Geometrical Theory of Diffraction

graduate course

Course Description

This is a one-semester graduate course on geometrical theory of diffraction (GTD). Covered topics include: (1) fundamentals of classical differential geometry, (2) geometrical optics (GO), (3) scattering from a PEC wedge, (4) asymptotic evaluation of integrals, and (5) GTD and its uniform version (UTD).

Course Material

The course material is based on two primary references. The first is the note “Differential Geometry for GTD Applications” by S. W. Lee, which has been retypeset in LaTeX. The second is the GTD lecture slide corresponding to Chapter 13 of Balanis’ textbook. Additional supplementary materials are provided as needed. I express appreciation to Professor Pathak for granting permission to reuse selected figures from his book in the preparation of the lecture slides on asymptotic evaluation of integrals.

  • Differential Geometry (Lee, Notes)
  • Geometrical Theory of Diffraction (Balanis, Slides;
    all slides are also available from the official website)
  • Scattering from a PEC Wedge (Slides)
  • Asymptotic Evaluation of Integrals (Pathak, Slides)

References

The primary reference for this course is Balanis’ “Advanced Engineering Electromagnetics”, Ch. 13. This chapter offers a concise introduction to the formulation of GO and GTD.

The following references are also recommended:

  1. Pathak and Burkholder present a rigorous treatment. Professor Pathak is one of the principal developers of UTD.
  2. McNamara, Derek, Albert, and Pistorius provide an accessible introduction, with clear derivations, particularly in the sections on GO.

[1] C. A. Balanis, Advanced Engineering Electromagnetics, 2nd ed., Wiley, 2012.
[2] P. H. Pathak and R. J. Burkholder, Electromagnetic Radiation, Scattering, and Diffraction, Wiley, 2021.
[3] D. A. McNamara, C. W. Pistorius, and J. A. G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction, Artech House, 1990.