1. Introduction

Metamaterial absorbers (MMAs), as the practical applications of the metamaterials, have been intensively investigated since they were firstly proposed by Landy [1]. MMAs are a kind of artificial plasmonic nanostructures which are usually composed of periodic subwavelength metallic and dielectric units. In these MMAs, the near-unity resonant absorption can be realized by manipulating the effective electric permittivity ε and magnetic permeability μ to get perfect impedance matching with free space, and with the loss dependent imaginary part of the refractive index as large as possible [2]. Both the transmissivity and the reflectivity are minimized simultaneously at the same wavelength region, which result in maximizing the absorptivity. Due to the advantages of perfect absorption, incident angle insensitivity and thin thickness, single-frequency absorbers have attracted much attention within a wide band ranging from the gigahertz [1] to terahertz range [3] as well as in the near-infrared region [4–9]. In addition, plasmonic filters with versatile functions have also obtained a lot of research interests, which are mostly absorptive-type filters [10–12].

However, the narrow band property greatly limits the potential application of currently available single-band absorbers. To obtain multiband MMAs with two or multiple absorption peaks, the absorbers may be designed by laterally arranging various sized subunits into one unit cell [13–17]or vertically stack multilayer composite structures [18–21]. The stacked trapezoidal structure with different geometrical dimensions can yield multiband or broadband absorption in the microwave [19] and terahertz regimes [3, 20]. However, those structures are extremely difficult to fabricate in nanoscale for the infrared region and the visible band [21]. Multiband or broadband MMAs at the infrared regime can also be realized by combining several different strips into a period which satisfy the subwavelength condition [22–25]. When the period of the structure is comparable to the wavelength, however, there will be diffracted order or surface plasmon polaritons (SPP) resonance, which deteriorate the LSPP modes under strips and decrease the absorption at resonance [22, 23].

Therefore, it is extremely desirable to design multi-band MMAs for infrared regime with perfect absorption, and flexible structure in fabrication. For this purpose, we design and investigate a dual-band perfect absorber in the mid-infrared region based on the T-shaped structure proposed by Chang [4]. Our design is an asymmetric T-shaped plasmonic array in which the LSPP modes are independently excited in each cavity of the structure. It is shown that the absorber has two distinct absorption peaks with high absorptivity, and remains almost unchanged over a wide range of incident angle. Furthermore, the resonant wavelength of the two bands can be tuned independently by varying the geometry of the asymmetric T-shaped structure. Different from previous works by using multi-sized or multilayer structures, our design employs a simple asymmetric T-shaped structure only with a much smaller period. Therefore, this MMA is much easier to fabricate and immunize against the effect of diffraction. In contrast to the previous works [11, 12], we present two comparison absorbers to reveal the origin of the dual-band spectral characteristic. Furthermore, the equivalent LC circuit model is used to explain the physical mechanism of the resonance and predict the resonance condition.

2. Structure design

The schematic of the unit cell of the proposed dual-band infrared absorber as well as the propagation configurations of the incident electromagnetic (EM) wave are shown in Fig. 1.The asymmetric T-shape array is periodically arranged on the metallic ground plane with a periodicity of $\Lambda =2.1$ μm. The width and thickness of the cap at the top of the T-shaped array are $W=1.75$μm and $h=0.1$μm, respectively. The SiO₂ layer is embedded between the T-shaped array on the substrate with the thickness of $t=0.1$μm. The width of two cavities which are between the top cap and the substrate are denoted by$w_1=0.95$μm and$w_2=0.55$μm, respectively. Thus the width of the post is $w_p=W-w_1-w_2$. The cavities in each sides of the post can be tuned independently. Importantly, the post of the T-shape array is not in the middle of structure but with a displacement, as denoted by the two dashed lines, therefore the whole structure turns to be an asymmetric T-shaped array. Different from the band gap structures proposed before [10, 26], there is no structure gap between the post and the ground plane. The whole structures are illuminated by a transverse magnetic (TM) polarized plane wave (the magnetic field is perpendicular to the incident plane), as shown in Fig. 1(a). The absorbance and reflectance spectra of the structure are calculated by using the rigorous coupled wave analysis (RCWA) method. The substrate is a continuous metallic layer with the thickness much larger than the skin depth in the infrared regime. Therefore, no light could transmit through the whole structure and the transmissivity $T(\omega )$ was close to zero. Thus, the absorptivity could be calculated by$A(\omega )=1-R(\omega )$, where $R(\omega )$ is the reflectivity. In this paper, the noble metal Silver is chosen as the material of the substrate and the T-shape structure. The frequency-dependent complex dielectric constants of silver (Ag) and SiO₂ are taken from [27].

 

Fig. 1 (a) Schematic structure of the proposed dual-band perfect absorber. The two dashed lines show the centers of the top cap and the post, respectively. (b) Another two absorber structures with only one cavity (i.e., w₂ = 0 or w₁ = 0) on either side of the structures for comparison. The cavity lengths are the same (i.e., w₁ and w₂ respectively) as the asymmetric T-shaped structure.

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3. Results and discussion

Figure 2 presents the absorption spectra of the dual-band perfect absorber at normal incidence for TM plane wave. There are two distinct absorption peaks located at 4.61 μm and 6.53 μm with absorptivities of 99.8% and 99.9%, respectively. What’s more, the off-resonance absorption is very small, which results in a wavelength selective infrared absorber with near-unity absorbance. Thus a dual-band infrared perfect absorber is realized in one period without the multi-sized or multilayer structures. The absorption spectra of the asymmetric T-shaped structure under TE polarization are also presented in Fig. 2 with green line. The absorptivity is less than 2% indicating no absorption occurs in our structure for TE polarization. Therefore the absorption is polarization dependent. Hence, metamaterial absorbers can be made wavelength selective and polarization dependent which are not possible in conventional bulk material based absorbers.

 

Fig. 2 Absorption spectra of the asymmetric T-shaped structure and two comparison absorbers at normal incidence. The red and blue curves represent the absorptivity of the structure with only one cavity on right or left side, as shown by the two insets.

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To reveal the origin of the dual-band spectral characteristics, we simulated the unit cells with only one cavity on the right or left side of the asymmetric structure, as shown in Fig. 1(b) and the inset of Fig. 2. The red and blue curves represent the absorptivity of the solely cavity to the right or left side of the structure, which have the absorption peaks located at 4.61 μm and 6.53 μm, respectively. The comparison of simulation results show that the absorption spectrum of the dual-band absorber is the superposition of those of each structure with one cavity only.

Additionally, the dual-band absorber is investigated by changing the cavity length in the asymmetric structure while the width of cap is fixed. Figure 3(a) denotes that the left side cavity length is varied from $w_1=0.65$μm to $w_1=1.05$ μm, while keeping the right side $w_2$ as a constant. Obviously, the absorption peak of the longer wavelength shifts from 5.2 μm to 6.83 μm, while the other absorption peak remains unchanged. Similarly, Fig. 3(b) shows the right side cavity length is modified from $w_2=0.35$ μm to $w_2=0.75$μm, with left side $w_1$ unvaried. Once again, only the shorter absorption wavelength linearly moves from 3.42 μm to 5.7 μm, while the higher wavelength absorption is almost unchanged. Therefore, the resonant absorption of each band can be tuned and optimized independently at desired wavelength with high absorptivity.

 

Fig. 3 Absorption spectra of the designed absorber with various cavity lengths (a) on left side and (b) on right side, while keeping the cavity length of the other side unchanged. Green triangles indicate the resonance wavelength calculated from the LC circuit model.

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The equivalent LC circuit model can be used to predict the resonance condition [28], as shown in Fig. 4.For our proposed structures, each cavity can be considered as an isolated unit as long as the thickness of the post is much greater than radiation penetration depth [29]. Here, parallel-plate capacitance $C_e={\epsilon }_{0}hl/(\Lambda -W)$ is used to approximate the gap capacitance between the neighboring T-shape array, and the capacitance between two metal surfaces of the cavity is given as $C_m=c_{\text{1}}{\epsilon }_d{\epsilon }_0{w}_{1,2}l/t$, where ${\epsilon }_0$ and ${\epsilon }_d$ are the free-space permittivity and the relative permittivity of the filling dielectric, respectively, and l is the length along the structure direction [30]. Importantly, $c_1$ is a numerical factor accounting for the non-uniform charge distribution at the metal surfaces. Typically in the calculation, $c_1$ is set to be 0.5 [31]. In addition, $L_e=(w_{1,2}+t/2)/({\epsilon }_0{\omega }_{\text{p}}^2\delta l)$ accounts for the contribution of the drifting electrons to the inductance, and $L_m=0.\text{5}{\mu }_0{w}_{1,2}t/l$ represents the mutual inductance of the top cap and substrate, where ${\omega }_p=1.364\times {10}^{16}rad/s$is the plasma frequency of Ag, and ${\mu }_0$ is the vacuum permeability. Furthermore, the power penetration depth $\delta =\lambda /4\pi \kappa$is frequency dependent, where $\kappa$ is the extinction coefficient of Ag. The total impedance of the LC circuit model can be expressed as

 

Fig. 4 Schematic of the equivalent inductor and capacitor circuit model. The arrows represent electric current flows in one cavity of the asymmetric T-shaped structure.

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The calculated resonance wavelengths based on the LC circuit model are depicted as green filled triangles in Fig. 3. As shown in Fig. 3(a), the predicted resonance wavelengths for the left side cavity at several $w_1$ values match well with the RCWA results. However, in Fig. 3(b), there exists relatively larger deviation for small cavity length of the right side$w_2$. The reason lies that the free electrons distribute uniformly, which needs a larger c₁ to provide better prediction. When cavity length is enlarged, electrons tend to accumulate at the corners of metallic surface [28]. The approximation of parallel capacitors therefore is appropriate. Hence, the cavity length dependence of enhanced absorption can be fully explained by the excitation of magnetic resonance.

We further investigate the influence of the cavity length difference $\Delta =w_1-w_2$ on the dual-band absorption performance. Figure 5 shows the absorptivity as a function of wavelength and the difference Δ, while the width of the post and the cap are fixed. It is seen that two distinct absorption peaks are obtained when difference Δ is large enough, e.g., for Δ = 0.4 μm. In this case, the two cavities perform as distinct resonators working at two different wavelengths. As the difference Δ decrease, the two absorption peaks move closely with lower absorptivity. For the case of Δ = 0 μm, the two absorption peaks combined together, which becomes a symmetric structure with single absorption band. Further decreasing the difference to negative will make the structure acting as an asymmetric structure again. Therefore it is necessary for constructing the dual-band absorption to use the asymmetric structure in this T-shaped array.

 

Fig. 5 Absorption spectra as a function of wavelength and the cavity length difference Δ varying from 0.4 μm to −0.4 μm.

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We also compare the absorption spectra between the convention sandwich structure (see the inset of Fig. 6) and the asymmetric T-shaped structure, as shown in Fig. 6. The absorption spectra are calculated at the incident angle of θ = 25°, due to the even-order harmonic modes can only be excited at oblique incidence. The geometric parameters of sandwich structure are adopted as follows: $\Lambda =3.6$ μm, $W=1.75$ μm, $h=0.1$ μm and $t=0.1$ μm. The period is chosen for combining two different strip antennas in one period. The strip width and the thickness of each layer are the same as those of the T-shaped structure, which dominantly determine the optical properties [6]. It is noted that the second harmonic mode occur at shorter wavelength and the absorption peak is at 3.39 μm for the convention sandwich structure. The absorption peak at 5.13 μm is due to SPP, which is corresponding to the large period containing two antennas. Therefore it is restricted to construct dual-band or broadband absorber by using the multi-sized structure [14, 22–25]. The proposed structure, however, have dual-band absorption peaks with low sideband absorption, which is due to the present of the post suppresses the multiple LSPP peaks.

 

Fig. 6 Comparison of absorption spectra between the convention sandwich and the asymmetric T-shaped structure with the incident angle θ = 25°. The convention sandwich structure is shown in the inset.

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In order to understand the nature of the dual-band absorption in our designed structure more clearly, we simulated the distributions of the magnetic field components at the two absorption peaks, as shown in Fig. 7.It is identified that different field distributions are observed for the resonances excited at two absorption peaks. Clearly, the field is localized under the cap and within a cavity which is open on one side and closed on the other side, thus the magnetic field has a node at the open side and an antinode at the closed side [4, 5].On one hand, the field is strongly confined in the cavities, and the field in the neighbor cavities which belong to different periods cannot affect each other, despite the small separation between the T-shaped array. On the other hand, the width of the post is larger than the skin depth in the infrared regime, therefore the two cavities in one period cannot couple to each other. It is evident that the incident electromagnetic energy can be efficiently confined to the respective cavity of the asymmetric structure at the corresponding resonance wavelength and dissipated by the ohmic loss within the metallic parts. Actually, the resonances are primarily associated with excitation of magnetic resonance because the circulating currents result in a magnetic moment which can strongly interact with the magnetic field of the incident light.

 

Fig. 7 Calculated distributions of the normalized magnetic field modulus ($\left|H_y/H_{inc}\right|$) at the resonant peaks of (a) 6.53 μm, and (b) 4.61 μm. The enhanced magnetic fields are confined within the respective cavity at the corresponding wavelength.

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We also investigate the incident angle dependence of our dual-band plasmonic absorber, since the wide-angle feature is very important for practical applications. Figure 8 shows the absorption spectra of our plasmonic absorber as a function of the indent angle ranging from positive (incident from the left half plane) to negative (incident from the right half plane) [29]. Clearly, the resonant absorptivity exhibits a symmetrical profile with respect to normal incidence and remains very high with the increasing incident angle. The absorption for the positive angles is nearly the same with that of negative angles, which can be understood by the fact that the magnetic resonance peaks are origin from the LSPP resonant mode and not change much with the angle of incidence. As our simulation results reveal, the designed dual-band absorber can operate well over a wide range of incident angles for both absorption peaks. The availability of wide-angle incidence is quite useful for applications such as infrared imaging and thermal bolometers

 

Fig. 8 Absorption spectra of the dual-band absorber change with the incident angle. The two red strips clearly show two strong absorption bands almost independent of the incident angle.

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The structure is easier to fabricate and the fabrication processes of the structures are briefly discussed [5, 10]. Firstly, the substrate Ag film and a 100 nm SiO₂ layer were deposited on a silicon substrate. Then a polymethyl methacrylate (PMMA) layer was spin coated on the SiO₂ layer. The grating pattern with a lattice constant Λ and line spacing w_p was exposed with electron beam lithography (EBL). The pattern was transferred to SiO₂ layer by a dry etching step. After etching a depth of t, a sliver film was then evaporated on the surface with a thickness of t. After removing the residual PMMA, another PMMA periodic structure with a period Λ, line spacing W, and displacement Δ/2 was formed by the alignment in the second EBL. Finally, a 100 nm thick silver film was deposited, and the asymmetric T-shaped structure was completed via a PMMA lift-off process.

4. Conclusion

In conclusion, we have designed a wide-angle dual-band infrared perfect absorber based on simple asymmetric T-shaped plasmonic array. The dual-band absorber realizes two distinct absorption peaks at the wavelength 4.61 μm and 6.53 μm with absorptivities more than 99%. The nature of the absorption is due to the LSPP mode excited in the cavities. Thus the two absorption peaks can be tuned independently by changing the cavity length of each cavity, which match well with the resonance condition predicted by the LC circuit model. In comparison to the multi-sized structure, the period of our structure is much smaller, which is immunized against the diffraction effect. Additionally, due to the present of the post, the multiple LSPP peaks are suppressed, which makes the sideband of dual-band absorption peaks very low.