Figure 1

Dispersion relations of MIM waveguides for TM modes propagating in the $z$ direction. The geometry, the coordinate system, and the field components of the TM mode are illustrated in the inset. The black solid curve shows the dispersion for a single interface, and colored ones those for low-energy modes for various $T$ values. We used the value of 2.1 and the reported values [27] for the dielectric constants of ${\mathrm{SiO}}_2$ and Au, respectively.Reuse & Permissions

Figure 2

Energy density distribution in a MIM waveguide with a finite length. The first-order resonance for $T=3.3\mathrm{nm}$ and $L=65\mathrm{nm}$. The thickness of the Au slabs in the $x$ direction is 150 nm. A TM ($x$)-polarized plane wave of $\lambda =970\mathrm{nm}$ is incident from the left. The dashed lines are the borders between Au, ${\mathrm{SiO}}_2$, and free space. Right: Electric and magnetic fields at $z=2\mathrm{nm}$ and $L/2$, respectively. These are typical profiles of the MIM guided mode. Below: Fields at $x=0$. The electric field shows the maximum amplitudes near both end faces, and the magnetic field exhibits a peak at the center; a typical standing wave of $m=1$. The fields are the snapshots at the moment of the maximum amplitude. The energy density and the fields are normalized by those of the incident wave. The energy was calculated taking account of the frequency dispersion of the dielectric constant of Au [16, 28]. Each corner of the model has a radius of 0.25 nm to avoid unphysically singular values.Reuse & Permissions

Figure 3

Scanning electron micrograph of a fabricated nanosheet plasmon cavity. $T=14\mathrm{nm}$, $L=107\mathrm{nm}$, and $W=3\mu \mathrm{m}$. Scale bar, 500 nm. Inset: The transmission electron micrograph of the cross section for $T=3.3\mathrm{nm}$. Scale bar, 20 nm. Although the ${\mathrm{SiO}}_2$ film is wavy due to the surface roughness of the first Au layer, this feature had no influence on the optical properties in this study. The ${\mathrm{SiO}}_2$ film looks duplicated because the microscope specimen has a finite thickness and the vicinities of convex and concave points of the film look brighter.Reuse & Permissions

Figure 4

(a) Measured reflectance for various $L$ values. $T=14\mathrm{nm}$ and TM polarization. The individual spectra are offset by 0.04 from one another for visibility. Arrows indicate the major dips. (b) Schematic drawing illustrating the incident, the collected scattered light, and the measurement area (diameter: $2\mu \mathrm{m}$). (c) Calculated reflectance (upper) and intensity enhancement at the center of the entrance surface (lower) for TM polarization for representative $T$ and $L$ values. The field is normalized by that of the incident light. The thin lines indicate the experimental reflection spectra for similar parameters (left: $L=106\mathrm{nm}$; right: 61 nm). The reflection dips and the field peaks are denoted by arrows. The fields in Fig. 2 correspond to the $m=1$ peak in the right panel. The $Q$ values of the resonances are 10–20.Reuse & Permissions

Figure 5

Experimentally obtained dispersion relations. Solid curves: Analytical dispersion of MIM waveguides. Dashed lines: Propagation in the media with refractive indices of $n$ drawn for reference. The non-negligible discrepancy between the analytical model and the experiment for $T=14\mathrm{nm}$ probably originates from an error in the thickness measurement.Reuse & Permissions