Electromagnetic Waves, Materials, and Computation with MATLAB®

194 Electromagnetic Waves, Materials, and Computation with MATLAB

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Case 2: q

1

imaginary

It can be shown that each of the rst and the fourth terms is zero. This is because the cor-

responding electric and magnetic elds are in time quadrature. Furthermore, the second

term is equal to the third term and each is equal to

(1/4) Re[( )( )]

T T T T*

E H

x y

Ψ Ψ

*

. Thus, the

power ow in the tunneling frequency band (Ω < 1/C) comes entirely from the cross-

interaction.

At Ω = 1, ε

p

= 0, and from Equation 10.88, B = 0 but A ≠ 0. From Equation 10.89, τ = 0. This

point exists only for the p wave.

At Ω = 1/C, A = 0, and B = 0. Evaluating the li