Light scattering by a coated infinite cylinder in an absorbing medium

The scattering formulation for a coated infinite cylinder in an absorbing medium is presented in this paper. The cylinder is subjected to an arbitrarily polarized plane wave propagating in a general direction at the cylinder. The refractive index and magnetic permeability of the host medium, as well as those for the core and coating of the cylinder, can be real or complex. The scattering and extinction efficiencies and the scattering amplitudes are derived for both the near field and the far field. As the medium is absorbing, the "true" extinction and scattering efficiencies are derived based on the radiative energy outflow at the surface of the cylinder. The radiative efficiencies in the far field are denoted as "apparent" properties because they include absorption by the intervening medium. The influence of the refractive index and permeability of the host medium on the scattering properties of a coated cylinder is illustrated by numerical examples.     

Finite-difference time-domain solution of light scattering by an infinite dielectric column immersed in an absorbing medium

The two-dimensional (2-D) finite-difference time-domain (FDTD) method is applied to calculate light scattering and absorption by an arbitrarily shaped infinite column embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. The single-scattering properties of the infinite column embedded in the absorbing medium, including scattering phase functions and extinction and absorption efficiencies, are derived by use of an area integration of the internal field. An exact solution for light scattering and absorption by a circular cylinder in an absorbing medium is used to examine the accuracy of the 2-D UPML FDTD code. With use of a cell size of 1/120 incident wavelength in the FDTD calculations, the errors in the extinction and absorption efficiencies and asymmetry factors from the 2-D UPML FDTD are generally smaller than approximately 0.1%. The errors in the scattering phase functions are typically smaller than approximately 4%. With the 2-D UPML FDTD technique, light scattering and absorption by long noncircular columns embedded in absorbing media can be accurately solved.     

Acoustic scattering of an incident cylindrical wave by an infinite circular cylinder

Exact scattered acoustic fields generated by an infinite circular cylinder in the presence of an incident cylindrical wave are derived for fluid media. Equations are given for the scattered field outside the cylinder and for the total field within.     

Mie scattering by a spherical particle in an absorbing medium

We show that the large-size parameter limit of the scattering efficiency of a spherical particle of relative refractive index m(r) embedded in an absorbing medium is equal to [m(r) - 1[2/]m(r) + 1]2 and not to zero as has been claimed in a recent article [J. Appl. Opt. 40, 1354-1361 (2001)].     

Electromagnetic scattering by an infinite cylinder of material or metamaterial coating eccentrically a dielectric cylinder

The electromagnetic scattering by an infinite cylinder of dielectric material or metamaterial, coating eccentrically another infinite dielectric cylinder, is treated in this work. The problem is solved using classical separation of variables techniques. No use is made of the translational addition theorem. For small eccentricities h = d/a(? 1), where d is the distance between the axes of the cylinders and a the radius of the outer cylinder, we use instead the cosine and the sine laws to satisfy the boundary conditions at the surface of the outer cylinder. Keeping terms up to the order h2 we finally obtain exact, closed-form expressions for the expansion coefficients g(1) and g(2) in the relation S(h) = S(0)[1 + g(1)h + g(2)h2 + O(h3)], giving the scattered field and the scattering cross sections of the problem, where S(0) corresponds to the coaxial geometry, with h = 0 (d = 0). Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters, corresponding to materials or metamaterials. Our method is an alternative of the one using the translational addition theorem in the case of small eccentricities h.     

Application of the exact solution for scattering by an infinite cylinder to the estimation of scattering by a finite cylinder

A new algorithm for cylindrical Bessel functions that is similar to the one for spherical Bessel functions allows us to compute scattering functions for infinitely long cylinders covering sizes ka = 2πa/λ up to 8000 through the use of only an eight-digit single-precision machine computation. The scattering function and complex extinction coefficient of a finite cylinder that is seen near perpendicular incidence are derived from those of an infinitely long cylinder by the use of Huygens's principle. The result, which contains no arbitrary normalization factor, agrees quite well with analog microwave measurements of both extinction and scattering for such cylinders, even for an aspect ratio p = l/(2a) as low as 2. Rainbows produced by cylinders are similar to those for spherical drops but are brighter and have a lower contrast.     

Debye series of normally incident plane-wave scattering by an infinite multilayered cylinder

We derive the formula of the Debye-series decomposition for normally incident plane-wave scattering by an infinite multilayered cylinder. A comparison of the scattering diagrams calculated by the Debye series and Mie theory for a graded-index polymer optical fiber is given and the agreement is found to be satisfied. This approach permits us to simulate the rainbow intensity distribution of any single order and the interference of several orders, which is of good use to the study of the scattering characteristics of an inhomogeneous cylinder and to the measurement of the refractive index profile of an inhomogeneous cylinder.     

Wave scattering by a circular cylinder half-immersed in water with an ice-cover

The problem of scattering of water waves obliquely incident on a fixed long circular cylinder half-immersed in deep water with an ice-cover is investigated here. The ice-cover is modelled as an elastic plate of very small thickness. The problem is formulated using the method of multipoles. This leads to an infinite system of linear equations which are solved numerically by truncation. The reflection and transmission coefficients are obtained and depicted graphically against the wave number for various values of the angle of incidence and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. The effect of ice-cover is seen to increase the reflection coefficient and to decrease the transmission coefficient.     

Oblique wave scattering by a circular cylinder submerged beneath an ice-cover

When a train of small-amplitude surface water waves is normally incident on a very long horizontal circular cylinder fully submerged in deep water with a free surface, it is well known that it passes over and below the cylinder with a change of phase without experiencing any reflection. However the cylinder does experience reflection for oblique incidence of the surface wave train. It is shown here that the same phenomenon also holds good when the deep water has an ice-cover instead of a free surface, the ice-cover being modelled as a thin elastic plate. Here, for oblique incidence, the reflection and transmission coefficients are obtained approximately and depicted graphically against the wave number in a number of figures.     

Numerical investigation of the radiation characteristics of a perforated cylinder in a circular chamber filled with an absorbing medium

A problem on radiant heat exchange in a circular chamber filled with an absorbing medium and containing a perforated cylinder is solved.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 6, pp. 995–998, June, 1985.     

Mie theory for light scattering by a spherical particle in an absorbing medium

Analytic equations are developed for the single-scattering properties of a spherical particle embedded in an absorbing medium, which include absorption, scattering, extinction efficiencies, the scattering phase function, and the asymmetry factor. We derive absorption and scattering efficiencies by using the near field at the surface of the particle, which avoids difficulty in obtaining the extinction based on the optical theorem when the far field is used. Computational results demonstrate that an absorbing medium significantly affects the scattering of light by a sphere.     

Radiation of an infinite isothermal cylinder with account of scattering

The radiation problem of a cylinder filled by a radiating, absorbing, and scattering medium is treated. The transport equation is solved analytically within the P₁ approximation for an arbitrary scattering indicatrix by the spherical harmonic method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 1, pp. 141–144, July, 1978.     

On wrinkling induced by surface stress at the boundary of an infinite circular cylinder

The effect of surface stress on an infinite linearly-elastic circular cylinder is examined in respect of the possible wrinkling of its boundary. Displacement fields involving wrinkling are exhibited, the form of this wrinkling being shown to be essentially a surface phenomenon independent of thermal stress.     

Light scattering by absorbing hexagonal ice crystals in cirrus clouds

An improved ray-optics theory for single scattering and polarization of hexagonal columns and plates randomly oriented in space has been developed by considering absorption and by using the Chebyshev solution for diffraction integrals. The vector-tracing method and statistics technique of random sampling are employed. The equivalent forms of Snell's law and Fresnel formulas for absorbing ice crystals are derived, and two equivalent optical constants, m' and m″, are obtained. Comparison is made of the computed results of our model and the Takano and Liou model for asymmetry factors, single-scattering albedos, and scattering phase matrix elements. Some characteristics of our model are discussed, and these analyses demonstrate that our ray-optics model is practical and much improved.     

Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium

The three-dimensional (3-D) finite-difference time-domain (FDTD) technique has been extended to simulate light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. When computing the single-scattering properties of a particle in an absorbing dielectric medium, we derive the single-scattering properties including scattering phase functions, extinction, and absorption efficiencies using a volume integration of the internal field. A Mie solution for light scattering and absorption by spherical particles in an absorbing medium is used to examine the accuracy of the 3-D UPML FDTD code. It is found that the errors in the extinction and absorption efficiencies from the 3-D UPML FDTD are less than approximately 2%. The errors in the scattering phase functions are typically less than approximately 5%. The errors in the asymmetry factors are less than approximately 0.1%. For light scattering by particles in free space, the accuracy of the 3-D UPML FDTD scheme is similar to a previous model [Appl. Opt. 38, 3141 (1999)].     

Stresses in an infinite medium with two similar circular cylindrical inclusions

Summary Stresses around two similar circular cylindrical inclusions in an infinite medium under the generalised plane strain conditions subjected to uniform far-field stresses are investigated in this paper. The analysis is based on the complex stress potentials of Muskhelishvili [1]. Stresses can be found with any clearance between the two inclusions. Special treatment has been made for the case in which the two inclusions are in contact with each other, leading to a closed form solution to the local stresses at the contact point. Stress singularities are established in two extreme cases of either rigid or void inclusions, complementing the results for the anti-plane problem [2]. It has been shown that for inclusions of finite modulus no stress singularity arises but different degrees of stress concentration around the contact point can be found instead depending on the Young's modulus ratio between the inclusion and the medium and the loading condition. Other effects, such as the clearance between the inclusions and the Young's modulus ratio between the inclusion and the medium on the distribution of the interfacial stresses, are also examined when the two inclusions are in contact or separate. Numerical results are shown and discussed and they tend to imply a wider applicability of the conclusions obtained in this paper than the idealised case as analysed.     

Wave scattering by a horizontal circular cylinder in a two-layer fluid with an ice-cover

In a two-layer fluid wherein the upper layer is of finite depth and bounded above by a thin but uniform layer of ice-cover modelled as a thin elastic sheet and the lower layer is infinitely deep below the interface, time-harmonic waves with a given frequency can propagate with two different wavenumbers. The wave of smaller wavenumber propagates along the ice-cover while wave of higher wavenumber propagates along the interface. In this paper problems of wave scattering by a horizontal circular cylinder submerged in either the lower or in the upper layer due to obliquely as well as normally incident wave trains of both the wave numbers are investigated by using the method of multipole expansions. The effect of the presence of ice-cover on the various reflection and transmission coefficients due to incident waves at the ice-cover and the interface is depicted graphically in a number of figures.     

Diffraction of torsional waves by a penny-shaped crack in an infinitely long cylinder bonded to an infinite medium

This paper contains an analysis of the interaction of torsional waves with penny-shaped crack located in an infinitely long cylinder which is bonded to an infinite medium. Both the cylinder and infinite medium are of homogeneous and elastic but dissimilar materials. The solution of the problem is reduced to a Fredholm integral equation of the second kind which is solved numerically. The numerical solution is used to calculate the stress intensity factor at the rim of the penny-shaped crack.     

Torsion of a non-homogeneous infinite elastic cylinder slackened by a circular cut

We consider the torsional deformation of a non-homogeneous infinite elastic cylinder slackened by an external circular cut. The shear modulus of the material of the cylinder is assumed to vary with the radial coordinate by a power law. It is assumed that the lateral surface of the cylinder as well as the surface of the cut are free of stress. The main object of this study is to establish the effect of the non-homogeneity on the stress intensity factor at the tip of the cut. The problem leads to a pair of dual series relations, the solution of which is governed by a Fredholm integral equation of the second kind with a symmetric kernel. This equation is solved numerically by reducing it to an algebraic system. It is concluded that for any degree of non-homogeneity and for D, the relative depth of the cut, greater than 0.6, the cylinder may be replaced by a half-space. However, as the non-homogeneity increases, D decreases.