Besides its amplitude is much larger than the waves

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Unformatted text preview: m ��j exp � jm ��i � � � � � � � � ki , � a � ˆ � C0 E ( � ,�, z) � 4 TE s 2 4 � ˆ E � hi 0 i �1 � 2cos ��i � � � � � � � �k a � i ,� ki ,� � 2 � exp( � jki ,� � � jki , z z ) �1 � 2 cos ��i � � � � � � Scattering from cylindrical objects 53 TE Scattering by a thin conducting cylinder � Consider the scattered electric field. It’s phase does not depend on angle. It’s amplitude is given below � E sTE ( � , � , z ) � ˆ E sTE (� ) exp( � jk i , � � � jk i , z z ) ,� � TE (� ) � � C0 Es ,� 4 � � ˆ � k a �2 E � hi i ,� 0 i ki ,� � �1 � 2 cos �� � �i � � � � EsTE ,� y ki �� Scattering from cylindrical objects �i � � �i x 54 TE Scattering by a thin conducting cylinder � Note that scattering is largest when cos �� � �i � � �1 � � � �i � � � This is the backward scattering case � � It is zero when � � �i � 2 EsTE ,� y � � �i � � �� Scattering from cylindrical objects �i x 55 Numerical experiments � Let us return to the exact result for TE case and again focus on the azimuthal component of the electric field � � ˆ EsTE ( r ) � � j Ei0 � hi exp � � jki , z z � ,� � � m ��� � ( � j )m J m � ki ,� a � (2) H m � � ki ,� a � (2) H m � � ki ,� � � exp � � jm �� � �i � � � � � We would like to compare this with the asymptotic result � This a difficult function to compute because of ‘bad’ behavior of Bessel functions of large order Scattering from cylindrical objects 56 Scattering by a perfectly conducting infinite cylinder � So let us consider the exact numerical result for the azimuthal component of the electric field � y We plot this function when �i � 0 � ki � � ki , x ,0, ki , z � , ki , � � ki , x Ei � ki , x ˆ ˆ hi � ˆ � y i EsTE ,� x ˆ Ei0 � hi � Ei0, y ˆ ˆ Ei (r ) � Ei0, y y exp � � jki � r � � Ei0, y y exp � � jki , x x � jki , z z � Scattering from cylindrical objects 57 Numerical experiments � For a thin cylinder we have the amplitude profile � /3 Ei ki ,� a � 0.25 ki , x Scattering from cylindrical objects 58 Numerical experiments � It is also instructive to look at constant phase fronts, at which phase(Q) � 0 ki ,� a � 0.25 Scattering from cylindrical objects 59 Numerical experiments � So in the far field, the phase fronts are almost circular in the xy plane: there is no angle-dependence of the phase of the scattered field, as found from the thin-film approximation � Also the amplitude is largest in case of backscattered waves, as found from the same approximation � � The amplitude becomes nearly zero when � � �i � 3 � Again this is in line with what we found before � So this approximation is quite accurate Scattering from cylindrical objects 60 TM Scattering by a thin conducting cylinder � For the TM case from a thin cylinder we have k i , � a � ka � 1 � For small arguments (consider positive or zero m’s) 1 �z� Jm � z � � � � m! � 2 � � m Lowest order in 2j (2) H 0 � z ...
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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.

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