Chapter 11, Problem 11.9P

An example of a nonuniform plane wave is a surface or evanescent wave, an example of which, in pharos form, is shown here, exhibiting diminishing amplitude with x while propagating in the forward z direction:

$E,\left(z\right)=E_0{e}^{-az}{e}^{-j\beta z}ay$

Such fields form part of the mode structure in dielectric waveguides, as will be explored in Chapter 13. (a) Assuming free-space conditions, use Eq. (23) to find the associated magnetic field, H,(z) (note that there will be two components), (b) Find a as a function of đ�›½, đ�œ”, e₀. and đ�œ‡_0: such that all of Maxwell’s equations are satisfied by the electric and magnetic fields.