Abstract

We use a quantum mechanical approach to derive a set of linear and nonlinear quantum conductivity coefficients for metal–insulator–metal structures with nanometer sized gaps. The immediate proximity of metallic objects generates a tunneling AC current density that endows the gap region with additional linear and nonlinear coefficients that in turn trigger linear and nonlinear absorption, and second- and third-harmonic generation. For example, a vacuum gap approximately 0.8 nm thick displays an effective $|{\chi }^{(2)}|\sim 0.1\mathrm{pm}/\mathrm{V}$ for adjacent objects composed of dissimilar metals and an effective $|{\chi }^{(3)}|\sim {10}^{-20}{\mathrm{m}}^2/{\mathrm{V}}^2$ for either similar or dissimilar metals, increasing exponentially for smaller gaps. Field localization inside the gap ensures that harmonic generation arising from the gap region overwhelms intrinsic metal second- and third-order nonlinearities.

© 2014 Optical Society of America

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