Plasmonic interaction of visible light with gold nanoscale checkerboards

Intersecting corners and checkerboards of negative refractive index materials (NRIM) represent highly singular electromagnetic systems that involve very highly enhanced local fields and the local density of modes. It is well known that plasmonic metallic systems can mimic the behavior of NRIM in the near-field limit at optical frequencies. Opaque gold films have been structured by focused ion-beam technologies at submicrometer scales in a checkerboard fashion and their optical properties measured. Subwavelength square holes in thick gold films placed in checkerboard fashion show a broadband extraordinary transmission of light at visible wavelengths. We find that the smaller the square holes, the larger is the transmission over a band of wavelengths from 650 to 950 nm suggesting that such structured surfaces have very unusual effective medium properties, which is confirmed by the band-structure diagrams computed with finite elements. Theoretical results also confirm the experimental transmission measured to be well over $80\%$ from 750 to 950 nm for a checkerboard with $150\mathrm{nm}\times 150$ nm square holes. This unusual broadband nature of checkerboard structured films is confirmed by the dark-field reflection spectra. Microscopic studies reveal that these structures have enhanced interaction of light at the edges and corners. These checkerboards are also found to give rise to an enhancement of fluorescence by imbedded dye molecules. There is a strong correspondence between the theoretical predictions and the experimental measurements.

Figure 1

Corners of negative refractive index act as perfect lenses. The pictures show the focusing of rays via negative refraction. The double intersecting corner reimages the rays from a source onto itself. This results in a highly singular situation with the rays circulating about the corner.

Figure 2

A point source located inside a perfect corner reflector consisting of eight infinite regions alternating positive and negatively refracting isotropic homogeneous media ($\varepsilon =\mu =\pm 1$) displays seven perfect images (one in each corner). In such a system, light goes around in closed trajectories and modes are infinitely degenerate. A large magnitude of the longitudinal electric field compared to the transverse magnetic field is noted. The working wavelength is 0.3 m. It is interesting to note that the power flow is apparently outwardly directed, which arises due to the perfectly matched layer boundary conditions.

Figure 3

The dependence of the spatial oscillations of the plasmonic fields on the dissipation in the medium. The number of spatial oscillations is evidently lowered as the dissipation is increased from ${10}^{-6}$ to ${10}^{-3}$. The plot shows that the number of oscillations vary inversely with the logarithm of the dissipation in the medium for the case of the perfect corner reflector shown in Fig. 2.

Figure 4

Band diagram for wave numbers describing the segments [BA] and [AC] of the first Brillouin zone ABC for a chessboard with alternating regions of relative permittivity of 1 and $-$1 for the transverse electric polarization (i.e., electric field orthogonal to the plane). The plots of the corresponding eigenfields around wave number C exhibit either an evanescent behavior in the square inclusions with negative permittivity and a Mie-type resonance in other inclusions (a hallmark of spoof plasmons reminiscent of metal plates with holes),[20] or the eigenfields exhibit Bloch-type (antiphase at wave number C) features across a periodic cell.

Figure 5

Electric fields associated with a line source located inside a finite square checkerboard consisting of alternating square regions of positively and negatively refracting isotropic homogeneous media ($\varepsilon =\mu =\pm 1$). (a) For a source very close to a corner, the field remains mostly confined near the corner. (b) For a source close to an edge, and located midway between two corners, a network of plasmon modes takes place.

Figure 6

Scanning electron microsope images of checkerboard structures made by FIB induced adhesion followed by peel off on (a) a 200-nm thick gold film: each square has a size of about $500\text{nm}\times 500$ nm, (b) a magnified picture of a part of the structure in (a) showing the connected nature of the checkerboard, and (c) a 200-nm thick silver film with each checkerboard square measuring about $450\mathrm{nm}\times 450$ nm.

Figure 7

Optical (white light) microscope images of the gold checkerboard structures at 100$\times$ magnification. Panel (a) shows the optical bright image while (b) shows the dark-field image of the checkerboard pattern shown in Fig. 6a. Panel (c) shows the bright-field image and (d) the dark-field image of a sample with unconnected square scatterers with the same periodicity and the same scatterer size. In case of (d), each square scatterer appears uniformly bright in contrast to (b). The film thickness is 200 nm in each case.

Figure 8

Broadband transmission through a 200-nm thick gold film with subwavelength square holes of size $200\mathrm{nm}\times 200\mathrm{nm}$ and $350\mathrm{nm}\times 350\mathrm{nm}$ placed in checkerboard fashion. Panel (a) shows a sample for the checkerboards that has a periodicity 400 nm, which corresponds to the thick curve in panel (b). The transmission across the spectral region 450 to 900 nm never exceeds 60% in panel (b) and the crossing with the thin curve for a checkerboard with periodicity 700 nm around the wavelength 750 nm is noted; the two curves display an antagonistic behavior, thereby suggesting the ratio between the wavelength and the unit cell’s size is crucial to determine the transmission properties.

Figure 9

Broadband extraordinary transmission obtained through a 200-nm thick gold film with subwavelength square holes of size($150\mathrm{nm}\times 150\mathrm{nm}$) placed in checkerboard fashion. The checkerboard has periodicity of 300 nm. There is broadband transmission well over 60$\%$ across the spectral region of 650 to 950 nm with a strong agreement between the computed transmittance (dotted curve) and the experimentally measured transmittance (thick curve). We note the similarity between these curves and the thick curve in panel (b) of Fig. 8.

Figure 10

The dark-field reflection spectra from checkerboard structured gold films with periodicities of 300, 700, and 1000 nm. The reflectances are normalized with respect to the reflectance from a thick aluminum film. While the larger periodicity samples show definite resonant peaks, the 300-nm periodic sample has a featureless broadband nature that monotonically increases across the visible frequencies up to 900 nm.

Figure 11

(a) Schematic diagram representing the periodic cell used in the finite element modeling. (b) Representation of a sample of the mesh taken from the side of the figure (a). (c) Schematic diagram for the observation of light transmittance. White light (represented by a rainbow color in the large arrow) illuminates a gold/silver checkerboard, and transmission measurements are made. (Inset) Unit cell used in the checkerboard structure.

Figure 12

Three-dimensional comsol calculations for the propagation of light having a wavelength of 580 nm across the unit cell shown in Fig. 11. We show the normalized total field of a 3D simulation for a periodic checkerboard with a periodicity of 1000 nm and thickness 200 nm, with a square hole of side of length 500 nm. The radiation is incident through the glass substrate. (a) shows the amplitude of the electric field in three dimensions. (b), (c), (d), (e), and (f) are cross-sectional plots of the electric field corresponding to the different $z$ positions as indicated in the panels.

Figure 13

Top panel: three-dimensional comsol calculations for the propagation of an $x$-polarized electromagnetic wave having a wavelength of 750 nm across the unit cell shown in Fig. 11. We show the normalized total field of a 3D simulation for a periodic checkerboard with a periodicity of 300 nm and thickness 200 nm, with a square hole of side length of 150 nm. (a) 3D plot, (b) 2D plot of the amplitude of the electric field on the vertical plane $y=150$ nm. (c) 2D plot of the amplitude of the electric field on the vertical plane $x=150$ nm. Bottom panel: three-dimensional comsol calculations for the propagation of light having a wavelength of 750 nm as in Fig. 13. Top: profile of the amplitude of the electric field along the red line. Bottom: plot of the amplitude of the electric field on the vertical plane $y=150$ nm.

Figure 14

Fluorescence emitted by Rhodamine-6G molecules imbedded in a PMMA film at a 20-$\mu$molar concentration and spin coated on plain glass, unstructured gold film, and checkerboard structures of block size $500\mathrm{nm}\times 500\mathrm{nm}$ and 1000-nm periodicity. The labels Checkerboard-1, -2 and -3 refer to three different samples with the excitation focus spot at different locations in the finite checkerboard structures. The enhancements depend on the exact location of the focus spot within the structures.