1. Introduction

Localized surface plasmon resonances (LSPRs) in metal nanoparticles arise from the collective oscillation of conduction electrons. The enhanced electric fields on the nanoparticle surface associated with LSPRs are very attractive for many applications [1,2], including infrared absorption [3,4], Raman spectroscopies [5,6], photovoltaics [7], and nonlinear photonics [8]. For some applications, besides enhanced electric fields, narrower resonant linewidth is also desirable. For instance, in biosensor applications based on RI change, the detection limit depends on not only the LSPRs sensitivity to the local dielectric medium, but also the resonant linewidth [9,10]. Narrower linewidth allows smaller shifts to be detected [11,12].

However, due to their strong radiative damping, the LSPRs usually have a broad linewidth [13], which significantly limits the performance of the LSPRs-based sensors. An effective way to suppress the radiative loss of LSPRs is by Fanolike resonances, namely coupling LSPRs to other resonant modes with a narrow linewidth. For example, by coupling the broad LSPRs to subradiative plasmonic modes, a RI sensitivity exceeding 1000 nm/RIU with a FOM reaching 5 in the near-infrared region was achieved [14]. The double Fano resonance effect has been proposed in the split ring resonators/Rod structure with very high RI sensing sensitivity and FOM, due to the strong interplay between the broad bright mode and the narrow dark modes [15]. Very recently, some novel plasmonic perfect absorbers consisting of nanoparticle/hole arrays on dielectric slab and mirror have also been proposed as high-quality LSPRs sensors [16,17]. Similarly, Shen et al. coupled the broad LSPRs to narrow lattice surface modes to realize narrower optical resonances with enhanced biosensing properties [18]. Such diffraction coupling effect of LSPRs is also used by our group to design high-performance LSPRs sensors [19,20]. And Lodewijks et al. showed that the Fano resonance between localized and propagating surface plasmon resonances can be exploited to dramatically increase the RI sensitivity [21]. Furthermore, improved sensor performance was also obtained through the combination of LSPRs with an optical microcavity [22].

In this letter, we for the first time propose a simple structure composed of a 2D gold nanoparticle array lying on a dielectric slab waveguide for high-performance RI sensing. Arising from the interference between the waveguide mode in the dielectric slab and the LSPRs of the metal nanoparticles, a sharp Fanolike resonance is created, which exhibits a RI sensitivity of 250 nm/RIU and FOM of 28, much higher than the reported values [23]. Moreover, it is found that for the interference to appear, the electric field of waveguide mode should be parallel to the polarization direction of the LSPRs. We hope that the proposed structure could offer great potential in realistic biosensing applications.

2. Results and discussions

The designed RI sensor is schematically shown in Fig. 1(a), which is composed of a 2D gold nanoparticle array lying on a dielectric waveguide layer (ITO, n_f = 1.949) supported on a substrate (silica, n_s = 1.459), where t = 140 nm denotes the thickness of the waveguide layer. The ellipsoidal gold nanoparticles have a long (short) axis of 140 nm (40 nm), and its height is 30 nm. The periodic arrangement of the Au nanoparticles can provide the necessary momentum for the incident light to excite the waveguide mode. The 2D nanoparticle array can be easily fabricated by the standard electron beam lithography [24,25], and the dielectric waveguide layer can also be easily prepared by the standard deposition method [26]. Figure 1(b) schematically shows the same nanoparticle arrays but directly lying on the silica substrate, to obtain the influence of the dielectric waveguide layer on the LSPRs in the gold nanoparticles.

 

Fig. 1 Schematic of a plasmonic structure for high-performance RI sensing. Gold nanoparticle array is placed on a dielectric waveguide layer (a) and directly placed on the substrate (b). P_x and P_y are the periods in the x and y directions, respectively. The polarization of the incident light is along the long axis of the ellipsoidal nanoparticle.

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Figure 2(a) shows the normal-incidence transmission spectra of the same Au nanoparticle arrays with P_x = 200 nm and P_y = 700 nm, which lie on the ITO layer (the solid red line) and the silica substrate (the black dotted line). The transmission spectra are calculated by the commercial software package COMSOL Multiphysics. In our numerical calculations, gold has a frequency-dependent permittivity described by the Drude model: ε_gold = 1 – ω_p²/[ω(ω + iω_c)], where the plasma frequency ω_p = 1.367 × 10¹⁶ rad/s and the collision frequency ω_c = 4.084 × 10¹³ rad/s [27]. For the Au nanoparticle arrays lying on the ITO layer, one can see two transmission dips indicated by the arrows, which are located at 856 nm and 1090 nm, respectively. The broad transmission dip (labeled as dip 1) corresponds to the extinction of LSPRs in individual nanoparticles, and the sharp Fanolike dip (labeled as dip 2) arises from the strong interference between broad LSPRs and a narrow waveguide mode [28]. For the Au nanoparticle arrays directly lying on the silica substrate, one can only see a broad tansmission dip of LSPRs, which is blue-shifted to 772 nm because of the relatively smaller permittivity of the silica substrate. But, the sharp Fanolike dip will disappear, due to the absence of the waveguide mode. Thus, we can conclude that the sharp Fanolike dip indeed arises from the strong interference between the LSPRs and the narrow waveguide mode instead of the coupling between the LSPRs and a lattice surface mode, which is due to the fact that for light propagating above and below the substrate, this refraction index mismatch results in different phase velocities and conditions for constructive interference [29,30].

 

Fig. 2 Normal-incidence transmission spectra of two structures schematically shown in Fig. 1, with P_x = 200 nm and P_y = 700 nm. (b) and (c) Normalized electric field intensity (E/E_in)² on the xoy plane across the center of the gold nanoparticles at the dip 1 and dip 2 resonances indicated in Fig. 2(a).

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Figures 2(b) and 2(c) plot the normalized electric field intensity distributions on the xoy plane across the center of the gold nanoparticles for the resonances at dip 1 and dip 2, respectively. At the dip 1 resonance, the electric fields have two obvious “hotspots” on the left and right ends of the gold nanoparticles, which are the typical characteristics of a dipole plasmon resonance. At the dip 2 resonance, although the field pattern is almost the same as at the dip 1 resonance, the maximum electric field is enhanced to be about 4351 times of the incident field, which is nearly 12 times stronger than the corresponding value at the dip 1 resonance.

To understand the physical mechanism of the sharp Fanolike resonance, in Fig. 3 we plot the x, y, and z components of the electric and magnetic fields at the dip 2 resonance. Clearly, the electric field of the waveguide mode is in the x direction, and its magnetic field is in the z direction. The electric field of the waveguide mode has the same direction as the polarization of the LSPRs. As a result, the waveguide mode can strongly interference with the LSPRs in individual Au nanparticles, when it propagates in the ITO layer. The interference is able to suppress radiative damping of LSPRs and thus forms the sharp Fanolike resonance at the dip 2, since the waveguide mode is confined within the ITO layer [28].

 

Fig. 3 (a)-(c) Normalized electric field components (E_x/E_in)², (E_y/E_in)² and (E_z/E_in)² on the xoy plane across the center of the gold nanoparticles at the dip 2 resonance. (d)-(f) The same as (a)-(c), but for normalized magnetic field components (H_x/H_in)², (H_y/H_in)² and (H_z/H_in)².

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Here, we note that in our proposal, the metal nanoparticles are exposed in air rather than buried within substrate, which is very helpful for applications in biosensing at the sharp Fanolike resonance associated with a huge enhancement of electric fields. To demonstrate this, Fig. 4(a) presents a set of transmission spectra for the refractive index (n) of the environment medium to be varied from 1.00 to 1.08. Both dip 1 and dip 2 have obvious red shift when n is increased. Figure 4(b) gives the spectral positions of two transmission dips for different n. We obtain the RI sensitivities of 250 and 200 nm/RIU for the sharp Fanolike resonance and LSPRs, respectively. In the practical applications, the FOM value is usually employed to evaluate the performance of a RI sensor, which is defined as the RI sensitivity normalized by the resonant full-width at half-maximum (FWHM) [31]. The FOM values of our designed sensor can reach as high as 28 for the sharp Fanolike resonance and 2 for the LSPRs, respectively. The FOM of the sharp Fanolike resonance is enhanced to be 14 times higher than that of the LSPRs, owing to the larger electric field enhancement and the narrower linewidth. Lastly, we note that although we have not optimized our designed plasmonic structure for biosensing, the predicted FOM value is also much larger than those of other types of Fanolike resonance caused by the interference of two LSPRs observed usually in individual or assembled nanostructures, where the FOM value is generally lower than 9 [32–34].

 

Fig. 4 (a) Transmission spectra of the designed RI sensor under different dielectric environment. (b) The dependence of the resonance wavelengths of dip 1 (black) and dip 2 (red) on the refractive index of the environment medium.

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3. Conclusion

In summary, we theoretically propose an alternative approach for high-performance RI sensing, by coupling LSPRs to waveguide modes. Arising from the strong interference between the waveguide mode propagating in a dielectric slab and the LSPRs of metal nanoparticles, a sharp Fanolike resonance is created and exhibits a RI sensitivity of 250 nm/RIU and a FOM value of 28, much larger than that of other type of Fanolike resonance that is caused only by the interference of two LSPRs, which is usually observed in individual or assembled nanostructures. Furthermore, the interference condition is also found, that is, the electric field of the waveguide mode must be parallel to the polarization direction of the LSPRs. Our designed RI sensor may find broad applications in biomedical sensing.