Dipole radiation in the presence of planar soft and hard surface

Soft and hard surface can be introduced in electromagnetic theory as a convenient idealized concept for the tuned corrugated surfaces and other corresponding structures. By use of the spectral-domain approach, the Weyl´s identity and the technique of exponential integral function, the accurate closed-form expression is derived for electromagnetic field of an arbitrarily oriented electric dipole in the presence of the planar soft and hard surface. The fields are expressed as the sum of three parts: primary field, image field reflected by a perfect electric conductor boundary and field created by a transmission-line current source. In addition, the expressions of the far-field and the related power are derived. The obtained result can serve as the foundation for the related practical electromagnetic problems in the presence of a soft and hard surface.