1. Introduction

Plasmonic metamaterials absorbers [1] (PMAs) have been rapidly developed in recent years due to their superior and controllable absorption properties in the visible and near-infrared realm that are intensively used in the area of energy harvesting [2], plasmonic sensor [3, 4] and nonlinear optics [5]. Although the underlying mechanism of the PMAs is overwhelmingly considered as the manipulations on the effective permittivity and permeability through the structuring [6], the gap plasmon mode [7, 8] and the destructive interference plasmonic mode [9–11] can also be used to explain the near unity absorption ability of PMAs. These plasmonic modes are the resonance interactions between the free electron and the electromagnetic fields [12–14], which gives rise to the application of the plasmonic sensors.

For detecting the concentration of molecule, the plasmonic sensors based on PMAs should be very sensitive to the refractive index of the surrounding medium [3]. Figure of merit in generalized form (FOM*) and figure of merit (FOM) introduced by J. Becker [15] are respectively denoted as FOM* = [dI(λ)/dn(λ)/I(λ)]_max and FOM = [dλ/dn(λ)/FWHM]_max, where I(λ) is the relative intensity of the measuring signal, dn is the refractive index change and FWHM is the full width of the half maximum of the absorption. Thus, a very narrow and perfect absorption band is always required for enhancing the performance of the plasmonic sensors. In fact, to enhance the sensitivity of the refractive index of the surrounding medium, the PMA with multiple and narrow absorption peaks should also be an alternative for the plasmonic sensors. The different plasmonic modes of the narrow multiband PMAs can improve the sensitivity and accuracy of the plasmonic sensors. However, multiband PMAs focused on the THz region [16–18] and infrared region [19] have been investigated and found to be easily realized due to its large scale size compared to that in the visible region. In the visible and near infrared region, most multiband absorbers are aimed at the broad absorption band [20–24], and some need an incident angle to excite the multiple absorption band [25]. Recent advances on the narrow band absorber demonstrated by Qiu et al show that the Ag has a good performance for the ultra-narrow band absorptions, which has great potential for the plasmonic sensors [26, 27], although the oxidizable problem of the Ag should be overcame. Here, we introduce the Ag based metal film-dielectric-metal structure (MIM structure) by utilizing a simple single structure to achieve a triple-band PMA in the visible and near-infrared region. We show that these triple-band PMAs can yield over 99% absorption in simulation. We analyze the different plasmonic modes in each absorption band through extracting the electric and magnetic intensity distribution and varying the spacer thickness. The triple-band PMA may have a positive performance for the sensor application due to the difference sensor sensitivity response of the different plasmonic modes.

2. Numerical investigation

The numerical simulations using finite difference time domain (FDTD, available from Lumerical software package [28]) algorithm were performed by employing the structures shown in Fig. 1(a). The top layer is an array of Ag particles and the bottom layer is bulk flat Ag film that eliminates the transmission. A thin dielectric layer separates the two Ag layers. The thickness of the cylinder Ag particle is denoted as t and its diameter as d. The thickness of the dielectric layer and the Ag film are denoted by h and w, respectively. The lattice constant is assumed to be a. Al₂O₃ was used as the dielectric and its refractive index is 1.75. The permittivity of Ag is extracted from Johnson and Christy’s work [29] in 1972 and simulated by Drude mode [25]. All materials are assumed to be nonmagnetic (i.e., μ = μ₀). A normal incident plane wave along the negative z direction was applied with the polarization along with the x direction.

 

Fig. 1 (a) The construction of the PMA. The green region is the Al₂O₃ layer while the gray regions are Ag. d and t are the diameter and thickness of the Ag cylinder particle, respectively. h and w denote the thickness of the Al₂O₃ layer and the Ag film, respectively. a is the lattice constant. The parameters of the PMA are set as a = 500 nm, w = 100 nm, t = 30 nm, d = 100 nm and h = 40 nm. (b) The absorption spectrum for the PMA with three peaks denoted as Peak 1, Peak 2 and Peak 3.

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Here, we set the parameters of the PMA as follows: a = 500 nm, w = 100 nm, t = 30 nm, d = 100 nm and h = 40 nm. As depicted in Fig. 1(b), there are three peaks with the maximum absorption over 99%, denoted as Peak 1, Peak 2 and Peak 3, arranged from the high frequency to low frequency.

To better understand the underlying mechanism of the three absorption peaks, the electric and magnetic fields were extracted from the simulated peaks on the x-z plane of the PMA with the thickness of the Al₂O₃ layer 40 nm, as shown in Fig. 2. Figures 2(a) and 2(b) are the electric and magnetic intensity distribution, respectively, extracted from Peak 1. The magnetic intensity shown in Fig. 2(b) is distributed between the grating-like Ag particles, which indicates that the surface plasmon polaritons (SPP) were excited by the incident waves coupled with the Ag grating structure [26]. Figure 2(d) shows that the magnetic field is localized around the Ag nanoparticles, which indicates that Peak 2 was induced by the destructive interference enhanced Ag nanoparticles absorption [11, 24]. The magnetic field intensity distribution of Peak 3, shown in Fig. 2(f), is localized between the Ag nanoparticles and the Ag film which indicates that the gap plasmon mode or the coupling between the Ag nanoparticles and the Ag film governs the absorption [25, 30]. However, when the Al₂O₃ layer is thick enough, the interaction between the Ag nanoparticle and the Ag film is very weak [25], and the destructive interference of the Ag/Al₂O₃ bi-layer enhanced Ag nanoparticle absorption will govern Peak 3 [11].

 

Fig. 2 The electric and magnetic field intensity distribution from the three absorption peaks on the x-z plane of the PMA with 40 nm Al₂O₃ layer in thickness. (a) and (b) are the electric and magnetic intensity distribution extracted from Peak 1, respectively. (c) and (d) are the electric and magnetic intensity distribution extracted from Peak 2 respectively while (e) and (f) are extracted from Peak 3.

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To further investigate the basic physics and the tunable properties of PMA, we simulated the absorption properties by varying the spacer thickness, h, from 20 nm to 110 nm while the other parameters are kept the same. Figure 3(a) shows the peak positions of the Peaks 1, 2, 3 and Fig. 3(b) shows the full width at half maximum (FWHM) as the function of the spacer thickness. As shown in Fig. 3(a), the position of the Peaks 1 and 2 red shifted as h increased, while the Peak 3 blue shifted first and then red shifted. Note that in the PMAs the gap plasmon mode induced near-perfect absorption peaks will blue shift [11, 25], while the destructive interference induced absorption peaks will red shift as the thickness of spacer layer increased [9]. For the Peaks 1 and 2, the red shifted tendency as h parameter increased reveals that the interference affects the two absorption peaks. It has been demonstrated that as the spacer layer increased the coupling between the top metal structure and the bottom metal film becomes weaker [25], that is, the gap plasmon mode is eliminated since the gap distance becomes bigger and the interference effect from the bottom Ag/Al₂O₃ bi-layer dominates the absorption [11]. According to the transformation from the gap plasmon mode to the interference mode, Peak 3 will blue shift first and then red shift later which conforms to the magnetic intensities distribution shown in Fig. 2(f). As shown in Fig. 3(b), all the FWHMs of Peaks 1, 2 and 3 become bigger first then smaller later as the spacer thickness growns. However, the FWHMs of the three peaks are very small, especially for the spacer thickness being 110 nm, all of the FWHMs are smaller than 10 nm.

 

Fig. 3 (a), (b) The peak positions and FWHMs of Peaks 1, 2, 3 as the functions of the spacer thickness of the Al₂O₃ layer varying from 20 nm to 110 nm.

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Here, to achieve the sensor properties of the PMAs, we extracted the FOM and FOM* parameters from the reflection spectra which are extreme values corresponding to the absorption peaks [15]. Here, the refractive index of the surrounding media is set as 1, and dn as 0.05. Note that for the perfect absorption case, the intensity of the reflection is near zero which leads to an infinite value to the FOM*. Such as, in the case of 60 nm spacer layer thickness in our structure, the reflection of Peak 1 is only 0.0003 at 538 nm, which leads to an extremely big value of FOM* = 45367, as shown in Fig. 4(b). Thus, we extract the value of the Max|dI(λ)/dn| as a function of the spacer thickness to investigate the intensities change versus the surrounding dielectric changing, shown in Fig. 4(a). The black square, red circle and blue triangle dash lines are represent for Peaks 1, 2 and 3, respectively. The value of Max|dI(λ)/dn| of Peak 1 increases as the spacer thickness growing first and then decreases later. The one of Peak 2 has the decreasing tendency as the spacer thickness growing. For Peak 3, the value of Max|dI(λ)/dn| increases as the spacer thickness growing. Figures 4(b) and 4(c) respectively show the parameters of FOM* (log scale in the vertical axis) and FOM of the each absorption peak varying with the thickness of Al₂O₃ layer from 20 nm to 110 nm. Due to the different plasmonic modes, the three absorption peaks respond differently to the perturbation of the neighboring medium refractive index. For the FOM parameter, which is related to the position variation of the absorption peaks, Peaks 1 and 2 show the high FOM when h = 20 nm, while the FOM of the Peak 3 was much lower. For the FOM* parameter, which is related to the intensity variation of the reflection dips, Peaks 2 and 3 keep the identical tendency while Peak 1 has a maximum value when h = 60 nm. Our simulation result shows that the sensitivities in terms of wavelength shift per unit refractive index are 289 nm/RIU, 452 nm/RIU and 157 nm/RIU for Peaks 1, 2, 3, respectively when the spacer thickness is 20 nm. It is noteworthy that the same resonance position shifts with wavelength unit will lead to the different shifts with the energy unit between the infrared realm and the visible realm. The characterized wavelength in our work mainly focuses on the visible region which is compatible to the current data of the plasmonic sensor [3, 15, 26, 31, 32] when we use the energy unit, while less than some of them [26] when use the wavelength unit. However, these different responses will enhance the sensitivity and accuracy for detecting the refractive index fluctuation of the surround environment.

 

Fig. 4 (a) Max|dI(λ)/dn|, (b) FOM* (FOM* = Max|dI/dn/I|) and (c) FOM (FOM = Max|dλ/dn/FWHM|) of the Peaks 1, 2, 3 as the functions of the spacer thickness of the Al₂O₃ layer varying from 20 nm to 110 nm.

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3. Conclusion

In summary, we have theoretically and numerically studied the triple-band PMAs for the visible and near infrared light. The absorption mechanisms are demonstrated as being induced by different plasmonic modes such as the grating, interference enhanced nanoparticle absorption and the gap plasmon mode. Each FOM* and FOM for the plasmonic sensors was calculated from the three absorption peaks. The proposed triple-band PMAs showed great advantage for the plasmonic sensors applying in the visible and near-infrared realm.