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Analyzing Dipole Scattering in Electromagnetic Theory

This note explores the principles of dipole scattering as part of an advanced course in electromagnetic theory. It discusses the relation between electric fields and dipole moments and incorporates the addition theorem for calculating scattered fields from dipole sources. The far-field approximation is analyzed, outlining the derivation of the scattered electric field in the far zone. Key assumptions and boundary conditions are highlighted, providing insights into how a single dipole radiates in free space. This study is beneficial for understanding the scattering phenomena that arise in various applications within the ECE field.

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Analyzing Dipole Scattering in Electromagnetic Theory

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  1. ECE 6341 Spring 2016 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 (from Notes 15):

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

  4. Dipole Scattering (cont.) Assume a scattered field (see the note below): B.C.’s: at Hence Note: We assume that the scattered field is TMz. This follows from the fact that we can successfully satisfy the boundary conditions.

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

  6. Dipole Scattering (cont.) Far-Field Calculation From ECE 6340 (far-field approximation): 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 ECE 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 From ECE 6340: In the far field of any antenna, we have so or

  12. Dipole Scattering (cont.) Hence We thus have with

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