Infinite Dielectric Cylinder Research Articles

Scattering by an arbitrary cylinder at a plane interface: broadside incidence

The problem of the determination of the fields scattered by an infinite dielectric cylinder of arbitrary cross section located at the interface between two semi-finite dielectric media is reduced to the solution of integral equations for unknown functions defined on the boundaries. These boundary functions are chosen so as to minimize their number. The incident field is that of a plane monochromatic wave. The derivation of the integral equations is given for the transverse electric (TE) mode for a dielectric cylinder and for a perfectly conducting cylinder. The exact electromagnetic fields are obtained from the solutions of the integral equations by integration, and the radar cross section can be computed from the far-field approximation. Sample outputs of the computer programs that implement this solution are shown. >

The discrete Fourier transform method of solving differential-integral equations in scattering theory

An accurate and efficient numerical method is presented for solving many differential-integral equations arising from electromagnetic scattering theory. It uses the discrete Fourier transform technique to treat both the derivatives and the convolution integrals which often appear in these equations. As a consequence, this method is extremely simple to implement, uses less computer memory than comparable methods, and yields accurate predictions. The differential-integral equation is recast into a periodic form conducive to application of the discrete Fourier convolution theorem. The differential operators are approximated by appropriate finite-difference and discrete-convolution operators. All these quantities are computed by using the fast Fourier transform. An approximate solution is obtained by using the conjugate gradient method. Results are compared to experimental data or analytical solutions for a 3 lambda *3 lambda metal plate (where lambda is the wavelength), a homogeneous and a layered infinite circular dielectric cylinder, and a dielectric sphere. The accuracy of the method is further illustrated by comparing predictions with independent measurements by R.A. Ross (1966) on a 2 lambda *1 lambda metal plate at grazing incidence. In all cases, agreement is excellent.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multiple scattering by two parallel dielectric cylinders

The solution of the multiple-scattering problem for two parallel infinite dielectric cylinders is considered for plane wave illumination perpendicular to the cylinder axes. Numerical results show the coupling effect with respect to cylinder size, separation, and orientation of the cylinder axes with respect to the incident wave. The coupling effect is illustrated by calculations of the internal and near-field intensity for end-on and broadside incidence. Results for circular cylinders with a size/wavelength ratio corresponding to a particular morphology-dependent resonance (size parameter = 45.329) show that the local effect of the resonance is completely damped when the two cylinders touch.

Scattering of vertically polarized electromagnetic waves from infinite dielectric cylinders embedded in a lossy medium

The problem of scattering of vertically polarized electromagnetic waves from underground cylindrical objects is investigated in this paper. The analysis used here can be considered to be an extension of previous integral-equation techniques dealing with the horizontal-polarization scattering problem from underground tunnels or conducting wires. Numerical data for the far-field region of buried cylindrical objects are plotted and some interesting conclusions based on these results are discussed and compared with those of the horizontal scattering problem.

Radiation pressure and 360° scattering diagrams for infinite cylinders

The general solution for the scattering of electromagnetic radiation by a tilted infinite dielectric cylinder is discussed. Angular scattering curves of 360 degrees for two polarizations are presented for given values of the size parameter and the incident polarization angle. The radiation pressure on tilted cylinders for arbitrary polarization is calculated and shown not necessarily to be within the incident plane.

Internal electric field distributions of a dielectric cylinder at resonance wavelengths

Calculations of the electric field distribution within and around an infinite circular dielectric cylinder, having a relative index of refraction of 1.53 and illuminated with plane-wave radiation of wavelength lambda, have been performed for size parameters ranging from 39 to 51. Results for size parameters that satisfy resonance conditions for various atural modes of oscillation of the cylinder (mode number n = 53; order numbers l = 1-5) clearly illustrate the physical significance of n and l and show that the internally reflected circumferential waves are localized near, but not confined to, the cylinder surface.

Calculation method for scattering cross section of a dielectric sphere considering resonance phenomena

AbstractThe scattering cross section of the dielectric sphere was expressed in infinite series by Stratton. However, this series is difficult to calculate. In the conventional calculation, the applicable ranges of parameters are limited and the number of terms required for infinite series calculation is not clear. Further, the relation between the resonance of dielectric spheres proposes a new calculation method. The fundamental nature of the resonance of the dielectric sphere is discussed and calculation methods for spherical Bessel functions of complex variables and spherical Hankel functions required for scattering cross‐section calculations are presented. The resonance characteristics of the dielectric sphere are calculated with various parameters and the method of determining the number of terms in the calculation of infinite series is examined. This method is applicable for the calculation of scattering wave from the infinite dielectric cylinder.

Radiation pressure on randomly oriented infinite cylinders

Expressions are developed for the radiation pressure on infinite dielectric cylinders caused by an oblique incidence as a function of the size parameter alpha = 2pialpha/lambda. It is shown that for nonabsorbing cylinders the radiation pressure is always perpendicular to the axis of the cylinder and thus not along the direction of the incident radiation except for the case of normal incidence. This result applies also for other small nonspherical particles. Consequently, the radiation pressure on a randomly oriented nonspinning group of small nonspherical particles causes the particles to spread away from the direction of propagation of the incident radiation. It is suggested that this conclusion should be taken into account when discussing the effect of the radiation pressure on small particles in space, as compared with other forces such as the dynamic pressure on the solar wind.

Electromagnetic scattering by an infinite inhomogeneous dielectric cylinder: New Green’s function and integral equations

The scattering of electromagnetic waves by an infinite dielectric cylinder with variable dielectric permeability presents, in general, certain mathematical difficulties regarding the construction of rigorous solutions. We give a new divergenceless tensor Green’s function, specially appropriate for cylindrical symmetry, and, in terms of it, present new scattering integral equations. We prove that the series for med by all successive iterations of those scattering integral equations converge under certain conditions. Suitable transformations lead to new integral equations with Hilbert–Schmidt kernels, which imply further rigorous results.

Raman and fluorescent scattering by molecules embedded in dielectric cylinders

Fluorescent and Raman scattering by molecules embedded in dielectric particles is strongly dependent on the morphology and optical properties of the particle and the distribution of active molecules within the particle. In this paper, the formalism is derived for the case where the scattering molecules are embedded in an infinite dielectric cylinder. Analytical results for the scattered fields are given for arbitrary angles of incidence. The general results, which involve an integral and a sum, are rather lengthy. Accordingly, the saddle-point method has been used to carry out the integration approximately. Numerical results are given for perpendicular incidence and for observation in the plane perpendicular to the cylinder axis, for single dipoles variously located within the cylinder, and for a uniform distribution of isotropic incoherent dipoles. The angular distribution and polarization of the scattered irradiance depends sensitively upon cylinder radius and refractive index, so that this effect must be considered if inelastic scattering signals are to be used as a diagnostic tool.

The size distribution of interstellar particles. II - Polarization

view Abstract Citations (58) References (30) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The size distribution of interstellar particles. Mathis, J. S. Abstract The linear and circular polarizations of infinite dielectric cylinders of the graphite-silicate mixture with a truncated power-law size distribution proposed by Mathis, Rumpl and Nordsieck (1977) as a model of interstellar particles are calculated. Particles above a specified minimum size are assumed to have perfect Davis-Greenstein alignment, and an index of refraction of 1.6 is used. Results are found to be in good agreement with observations of interstellar extinction between 0.1 and 1 micron, the wavelength dependence of linear and circular polarization, and the albedo and phase function of diffuse galactic light between 0.18 and 0.6 microns, for a maximum particle size of 0.28 micron, a minimum particle size of 0.005 micron and a minimum aligned particle size of 0.08 micron. Observations of mass loss in carbon- and oxygen-rich stars are also noted in support of the proposed graphite-silicate composition of the interstellar grain mixture. Publication: The Astrophysical Journal Pub Date: September 1979 DOI: 10.1086/157335 Bibcode: 1979ApJ...232..747M Keywords: Circular Polarization; Dielectric Polarization; Graphite; Interstellar Matter; Linear Polarization; Mass Distribution; Particle Size Distribution; Spatial Distribution; Carbon; Interstellar Extinction; Mathematical Models; Oxygen; Particle Density (Concentration); Particle Mass; Silicates; Stellar Mass Ejection; Astrophysics; Interstellar Grains:Sizes; Interstellar Matter:Polarization full text sources ADS |

Scattering from an infinite dielectric cylinder embedded into another

In this work the scattering from an infinite dielectric cylinder embedded into another cylinder is considered. In the case of an eccentric circular cylinder the problem is solved using the classical separation of variables techniques combined with related translational addition theorems. When the difference in the indices of refraction of the cylinders is small, a perturbation series is developed up to second order. For non-circular arbitrary inhomogeneities, an integral equation method is developed by employing the homogeneous scatterer Green function. Numerical results are computed for circular cylindrical inhomogeneities; the convergence of the perturbation series and the properties of the scattered field are discussed.

The absorption of light in an idealized photoreceptor on the basis of waveguide theory: I—The infinite dielectric cylinder

As an approximative model of a photoreceptor, the electromagnetic excitation of an infinite dielectric cylinder by plane light waves has been investigated. The angle of incidence and the direction of polarization have been varied. The solution has been worked out on the basis of the theory of Maxwell, the absorbing medium being described by a complex dielectric constant. For three different values of the absorption and the receptor diameter the energy absorbed in the receptor has been calculated as a function of the angle of incidence and the direction of polarization. This has been done for the relative energies in the individual modes and for the total energy. The results are compared with the predictions of the geometrical optical theory which proves that the latter does not describe correctly the absorption.

Sur la diffraction d'une onde plane par un cylindre dielectrique

A differential method to investigate the diffraction of an electromagnetic wave by an infinite dielectric cylinder of arbitrary cross section is given. Assuming that the cylinder radius and the wavelength are of the same range, the method has been tested on some numerical examples.

Diffraction by an infinite dielectric cylinder due to a normally incident cylindrical wave

The asymptotic value of the electric field diffracted by an infinitely long dielectric cylinder due to a normally incident cylindrical wave is computed by the geometrical theory of diffraction and shows excellent agreement with previous experimental results as well as the exact solution.

The Efficiency of Excitation of a Surface Wave on a Dielectric Cylinder

This paper presents a theoretical and experimental study of the excitation of the lowest order TM surface wave on an infinite dielectric cylinder. The source is a circular filament of magnetic current within the dielectric rod. The integral solution for the field is evaluated as a contour integral by applying Cauchy's theorem. The far zone radiation field is obtained by means of a saddle pointintegration. Curves are presented which show excitation efficiency as a function of k/sub 0/a, the normalized circumferential length of the filament. A filament 0.83 wavelength in diameter will launch the TM mode with an efficiency of 95 per cent. A narrow annular slot in a large metal sheet was used to approximate the magnetic current filament and efficiency was measured using Deschamps' method for a two-port junction. The experimental measurements verify the theoretical analysis. In addition, it was found that the slot launching efficiency was essentially independent of the ground plane dimensions.

The field due to an infinite dielectric cylinder between two parallel conducting planes

This paper shows that, whatever the distance of the cylinder from the planes, this field can be calculated by first solving an infinite set of linear equations with comparatively simple coefficients. By neglecting all except the first few unknowns, a good approximation to the correct solution is obtained. The simplest approximation is sufficient for most practical purposes, and it is shown that the increase in capacity between the planes due to the presence of the cylinder is nearly proportional to the cylinder radius squared times a simple function of its dielectric constant, provided that this radius is small compared with the distance between the planes.