Mithat Idemen

Diffraction of a whispering gallery mode by the edge of a thin concave cylindrically curved surface

When a cylindrically curved perfectly conducting concave surface is terminated abruptly, an incident whispering gallery (WG) mode undergoes diffraction. This phenomenon is studied here for the canonical problem of a thin boundary and an edge that is parallel to the cylinder axis. To confine attention to diffraction by a single edge, it is assumed that the boundary extends to infinity in an infinitely extended angular space that is equivalent to placing along some radial plane intersecting the boundary a perfect absorber for angularly propagating waves. The problem can then be phrased as a functional equation problem of the Hilbert type which is solved exactly. An asymptotic approximation in the high frequency limit ka \gg 1 , where k is the wavelength and a the radius of curvature, is obtained in explicit form and phrased so as to exhibit the diffraction coefficient for edge-diffracted rays and the launching coefficients for creeping waves on the convex side as well as WG modes on the concave side. These quantities are of interest for placing the results within the context of the geometrical theory of diffraction (GTD) and are relevant to the analysis of curved two-dimensional reflectors of finite width, where WG modes excited by diffraction of the incident field at one edge provide illumination of the other edge. The induced surface current density function is also derived. The asymptotic results, including an observed shift of the shadow boundary relative to the direction of incidence of the WG mode, are explained completely in terms of half-plane diffraction of one of the modal ray congruences, thereby confirming via this canonical problem the validity of the GTD for diffraction of modal fields. For the limiting case a \rightarrow \infty , all expressions are shown to reduce to those for the classical half-plane problem.

Universal Boundary Relations of the Electromagnetic Field

In the present paper it is shown that a set of universal boundary relations which give the discontinuities of the electromagnetic field across any regular surface can be written via the distribution concept. All specific boundary conditions are then derived from these universal relations as particular cases. It is also shown that any set of linear relations written on a regular surface can not always be the boundary relations of an electromagnetic field. In the case of monochromatic fields the necessary and sufficient conditions for a set of linear equations to be the boundary conditions are given in three theorems. These theorems are applied to the discussion of the validity of boundary conditions of impedance type and show that such conditions can only be valid at certain critical frequencies.

Confluent edge conditions for the electromagnetic wave at the edge of a wedge bounded by material sheets

Abstract The edge conditions which dictate the asymptotic behaviour of the electromagnetic field near the edges play a crucial role in solving boundary-value problems involving boundaries having edges. In analytical studies they permit one to determine some unknown functions while in numerical investigations they enable one to improve the convergence of some processes by introducing beforehand the edge singularities into the field functions. In spite of its importance, the subject has not yet been studied sufficiently and accurately for new types of boundary conditions which are important for practical applications. This work is devoted to the analysis of wedge configurations bounded by material sheets having different constitutive parameters. The cases where the electric or the magnetic field is parallel to the edge are considered separately. It is shown that for each of these cases 81 physically different configurations are possible. However, from mathematical point of view all these configurations can be reduced only to nine canonical types. These canonical types are investigated in full detail by introducing the confluence concept which permits one to reveal also the logarithmic singularities, if any.

Diffraction of the creeping waves generated on a perfectly conducting spherical scatterer by a ring source

To analyze the diffraction of high frequency waves one turns often to the geometrical theory of diffraction (GTD) whose aim is to describe this phenomenon in terms of certain factors. These factors involve, among the others, several diffraction coefficients showing the modifications to be considered when a ray is transformed into another one at a diffraction point. The aim of this paper is to analyze the diffraction of creeping waves generated on a perfectly conducting spherical reflector, and thereby to obtain explicit expressions for certain coefficients related to the diffractions occurring at the edges of spherically curved reflectors. The analysis is performed by using an integral transform technique recently developed by one of the authors. Various ray contributions are isolated, and fairly simple nonuniform expressions for the diffraction coefficients are obtained.

The Maxwell's equations in the sense of distributions

It is well known that there is no direct one-to-one correspondence between the electromagnetic theory based on the physical laws and that based on the Maxwells differential equations. For example, in order to derive the boundary conditions from the Maxwells differential equations, one assumes that some integral identities derived from them are valid even when the field components (or material parameters) are discontinuous. This assumption violates, in a sense, the completeness of the theory of electromagnetism based on the Maxwells differential equations. We will prove that if one postulates that the Maxwells equations are valid in the sense of distributions, then this incompleteness will be removed and the boundary conditions will appear implicitly in the basic differential equations.

High-frequency surface currents induced on a perfectly conducting cylindrical reflector

An explicit expression for the surface current induced by sources on a perfectly conducting cylindrical reflector is obtained by taking into account the locality of the high-frequency diffraction phenomenon. The results show that the component previously conjectured by Ufimtsev involves several components having different propagation behaviors that can be separated into three main groups. When the reflector becomes infinitely large, the currents excited by edge diffraction are shown to reduce to those for the classical half-plane problem. The results are independent of the actual source configuration and may thus be useful in more complicated situations.

Some Diffraction Coefficients Related to Diffractions at the Edges of Curved Reflectors

To analyse the diffraction of high frequency waves one recourses often to the Geometrical Theory of Diffraction whose aim is to describe this phenomenon in terms of rays and certain factors. These latters involve several diffraction coefficients showing the modifications which occur when a ray is transformed into another one at a diffraction point. The aim of this paper is to give explicit expressions for certain coefficients related to diffractions occuring at the edges of cylindrically curved reflectors. On account of the locality of high-frequency diffraction phenomenon, all the coefficients given here can also be used, with some precautions, to calculate diffracted fields even when the reflector is not cylindrical.

Relativistic Scattering of a Plane-Wave by a Uniformly Moving Half-Plane

We discuss the effect of motion on the scattering by an edge. To this end, one considers the simplest canonical structure formed by a uniformly moving perfectly conducting half-plane illuminated by a time-harmonic plane wave and investigates the effect of the motion on the reflection and shadow zones, aberration, Doppler shift, edge-diffracted wave, etc. The cases where the velocity is parallel and normal to the half-plane are considered separately. Some of the interesting results which were obtained, in addition to the classical Doppler shift and aberration phenomena, are that (i) the edge-excited wave is never time-harmonic while the waves excited by the plane (both in the shadow and in the reflection zones) are always time-harmonic, (ii) the shadow and reflection boundaries are not parallel to the incident and reflected rays, (iii) at certain values of the velocity and incidence angle, a shadow region appears in the apparent illuminated region while a lit region appears in the apparent shadow region, (iv) the moving half-plane provides, sometimes, energy to the reflected wave. The cases of upsiLtc and upsi~c are examined in detail

Scattering of electromagnetic waves by a rectangular impedance cylinder

Abstract A uniformly valid asymptotic solution is developed for the diffraction of a high-frequency wave by an infinitely long rectangular cylinder having different impedance walls. The incident wave is generated by a line source located parallel to the cylinder. The problem is reduced first to a system of modified Wiener–Hopf equations involving infinitely many unknown constants and then to a couple of infinite system of linear algebraic equations which are solved numerically. Explicit expressions of the dominant wave components existing in different regions are found. Some illustrative examples show the capability of the approach.

Two-dimensional inverse scattering problems connected with bodies buried in a slab

A general theory of two-dimensional scalar inverse scattering problem, whose aim is to recover the geometrical as well as the physical (electromagnetic) properties of a cylindrical body buried in a slab, is established through a continuous spectral representation of the scattered field. The slab as well as the half-spaces below and above it are supposed to be filled with non-magnetic lossless simple materials. Then the theory permits one to determine with Born approximation the permittivity and conductivity of the body which is also supposed to be non-magnetic. The reflections from two sides of the slab give rise to the interaction of the body in the spectral domain with four waves, which makes the problem interesting from both mathematical and physical points of view. An illustrative example shows the practical applicability of the theory.