Since the discovery of the extraordinary optical transmission through nanohole arrays in metallic films by Ebbesen, a wealth of research has been sparked in the experimental and theoretical investigation of the localized electromagnetic field enhancement and the optical transmission enhancement in subwavelength nanostructures. However, there has been a long debate on the interpretation of the enhancement effect since Ebbesen's work. In addition, a quantitative analysis of the enhancement is still widely open. In this talk, using two-dimensional slits as a prototype, I will present mathematical studies of both the field enhancement and transmission enhancement in the subwavlength structures. Based upon the layer potential technique, asymptotic analysis, different types of enhancement mechanism are unveiled, which includes Fabry-Perot resonance, surface waves, and Fano resonances. This is a joint work with Junshan Lin from Auburn University.
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