(4.9a) shows the direction of propagation is along the x‐axis, and wave impedance is defined in the (y‐z) plane. It is also called the intrinsic impedance η0 of free space and intrinsic impedance η of material filled homogeneous space. The following expression is obtained for the wave impedance η, for y‐polarized waves, from equation (4.5.25a):
(4.5.26)
Equation (4.5.25b) provides the following wave impedance for the z‐polarized waves:
(4.5.27)
The positive wave impedance of the (Ey, Hz) or (−Ez, Hy) fields corresponds to a wave traveling in the +x direction. However, for the (Ez, Hy) fields, the wave impedance is negative showing the wave propagation in the negative x‐direction. Under certain conditions, a medium can have an imaginary value of propagation constant, i.e. βx = − jp. In this case, the wave impedance becomes reactive, and there is no wave propagation. Again, the wave equation (4.5.20) is reduced to Ei = E0ie−px ejωt and Hi = H0i e−px ejωt for the wave propagation in the positive x‐direction. These are decaying nonpropagating evanescent mode waves. These are only decaying oscillations.
The wave equations (4.5.13a) and (4.5.13b), for the Ey and Hz field components, are solved to get the total solution as a superposition of two waves traveling in opposite directions:
In the above expression,
Figure (4.9d) shows the propagating EM‐wave in an arbitrary direction of the wavevector
where
(4.5.30)
The second terms of the above equations show wave propagation in the negative x‐direction. The wave equations show the decaying propagating waves. For the case α = 0, the above equations are the same as that of equations (4.5.28).
4.5.4 Vector Algebraic Form of Maxwell Equations
Maxwell’s equations in the unbounded medium could be also written in the vector algebraic form. The del operator can be replaced as follows:
Set #I for the isotropic medium:
Set #II for the anisotropic medium:
Equations (4.5.31a) and (4.5.31b) show that for the positive values of μ and ε, the triplet
