Time-domain analysis of the Sommerfeld VMD problem based on theexact image theory

A novel time-domain solution of the Sommerfeld half-space problem is constructed through the exact image theory. The radiation from a vertical magnetic dipole (VMD) above the planar interface of two lossless and dispersionless dielectric media is analyzed. The reflection field is given as a Laplace transform when the refraction index of the lower medium is greater. The converse case of refraction indexes is also studied, and the reflection field is written as originating from an image source located in homogeneous space. The present theory is seen to lead to a numerically efficient result, which is demonstrated with examples