by different broadening constants. On the basis of the results obtained it has been shown that it is possible to diagnose the plasma and determine the degree of its inhomogeneity and reabsorption by the parameters of the self-reversed profiles of the spectral lines. To diagnose the plasma in the absence of self-reversal, we propose to use the line intensities in the emission spectra of the plasma, including those obtained by probing it by its self-radiation. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 3, pp. 404–411, May–June, 2005.     

Effect of twist inhomogeneity on soliton spin excitations in a helimagnet

The effect of twist inhomogeneity on the soliton spin excitations in a one-dimensional inhomogeneous helimagnet in the semiclassical limit is investigated by solving a generalised perturbed fourth order nonlinear Schrödinger equation in the continuum limit. A multiple scale perturbation analysis shows that the amplitude of the perturbed soliton depends on the nature of the inhomogeneity, but its velocity remains constant.     

Macroscopic effect of the shadow of the electromagnetic field of relativistic electrons

The effect of the “formation zone” (“shadow” effect) on the characteristics of coherent diffraction radiation from a relativistic electron bunch passing near two conducting targets has been investigated experimentally as a function of the distance between the targets. The effect of the shadow behind absorbing and conducting screens on the diffraction radiation intensity has been studied in the experiments. In both cases, the same decrease in the diffraction radiation intensity almost to zero is observed with a decrease in the distance between the shadow source and target. The results indicate that two interpretations of the observed effect—the formation zone and shadow effect—are not equivalent.     

The mixed finite element method as applied to waveguide diffraction problems

A mixed finite element algorithm for solving the vector problem of diffraction by an inhomogeneity in a waveguide is constructed and implemented. Partial radiation conditions are used to proceed to a bounded domain.