Fundamental behavior of electric field enhancements in the gaps between closely spaced nanostructures

We demonstrate that the electric field enhancement that occurs in a gap between two closely spaced nanostructures, such as metallic nanoparticles, is the result of a transverse electromagnetic waveguide mode. We derive an explicit semi-analytic equation for the enhancement as a function of gap size, which we show has a universal qualitative behavior in that it applies irrespective of the material or geometry of the nanostructures and even in the presence of surface plasmons. Examples of perfect electrically conducting and Ag thin-wire antennas and a dimer of Ag spheres are presented and discussed.

Figure 1

Schematic diagram of a thin-wire antenna. The parameters shown are discussed in the text.

Figure 2

$\left|\mathbf{E}\right|{}^2$ enhancements as a function of gap size for PEC thin-wire antennas with parameters given in the text. Solid lines are used to connect the actual data points (symbols).

Figure 3

$\left|\mathbf{E}\right|{}^2$ enhancements as a function of gap size for a 3D Ag thin-wire antenna and a dimer of Ag spheres with parameters given in the text. Solid lines are used to connect the actual data points (symbols).

Figure 4

Intensities of $\left|\mathbf{E}\right|{}^2$ and the incident component of $\mathbf{E}$, $\left|E_x\right|{}^2$, in the gaps of a (top) 3D Ag thin-wire antenna and (bottom) Ag sphere dimer with parameters discussed in the text. The inset white scale bars correspond to $1$ nm. Note that the intensity values have been rescaled relative to Fig. 3 to fit clearly on the same scale, and the fields inside of the structures have been set to $0$.