The use of vector transforms in solving some electromagnetic scattering problems

It is shown that there exists a class of vector transforms and vector series expansions that are independent of their scalar counterparts. They can be used to simplify the solutions of a class of vector electromagnetic scattering problems. The applications are shown of vector Fourier, Hankel, and Mathieu transforms and series expansions to the formal solutions of scattering by rectangular, circular and elliptical disks and open-ended waveguides. The problems solved are canonical problems, however, more complex problems for applications in microwaves, microstrip integrated circuits, geophysical probing, etc. can be solved in a similar fashion.