The T-matrix method is one of the most powerful and widely used theoretical techniques for the computation of electromagnetic scattering by single and composite particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper presents a comprehensive database of T-matrix publications since the inception of the technique in 1965 through early 2004.

T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database

One method of analyzing radiation and propagation above a surface is to employ an effective surface impedance to describe the effect of the boundary In this paper an expression is derived for the effective impedance at grazing incidence of a slightly rough interface between air and a finitely conducting medium for which the Leontovich boundary condition is applicable The perturbation technique of Rayleigh and Rice is employed, and attention is restricted to vertical polarization The resulting effective surface impedance consists of two terms, the impedance of the lower medium when the surface is perfectly smooth and a term accounting for roughness The latter term can be complex in general and depends on the strengths of the roughness spectral components present The result is applicable to either deterministic periodic surfaces or random rough surfaces Various alternate definitions of the effective surface impedance are examined and are seen to be equivalent The analysis of power flow at the surface permits the interpretation of the interaction process in terms of scattered fields

Theory of HF and VHF Propagation Across the Rough Sea, 1, The Effective Surface Impedance for a Slightly Rough Highly Conducting Medium at Grazing Incidence

The scattering of waves from periodic surfaces is studied. We give a general review of this problem and compare three analytical methods for a conducting sinusoidal surface in detail for both TE and TM polarized waves. The three methods are: 1) the method developed by Masel, Merrill, and Miller (MMM); 2) the Modified Physical Optics (MPO) method; and 3) Waterman's Plane Harmonics (WPH) approach. We find the MMM method to be the most efficient one in terms of the rate and range of convergence. For dielectric media with periodic rough surfaces, an improved method is developed for calculating the reflected and transmitted powers. The results are used to compare with experimental data obtained at optical frequencies. It is shown that good agreement is achieved when the complex permittivity of the metal for the grating at the corresponding frequency is used.

Scattering of waves from periodic surfaces

The Rayleigh hypothesis in the theory of scattering by a cylindrical obstacle of arbitrary cross section is investigated analytically. The hypothesis asserts that outside and on the obstacle the scattered field may be expanded in terms of outward-going wave functions of the circular cylinder. As such, it is analogous to the assumption made by Lord Rayleigh in his treatment of diffraction by a reflection grating. We show that the validity of the Rayleigh hypothesis is governed by the distribution of singularities in the analytic continuation of the exterior scattered field. Conditions are derived under which the Rayleigh hypothesis is rigorously valid. As examples, the elliptic cylinder and the perturbed circular cylinder are considered in detail.

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The Rayleigh hypothesis in the theory of diffraction by a cylindrical obstacle

An initial effort is described to develop an antenna synthesis procedure by which the shape of a surface of rotation and its current density are deduced from a given far-field radiation pattern which satisfies the conditions of a characteristic mode. Typical results obtained to date are presented to substantiate the method and to illustrate some antenna shapes. A variety of research topics suggested by present efforts are discussed and suggested for future investigation.

Antenna shape synthesis using characteristic modes

Methods based on the Rayleigh hypothesis (e.g. the point-matching method) for numerically solving wave-diffraction problems are shown to be equivalent to the exact extended-boundary-condition method. It is concluded that the Rayleigh hypothesis is exact, although, in general, it is necessary to interpret it in the generalised function sense.

Equivalence of the Rayleigh solution and the extended-boundary-condition solution for scattering problems

The electromagnetic field scattered by a conducting circular cylinder is expressed as an outward-going wave expansion in an eccentrically placed polar-co-ordinate system. It is shown that the expansion is always valid on the cylinder surface in the generalised-function sense but not in the conventional-function sense.

Example of the generalised-function validity of the Rayleigh hypothesis

A finite-difference method of computing the field scattered by conducting cylinders of arbitrary cross-section has recently been proposed by Patwari and Davies. The advantage claimed for their method—essentially that it overcomes the fundamental objection to the Rayleigh method—is shown to be unjustified and the two methods are, in fact, shown to be identical.

M.L. Burrows

Papers

Equivalence of the Rayleigh solution and the extended-boundary-condition solution for scattering problems

Example of the generalised-function validity of the Rayleigh hypothesis

Comment: Scattering by infinite cylinders of arbitrary cross-section by the method of finite differences [and reply]