1 Introduction

Metamaterials, also known as artificially manufactured materials, have attracted great attention in the last decades with unique properties that are not available in nature [1]. Since the impedance of metamaterials \((z=\sqrt{\mu / {\epsilon }}=1\)) can be simply adapted to the surrounding media, by satisfying maximum power transfer from the incoming light into surface plasmon. Therefore near-perfect absorption of light can be achieved. Metal-based plasmonic metamaterials have attracted a lot of attention in recent years, such as biosensing [2], negative refractive index [3], stealth technologies [4], and optical filtering [5]. These plasmonic structures have a unique ability to manipulate light by releasing an electromagnetic wave oscillation along with the metal–insulator interface by the interaction of the electromagnetic field and free electrons between the same interface [6]. These properties yield Metal–Insulator–Metal (MIM) structures to get great attention in many research areas, and the potential of light control in nanoscale dimensions has been demonstrated with different applications based on single [7], double [8], and multiple-band MIMs [9]. However, single-band absorbers are disadvantageous in the sensitivity and detection of different spectral fingerprints in imaging, filtering, and spectroscopic applications [10]. To overcome these disadvantages, many researchers have recently focused on high-performance dual or multi-band absorbers [11].

In recent studies, plasmonic filters, including low-pass [12], high-pass [13], band-pass [14], or band-stop filter [15] structures, have been investigated. In previous studies, aperture- and temporal-coupling mechanisms are most commonly used in plasmonic absorber designs. However, the static tunability of aperture-based absorbers is challenging due to tuning the gap length and tuning to different output waveguides at resonant wavelengths [16]. Particle or resonator-based absorbers are preferred for spectroscopic detection and filtering with their simple structure than the cavity and waveguide structures with more challenging dimensions control.

In this study, a narrowband metamaterial absorber (MA) with nearly perfect absorption at five different wavelengths is designed in the mid-IR region. The MA under study consists of a thick Au optical mirror, SiO2 dielectric material, and a Pi-Inverted Pi-shaped Au resonator on top. Pi-Inverted-Pi resonators are geometrically optimized to get a nearly perfect absorption at five resonance peaks associated with each part of the Pi-Inverted-Pi antenna structure. The electric field and charge distributions of the antennas at resonance wavelengths are also investigated. The relations between the charge distribution and the electric field are evaluated numerically. In addition, the TE and TM polarization performance of the MA is examined, and its polarization dependence is shown. The Q-factor of the designed MA structure is calculated, and a high Q factor (118.61) is obtained. Our designed MA system with its simple structure, simultaneous perfect absorption at five bands, and high-Q factor can be used in many potential applications, such as absorption filtering, spectroscopic sensing, and narrowband photodetector.

2 Material and methods

2.1 Numerical analysis

A schematic view of the proposed quintet-band MA is shown in Fig. 1a. The unit cell of MA structure consists of 120 nm SiO2 dielectric layer sandwiched between 200 nm Au layer and 60 nm thick Au Pi-inverted-Pi shaped resonators. The bottom Au layer serves as an optical mirror to minimize the leakage of the incoming wave. The geometrical parameters of the MA platform are as follows: H and L represent the horizontal and vertical lengths of the big Pi-structure, while K and M indicate the horizontal and vertical lengths of the small Pi-structure. The absorption strength can be improved slightly for an optimized value of w for small and big Pi, individually. The width (w) of the structure is set to 140 nm for simplicity.

Fig. 1
figure 1

a Schematic of the quintet band metamaterial absorber. b Calculated absorption spectrum with 200 nm thick Au layer as an optical mirror, 120 nm thick SiO2 dielectric layer, and 60 nm thick Au resonators. The parameters of the part of the inverted-Pi-shaped antennas are H = 1000 nm, L = 655 nm, M = 400 nm, K = 700 nm, and w = 140 nm, respectively. The periodicity of the antennas is 1750 nm

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The spectral response of the proposed MA has been numerically studied by the Finite Difference Time Domain (FDTD) method by the Lumerical program. In numerical calculations, the Palik reference was used for Au and SiO2 dielectric constants [17]. In the simulation, a single unit cell consisting of two different elements of big and small Pi-shaped antenna has been computed with periodic boundary conditions in x- and y-directions, and a perfectly matched layer is chosen for the z-direction. A plane wave light source is set along the z-direction.

The calculated absorption spectra of the designed MA have five narrow resonance bands at peak positions of λ1 = 1817.52 nm, λ2 = 1968.38 nm, λ3 = 2721.31 nm, λ4 = 3765.6 nm, and λ5 = 5740.63 nm as depicted in Fig. 1b. The absorption strengths for the associated resonance wavelengths are 96% (at λ1), 97.15% (at λ2), 94.5% (at λ3), 99.7% (at λ4), and 93.6% (at λ5). The full-width at half maximum (FWHM) and the quality factors (\(\frac{{\lambda }_{0}}{\mathrm{FWHM}}\)) of individual peaks are 15, 37, 85, 114, and 179; 118.7, 53, 32, 33, and 32, respectively. The narrower the peak, the higher the quality factor Q; therefore, it offers better optical performance. The designed MA structure has nearly perfect absorption in almost all five resonances and high Q-factor than those reported in Table 1. These results reported in the table are obtained in a near-IR regime from 640 to 1644 nm, and the highest Q-factor is 87.6, which is almost two orders of magnitude small than our structure. In the longer wavelength regime, the FWHM increases due to the broadening of the bands; therefore, our structure has the highest Q-factor among its counterparts to the best of our knowledge.

Table 1 Comparison of our metamaterial absorber performance with the reported studies so far
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The tuning capacity of the proposed MA has been investigated with the same FDTD method. It has been shown that the resonance peaks can be tuned spectrally depending on the geometric parameters (H, L, K, M, and P), as shown in Fig. 2. The change in the length (H) of the big Pi-antenna affects the spectral positions of the three resonances at λ1, λ3, and λ5. The spectral shift for resonance at λ1 has almost no change; however, absorption strength has significantly decreased as the H value changes from 1000 to 1300 nm. The spectral positions and the absorption strength of the resonances at λ2 and λ4 have no change at all. The spectral positions are the same for the value of 1100 nm and 1200 nm for the H-value at λ5 with a strong decrease for H = 1100 nm. As the L parameter increases, the resonance wavelengths of λ3 and λ5 are red-shifted while the spectral positions at other resonances remain fixed, as shown in Fig. 2b. The near-unity perfect absorption can also be achieved at λ1 (only for L = 595 nm), λ4 (for all parameters), and λ5 (only for L = 545 nm).

Fig. 2
figure 2

The calculated absorption spectra of Pi-inverted-Pi-shaped metamaterial absorber. Spectral tuning based on geometrical parameters are given. a H parameter varies at fixed parameters of L = 655 nm, K = 700 nm, and M = 400 nm. b L parameter varies at fixed parameters of H = 1000 nm, K = 700 nm, and M = 400 nm. c K parameter varies at fixed parameters of H = 1000 nm, L = 655 nm, and M = 400 nm. d M parameter varies at fixed H = 1000 nm, K = 700 nm, and L = 655 nm. e The period varies at fixed parameters of H = 1000 nm, K = 700 nm, L = 655 nm, and M = 400 nm. The period is set as 1750 nm for a, b, c, and d for calculating the effect of other parameters

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The resonance wavelength at λ3 and λ5 has no shift, while the other resonance has slight changes as the length K (varying between 580 and 760 nm) and M (ranging between 300 and 460 nm) as depicted in Fig. 2c and d. Also, the absorption strength is stable at λ3, λ4, and λ5 with a change in the K value. The absorption strength decreases as M increases with a redshift. Also, the spectral tunability of resonance at λ3 strongly depends on the M parameter. Figure 2e shows almost no effect of the period on the spectral position of the quintet resonances except at λ5. These results show that the proposed structure is beneficial for frequency selective absorber applications with its single layer, easily controllable spectral positions, and simple structure.

The spectral response of the quintet absorber is almost stable with changing parameters of h, s, and k as shown in Fig. SI (1). This structure can be easily fabricated since the little variations in between the legs of each Pi and the gap between the Pi antennas has almost no effect on the spectral positions at five individual bands. Also, absorption strength does not change significantly at λ1, λ2, λ3, and λ4; however, at λ5 it decreases to half.

2.2 Field enhancements

In order to understand the physical origin of quintet resonance behavior, the field and charge distributions have been studied with the same FDTD method. Figure 3 shows the electric field intensity distributions at resonance wavelength at λ1, λ2, λ3, λ4, and λ5 in the metal layers. Figure 3a shows the electric field intensity of the five resonance values. Based on the electric field enhancements in Fig. 3b, the resonances at λ1 = 1817.52 nm is due to the coupling of small Pi and the legs (L) of the big Pi antennas. The resonance at λ2 = 1968.38 nm is completely due to the K length of the small Pi antennas as depicted in Fig. 3c. The field enhancement shows that the resonance at λ3 = 2721.31 nm is due to the big Pi antenna (H and L parameter), as shown in Fig. 3d. From the field distributions, the resonance at λ4 = 3765.6 nm is due to the small Pi antenna (K and mostly M parameter). From Fig. 3f, the E-field is mostly localized in the legs (L) of the big-Pi antennas; therefore, the resonance at λ5 = 5740.63 nm is due to the big-Pi antenna.

Fig. 3
figure 3

Field enhancements at the interface between the dielectric layer and top metallic antennas for the proposed five-band Pi-inverted-Pi-shaped nano-antennas. The geometric parameters are H = 1000 nm, L = 655 nm, K = 700 nm, w = 140 nm, M = 400 nm, and s = 140 nm. The field enhancements of a all resonances, b resonance at λ1, c the resonance at λ2, d the resonance at λ3, e the resonance at λ4, and f the resonance at λ5

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2.3 Charge distributions

In order to fully understand the physical origin of electric and magnetic resonance occurring in Pi-inverted-Pi-shaped antennas, the charge distributions of five nearly perfect resonance peaks are investigated by the FDTD method. Figure 4a shows the charge distributions of resonance peaks at λ1, λ2, λ3, λ4, and λ5 in the resonator. It can be seen from the same figure that equal sizes of different charge polarities are accumulated at the opposite side of the Pi-inverted-Pi antennas, indicating that the electric dipole is excited. The electromagnetic dipole of the structure at each resonant wavelength is excited by a strong electric field at both Pi structures. Figure 4b shows the charge distribution at the first resonance wavelength of 1817.52 nm. The charges of different polarities are accumulated at the end of the base and the tip of the legs of the small Pi antenna. In the same figure, the charges with opposite signs are accumulated left and right legs with the same polarity of the charges in the big Pi-antennas indicating that electric dipoles excitations. Also, the charge accumulation at the base of big P-antennas (a negative and positive charge) at the left and right parts, respectively, is mainly due to the coupling of the adjacent cell. The charge distributions at λ2 (1968.38 nm) and λ3 (2721.31 nm) indicate the excitation of two dipoles at the small and big Pi-antennas, respectively, as shown in Fig. 4c and d. The two poles of excited dipoles can be seen in the charge distributions at the resonance wavelengths of λ4 (3765.6 nm) and λ5 (5740.63 nm) in Fig. 4e and f, respectively. These charge accumulations given in Fig. 4 indicate the electric dipole excitations supported by the electric field enhancement due to surface plasmons.

Fig. 4
figure 4

Charge distributions of Pi-inverted-Pi-shaped nano-antennas. The geometric parameters H = 1000 nm, L = 655 nm, K = 700 nm, M = 400 nm, w = 140 nm, and s = 140 nm are used for calculations. a The charge distributions of all resonances. b The charge distribution at λ1 resonance. c The charge distribution of resonance at λ2. d The charge distribution of the λ3 resonance. e The charge distribution at λ4 resonance. f The charge distribution at λ5 resonance

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2.4 Polarization dependence of the metamaterial absorber

Polarization sensitivity analysis is carried out to justify the choice of design structure. For TM polarization (90° polarization angle), the structure offers five absorption bands at 1817.52 nm, 1968.38 nm, 2721.31 nm, 3765.60 nm, and 5740.63 nm with the absorption level of 96.03%, 97.15%, 93.54%, 99.66%, and 93.60%, respectively. The structure is partially sensitive to polarization with 60%, 58%, and 50% absorption at 1817.52 nm, 1968.38 nm, and 50% at 2721.31 nm, respectively for TE polarization (0° polarization angle), as shown in Fig. 5. The peaks at 3765.6 nm and 5740.63 nm are disappeared for TE polarization. The structure was partially sensitive to polarization due to its asymmetrical design. The important design contribution of this work is that a single layer MA offers five and three significant absorption bands for TM and TE polarization, respectively. The proposed quintet band MA has potential applications in Mid-IR spectroscopy, bandpass filters, and optical filtering, etc.

Fig. 5
figure 5

Polarization dependence of Pi-inverted-Pi antennas. When the antenna was illuminated with TM and TE polarization, deep dips were obtained in TM polarization, while lower peaks were observed in TE polarization

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3 Conclusion

In summary, a quintet-band metamaterial absorber based on Pi-inverted-Pi-shaped nano-antennas is proposed, and the absorption characteristics of the structure are numerically analyzed. The numerical results show that the absorption spectra of the proposed structure have five absorption bands at 1817.52 nm, 1968.38 nm, 2721.31 nm, 3765.6 nm, and 5740.63 nm. Near-perfect absorption is achieved at almost each of the five resonance wavelengths, simultaneously. Our numerical analyzes demonstrate that the origin of five resonances is due to the field coupling in the Pi-inverted-Pi-shaped antenna. The results also show that by changing the dimensions of the Pi-type resonator, the spectral position, number of peaks, and absorption strength of the five resonances can be controlled. It has also been shown that the MA has high Q factors for each resonance as follows 118.7, 53, 32, 33, and 32, which is beneficial for bio-chemical detections where complex compounds are needed to be identified accurately. Our proposed structure is partially dependent on polarization; therefore, this structure can be used for frequency selectivity, optic absorber and modulators, bio-sensors, active filters, and Raman applications.