1. Introduction

Recently Fano resonance in plasmonic nanostructure complexes has attracted much attention, owing to its sharp spectral response, high field enhancement and highly designable optical response of plasmonic nanostructures. It has been reported that by engineering plasmonic nanostructures, Fano resonance can be achieved over a broad range of frequencies: from the visible to the terahertz region [1–10]. Fano resonance in mid-infrared (MIR) region is of great interest for biosensing applications because many materials possess MIR vibrational fingerprints that can be used for their identification, while the high-Q Fano resonance enhances field-matter interaction and enables sensitive bio-detection [11].

In this paper, we will demonstrate a Fano resonance in concentric two-ring apertures in metallic films. We have recently demonstrate an extraordinary optical transmission (EOT) effect [12, 13] in subwavelength metallic ring apertures which is polarization-independent [14], where over 60% optical transmission is observed when the area of the aperture is only 1.4% of the total area. The EOT effect results from the excitation of a bright dipole mode (the TE₁₁ mode when the ring aperture is viewed as a coaxial waveguide) by a linearly polarized incident light. When two concentric ring apertures are placed close to each other, the near-field coupling between them gives rise to two hybridized modes: a broadband bright mode and a narrowband dark mode [15]. Due to the local asymmetry (different radii) between the two ring apertures, the two hybridized modes are not exactly orthogonal to each other. The coupling between the two hybridized modes results in the characteristic Fano line shape in the transmission spectra. Given the symmetry of the structures, the Fano resonance is independent of the polarization of the incident light. By fitting the simulated and measured transmission spectra to a coupled optical resonator model, we find the Q of the dark mode to be 3~6 times higher than that of the bright mode depending on the dimensions of the apertures. We will also show in this paper that the dark mode can be selectively disabled without affecting the bright mode due to its unique current flow pattern.

2. Simulated and analytical results

The structure we use consists of an array of two concentric metallic ring apertures with subwavelength dimensions in a metal film. Figures 1(a)-1(e) show the 3D FDTD simulation of the two-ring aperture arrays in a gold film with the thickness of h = 100 nm on a silicon substrate, which is excitated by a normal-incident light polarized along the x-axis. The two concentric ring apertures have radii of r₁ = 950 nm and r₂ = 700 nm, widths of w = 100 nm and an edge-to-edge gap between them of d = 150 nm. The structure has two resonant modes: a bright mode where the E-fields in the two apertures are in-phase, and a dark mode where the E-fields have opposite phase. Figure 2(a) shows the schemes of charge distribution of hybridized modes. Figure 1(a) shows the top-view of the electric field (the E_x component) distribution of the dark mode. Figures 1(b) and 1(c) show the side-view of the field distribution for the bright and dark modes respectively. The peak E-field intensity (|Ex|²) in the aperture is 200 times higher than that of the incident wave when the dark mode is excitated. The periodic boundary condition with a period of p = 2.6 µm is used in the simulation.

 

Fig. 1 (a) Top-view of Ex field amplitude distribution at frequency of 760 cm⁻¹ when the dark mode is excitated in the concentric ring apertures. (b) and (c) show the cross-sectional Ex field distribution of the bright mode (excitated at frequency of 980 cm⁻¹) and the dark mode, respectively, with the cross-section cut along the horizontal dashed line in (a). Black arrows indicate the field direction, and red circles indicate the charge distribution. (d) The simulated power transmission spectrum for the concentric two-ring apertures is shown as the solid red line, which is fitted by a coupled optical oscillator model (dotted black line). The dashed blue and dashed green lines are the transmission spectra of the single ring apertures. (e) The phases of the Ex field in the two apertures (the dashed lines) and their difference (the solid line). (f) Solid lines: energies in the dark mode (the red line) and the bright mode (the black line) calculated from the analytical model, which are normalized to the maximum energy in the dark mode. Blue dashed line: absorption of the structure calculated from FDTD simulation.

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A sharp Fano resonant dip around the central frequency of 840 cm⁻¹ can be clearly seen on the simulated transmission spectrum shown as the red line in Fig. 1(d). In comparison, a single-ring aperture shows only a peak on the transmission spectrum due to the EOT effect. The dashed lines show the transmission spectra when only the external ring aperture or only the internal ring apertures is present. The small features on the spectra at ~1100 cm⁻¹ are due to the grating effect determined by the periodicity of the array [12]. The phases of the E-field in the two apertures and their differences are plotted in Fig. 1(e). One can see that the phases at aperture r₁ (the blue line) and r₂ (the green line) differ by ~π around the Fano resonance dip, confirming that the dark mode is excitated there. In addition, the absorption peaks at around 760 cm⁻¹ which is near the Fano resonance dip in transmission spectrum, shown as the blue dashed line in Fig. 1(f), which also confirms dark mode excitation.

The dark mode does not couple directly to the far field and cannot be directly excitated because the radiations from the two apertures destructively interfere with each other. However, due to the asymmetry in the lengths of the inner and outer apertures, the field intensity inside each ring apertures would be different, and therefore the dark mode can couple to the bright mode, which gives the Fano resonance that can be seen in the far-field transmission spectrum. The coupling process between the dark and bright modes can be analyzed with a coupled optical resonator model [16, 17]. We assume two optical resonances representing the bright mode and dark mode are oscillating with amplitudes a₁ and a₂ at frequencies ω₁ and ω₂, respectively. The intrinsic photon lifetimes of the two resonances are τ₁ and τ₂, and the two resonances are coupled to each other with a coupling rate κ. Only the bright mode directly couples to the input and output waves. The time evolution of the amplitudes of these two modes can be described as follows:

Under the steady state ($d{a}_1/dt=d{a}_2/dt=0$), we can get the expressions of amplitudes a₁ and a₂ of the resonant modes as well as the transmission

The analytical model is used to fit the transmission spectrum from both simulations and measurements to find the basic properties of the bright and dark modes. The black dotted line in Fig. 1(d) shows that the analytical model fits very well with the FDTD simulation results. From the fitting parameters, we find that the bright mode resonates at the center frequency of 982 cm⁻¹ with a photon lifetime of ~26 fs (Q₁ = 4.8), and the dark mode resonates at the center frequency of 827 cm⁻¹ with a photon lifetime of ~127 fs (Q₂ = 19.8). The Q of the dark mode is ~4 times higher than that of the bright mode since the dark mode is not directly coupled to the far-field radiation. The Q of the dark mode is limited by the intrinsic metal loss. The coupling lifetime (1/κ) between the two modes is ~36 fs. The energies at different frequencies in each mode are proportional to |a₁(ω)|² and |a₂(ω)|², respectively, which are plot as solid lines in Fig. 1(f). One can see that the dark mode shows a stronger resonance and higher amplitude than the bright mode. At the center of the dark mode resonance, the amplitude of the bright mode reaches close to zero, showing that almost all the optical energy has been transferred from the bright mode to the dark mode, even though the dark mode does not directly couple to the incident wave. We also notice that the sum of the energies in each mode from the fitted analytical model agrees with the total absorption loss from the simulation results (blue dashed line in Fig. 1(f)).

Since there are multiple unknown parameters in Eq. (7), understanding how each parameter affects the spectra is important to obtain a correct fitting. By tweaking each parameter, we found that the envelop of the overall peak (excluding the Fano dip) from the broad bright mode is mainly determined by τ₁, k₁ and k₂, while the Fano dip is mainly determined by the coupling rate κ and photon lifetime τ₂. The information of bright mode (ω₁, τ₁, k₁ and k₂) can be obtained from the modified structure with dark mode suppressed, which will be talked in detail later. In general, higher τ₁ leads to higher and narrower envelop of the overall transmission peak, while higher k₁ or k₂ leads higher and broader envelop. And higher κ leads to a broader but deeper lineshape of Fano dip. Higher τ₂ also leads to a higher extinction ratio of the Fano dip but its total width is almost not affected.

The Q of the bright and dark modes (Q₁ and Q₂) can be tuned by varying the dimensions of the concentric two-ring apertures. Figures 2(b)-2(e) show how the Q’s of the two modes depend on the radii of the rings, the metal thickness, the width of the aperture and the gap between two ring apertures. Among those geometric parameters, the Q of dark mode (Q₂) is most sensitive to the metal thickness. As the metal thickness increases, Q₂ increases significantly while Q₁ remains almost constant, which is shown in Fig. 2(b). When the gap between the two ring apertures increases, the larger asymmetry of the local field inside the two ring apertures leads to higher coupling rate κ between the bright and dark modes. Higher κ would increase the optical power transferred from bright mode to dark mode, giving a broader but deeper Fano resonance dip. Therefore, Q₂ peaks at a particular gap d = 300 nm, as shown in Fig. 2(c). The two Q’s do not vary significantly with the aperture width or the overall dimension (radii) of the structure, as shown in Figs. 2(d) and 2(e).

 

Fig. 2 (a) Hybridization schemes. (b)-(e) Quality factors for the dark (red) and the bright (black) modes extracted from the simulated transmission spectra by fitting them with the analytical model. Unless otherwise specified by the x-axis of each panel, the geometric parameters of the device are h = 100 nm, r₁ = 950 nm, r₂ = 700 nm, w = 100 nm, d = 150 nm, p = 2.6 µm. (b) Q versus the metal thickness h. (c) Q versus the gap size d between the two apertures. (d) Q versus the width of the aperture w. (e) Q versus radius r₁ when r₁, r₂ and w are scaled with the same factor. The resonant wavelength scales proportional to the radii.

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3. Experimental results

We fabricate periodic arrays of the concentric two-ring apertures arrays by the E-beam lithography. The rings are first defined on a negative E-beam resist (Dow Corning XR-1541) on top of a 100-nm-thick polymethyl methacrylate (PMMA) layer on a lightly doped silicon substrate. The ring pattern is then transferred to the PMMA layer by oxygen plasma etching, and a reactive ion etching for a 20-nm-thick silicon layer is performed. A 40-nm-thick gold film is then evaporated followed by a lift-off process with Acetone. Thus, the 40-nm-thick apertures are partially filled by a 20-nm-thick silicon layer. Figure 3(a) shows the SEM picture of the fabricated periodic arrays of the concentric two-ring apertures with various radii in the gold film on a silicon substrate. The total size of each array is 100 µm × 100 µm.

 

Fig. 3 (a) An SEM picture of fabricated concentric two-ring apertures. (b) Red solid line shows measured power transmission spectrum for the concentric two-ring apertures with r₁ = 600 nm and r₂ = 350 nm. The dashed lines are the measured transmission spectra of single-ring apertures (blue: r = 600 nm, green: r = 350 nm). The spectra are normalized to the transmission of a bare silicon substrate. The black dotted line is analytical fitting of transmission of concentric two-ring apertures using coupled optical resonator model.

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The transmission of the device, measured using a Nicolet Fourier-transform Infrared Microscope [18], confirms the simulation results. Figure 3(b) compares the measured transmission spectra of a two-ring aperture array (red line) and single-ring aperture arrays (blue and green dashed lines). All the spectra are normalized to transmission of a bare lightly doped silicon wafer which has ~50% absolute transmission. The two ring radii are r₁ = 600 nm, r₂ = 350 nm. The width of each ring is w = 70 nm and the distance between the two rings is d = 180 nm. A Fano resonance dip centered at 1190 cm⁻¹ can be clearly identified. By fitting the measured transmission spectrum with the coupled optical resonator model (the black dotted line in Fig. 3(b)), the bright mode is found to resonate at 1356 cm⁻¹ with a photon lifetime of ~14 fs (Q₁ ≈3.7), and the dark mode resonates at 1168 cm⁻¹ with a photon lifetime of ~52 fs (Q₂ ≈11.5). The coupling lifetime between the two modes is 16 fs. The quality factor of the dark mode is over 3 times higher than that of the bright mode. Therefore, the dark mode is expected to create stronger interaction with the material in the aperture. Note that the small dip at 1550 cm⁻¹ in the measured spectra is due to the grating effect determined by the periodicity of the array.

The bright mode and the dark mode have very different patterns of charge motion (current flow). In the bright mode, the charges in the metal between two apertures oscillate along the radial direction; while in the dark mode, the charges move along the azimuthal direction. and the current flow is the strongest at the minimum E-field positions. Therefore, if the metal between two ring apertures is cut at the minimum E-field positions (top and bottom portion of the rings) as shown in Fig. 4(a), the azimuthal current flow of the dark mode is stopped and the dark mode is suppressed. These cuts have little effect on the bright mode whose radial current flow is not interrupted. As a result, the Fano resonance dip disappears due to the absence of the dark mode while the resonance peak from the bright mode remains, which is experimentally observed as the red line in Fig. 4(c) shows.

 

Fig. 4 (a) Scheme of charge motions for the dark mode with a cut between the apertures. (b) An SEM picture of fabricated concentric two-ring apertures with a cut between the apertures. (c) Measured transmission spectra of concentric two-ring apertures with a cut in the metal between the two apertures, as shown in (b), with different polarization of incident light. The transmission is normalized to the transmission of a bare silicon wafer.

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When the polarization of the incident wave is rotated 90°, the cuts are now at the maximum E-field location where the azimuthal current flow of the dark mode is zero. Therefore the dark mode is not affected by the cuts and the Fano resonance reappears as the black line in Fig. 4(c) shows. With this structure, one can selectively turn on and off the Fano resonance and create dramatically different spectra features by changing the polarization of the incident light.

5. Conclusions

We show a Fano resonance in subwavelength concentric two-ring apertures in metallic films, which arises from the coupling between a dark mode and a bright mode enabled by the intrinsic asymmetry between the two concentric rings. The Q of the dark mode is 3−6 times higher than that of the bright mode. The extraordinary transmission of the two-ring apertures is independent of the polarization of the incident light. In a modified structure, however, we show that the dark mode can be switched on and off without affecting the bright mode by varying the polarization of the incident light.