Unformatted text preview: 12.24 CHAPTER 12. WAVES AT PLANE BOUNDARIES a. Write an expression for the incident TE wave. Hint: It may help to make a sketch of the geometry.
b. Find the frequency below which the wave is totally reﬂected as a function of the angle of incidence 01 for the TE wave. This is called the the cutoff frequency, we.
Hint: Think about what is required to get l"l = 1. Although this problem is not
about total internal reﬂection, you may want to study carefully how IF becomes unity in the case of total internal reﬂection.
c. Is the cutoff frequency of a TE wave at oblique incidence larger or smaller than the plasma frequency we?
(1. Now suppose a TM wave is incident at an angle of incidence 0i. Write an expression for the incident TM wave and then ﬁnd the cutoff frequency as a function of the angle
of incidence for the TM wave. Is the cutoff frequency now larger or smaller than the plasma frequency we? Problem 12.14: An electromagnetic wave is incident from free space upon a uniaxial
medium whose permittivity tensor is speciﬁed by 9 0 0
5:50 0 4 0
0 0 9 a. Assume ﬁrst that the incident wave is given by Fiﬁ") = Eoe‘jk‘zi (polarized a: di
rection). If the reﬂected wave is EG‘ ) = Fone‘ijk‘zi, what is the reﬂection coefficient
I}? Give a numerical value. b. Assume now that the incident wave is polarized in the y direction and given by
EG“) = Eoe‘jk‘zy. If the reﬂected wave is Fiﬁ) = FyEoe+jkizy, what is the reﬂection
coefﬁcient I‘y? Give a numerical value. (3: Now assume that the incident wave has both :1: and y components and is given by
E(f') = (%x) Eoe‘jk‘z. Write an expression for the electric ﬁeld of the reﬂected wave.
(1. What is the angle between the electric ﬁeld polarization directions of the incident
and reﬂected waves? Give a numerical value. Has the electric ﬁeld rotated upon reﬂection? Problem 12.15: Consider an incident TE wave for which the electric and magnetic
ﬁelds are Esra—1E“? and [Hui + Hie] e‘ﬁri’
The electric ﬁelds of the reﬂected and transmitted waves are: '11}? 4125? Ewye" and Etyye The magnetic ﬁelds of the reﬂected and transmitted waves are: v iHrmﬁ + Hrzﬁl 91%"? and [Hmfc + Hui] e_ﬁ:i'i" :1. Find the following ratios (the reﬂection and transmission coefﬁcients for each com
ponent of the magnetic ﬁeld): ...
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 Fall '06
 RANA
 Electromagnet

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