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Unformatted text preview: ¿½s , ï¿½ sin ï¿½s ï¿½ ï¿½ Î¸s , ï¿½ ï¿½ sin ï¿½s ,cos ï¿½s ,0 ï¿½ ï¿½ Ë† s (1.13) Ë†
Ï†s Ë†
ks
Ë†
Î¸s
z ï¿½s h y ï¿½s
x
2a kË†i ï¿½ zË† Ë†
E i0 ï¿½ E 0 x Problem 3:
Consider a plane wave traveling in free space. The wave is incident upon a certain dielectric
object of arbitrary shape with a dielectric constant ï¿½ ï¿½ r ï¿½ generating equivalent currents inside the object. Let E s , H s denote the scattered field, i.e., the field induced by these equivalent
currents. In the far field zone the scattered electric field is given by: E sf (r ) ï¿½ exp ï¿½ ï¿½ jkr ï¿½
Ë†
Q ï¿½ kË†s , k i
r ï¿½ ï¿½
ï¿½ Ë†
Ë†Ë†
W here k ï¿½ ï¿½ ï¿½ 0 ï¿½0 , k s denotes the direction of scattering and Q ï¿½ k s , k i ï¿½ is the vector scattering amplitude (see the powerpoint slides for a description). Using the reciprocity theorem
of electromagnetic theory show that kï¿½ ï¿½
Ë†Ë†
Ë†
e0 ï¿½ Qï¿½ ks , ki ï¿½
ï¿½ e0 ï¿½ ï¿½ n ï¿½ E s ï¿½ r ï¿½ ï¿½ exp ï¿½ jks ï¿½ r ï¿½ dS ï¿½
ï¿½
4ï¿½ j ï¿½ ï¿½ ï¿½
S ï¿½ ï¿½ ï¿½
Ë†ï¿½
h0 ï¿½ ï¿½ ï¿½ H s ï¿½ r ï¿½ ï¿½ nï¿½ exp ï¿½ jks ï¿½ r ï¿½ dS ï¿½
ï¿½
ï¿½
S Ë†
Ë†
W here e0 is any arbitrary constant vector with ks ï¿½ e0 ï¿½ 0 , and h0 ï¿½ ï¿½ ï¿½1/ ï¿½ ï¿½ ks ï¿½ e0 ,
ï¿½ ï¿½ ï¿½0 / ï¿½ 0 , and S is any arbitrary closed surface surrounding the object. (See figure...
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This note was uploaded on 02/26/2013 for the course EE 25227 taught by Professor Akbabi during the Spring '13 term at Sharif University of Technology.
 Spring '13
 akbabi

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