2.1 Basic Equations

We consider only time harmonic electromagnetic fields with a time dependence specified by the factor e ^jwt which is omitted. In a stationary, linear. isotropic, homogeneous medium which is free of sources, the field is described by Maxwell's equations

(2.1)

where E and H are the complex phasors representing the electric and magnetic fields respectively, Z = l /Y = is the intrinsic impedance of the medium, and k = ? is the propagation constant or wave number. The permittivity and permeability of the medium are ? and ? respectively, and these may be complex, incorporating the effect of losses. In the particular case of a vacuum, Z = 120 ? ohm, and we distinguish the corresponding parameters by the suffix "o". SI units are used throughout.

A consequence of (2.1) is

(2.2)

and by eliminating H or E from (2.1) it follows that

(2.3)

We observe that all of the above equations are invariant under the transformation

E ? H, H ? - E, ? ? ?, Z ? Y

and this is referred to as the duality of Maxwell's equations.

At an interface between two media, the properties of the overall medium change discontinuously, and this may result in discontinuities in some components of the field. The transition conditions (generally referred to as boundary conditions) relating the fields on the two sides of the interface can be deduced from...