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Understanding Dipole Scattering in Electromagnetic Fields

This document discusses the concept of dipole scattering in electromagnetic fields, exploring the implications of varying parameters and coordinates. Key topics include the evaluation of scattered fields, far-field calculations, and the application of the addition theorem. The analysis provides insights into how a dipole radiates in free space, and the formulation allows for understanding the scattered electric field components. This material is part of the advanced electrical engineering curriculum, focusing on wave propagation and scattering phenomena.

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Understanding Dipole Scattering in Electromagnetic Fields

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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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