Advanced electromagnetics

• explain Maxwell’s equations, boundary conditions, Poynting theorem, as well as the concepts of electromagnetic energy and power in the presence of electric as well as magnetic sources.
• explain wave-matter interactions through conduction, polarization, and magnetization, with particular emphasis on the harmonic oscillator model and dispersion in dielectric materials.
• define vector potentials, establish their differential equations, and derive integral expression solutions representing radiation integrals.
• solve wave equations by the method of separation of variables for rectangular, cylindrical and spherical coordinates and explain the underlying wave solutions.
• explain and apply electromagnetic principles and theorems such as uniqueness, duality, image principles, reciprocity theorem, and equivalence principles.
• derive and understand integral equations for open and closed boundary value problems.
• explain and apply method of moments technique for numerical solution of integral equations.
• explain the concept of ill-posedness and regularization of inverse problems, and describe the Kirsch-Kress decomposition method for the numerical solution of inverse scattering problems.
• explain spectral expansions of fields in cylindrical and spherical coordinates, and apply them to solve simple 2-D and 3-D canonical scattering problems.
• determine radiated fields from simple as well as complex sources, and investigate their near- and far-fields.
• explain and apply analytical and numerical computational techniques, and assess their region of validity and accuracy.

Selected parts of the course content may vary from year to year. The course concerns the radiation and propagation of electromagnetic waves and their scattering from, and interaction with, objects composed of complex geometries and/or complex materials:
1. Maxwell’s equations with magnetic sources and boundary conditions
2. Electromagnetic properties of matter
3. Radiation from sources, vector potentials and radiation integrals
4. Wave equation and its solution in rectangular, circular-cylindrical, and spherical coordinates
5. Electromagnetic theorems and principles
6. Integral equations and method of moments
7. Plane wave scattering from two- and three-dimensional conducting and dielectric objects
8. Inverse scattering

10036/30400/31400, The participants must possess qualifications in fundamental electromagnetism corresponding to a typical undergraduate course comprising: electro- and magnetostatics; conductors, dielectrics and magnetic materials; time-varying fields; Maxwell’s equations in differential and integral forms; propagation of plane waves and their reflection and transmission at plane interfaces.

Furthermore, the participants should feel confident with: rectangular, circular cylindrical, and spherical coordinate systems in three-dimensional space; vector analysis with the gradient, divergence, and curl operators and related integral theorems; and phasor notation for time-harmonic fields.

It is moreover beneficial to be well-acquainted with introductory concepts and methods for partial differential equations.

The course is comprised of lectures; group tutorials; and a project work.

The course is a prerequisite for 30430 Advanced Antenna Techniques and Measurements and provides a strong background for special courses and master’s thesis projects within applied electromagnetics.