Fundamentals of the Physical Theory of Diffraction, 2nd Edition

1 Basic Notions in Acoustic and Electromagnetic Diffraction Problems

1.1 Formulation of the Diffraction Problem

In this book the physical theory of diffraction (PTD) is developed for both acoustic and electromagnetic waves diffracted at perfectly reflecting objects.

In two-dimensional problems, this theory is valid for both electromagnetic and acoustic waves.

First we present the theoretical fundamentals for acoustic waves and then for electromagnetic waves. In the linear approximation, the velocity potential u of harmonic acoustic waves satisfies the Helmholtz wave Equation (Kinsler et al., 1982; Pierce, 1994):

(1.1)

Here k = 2π/λ = ω/c is the wave number, λ the wavelength, ω the angular frequency, c the speed of sound, and I the source strength characteristic. The time dependence is assumed to be in the form exp ( − iωt) and is suppressed below. The acoustic pressure p and the velocity v of fluid particles, caused by sound waves, are determined through the velocity potential (Kinsler et al., 1982; Pierce, 1994),

(1.2)

where ρ is the mass density of a fluid. The power flux density of sound waves, which is the analog of the Poynting vector for electromagnetic waves, equals

(1.3)

Its value averaged over the period of oscillations T = 2π/ω equals

(1.4)

Two types ...