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 cut-off 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 cut-off 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