M 2 j 2m m 2 2 h m 0 z h m 1 z h m z z

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Unformatted text preview: jm�i � M m ,ki , z ( � , � , z ) 41 Exact solution of the problem (TE polarization) � Explicit form in components � ˆ E ( r ) � E � hi TE s ,� � � m 0 i � exp � � jki , z z � ki , � � � ( � j ) m J m � ki , � a � (2) H m � � ki , � a � m ��� � (2) H m � ki ,� � � exp � � jm �� � �i � � � � � ˆ EsTE ( r ) � � j Ei0 � hi exp � � jki , z z � ,� � � m ��� � ( � j ) m J m � ki , � a � (2) H m � � ki , � a � Scattering from cylindrical objects (2) H m � � ki ,� � � exp � � jm �� � �i � � � � 42 Exact solution of the problem (TE polarization) � The magnetic field in the TE case � j � um J m � ki ,� a � H H (r ) � � � N m , ki , z ( � , � , z ) (2)� � m��� H m � ki ,� a � TE s � In components: ˆ � jki , z � exp � � jk z � H ( r ) � E � hi � i ,z k� � � � � (� j)m J � k a m � i ,� � (2) H m � � ki ,� � � exp � � jm �� � �i � � � H (2)� k a � � m ��� m � i ,� � TE s ,� � Scattering from cylindrical objects 0 i � 43 Exact solution of the problem (TE polarization) exp � � jki , z z � ˆ � ki , z � H ( r ) � E � hi � �k � ki , � � � � � TE s ,� � � m ��� m � 0 i � ( � j ) m J m � ki , � a � (2) H m � � ki ,� a � (2) H m � ki ,� � � exp � � jm �� � �i � � � � ˆ � ki ,� � exp � � jk z � H ( r ) � � E � hi � i ,z �k � � � � ( � j )m J � k a m � i ,� � (2) H m � ki ,� � � exp � � jm �� � �i � � � H (2)� � k a � � � m ��� m i ,� TE s,z � Scattering from cylindrical objects 0 i � 44 Exact solution of the problem (TM polarization) � For the TM case we have EsTM ( r ) � � � m ��� H bm N m,ki , z ( � , � , z ) J m � ki , � a � � � � � vm (2) H m � ki , � a � m ��� k ˆ � � E � vi � ki , � 0 i � � H N m,ki , z ( � , � , z ) J m � ki , � a � (2) H m � ki ,� a � m ��� Scattering from cylindrical objects H ( � j )m exp � jm�i � N m,ki , z ( � ,� , z ) 45 Exact solution of the problem (TM polarization) � Explicit form in components E TM s ,� � � � jki , z � ˆ ( r ) � � E � vi � � � � exp � � jki , z z � � k� 0 i ( � j ) m J m � ki , � a � (2) H m � ki , � a � m ��� E TM s ,� � ki ,z � exp � � jki , z z � ˆ ( r ) � � E � vi � � � k� ki ,� � � � 0 i � � m ��� (2) H m � � ki ,� � � exp � � jm �� � �i � � � � m ( � j ) m J m � ki , � a � (2) H m � ki , � a � Scattering from cylindrical objects (2) H m � ki ,� � � exp � � jm �� � �i � � � � 46 Exact solution of the problem (TM polarization) � Explicit form in components E TM s,z � � m ��� � � ki , � ˆ ( r ) � � E � vi � � �k 0 i ( � j ) m J m � ki , � a � (2) H m � ki , � a � � � exp � � jki , z z � � (2) H m � ki ,� � � exp � � jm �� � �i � � � � The magnetic field J m � ki ,� a � j� TM...
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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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