1. Introduction

Recently, plasmonic structures have been investigated extensively, due to their novel functions and unordinary properties [1–11]. It can be used in various fields, such as photonic modulators [12], optical filters [13], bio-sensors [14], and absorbers [15]. Most of these applications greatly benefit from the unique properties of nano structured metals supporting plasmonic resonance modes [2,4,7], which can be controlled by the size [6], shape [2], plasmonic materials [17], and surrounding dielectric media [16–19]. Based on plasmonic structures, perfect absorbers [18,20] have been realized in the infrared regime, and other electromagnetic regimes. These absorbers can be categorized into narrowband and broadband types. Broadband absorbers are widely used in thermo harvesting and solar power harvesting [21], as well as thermo emission [22]. While narrowband absorbers are generally applied for sensing [2, 12, 18, 23], detection, and thermal radiation tailoring [7,20,22].

Combining the perfect absorber structure and the plasmonics resonance, which is dependent on the surrounding dielectric, Liu et al. realized a refractive index sensor [18]. For plasmonic sensing applications, surrounding dielectric refers to the test sample, of which refractive index is to be measured on top of the metallic periodic surface, and the sample is usually liquid or gas [14, 18, 19, 24]. Sensing sample solutions containing the lossy nanoparticles, which is referred to colloidial, have potential in biological and medical applications, electronic conductors and catalysis, of which optical and electronic properties are tunable by changing the size, shape, surface chemistry, or aggregation state [25]. As a refractive index sensor, both narrow linewidth and large modulation depth are necessary to enhance its sensitivity [2,4,16–19]. Due to metals in optical regime have inherent losses, their resonance bandwidths are relatively broad (≥ 40 nm), and it is rather challenging to design ultranarrow plasmonic absorbers in the optical regime. Several methods have been proposed to narrow the linewidth with deep modulation depth [2,7,16,19]. In the previous investigations, researchers mainly studied the gap plasmonic resonance [26] or magnetic dipole resonance and its sensing applications [16–19]. Surface lattice resonance (SLR) with sharp spectrum features have been reported in recent years [27]. The SLR mode of all-metal structures has narrow band linewidth [23,28]. The metal-dielectric-metal structure has been well studied for absorption based on gap resonance (GR) and related sensing applications [17–19], however, there is little attention paid to the perfect absorption property and sensing applications of its SLR mode.

Here, we investigate numerically perfect narrowband (narrower than 10 nm) absorption properties of the metal–dielectric–metal structure, of which absorption dip is owing to the lattice resonance. This feature is different from those in most literatures [16–19]. As a refractive index sensor, the bulk figure of merit [19] can be one order larger than that based on plasmonic gap resonance, while the surface figure of merit [32] can be two times larger. This narrow bandwidth and perfect absorption properties have potential in sensing applications [18,24].

2. Results and discussion

2.1. MRAM structure

Figure 1 shows the investigated metal-dielectric-metal structure which consists of a top periodic metal nanoring array, a middle dielectric layer, and a bottom metal plate. This metal nanoring array backed by metal structure is abbreviated as MRAM. The whole structure locates on top of a glass substrate. The middle dielectric layer has low refractive index value, such as MgF₂ [29], and SiO₂ [30]. The liquid or gas sample is distributed on top of the periodic surface, which is denoted by the transparent light blue color and marked out by the red dashed line box, while the device is operated as a refractive index sensor. Parameters of MRAM structure include nanoring outer diameter D, inner diameter d, thickness t, period in the x direction p_x, period in the y direction p_y, middle dielectric layer thickness h, and metal plate thickness L. The incoming light is transverse magnetic polarization with electric vector along the x axis, and incidents normally to the top metallic periodic surface.

 

Fig. 1 Schematic of the MRAM structure. “DL” denotes Dielectric Layer. As a refractive index sensor, the measured sample is distributed on top of the periodic surface, which is denoted by the transparent light blue color in the red dashed line box.

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2.2. Results and performance

In calculations, we use finite difference time domain methods. We divided the calculated domain into several parts, and utilized the un-uniform mesh of which maximum and minimum meshes are respectively 10 nm and 0.5 nm in the domain including nanoring array, middle dielectric layer, and metal substrate. Here, the metal nanoring array has square lattice, i.e. p_x and p_y are both equal to p. We set periodic boundary conditions in the x and y directions, and perfect matched layers in the z direction. Metal is set as Gold, of which the dielectric constant is from Reference [31]. The reflectivity (R) spctrum of the MRAM is shown in Fig. 2(a). In the reflectivity curve, there are two significant dips with extremely small values, which are labeled as A and B, represent two distinct types of resonance. These two narrow dips result from the surface lattice resonance and gap plasmonic resonance, respectively. The shallow dip with large reflectivity between A and B is due to the nonlinear fit of the refractive index of Gold. For the metal plate thickness is larger than the skin depth in the optical regime, the absorption A = 1−R (here, T ≈ 0.). Therefore, the absorption at resonance A and resonance B are 98.06% and 99.66%, respectively.

 

Fig. 2 (a) Reflective, transmission, and absorption spectra of the MRAM structure. LR and GR represent surface lattice plasmonic resonance and gap plasmonic resonance, respectively. (b)–(i) Electric field and magnetic field distributions at resonances A and B. Parameters: p = 0.9 μm, D = 0.366 μm, d = 0.2 μm, t = 57 nm, h = 35 nm, and L = 0.1 μm. In calculations, maximum mesh sizes in the x, y, and z directions are all set as 0.01 μm.

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For comparing the difference between the two resonances, we calculate the electromagnetic field distributions of the both modes. Results are shown in Figs. 2(b)–(i). At the wavelength 0.9315 μm, the electromagnetic field distribution features the lattice resonance [28]. It is shown in Figs. 2(b) and 2(c) that the electric field distributions mainly concentrate on the top surface and external edges of the metal nanorings in the x direction. Figures 2(d) and 2(e) present that the maximum magnitude of the magnetic field is between the ring arrays in the x direction and along the line of rings in the y direction. Whereas, at the wavelength 1.7607 μm, the electric field concentrate in the cavity between the nanoring array and the ground plane, as shown in Figs. 2(f) and 2(g). Magnetic field distribution profiles a gap plasmonic resonance [26] or magnetic dipole resonance [17, 18], which features an enhanced magnetic field in the microcavity between the nanoring stripe and the metal substrate, as shown in Figs. 2(h) and 2(i). Its nearly perfect absorption well utilizes the Ohmic loss in the metal. The resonance can be tuned by the geometric parameters of the structure [5,16,25].

2.3. Sensing properties

For that the lattice resonance of the MRAM structure has narrower bandwidth of reflective spectrum than the magnetic dipole resonance, a slight spectral shift can give rise to large intensity variation. In sensing applications, we usually define the sensing capabilities as follows [17–19]:

Figure 3(a) shows that the resonant wavelength redshift linearly with increasing the refractive index of the surrounding dielectric. At the resonant wavelength, the absorption is maximum, and FOM ≈ 25, which is larger than the value based on the gap resonance mode [17–19]. Also, the perfect absorption of the MRAM structure can lead to a large value of FOM^* as high as 120. Therefore, the sensitivity capability of the MRAM structure based on the lattice resonance plasmon is better than that based on the gap plasmon resonance of the same structure.

 

Fig. 3 (a) Resonance wavelength as a function of the sample refractive index on top of the MRAM structure. (b) Reflective spectrum (n = 1.312) and FOM^* curve. Parameters: p = 900 nm, t = 57 nm, d = 200 nm, D = 366 nm, h = 35 nm, and L = 100 nm.

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Inspired by References [32–34], we have investigated the surface sensitivity while the protein sample is adsorbed only on the gold nanorings surface of the MRAM structure, as shown in the inset of Fig. 4(a). The protein layer thickness is set as 8 nm, while its refractive index is set as 1.45 [35]. Figure 4(a) shows the reflective spectra of the MRAM structure with bare nanorings and with nanorings adsorbed by thin protein layer, respectively. After the MRAM structure with nanorings adsorbed by the 8–nm–thickness protein layer, the wavelength shift for SLR mode is 4.1 nm, which is weaker than the shift value of 37 nm for the GR mode. However, based on Eq. (1), the surface FOM for SLR mode is two times larger than that for GR mode at this protein layer thickness, i.e. 0.42: 0.20 at the 8-nm-thickess protein layer. This can be explained by the electric field concentrated on the top surface of the nanorings for LSR, as shown in Fig. 2(b), whereas the field is concentrated in the middle dielectric layer for GR, as shown in Fig. 2(g). Figure 4(b) shows that the surface sensitivity [34] is nearly linear increasing while the protein layer thickness is increased from 8 nm to 108 nm, while the absorption is deteriorated. The bulk FOM [19] can be one order larger than that based on plasmonic gap resonance, while the surface counterpart [32] can be two times larger at the adsorbed protein thickness of 8 nm. More importantly, the electric field of the lattice resonance mode is concentrated on the nanoring surface thus easily accessible for the measuring target biomelecules.

 

Fig. 4 (a) Reflective spectra for SLR. Inset shows the cross section of the MRAM when the protein sample is adsorbed only on the gold nanorings surface. BNR and PL refer two different cases, which are the abbreviations of MRAM with bare nanorings and MRAM with nanorings with the adsorbed thin protein layer, respectively. The sample layer thickness is set as 8 nm. (b) Surface sensitivity and reflectivity dip for SLR mode as a function of the thickness of adsorbed protein layer. Parameters: p = 900 nm, t = 57 nm, d = 200 nm, D = 366 nm, h = 35 nm, and L = 100 nm.

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Conclusion

In conclusion, we have investigated numerically the lattice-resonance-based narrow band absorption properties of the metal-dielectric-metal structure. The unit cell of the periodic structure is metal nanoring. Based on the lattice plasmon resonance, the structure offers a bulk sensing performance is an order of magnitude larger than that based on gap plasmon resonances. These lattice resonances can be tuned over a wide spectral range by tuning the array period, the nanoring thickness, and the thickness of centre dielectric layer. The surface figure of merit can be two times larger than that based on the plasmonic gap resonance mode. The narrowband and perfect absorber properties have potential applications in sensing and filtering applications in the near infrared region.