Antenna and Aperture Relationship

In the earlier sections we considered different near-field structures. These structures were one of three types apertures, antennas, and hybrid structures. The apertures have a finite dielectric opening in a metal thin film. The resonant near field of interest is located within and in the vicinity of the opening. Anteimas are finite metallic structures located in an infinite dielectric region. The resonant near field of antennas is located around the metallic structure. Then there are hybrid structures such as a metal-coated, tapered optical fiber, which on one hand do not have an aperture and on the other have metal going to infinity. In such hybrid structures, the fact that the metal 

If we interchange the dielectric in the aperture opening and the thin film metal, we get a complementary structure, which is an antenna. Is there any relation between the resonance properties of the two structures If we assume that the aperture metal film is infinitesimally thick, and that the metal is a perfect electrical conductor (PEC), the aperture and the complementary antenna structure are connected by a form of Babinet s principle. Supgose that the aperture is illuminated by an incident electric field Ei The interaction with the aperture will set up a total electric field E. Now, suppose that the complementary antenna structure is illuminated by an incident magnetic field that is vectorially equal to the incident electric field in the aperture case. Thus, the mcident magnetic field in the anteima case is E. In this case, let H2 be the total magnetic field. The particular form of Babinet s principle states that 

Of course, in the case of a real metal film that is not infinitesimally thick, the principle is not expected to be perfectly satisfied. 

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