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## Scattering of waves from an electric dipole over an impedance wedge

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This chapter deals with scattering of the electromagnetic wave emitted by a Hertzian dipole by an impedance wedge. Using a plane-wave expansion of the dipole field and the newly obtained exact solution of diffraction of a skew-incident plane electromagnetic wave by the same canonical body enables us to deduce an integral representation for the total field. Then by evaluating the multiple integral the far-field expressions are derived and studied. The formulation and the basic steps of analysis are presented. In particular, the far-field expressions for the geometrical-optics and the edge-diffracted waves, including a uniform asymptotic version of the far field are given. The numerical calculation and physical interpretation of the analysis are also carried out.

Chapter Contents:

• 3.1 Formulation of the problem and plane-wave expansion of the incident field
• 3.1.1 Statement of the problem
• 3.1.2 The Hertz vector and plane-wave expansion of the incident field
• 3.2 The integral representation of the total field
• 3.2.1 Integral formulation
• 3.2.2 Formulation of the problem for (r, φ, α, β)
• 3.2.3 Representation for the spectral functions
• 3.3 Deformation of the contours of integration and the geometrical-optics (GO) field
• 3.3.1 Saddle points, polar singularities, and residues
• 3.3.2 Branch cuts for auxiliary angles
• 3.3.3 The geometrical-optics field
• 3.4 The diffracted wave from the edge of the wedge
• 3.4.1 Nonuniform expression
• 3.4.2 The UAT formulation
• 3.5 Expressions for surface waves
• 3.5.1 Surface waves excited directly by the dipole
• 3.5.2 Surface waves excited at the edge by an incident space wave
• 3.6 Numerical results
• 3.7 Appendices
• 3.7.1 Appendix A. Multidimensional saddle-point method
• 3.7.2 Appendix B. The reciprocity principle

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