In studying the wave behavior in a straight waveguide having a uniform but arbitrary cross...

In studying the wave behavior in a straight waveguide having a uniform but arbitrary cross section it is expedient to find general formulas expressing the transverse field components in terms of their longitudinal components. We write

E = Er + aZEz

H = HT + aZHZ,

where the subscript T denotes “transverse.” Prove the following relations for time-harmonic excitation:

a)

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b)

where h2 is that given in Eq. (10-15).