Fundamentals of the Physical Theory of Diffraction, 2nd Edition

8 Ray and Caustic Asymptotics for Edge Diffracted Waves

8.1 Ray Asymptotics

The following relationships exist between the acoustic and electromagnetic diffracted rays:

where is tangent to the edge at diffraction point ζ. Here the relationships u^{(0, 1)}_s = E_t^{(0, 1)} are valid only in the absence of polarization coupling in the PO field.

8.1.1 Acoustic Waves

The theory of EEWs is employed here for the calculation of scattering at a smoothly curved edge L with a slowly changing angle α(ζ) between its faces (Fig. 8.1). In close proximity to point ζ on the edge, an arbitrary incident field

(8.1)

Figure 8.1 Element of a scattering edge L with a curvilinear coordinate ζ along the edge; is the unit vector tangential to the edge at point ζ.

can be considered locally as a plane wave propagating in the direction

(8.2)

Therefore, replacing the quantity u^inc(ζ) in Equations (7.89) ...