Wedge Diffraction: Exact Solution and Asymptotics

As the wedge diffraction problem is the basis for the construction of physical theory of diffraction (PTD), its solution is considered in this chapter in detail. First its solution is derived in the form of infinite series and then converted it to Sommerfeld integrals convenient for asymptotic analysis namely, Sommerfeld asymptotics and Pauli asymptotics. The chapter provides the expressions that relate to the excitation of the field by a cylindrical wave, with a specific source term around the wedge in a specific region. These expressions can be modified for excitation by a plane wave. The chapter shows the derivation of asymptotic expressions under the condition that the incident wave does not undergo double and higher-order multiple reflections at faces of the wedge; this is an extension of the Pauli technique. It also demonstrates the use of magic-zero procedure for fast convergent integrals and uniform asymptotics.