{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

chap12 006

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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): ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern