Electromagnetic Field Enhancement in Small Gaps: A Rigorous Mathematical Theory

This paper is concerned with the field enhancement when an electromagnetic wave passes through subwavelength metallic gaps. We focus on a particular configuration when there is extreme scale difference between the wavelength of the incident wave, the thickness of metal films, and the size of gap apertures. Based upon a rigorous study of the perfect electrical conductor model for the transverse magnetic ploarization, we show that enormous electric field enhancement occurs inside the gap if the gap size is sufficiently small. (There is no electromagnetic field enhancement for the transverse electric polarization case, of which the mathematical results are less interesting and they are not presented in this paper.) Furthermore, when the gap size approaches zero, there is a limit on the ultimate enhancement strength, which is proportional to the ratio between the wavelength of the incident wave and the thickness of the metal film. On other hand, it is demonstrated that there is no significant magnetic field enhancement inside the gap.