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Prof. David R. Jackson ECE Dept.

ECE 6341. Spring 2012. Prof. David R. Jackson ECE Dept. Notes 16. Dipole Scattering. z. y. x. Note: We can replace z with z - z ' and  with  -  ' at the end, if we wish. Dipole at origin :. Dipole Scattering (cont.). Dipole at. Now use addition theorem:. Hence.

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Prof. David R. Jackson ECE Dept.

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  1. ECE 6341 Spring 2012 Prof. David R. Jackson ECE Dept. Notes 16

  2. Dipole Scattering z y x Note: We can replace z with z-z' and  with  -'at the end, if we wish. Dipole at origin:

  3. Dipole Scattering (cont.) Dipole at Now use addition theorem: Hence Valid for  < 

  4. Dipole Scattering (cont.) Assume a scattered field: B.C.’s: at Hence

  5. Dipole Scattering (cont.) or We then have

  6. Dipole Scattering (cont.) Far-Field Calculation or since

  7. Dipole Scattering (cont.) Note: Instead of taking the curl of the incident vector potential, we can also evaluate the incident electric field directly, since we know how a single dipole in free space radiates. From 6340:

  8. Dipole Scattering (cont.) Now we need to evaluate the scattered field in the far-zone. Switch the order of summation and integration:

  9. Dipole Scattering (cont.) Use the far-field Identity: Then we have

  10. Dipole Scattering (cont.) Hence, we have The scattered field is clearly in the form of a spherical wave.

  11. Dipole Scattering (cont.) We now calculate the scattered electric field as Possible components: Note: E is the same in cylindrical and spherical coordinates. Hence, in the far-field we only have

  12. Dipole Scattering (cont.) Calculate H : Hence Keeping the dominant term:

  13. Dipole Scattering (cont.) so Also, Hence

  14. Dipole Scattering (cont.) so or Compare with:

  15. Dipole Scattering (cont.) Summary Note: We could also get this from the ECE 6340 far-field equation:

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