Teaching

Introduction to the Mathematical Theory of Diffraction

University of Manchester – Department of Mathematics
PhD Course, Spring 2026

Lecture	Topics	Notes	Video recordings (Youtube)
1	Governing equations; Laplace operator; Green’s function of Helmholtz equation; plane waves; plane wave decomposition; far-field asymptotics	PDF	Part 1 Part 2
2	Mathematical statement of diffraction problem; boundary conditions; Sommerfeld radiation condition; limiting absorption principle; Meixner series	PDF	Part 1 Part 2
3	Ray approximation; geometric theory of diffraction; canonical problems; Half-plane problem (problem statement)	PDF	Part 1 Part 2
4	Solution of Half-plane problem using Sommerfeld integral	PDF	Part 1 Part 2
5	Solution of Half-plane problem using the Wiener–Hopf method	PDF	Part 1 Part 2
6	Parabolic equation of diffraction theory; Green’s function; Propagator formula; Half-plane in parabolic approximation	PDF	Part 1 Part 2
7	Parabolic equation in polar coordinates; Diffraction by a cylinder; Airy equation; V. A. Fock solution	PDF	Part 1 Part 2
8	Diffraction by a cylinder; Asymptotic analysis V. A. Fock solution; Saddle point method; Creeping waves	PDF	Part 1 Part 2
9	Waveguides; Modes of plane waveguide; Green’s function of a waveguide; Cylindrical waveguide; Diffraction by open-ended plane waveguide	PDF	Part 1 Part 2

Recommended literature for the course:

J.B. Keller. Geometrical theory of diffraction. J. Opt. Soc. Am., 52:116–130, 1962.
V. M. Babich, V. S. Buldyrev. Short-Wavelength Diffraction Theory: Asymptotic Methods Springer, 1991.
A. Sommerfeld. Optics, Academic Press, 1954 (English translation).
B. Noble. Methods Based on the Wiener–Hopf Technique Pergamon Press, 1958
V. A. Fock. Electromagnetic diffraction and propagation problems. — London: Pergamon Press, 1965.
F. W. J. Olver. Asymptotics and Special Functions. - Academic Press, 2014
L. A. Weinstein. Open Resonators and Open Waveguides. Pp. 439, Golem Press, Boulder, Colo., 1969.