ECE 6114 Advanced Analytical Electromagnetics | ECE | Virginia Tech


Course Information


This course comprises PhD-level material covering exact and asymptotic analytical techniques for the solution of advanced electromagnetic problems involving wave propagation and scattering by finite and extended media inhomogenieties.

Why take this course?

The application of advanced computing techniques and fast desktop computers to the solution of highly complex wave propagation and scattering problems relating to the design of radar, communication systems, and remote sensors is rapidly increasing. As the computer codes become more sophisticated and the problems more complicated, there is an increasing need to be able to understand and use analytical and asymptotic results as checks on the computer results. Student must not only be aware of these alternative results but they must appreciate their capabilities and limitations.



A thorough understanding of Maxwell’s equations, boundary conditions, radiation, and electromagnetic theorems dealing with equivalent boundary value problems, as covered in 5106, is essential background for this course.

Major Measurable Learning Objectives

  • Determine the exact and asymptotic solutions for wave scattering by classical shaped dielectric, magnetic, and perfectly conducting bodies and extended surfaces.
  • Integrate exact and asymptotic analyses with computer based methods to provide checks on the solutions of complex electromagnetic systems problems.
  • Devise measurement campaigns to evaluate electromagnetic problems, using the predictions provided by asymptotic and analytic solutions of canonical problems.
  • Apply advance analytical methods to designing electromagnetic systems involving radiation, wave guiding, and scattering.

Course Topics


Percentage of Course

Review of Fundamental EM Theorems 5%
General Solution Approaches 15%
Modal Expansions
Differential Equations
Integral Equations
Approximate Analytical Solution Techniques 3.
Quasi-Static Approximation 5%
Rayleigh and Perturbation Methods 5%
Spectral Approach via Weyl Representation
Rayleigh-Gans Approximation for Penetrable Bodies 10%
Geometric Optics Asymptotes 20%
Ray Propagation and Conservation of Energy
Physical Optics 10%
Stationary Phase Approximation
Diffraction Approximations 10%
Fock (Smooth Surface Diffraction)
Geometrical Theory of Diffraction (Keller)
Physical Theory of Diffraction (Ufimstev)
Infinite Periodic Surfaces and Reactive Surfaces 10%
Floquet’s theorem and Consequences
Dipole Over a Lossy Earth
Types of waves
Surface Waves (Zenneck & Norton)
Leaky Waves
Lateral Waves
Radiated Waves
Random Surfaces 10%
Statistical Quantities
Techniques (Classical vs. Modern)
Physical Optics
Multiple Scattering