Introduction

Surface plasmon polaritons (SPPs) refer to electromagnetic (EM) waves that are confined and transmitted at the boundary between a metal and a dielectric material [1,2,3,4,5]. SPPs can be controlled using waveguides and resonators and have the potential to be useful in a variety of nanophotonic applications such as optical sensing, optical communication, photonic energy harvesting, and the development of integrated optical circuits (IOCs), due to their ability to concentrate and direct EM energy at the nanoscale [6,7,8]. In recent years, metamaterials have gained significant attention for their unique optical properties and have been successfully incorporated into a variety of meta-devices for use in different areas of nanophotonics [9,10,11,12].

Plasmonic metamaterial absorbers (PMAs), which are a type of metamaterial, have shown remarkable abilities to manipulate electromagnetic waves, which typically consist of periodic sub-wavelength metallic and dielectric units [13, 14]. These PMAs are designed to efficiently harvest EM radiation through an impedance-matching mechanism [15]. Compared to traditional absorbers, PMAs offer several advantages, such as greater miniaturization, improved adaptability, and increased effectiveness [16, 17]. Furthermore, PMAs have potential for use in a diverse range of applications, such as emitters, sensors, modulators, infrared camouflage, optical communication, and more [18,19,20,21].

PMAs are designed with a specific structural design that enables them to absorb light from a particular wavelength range with high efficiency [19]. In the microwave region (wavelengths of several millimeters to a few centimeters), PMAs can be designed using periodic arrays of metallic structures, such as split-ring resonators, to achieve strong absorption [22]. In the optical wavelength range (typically in the range of hundreds of nanometers), PMAs can be designed using structures such as nanowires, nanorods, and nanodisks [23]. The mid-infrared range is highly suitable for biosensing because it includes molecular vibrations that uniquely characterize the biochemical components of living organisms [24]. In the mid-infrared wavelength range (typically between 2 and 20 µm), various strategies have been developed to design PMAs, including composite grating superabsorbers, photonic crystal superabsorbers, and broadband nanoresonator absorbers [25]. These strategies involve designing complex structures that can efficiently trap and absorb light of different wavelengths in this range. The improved sensitivity of PMAs in chemical and biological sensing applications is due to their ability to absorb light in a specific wavelength range and interact with the surrounding environment in a controlled way. This makes PMAs useful in a wide range of sensing applications, including environmental monitoring, medical diagnostics, and food quality control [26, 27].

Based on this assumption, achieving perfect dual or multiband absorption requires a compound unit cell compound or a multilayered structure, making the manufacturing process more complex [15]. Consequently, there is a need to design a relatively simple structure that exhibits dual or multiband perfect absorption while being insensitive to polarization. This feature has been less demonstrated in previous research studies and is highly desirable.

Numerous research groups have utilized various techniques to enhance the performance by manipulating the parameters of materials and geometries, as well as by hybridizing plasmonic and electromagnetic wave coupling. Porous and tubular metal nanostructure arrays have garnered significant attention in the development of biosensors [28, 29]. These structures possess an open surface morphology and provide a conducive environment for label-free biosensing on metal nanoparticle surfaces, thereby offering multiple advantages. Han et al. developed a plasmonic absorber by decorating a hexagonal array of silicon nanowires (SiNW) with Au nanoparticles, achieving a broadband absorption of more than 80% in the range of 400 to 1000 nm [30]. The wideband absorption was due to cavity modes in the SiNWs and surface plasmon polaritons on the AuNPs. Liu et al. created an ultra-narrow band perfect absorber using a periodic structure, which operated in the near-infrared region [31]. Cao et al. proposed a perfect plasmonic absorber (PMA) consisting of a metal substrate and a periodic array of silicon nanorod resonators (SNRRs) for visible light, achieving an absorbance exceeding 92.2% [32]. Cheng et al. designed a triple narrowband PMA with vertical square split ring (VSSR) resonators with polarization-insensitive vertical polarization, achieving a maximum absorptance of 99.80% [33]. Luo et al. numerically investigated a perfect narrow-band absorber based on a metal–metal-dielectric-metal structure that consists of periodic metallic nanoribbon arrays. Their absorber presents a nearly perfect absorption of more than 99.9% in the infrared region [34]. Note that single-band PMAs are not suitable in some areas, such as spectroscopic detection and phase imaging, which require distinct absorption bands [35]. Therefore, research on more advanced multiband perfect MAs is necessary, and now has become a hot area.

A PMA can induce electric and magnetic resonances simultaneously to ensure impedance matching with the surrounding medium. This leads to nonreflection at the incident interface. There are two main types of PMAs: narrowband and broadband [36, 37]. Metamaterial absorbers are a viable option to enhance the performance of photodetectors. However, achieving narrowband absorption with multiple working wavelengths, particularly in the near and mid-infrared regions, is still a challenging endeavor. This study was motivated by previous articles and focused on the important topic of light-matter interaction at the PMA interface. The aim of the study was to design a quintuple narrowband plasmonic perfect absorber with a periodic structure that could function as an ultrasensitive RI sensor in the visible, near-infrared, and mid-infrared regions. The absorber was created using a dielectric layer sandwiched between a metallic nanobar array and a thin Ag film, supported by an assembly of six alternative Si-Ag films. The absorbance was over 90% at five different resonance frequencies under normal incidence. The perfect absorption was analyzed through electric- and magnetic-field distributions using COMSOL Multiphysics, and the working band and range of the absorptance peaks could be actively tuned by changing material parameters. The absorptance peak also showed high sensitivity to the variation of RI in the ambient medium. The designed sensor based on the perfect plasmonic absorber had a high sensitivity of around 98.02%, 99.47%, 98.02%, 99.47%, and 96.09% for modes 1–5, respectively. Thus, the quintuple narrowband perfect absorber has the potential for use in enhanced sensing and spectroscopy applications.

Simulation Models and Fundamental

In the near-infrared or mid-infrared region, PMAs usually consist of a trilayer structure [38]. In Fig. 1(a), the 3D view of the unit cell for the five-band PMA configuration. The PMA system within the unit cell exhibits a hybridization of the surface plasmon resonance (SPR) and cavity plasmon resonance (CPR) nanostructure, which comprises a periodic array of a pair of Ag nanobars adhered to a sandwich of MgF2/Ag/MgF2 layers on a bottom Ag film. The top of the Ag layer can serve as a resonator, which can generate the SPR effect to help the impedance matching condition. The dielectric layer can form a resonance cavity and result in the CPR effect, which benefits the absorbance of the incident EM wave. The bottom Ag film acts as a mirror to prevent transmission and serves as a reflective layer to achieve maximum absorption and reduce reflection. Figure 1(b) shows the cross section of the unit cell and the geometrical parameters. The geometric parameters include the period (P), the width of the Ag nanobar (L), the gap between a pair of Ag nanobars (g), the thickness of a pair of Ag nanobars (d1), the thickness of the first layer of MgF2 film (d2), the thickness of the the the first layer of Ag film (d3), the thickness of the the the second layer of the MgF2 film (d4), and the thickness of the the bottom layer of Ag film (d5). We use COMSOL Multiphysics [39, 40], a commercially available FEM-based software, with a 2-D simulation model because the z-axis in Fig. 1 is infinite compared to the x and y-axes. The incident EM wave polarizes on the x-axis from the top plane of the proposed PMA, with normal incidence.

Fig. 1
figure 1

Unit cells and geometrical parameters of the proposed PMA structures, (a) 3D view and (b) the cross section of the 2D view and the design parameters of the structure. (c) Schematic of the equivalent LC circuit for the proposed PM structure

Full size image

To mimic an infinite array of the unit cell system, periodic boundary conditions are considered in the x-direction, while perfectly matching layers are applied along the y-direction to absorb reflection waves at boundary interfaces. Ag permittivity of Ag is obtained from references [41, 42], and the RI of the MgF2 layer is 1.37. Absorptance, which is the amount of incident radiation absorbed by the PMA, can be expressed as A(ω) = 1—R(ω)—T(ω), where R(ω) =|S11(ω)|2 and T(ω) =|S21(ω)|2 represent reflectance and transmittance, respectively. The full width at half maximum (FWHM) is defined as the bandwidth value between the left and right of the transmittance spectrum's half-maximum position. The dipping strength (ΔD) represents the variation between the maximum and minimum transmittance, calculated as ΔD = (Tmax – Tmin) × 100% [43]. Furthermore, the quality factor (QF) can be calculated as QF = λres/FWHM, where QF represents the sharpness of the resonance peak.

The proposed PMA's absorptance resonant peaks can be explained by the equivalent LC circuit model (shown in Fig. 1(c)) [15, 17, 44,45,46]. The model includes the capacitance between the nanobars in adjacent unit cells, which can be calculated as Cgap = ε0d1/(P–2L − g), where ε0 is the permittivity of the permittivity of the surrounding medium's permittivity [45]. Additionally, the capacitance Cm = c1ε2ε0(2L + g)/d2 represents the capacitance between the nanobars and the Ag film. The coefficient c1 accounts for the nonuniform charge distribution on the metal surface, and ε2 is the permittivity of the dielectric layer. This model provides a clear understanding of the PMA's absorptance behavior.

The total impedance is [31].

$${Z}_{tot}=\frac{i\omega ({L}_{m}+{L}_{e})}{1-{\omega }^{2}{C}_{gap}({L}_{m}+{L}_{e})}-\frac{2i}{\omega {C}_{m}}+i\omega ({L}_{m}+{L}_{e})$$
(1)

where the corresponding parameters are listed in Table 1.

Table 1 The corresponding parameters of the LC circuit model
Full size table

The effect of the the second layer of MgF2 film (d4) and the bottom layer of the Ag film (d5) can be ignored since Cgap is less than Cm [14, 15, 20, 31, 45]. Magnetic resonance occurs when the circuit has zero impedance. Therefore, the resonance condition of the PMA can be solved by setting Ztot equal to zero. Then, the λres is [44]

$$\lambda_{res} \approx 2\pi\; \varepsilon_{0}\; ((L_{m}+L_{e}) C_{m})^{1/2}$$
(2)

The design of the PMA configuration is suitable for fabrication using e-beam lithography, which has a resolution below 5 nm [47]. Furthermore, the grinding of the ion beam can also be used to make PMA, which is a common technique in nanotechnology [48,49,50,51]. Furthermore, spacer lithography is a promising technique for creating nanoshell arrays with uniform patterns and thicknesses of sub-10 nm [52, 53], making it compatible with the proposed design. Therefore, the designed PMA can be fabricated using existing nanofabrication techniques, which is essential for practical applications.

Inspection of the Structure Mechanism and the PMA Performance

Figure 2 illustrates a comparison between the absorptance spectra of the designed PMA in two cases: without (top panel, referred to as case 1 hereafter) and with (bottom panel, proposed PMA) a pair of Ag nanobars. FEM simulations used the structural parameters listed in Table 2.

Fig. 2
figure 2

Comparison of absorptance at resonance wavelength of the PMA without a pair of Ag nanobar (upper panel, case 1) and with a pair of Ag nanobar (bottom panel, proposed PMA), respectively. The structural parameters used for the FEM simulations are provided in Table 1

Full size image
Table 2 Initial structural parameters of the proposed PMA
Full size table

The significant difference in the absorptance peaks between the two cases can be attributed to the hybridization of SPR, gap plasmon resonance (GPR), and CPR occurring in the proposed PMA. The absorptance spectrum and ∆D reveal that the case 1 only has one absorptance peak with low absorptance (17.23%) at λres = 670 nm. On the contrary, the proposed PMA exhibits quintuple-band absorptance with absorptance ranging from 90.66% to 99.11% at λres = 1240 nm, 1400 nm, 1910 nm, 2250 nm, and 6370 nm, corresponding to modes 1 to 5, respectively. The proposed PMA structure shows a remarkable improvement in absorptance peaks, Q-factor, ∆D, and small FWHM compared to the case 1. This improvement is due to the dielectric cavities formed by MgF2 between a pair of Ag nanobars and Ag layers, which can enhance the effects of CPR and GPR, and the top and edge surface of a pair of Ag nanorods that can provide an excellent light-matter intersection to enhance SPR [54, 55].

The remarkable improvement in absorptance in the proposed PMA structure results in SPPs in the unit cell center that provide quintuple-band near perfect absorptance and suppress intrinsic Ohmic losses in the plasmonic system [56]. By minimizing reflectance and eliminating transmittance, we achieved a nearly perfect absorber. Additionally, the redshifts observed in the proposed structure can be ascribed to the effective increase in capacitance and inductance of the resonant PMA, leading to an enhanced light-matter interaction. Table 3 summarizes the resonance wavelength (λres in nm), full width at half maximum (FWHM in nm), absorptance (A in %), Q factor and ∆D of the cases 1 and proposed PMA structures corresponding to their respective resonance modes (that is, at λres).

Table 3 The λres (nm), FWHM (nm), A (%), Q factor, and ∆D of the cases 1 and proposed PMA structures corresponding to their resonance modes (i.e., at λres)
Full size table

Figure 3(a), (b) provide a detailed visualization of the magnetic field intensity (|H|, A/m) and the electric field intensity (|E|, V/m) for Case 1 (Fig. 3(a)(1))) and the proposed PMA (Fig. 3(a)(2)–(6)) at λres. The four layers of Ag-nanobar/MgF2/Ag/MgF2 are designed to minimize reflection by matching the impedance at different material interfaces, while the bottom Ag layer acts as a mirror to prevent light transmission. It is evident that incident EM waves are efficiently confined to the respective metal surfaces, cavities, and edges at the corresponding λres. Compared to case 1, the fields | H | and | E | in the proposed PMA are much stronger and are concentrated in the gaps, edges, and top surfaces of a pair of Ag nanobars in the form of SPR and GPR, and in the MgF2 layer in the form of CPR. The proposed PMA shows a notable in the confinement of plane enhancement in |H| and |E| in the gaps, dielectric cavities, and metal surfaces and a remarkable out-plane enhancement following the surface and edge enhancement adjacent to their external borders. Additionally, the pattern of | H | and | E | fields on metal surfaces, edges, and dielectric cavities is different from case 1 due to the presence of a pair of Ag nanobars in the proposed PMA, and the different λres. At shorter λres = 1240 nm, the enhanced SPR effect is obvious (Fig. 3(a)(2), (b)(2)), while at longer λres, a strong CPR effect is remarkable (Fig. 3(a)(4), (b)(4)). The gaps and cavities in the proposed PMA conduct the SPP sources and generate the GPR and CPR modes, while the surfaces of Ag nanobars and Ag layers contribute the SPR modes. Therefore, the proposed PMA significantly enhances the light-matter interaction and contributes to the quintuple-band absorptance peaks. Localized | H | and | E | fields induce an induced current loop, which can be understood by the magnetic polaritons and the LC circuit model [57].

Fig. 3
figure 3

a Magnetic field intensity distributions (|H|, A/m) and b electric field intensity (|E|, V/m) at resonance wavelength of the proposed PMA without a pair of Ag nanobars (case 1, see (1)) and with a pair of Ag nanobars (proposed PMA, see (2)–(6)), respectively

Full size image

Figure 4 illustrates the distribution of the enhanced electric field by mapping the distribution of positive and negative surface charge densities, electric force lines, and energy flow arrows. At the corresponding λres, the line charge density (Coulomb / m), the electric force lines (green lines), and the energy flow (red arrows) for cases 1 and the proposed PMA are shown. In cases 1 (Fig. 4(1)), the density of (+ -) charge pairs is much weaker than in the proposed PMA, resulting in blurred charge pairs on the metal surface. In contrast, the proposed PMA (Fig. 4(1)–(6)) exhibits a more extensive distribution of charge pairs on the Ag surface between the second and last layers of MgF2. The dipole-like charge pattern on the surface of the proposed PMA is controlled by hybridization of the SPR, GPR, and CPR modes, which is significant. The Ag surface between the second and last layers of MgF2 is crucial in connecting the (+ -) charge pairs in the plasmonic system, resulting in a stronger dipolar effect and increased mutual inductance on the metal surfaces, as well as capacitive coupling in resonant cavities.

Fig. 4
figure 4

Line charge density (Coulomb/m), electric force lines, and energy flow arrows of Case 1 (1) and the proposed PMA (2)–(6) in corresponding λres, respectively

Full size image

The structural parameters have a great impact on the absorptance spectrum of the designed PMA. By varying the geometrical parameters, one can tune the absorptance peak wavelengths that range from near-infrared to mid-infrared, showing the tunability and feasibility of the designed PMA. The function of the bottom Ag layer is the mirror surface. Since d5 = 100 nm, the transmittance channel will prevent near-infrared and mid-infrared. In the following simulations, we keep d5 = 100 nm and vary one of the other structural parameters (i.e., L, g, d1, d2, d3, and d4) while keeping the other parameters intact. The default parameters are shown in Table 1.

First, we investigate the influence of L and g, on the absorptance spectrum, as shown in Fig. 5(a), (b), respectively. In Fig. 5(a), the varying L shows a great influence on the absorptance peaks. The absorptance peak of mode 1 redshifts with increasing L (from λres = 1380 nm to λres = 6370 nm), and the number of λres that absorptance exceeds 90% (labeled by number) increases with increasing L (from 0 to 5). This phenomenon can be described by the significant bound states of SPR on the top surface of longer Ag nanobars originating from the mechanics of the equivalent LC circuit. In the LC model (see Eq. (2) and Table 1), the λres increases with increasing L. In Fig. 5(b), the available ranges of g based on the desired working λres in the near and mid infrared regions and ΔD are 200 nm < g < 540 nm. Variation in g supports the coupling plasmon mode between a pair of Ag nanobars on the top surface.

Fig. 5
figure 5

Comparison of the absorptance spectrum of the proposed PMA by varying (a) L and (b) g, respectively

Full size image

The thickness of Ag nanobars (d1), the first layer of MgF2 (d2), the thin layer of Ag (d3) and the second layer of MgF2 (d4) can mediate the coupling effect of the SPP modes and significantly influence the performance of the absorptance spectrum. Figures 6(a), (b) and 7(a), (b) depict the absorptance spectrum of varying d1, d2, d3, and d4, respectively. As seen, the variations of d2 (Fig. 6(b)) and d3 (Fig. 7(a)) reveal a more significant blue shift with the increase of d2 (from 8580 to 4070 nm) and d4 (from 7640 to 5340 nm) when d2 and d4 increase from 5 to 40 nm. Note that there is a weak absorption peak at λres around 4000 nm. When the parameters of d2 are changed, it will strongly couple with mode 1, resulting in a significantly enhanced plasmon mode. This is because an increase in d2 forms an effective resonance cavity between the Ag nanobar and the Ag thin layer, leading to improved cavity plasmon resonance (CPR) and facilitating coupling with mode 1.

Fig. 6
figure 6

Comparison of the absorptance spectrum of the proposed PMA by varying (a) d1 and (b) d2, respectively

Full size image
Fig. 7
figure 7

Comparison of the absorptance spectrum of the proposed PMA by varying (a) d3 and (b) d4, respectively

Full size image

At the relevant wavelength, the skin depth of the Ag film measures approximately 11 nm. Figure 7(a) indicates that absorptance peaks shift towards the red with increasing thickness of the first layer of Ag, denoted as d3. The thickness of the first layer of Ag (d3) has a significant impact on resonance peaks. When d3 exceeds 20 nm, there is almost no transmission power. The number of peaks remains at 3 for d3 values greater than or equal to 15 nm. However, for d3 values of 5 nm and 10 nm, the number of peaks is 4 and 5, respectively. The thickness of d3 can influence the CPR effect between the Ag nanobar (with thickness d1) and the Ag film (with thickness d3) due to the different degrees of SPR effect resulting from varying d3 thicknesses. According to Figs. 6 and 7, the available ranges of d1, d2, d3, and d4 based on the labeled numbers and desired λres in the near- and mid-infrared regions are 25 nm < d1 < 200 nm, 5 nm < d2 < 40 nm, 5 nm < d3 < 40 nm, and 50 < d4 < 400 nm, respectively, revealing reliability and tolerance in the fabrication of the proposed PMA structure, giving robust performance against fabrication imperfections. Therefore, the proposed PMA is favorable for practical application due to its outstanding robustness.

The LC model as seen in Eq. (2) and Table 1 shows that an increase in the width (L) and permittivity of the dielectric layer (ε2) results in an increase in the λres. On the other hand, an increase in the thickness of the dielectric layer (d2) leads to lower values of LeCm, while the term LmCm remains independent of d2. Similarly, an increase in the thickness of the first layer of the dielectric (d1) results in smaller values of LeCm, while the term LmCm remains unaffected by d1. As a result, the λres decreases as the thickness of d1 and d2 increases. These predicted λres match well with the simulated results shown in Figs. 5, 6 and 7, which demonstrate the impact of d2, L, and d1. The thickness of the dielectric layer (d1) solely influences the value of Cg = πε0/(g/d1), which is a weak factor. Therefore, the impact of g on the λres may be negligible, aligning with the simulated results shown in Fig. 5(b).

Conclusion

Using FEM simulation, we designed a periodic structure that comprises of a metallic nanobar array, a thin Ag film, and a dielectric layer. This quintuple band nearly perfect metamaterial absorber (PMA) operates in the near- and mid-infrared regions. We explored the influence of various structural parameters on the PMA's performance. The absorptance of the PMA we designed can reach 98.02%, 99.47%, 98.02%, 99.47%, and 96.09% for modes 1–5, respectively. Moreover, the PMA exhibits strong electric field confinement and enhancement in a nanogap region. The high absorptance is due to the hybridization of localized gap, cavity and surface plasmon resonance, which are influenced by the dielectric layer structure parameters. The proposed PMA significantly enhances the light-matter interaction and contributes to the quintuple-band absorptance peaks. The localized | H | and | E | fields induce an induced current loop, which can be explained by the magnetic polaritons and the LC circuit model. By adjusting the working wavelength, this design can be extended to other energy conversion applications. In conclusion, our study reveals that this PMA structure has multiple absorption channels and exhibits excellent performance.