Ultimate terahertz field enhancement of single nanoslits

A single metallic slit is the simplest plasmonic structure for basic physical understanding of electromagnetic field confinement. By reducing the gap size, the field enhancement is expected to first go up and then go down when the gap width becomes subnanometer because of the quantum tunneling effects. A fundamental question is whether we reach the classical limit of field enhancement before entering the quantum regime, i.e., whether the quantum effects undercut the highest field enhancement classically possible. Here, by performing terahertz time domain spectroscopy on single slits of widths varying from 1.5 nm to 50 µm, we show that ultimate field enhancement determined by the wavelength of light and film thickness can be reached before we hit the quantum regime. Our paper paves way toward designing a quantum plasmonic system with maximum control yet without sacrificing the classical field enhancements.

Figure 1

Schematics of the field enhancement change in the metallic nanogap structure. (a) By reducing the gap size, the field enhancement is expected to first go up and then go down when the gap size becomes subnanometer because of the quantum tunneling effect. (b) A fundamental question is whether we reach the classical limit of field enhancement before entering the quantum regime.

Figure 2

(a) Schematic of an infinite single slit. The structure is illuminated by normally incident $p$-polarized terahertz waves. The inset is a transmission electron microscopy (TEM) image of a 1.5 nm $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ gap fabricated by atomic layer lithography. (b) Top views of SEM images for single slits with three gap sizes: $w=2\mu \mathrm{m}$ (top), 200 nm (middle), and 2 nm (bottom). (c) Cross-sectional views of SEM images for 10, 5, 2.5, and 1.5 nm gaps (from left to right).

Figure 3

(a) Time traces of the transmitted terahertz electric field through a sapphire substrate with a 1 by 1 mm aluminum aperture (black) and a 5 nm gap sample with the same aperture (red). The direct transmission of Au film is subtracted in the sample data. (b) Normalized transmitted amplitudes (left axis) and field enhancement (right axis) of a 5 nm gap as a function of frequency. The fit (black dashed line) indicates 1/$f$ dependence. (c) Field enhancement as a function of gap size $w$ for several frequencies. The solid lines are the theoretical calculation of the modal expansion formalism. (d) Horizontal electric field (left) and magnetic field (right) around a 1.5 nm gap with an area of 500 by 500 nm simulated by FDTD. The frequency is fixed at 0.15 THz.

Figure 4

(a) Field enhancement as a function of the gap size $w$. Transition of the field enhancement by decreasing the gap size $w$ at 0.3 THz. The gap thickness $h$ is fixed at 150 nm. Three regimes are identified for different values of $w$. The black dot is experimental data, and the black solid line is the result by modal expansion. For the regime of $w\ll h(\ll \lambda )$, the field enhancement shows a saturation behavior reaching to the ultimate limit estimated by a simple capacitor model (red line). The regime for $w\sim h(\ll \lambda )$ and that for $w\gg h$ and $w<\lambda$ are close to the dependence of $1/w$ (green line) and $1/\sqrt{w}$ (blue line), respectively. (b) Two components of the induced current density, $J_x$ (top) and $J_z$ (bottom), in 150-nm-thick Au film for $w$ of 200 nm (right) and 1.5 nm (left). (c) Schematics of the induced current density depicted with black arrows in a metal film and the accumulated charges near the slit edges for two gap sizes: $w\sim h(\ll \lambda )$ (right) and $w\ll h(\ll \lambda )$ (left). (d) Electric field enhancement of a 5 nm gap as a function of the gap thickness $h$. The solid line is the calculation of modal expansion. The schematics indicate that 1/$h$ dependence of the field enhancement results from an increased surface charge density due to the constant value of the induced surface current $K$.