Introduction

Both localized surface plasmons (LSPs) and propagating surface plasmons polaritons (SPPs) are the collective oscillations of conduction electrons around the metals coupled with incident electromagnetic field. LSPs, easily excited in nanoparticles with size much smaller than the incident wavelength, are highly sensitive to nanoparticle’s composition, shape, size, and local dielectric environment [1]. While SPPs, as propagating electromagnetic waves bound to the interfaces between metals and dielectrics [2], are also very sensitive to the surrounding. In this context, either LSPs or SPPs resonance can be used as a label-free and high-sensitivity sensor for measuring environment change and biomolecular interaction [3–6]. However, due to the broad linewidth of localized surface plasmons resonance, the sensitivity of LSPs-based sensor is usually among 200-800 nm/RIU and the figure of merit (FoM) is relatively low (generally lower than 6) [4]. On the other hand, although SPPs-based sensor possesses high sensitivity and FoM, the conventional SPPs sensors are often expensive with complicated configuration, such as Kretschmann configuration [7]. Therefore, it is still a great challenge to make high quality plasmonic sensors with simple structures.

Recently, Fano resonance has been proposed as a promising candidate for sensors of high-sensitivity and high FoM [8–10], because it possesses resonant suppression in a narrow frequency window, a typical asymmetric line shape, and high sensitivity to the change of the environment. A variety of Fano resonances have been realized in plasmonic systems so far through the hybridization of different plasmon modes [11–15]. It is noted that most of previous works focused on the in-plane near-field coupling between the narrow dark and broad bright plasmonic modes, but in this case the interval distance between the nanostructures needs to be precisely controlled and fabricated [13–15]. Hence, a direct coupling between LSPs and SPPs should be the most efficient way to construct Fano interference for the frequency modulation, the local enhancement and the lineshape engineering [16–18].

In this work, we propose a new plasmonic structure consisting of a gold nanobar array and a thick gold film, separated by a silica dielectric layer. We have found that, upon the light irradiation, apart from the excitation of LSPs in the nanobars, the SPPs can also be excited simultaneously at the interface between the gold film and the silica layer, where the nanobar array acts as a grating coupler. The spectral behaviors as well as the coupling of LSPs and SPPs are investigated systematically by deliberately changing the nanobar length, the array periodicity and the dielectric spacing. It is demonstrated that the Fano-like asymmetric lineshape can indeed be achieved by controlling the interaction between LSPs and SPPs. Furthermore, the sensitivity and FoM of the designed sensor can reach as high as 936 nm/RIU and 112 respectively, much better than what have been reported [4]. Our design strategy offers a promising simple and efficient way to obtain the desired modes coupling and lineshapes. The proposed structure is ready to be used as a high-performance environment sensor.

Results and discussions

The structure under study is schematically depicted in Fig. 1(a). It consists of an infinite rectangle array of gold nanobars placed on a silica spacer layer (the thickness is t), and a 200 nm-thick gold film sat on semi-infinite silicon substrate, acting as a mirror underneath to prevent light transmission. The periods of the array along x and y axes are P_x and P_y, and the length and width of the nanobar are L_x and L_y, respectively. In this work, L_y and P_y are fixed at 100 nm and 600 nm, and the height (h) of the nanobar is 50 nm. Finite-difference time-domain (FDTD) algorithm (Lumerical Solutions Inc., Canada) is adopted for rigorous 3D electromagnetic calculations. The plane wave is normally incident from the top and polarized along x-axis, as indicated in the Fig. 1(a). Periodic boundary conditions are used in x and y axes, and perfectly matched layers (PML) are applied along the direction of the illumination source. In the simulation, auto-uniform conformal mesh technology is used for full considering the metal/dielectric interface, and the grid size is set to 2.5 nm for the metal region. The numerical calculations are performed with extremely well convergence conditions with different mesh sizes. The optical response of gold, silicon and silica were modeled through the fitting of Palik’s experimental data by multi-coefficient models [19].

 

Fig. 1 (a) Schematics of the proposed plasmonic structure. P_x (P_y) represents the period distance along x(y) direction. L_x and L_y are the length and width of the nanobar, respectively. t is the thickness of the silica spacer layer. (b) Reflection spectra of the designed structure with different nanobar lengths while P_x = 1000 nm, P_y = 600 nm, L_y = 100 nm, h = 50 nm and t = 50 nm. The spectra have been vertically offset by unit for clarity.

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Figure 1(b) shows the representative optical responses of this system when P_x = 1000 nm. As can be seen, there are two distinct reflection dips in each curve. The lower-energy reflection dip, referred as Mode I, reaches nearly to zero with a broad linewidth. Its position is strongly associated with the nanobar length, as indicated by the noticeable blueshift from 1846 nm to 1133 nm when the nanobar length decreases from 400 nm to 200 nm. This mode has been attributed to the excitations of electric resonance and magnetic resonance simultaneously, which are related to the LSPs in the nanobar as well as the circulating current formed between the nanobar and the gold mirror [20–22]. However, another dip, denoted as Mode II here, has attracted little attention so far to our knowledge. It has a rather narrow linewidth with a position nearly independent of the nanobar length. One can thus relate it to the SPPs at the metal/dielectric interface, which can be excited by the light coupled from the periodic nanobar array.

To identify the origins of the above modes, we have calculated their corresponding near-field distributions. Typical results for L_x = 360 nm are shown in Figs. 2-3. From Fig. 2(a), it can be seen that the electric field distribution of Mode I at λ = 1698 nm exhibits a characteristic of electric dipole resonance. The opposite charges accumulated at the opposite ends of the nanobar create the intrinsic property of LSPs excitation. Moreover, the magnetic field is also found to be significantly enhanced and confined between the gold nanobar and the mirror, as illustrated in Fig. 2(b), demonstrating a strong magnetic response simultaneously in this plasmonic system.

 

Fig. 2 The near-field distribution for Mode I resonance at λ = 1698 nm for L_x = 360 nm, P_x = 1000 nm, P_y = 600 nm, L_y = 100 nm, h = 50 nm and t = 50 nm. (a) Electric field |(E)|, (b) magnetic field |(H)|, (c) displacement current (J) (the colormap represents the amplitude and the arrow denotes the current direction), and (d) power loss per volume (in log10 scale) distribution.

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Fig. 3 The near-field distribution for Mode II resonance at λ = 1044 nm for L_x = 360 nm, P_x = 1000 nm, P_y = 600 nm, L_y = 100 nm, h = 50 nm and t = 50 nm. (a) Electric field |(E)|, (b) magnetic field |(H)|, (c) displacement current (J) (the colormap represents the amplitude and the arrow denotes the current direction), and (d) power loss per volume (in log10 scale) distribution.

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Figure 2(c) shows that the circulating current, related to the excitation of the magnetic resonance, can be produced in this layered plasmonic system, in which the anti-parallel displacement current vector is distributed in the nanobar and the mirror. Note that the metallic film mirror is essential for the excitation of the magnetic resonance, because it supplies not only the image charges for the collective conduction electrons in the nanobar but also the closed circuit for the displacement current. It has been found that, when the mirror is removed, the reflection spectrum will exhibit a characteristic localized plasmon resonance peak rather than the dip observed in Fig. 1(b) [23]. We also calculated the power loss per unit volume with $P_{loss}(\omega )=\frac{1}{2}\omega |E(\omega ){|}^2\mathrm{Im}(\epsilon (\omega ))$, for this system on the resonance condition [24]. As shown in Fig. 2(d), most of the energy dissipation occurs in the lower part of the nanobar and the top region of the mirror. This implies that the optical energy trapped inside the layered structure (Figs. 2(a) and 2(b)) is dissipated completely by Ohm losses in the metallic structures, and thus leading to the nearly zero reflection.

Figures 3(a) and 3(b) give the electric and magnetic field distributions for Mode II, respectively. It is found that the fields are confined at the interfaces, especially for the magnetic component. The interface-bounded magnetic field is enhanced significantly at the interfaces of gold/air and gold/silica, demonstrating the clear characteristic of SPPs. It has been pointed out that the SPPs at the interface of gold film and silica is excited through the grating of the periodic nanobar array and, due to its large decay length (estimated to be ~500 nm for λ = 1044 nm according to$L_z=\frac{1}{\left|k_z\right|}=\frac{1}{\sqrt{|\beta {|}^2-{\epsilon }_d{(\frac{\omega }{c})}^2}}$), it can tunnel through the silica layer and couple with the surface plasmons in the nanobars. Therefore, we expect that the characteristic of the SPPs can also be tuned by the nanobars. This is consistent with the result shown in Fig. 1(b), in which the dip position is slightly blue-shifted as the dip of the LSPs gets closer in energy. The displacement current of Mode II is shown in Fig. 3(c). In contrast to the results of Mode I in Fig. 2(c), it distributes dominantly on the top region of the mirror and its direction changes alternately along the x-axis, resulting in available nodes to facilitate the charge accumulation. Figure 3(d) displays that most of the energy dissipation at the resonance frequency of Mode II occurs near the interfaces of gold/silica and gold/air. This is also another basic feature of the interface-bounded SPPs. It can thus be concluded that the Mode II is dominantly correlated to the SPPs bounded mode and we can achieve huge absorption in the specially designed plasmonic structure by tuning the coupling conditions.

In order to further understand the characteristics of these modes, we have also systematically investigated the effects of nanobar length and array period on the optical response of this plasmonic structure, while the thickness of the silica, t, is kept at 50 nm. The spectral response was found to be easily tunable by changing either the nanobar length or the array periodicity. As shown in Fig. 4(a), when P_x is fixed at 1000 nm and the nanobar length L_x decreases, the resonance frequency of the LSPs obviously moves to the higher energy. This feature can be attributed to the increased restoring forces of electrons in the nanobar. In sharp contrast, the resonance frequency of the SPP (1, 0) order is always near 1044 nm, showing very weak dependence on the nanobar length. Moreover, we note that, as the nanobar length keeps decreasing, the interval between the energy dip positions of the LSPs and SPPs also decreases, and a strong spectral overlap of them emerges when L_x approaches 200 nm. Meanwhile, the linewidth of the LSPs becomes narrower with decrease of L_x, which is resulted from the stronger modes coupling of these two modes. With further decreased L_x, a noticeable anticrossing of the LSPs and SPPs appears, as denoted by the circle in Fig. 4(a). The inset shows the corresponding enlarged reflection spectrum for the structure with L_x = 180 nm. As seen, due to the coherent interference of the LSPs and SPPs, a Fano-like resonance with an asymmetric lineshape can be clearly observed.

 

Fig. 4 (a) Calculated reflection contour map for the plasmonic structures of different L_x with P_x = 1000 nm and t = 50 nm. The inset shows the enlarged reflection spectrum for L_x = 180 nm. (b) Reflection contour map for different array periods (P_x) for the structures with L_x = 360 nm and t = 50 nm, the SPPs order is denoted as the index. The inset shows the enlarged reflection spectrum for P_x = 1600 nm.

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Similarly, both the LSPs and SPPs modes can be tuned by the array period. As shown in Fig. 4(b), when L_x is kept at 360 nm, the resonance dip position of the LSPs is nearly independent of P_x and always locates around 1698 nm. However, because the larger period nanobar array can excite lower-energy SPPs by supplying smaller momentum, the reflection dip position of the SPPs is apparently red-shifted with increasing P_x. Eventually, the overlap and even anticrossing between the LSPs and SPPs takes place, similar to the results given in Fig. 4(a). Again, the asymmetric lineshape of Fano-like interference can be produced by increasing P_x (the circle in Fig. 4(b) and inset figure). Therefore, we can conclude that the special modes with interesting lineshapes and resonance positions can be readily constructed by tailoring the coupling between LSPs and SPPs in our proposed plasmonic structure.

We have also examined the effect of the silica layer thickness, t, on the coupling between the SPPs and LSPs. Figure 5(a) illustrates the dispersion relationship of (1, 0) SPP mode for the structure with P_x = 1000 nm and L_x = 360 nm. It is obvious that, as the thickness of the layer increases, the dispersion curve of the SPPs gets much closer to the light line of silica, which is a tendency similar to that of metal-insulator-metal waveguide [25, 26]. Figure 5(b) gives the spectra of the SPPs and LSPs with the variation of the silica layer thickness. It can be seen that, when the silica thickness increases, the resonance dip of the SPPs shows blueshift, which can be well understood from its dispersion behavior shown in Fig. 5(a). On the contrary, as the spacer layer becomes thinner, the resonance position of the LSPs starts to blue-shift as the result of the increased effective restoring forces induced by the conduction electrons in nanobar and their image charges in the mirror [16]. Moreover, we have found that, when the spacer layer is removed, the resonance dip of the LSPs mode disappears. This is because the image charge for the magnetic resonance cannot be excited under this condition. All above results indicate that the spacer layer is essential for obtaining effective modes excitation and managing their coupling efficiency.

 

Fig. 5 (a) The dispersion relationship of the SPPs for the structures with L_x = 360 nm and different silica thicknesses t, as extracted from the period-dependent reflection dips of the SPPs. The dashed lines denotes the light in air (black) and silica (red), and the solid lines denote the SPPs at semi-infinite gold/air (black) and gold/silica (red) interfaces, respectively. The inset gives the schematics. (b) Reflection contour map for the structures of various spacer layer thicknesses with P_x = 1000 nm and L_x = 360 nm.

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It is well known that both SPPs and LSPs can be used for sensing the refractive index (n) variation of the environment by monitoring their spectral changes. The sensitivity (S) of the plasmonic sensors is determined by$S=\frac{\delta {\lambda }_{\mathrm{Re}s}}{\delta n}$, where ${\lambda }_{\mathrm{Re}s}$is the resonance wavelength, and n is the refractive index of the surrounding medium [3]. In this context, we have calculated the optical responses of our two plasmonic structures with L_x = 360 and 240 nm respectively when n changes from 1.0 to 1.4. As shown in Fig. 6, both the reflection dip positions of the LSPs and SPPs exhibit good linear relationships with the refractive index. As compared to the LSPs, the SPPs possess not only narrower linewidth but also high sensitivity. For the L_x = 360 nm structure shown in Fig. 6(a), the sensitivity is estimated to be 936.1 RIU/nm for SPPs and 504.9 RIU/nm for LSPs, respectively, and it becomes 937.4 RIU/nm for SPPs and 563.46 RIU/nm for LSPs when L_x = 240 nm (Fig. 6(b)). As for the practical applications, the figure of merit (FoM) of a sensor is another important parameter to evaluate its performance, which is defined as the resonance shift upon a change in the refractive index of the dielectric surrounding normalized by the resonance linewidth [6]. In this regard, the FoM of our plasmonic structure with L_x = 360 nm can reach as high as 112.2 (936.1 RIU/nm/8.34nm) for SPPs and 3.5 (504.9 RIU/nm/145.7nm) for LSPs, respectively. And due to the stronger modes coupling for L_x = 240 nm, the linewidth of the LSPs is narrower, and the FoM of the LSPs is improved to 10.42 with the FWHM = 48.5 nm for n = 1.4. Note that, although we have not optimized our plasmonic structure for sensing application, the high sensitivity and FoM achieved now is among the highest level of the recently reported plasmonic sensors [4].

 

Fig. 6 (a) Reflection contour map for a structure with P_x = 1000 nm, t = 50 nm and L_x = 360 nm plotted as a function of environmental refractive index. (b) Reflection contour map for a structure with P_x = 1000 nm, t = 50 nm and L_x = 240 nm plotted as a function of environmental refractive index.

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Finally, it should be pointed out that, although the SPPs mode can also be excited when the gold nanobar array are replaced by the dielectric one, the SPPs reflection dip is rather shallow (the reflection dip intensity is about 0.97) compared to the results presented above. Consequently, the signal-to-noise ratio of such a SPPs sensor degrades severely, which is not appropriate for the practical applications. Additionally, the resonance in lower frequency is no longer observable due to the absence of image charges, as it is known to be the prerequisite to form the magnetic resonance.

Conclusion

In summary, we have demonstrated how to manipulate the plasmonic lineshape and modes coupling in a simple layered metal-dielectric-metal system through the direct interaction of the localized and propagating modes. We show that the LSPs are closely dependent on the nanobar length and the SPPs are more sensitive to the array periodicity. Besides, the thickness of the silica spacer layer has a great effect on both spectral and spatial overlaps of the two modes. Active control of these factors can efficiently tailor the spectral features and modes coupling of the system, especially getting into the Fano-like regime. As an example, the sensitivity and FoM of our plasmonic system can be as high as 936 nm/RIU and 112 respectively for L_x = 360 nm and P_x = 1000 nm. The design strategy allows to simply but efficiently controlling the modes coupling and spectral feature of a plasmonic system that is easy to fabricate and widely applicable in controllable optical response engineering, novel plasmonic sensors and double-resonance SERS [27].