Electromagnetic field due to a loop antenna buried in a medium with complex boundaries

The radiation of a loop antenna embedded in a dissipative medium with complex boundaries is analyzed by a perturbation method and an efficient fast multiple-integration technique. But the perturbation method can not be used directly because there is a finite-length metal cylinder in the vicinity of the loop antenna. The prolate ellipsoid equivalence of the metal cylinder is made, then the cylinder may be removed and the perturbation method is valid. Numerical results indicate that the approach is accurate at low frequencies and stable.