Fundamentals of the Physical Theory of Diffraction, 2nd Edition

Appendix to Section 7.9.2 Field Radiated by Modified Uniform Currents Induced on Elementary Strips

Here we investigate the field radiated by the currents induced by the incident wave (7.128) on the finite elementary strips (0 ⩽ ξ_{1, 2} ⩽ l) belonging to the finite plane faces of a scattering object (Fig. 7.3). These currents are defined as those induced on the illuminated faces of the tangential half-planes (φ = 0 and φ = α); that is, .

In this investigation we employ the right-hand Cartesian coordinates x, y, z and x′, y′, z associated with faces 1 and 2, respectively. The axes x and x′ belong to faces 1 and 2, respectively, and they are parallel to tangents τ₁ and τ₂. According to the solution of the half-plane diffraction problem presented in Chapter 2, the current on strip 1 is described as

(A.1)

(A.2)

with

(A.3)

(A.4)

The current components and on strip 2 are ...