Fundamentals of the Physical Theory of Diffraction, 2nd Edition

3 Wedge Diffraction: The Physical Optics Field

The relationships u⁽⁰⁾_s = E_z⁽⁰⁾ and u⁽⁰⁾_h = H_z⁽⁰⁾ exist between the PO acoustic and electromagnetic fields. An exception is for an oblique incidence (see Section 4.3).

Exact expressions for the scattered field were derived in Chapter 2. In the present chapter we calculate the physical optics part of the scattered field, that is, the field generated by the uniform component of the induced surface scattering sources. It will be used in Chapter 4 to examine the field radiated by the nonuniform sources as the difference between the exact and physical optics fields.

3.1 Original PO Integrals

The geometry of the problem is shown in Figure 3.1. A perfectly reflecting wedge located in a homogeneous medium is excited by a plane wave,

(3.1)

where we assume that 0 ⩽ φ₀ ⩽ π. In the PO approximation, the surface sources (induced on the face φ = 0) are determined according to Equation (1.31):

(3.2)

Equation (1.32) determines the field radiated by these sources:

(3.3)

(3.4)

Here we use the denotations

(3.5)

where ∇' and ∇ are the ...