Surface equivalence principle

[3] Being a more rigorous reformulation of the Huygens–Fresnel principle, it is often used to simplify the analysis of radiating structures such as antennas.

It is an extension of Huygens–Fresnel principle, which describes each point on a wavefront as a spherical wave source.

correspond to the imaginary current sources that are impressed on the closed surface.

Both the original and imaginary currents should produce the same external field distributions.

Thus, the surface currents are chosen as to sustain the external fields in the original problem.

A similar formulation for a perfect magnetic conductor would use impressed electric currents.

[1] The equivalence principles can also be applied to conductive half-spaces with the aid of method of image charges.

[1][4] The surface equivalence principle is heavily used in the analysis of antenna problems to simplify the problem: in many of the applications, the close surface is chosen as so to encompass the conductive elements to alleviate the limits of integration.

[2][12][13][14] The principle has also been used in the analysis design of metamaterials such as Huygens’ metasurfaces[15][16] and plasmonic scatterers.

Illustration of the equivalence principle for an imaginary closed surface with impressed electric and magnetic current sources: original (a) and equivalent (b) problems over the imaginary surface, . and represent the original source distributions inside the surface. The equivalent formulation yields the same external electric and magnetic fields distribution as in the original problem. The internal fields and surface currents are chosen to enforce the boundary conditions .
Illustration of Love and Schelkunoff equivalence principles: a) The original problem, b) Love equivalent problem, c) Schelkunoff equivalent problem with perfect electric conductor, d) Schelkunoff equivalent problem with perfect magnetic conductor. All problems have the same external fields.