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chap12 006 - 12.24 CHAPTER 12 WAVES AT PLANE BOUNDARIES a...

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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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