Quantum tunneling in plasmonic nanostructures has presented an interesting aspect of incorporating quantum mechanics into classical optics. However, the study has been limited to the subnanometer gap regime. Here, we newly extend quantum plasmonics to gap widths well over 1 nm by taking advantage of the low-frequency terahertz regime. Enhanced electric fields of up to 5 V/nm induce tunneling of electrons in different arrays of ring-shaped nanoslot antennas of gap widths from 1.5 to 10 nm, which lead to a significant nonlinear transmission decrease. These observations are consistent with theoretical calculations considering terahertz-funneling-induced electron tunneling across the gap.

Metal-graphene-metal hybrid structures allow angstrom-scale van der Waals gaps, across which electron tunneling occurs. We squeeze terahertz electromagnetic waves through these λ/10 000 000 gaps, accompanied by giant field enhancements. Unprecedented transmission reduction of 97% is achieved with the transient voltage across the gap saturating at 5 V. Electron tunneling facilitated by the transient electric field strongly modifies the gap index, starting a self-limiting process related to the barrier height. Our work enables greater interplay between classical optics and quantum tunneling, and provides optical indices to the van der Waals gaps.

We investigated optical nonlinearity induced by electron tunneling through an insulating vertical gap between metals, both at terahertz frequency and at near-infrared frequency. We adopted graphene and alumina layers as gap materials to form gap widths of 3 Å and 1.5 nm, respectively. Transmission measurements show that tunneling-induced transmittance changes from strong fields at the gaps can be observed with relatively weak incident fields at terahertz frequency due to high field enhancement, whereas nonlinearity at the near-infrared frequency is restricted by laser-induced metal damages. Even when the same level of tunneling currents occurs at both frequencies, transmittance in the terahertz regime decreases much faster than that in the near-infrared regime. An equivalent circuit model regarding the tunneling as a resistance component reveals that strong terahertz nonlinearity is due to much smaller displacement currents relative to tunneling currents, also explaining small nonlinearity of the near-infrared regime with orders of magnitude larger displacement currents.

Quantum tunnelling becomes inevitable as gap dimensions in metal structures approach the atomic length scale, and light passing through these gaps can be used to examine the quantum processes at optical frequencies. Here, we report on the measurement of the tunnelling current through a 3-Å-wide metal-graphene-metal gap using terahertz time-domain spectroscopy. By analysing the waveforms of the incident and transmitted terahertz pulses, we obtain the tunnelling resistivity and the time evolution of the induced current and electric fields in the gap and show that the ratio of the applied voltage to the tunnelling current is constant, i.e., the gap shows ohmic behaviour for the strength of the incident electric field up to 30 kV/cm. We further show that our method can be extended and applied to different types of nanogap tunnel junctions using suitable equivalent RLC circuits for the corresponding structures by taking an array of ring-shaped nanoslots as an example.

We report the effect of geometrical factors governing the polarization profiles of near-field scanning optical microscope (NSOM) probes. The most important physical parameter controlling the selective electric or magnetic field sensitivity is found to be the width of the metal rim surrounding aperture. Probes with metal rim width w < λ/2 selectively senses the optical electric field, while those with w > λ/2 selectively senses the optical magnetic field. Intensity variation of optical Hertz standing wave formed upon reflection at oblique incidence shows a phase difference of π/2 between electric and magnetic probes: an analogue of the classical Wiener's experiment. Our work paves way towards electromagnetic engineering of nanostructures.