1. Introduction

Metamaterial absorbers(MAs) are a kind of artificially constructed meta-surfaces composed of periodic sub-wavelength metallic and dielectric units, which exhibit extraordinary electromagnetic properties that cannot be achieved with naturally occurring materials and have numerous relevant applications. The first proposed MA is realized by combining the electric ring resonators(ERRs) with cut wires in a parallel plane separated by a dielectric layer, and works for the TM polarization at microwave frequencies [1]. For infrared or optical frequencies, the MA can be simplified as a trilayer structure made of a patterned metallic layer above the homogeneous metallic substrate with a dielectric spacing layer [2–7]. Typically, almost all of the one-dimensional(1D) trilayer structures can only highly absorb the TM polarized electromagnetic wave [8, 9], due to the excitation of the magnetic resonances or surface plasmon polaritons(SPPs) requiring a magnetic-field component perpendicular to the cross section of the structure. For this reason, only few special designs can achieve high absorption for the TE polarization [10, 11]. Thus, it is challenging to realize the polarization independent perfect absorption by using only a 1D structure without the fourfold rotational symmetry [12, 13]. More recently, numerical results show that it is possible to reduce the complexity of the polarization independent MAs from two dimensions to one dimension through different absorption mechanisms as well as carefully designed geometries [14, 15]. Although the 1D polarization independent MAs seem to be simple, their performance is strongly dependent on the spacing distance between the stacks and the filling medium into the groove, which makes the fabrication complex in practice [15–18].

In this paper, we propose a wide-angle, polarization independent and fabrication-tolerant perfect absorber based on a 1D simple stacked array without slit filling. This absorber has very high absorption for both TM and TE polarizations simultaneously, which are attributed to the excitation of the magnetic resonance(MR) and the guided mode resonance(GMR), respectively. Moreover, this 1D absorber is almost independent on the spacing distance between the neighboring stacks and the metallic strip thickness, which releases degrees of freedom in design. Also, the operating wavelength could be finely tuned by varying the geometry of the structure or changing the dielectric medium. Comparing with those MAs designed in two dimensions [3–6], our current structure not only achieves the similar functions, but also is greatly simplified since it is periodic in one dimension only, which is suitable for flexible and high-throughput fabrication with large dimension and amount by interference lithography(IL) [19]. This is also superior to those 2D designs in practical situation, which usually need expensive and time-consuming UV lithography or electron beam lithography with the use of unchangeable and limited photomasks [20] or complex optical systems [3–5]. What’s more, our structure and fabrication are also suitable to extend to the microwave and terahertz regime.

2. Structure design

The illustration of the suggested 1D absorption structure as well as the propagation configurations of the incident electromagnetic wave are presented in Fig. 1. As depicted in Fig. 1, two pairs of strip-patterned metal-dielectric bilayers are periodically arranged on the metallic ground plane with a period of Λ = 1.55 μm. The width of the vertically cascaded stack is w = 0.55 μm and the thickness of each metallic strip is h = 0.05 μm. The upper dielectric strip plays an important role as the waveguide layer for the TE polarization, while the lower dielectric strip is used as the significant spacer layer for the TM polarization. The thicknesses of the two dielectric strips are d = 0.72 μm and t = 0.16 μm, respectively. The dielectric strips are both germanium (Ge). Within the considered wavelength range, Ge is a lossless material with a refractive index of n = 4 [21]. Silver is chosen as the metallic components, and the frequency-dependent complex dielectric constants are taken from Ref [21]. The absorption and reflection spectra of the absorber are calculated by using the rigorous coupled wave analysis (RCWA) method [22]. In the calculation, a total of 101 Fourier components are used to represent the dielectric function in the grating region. The thickness of the continuous metallic substrate is much larger than the skin depth in the infrared regime, which prevents all light from transmitting through the whole structure. Thus the transmissivity T is set to be zero, and the absorptivity could be calculated by A = 1 − R, where R is the reflectivity.

 

Fig. 1 (a) Schematic of the one-dimensional absorber based on a stacked array consisted of vertically cascaded two pairs of metal-dielectric bilayers. The magnetic field (TM polarization) is confined in the spacer strip, while the electric field (TE polarization) is localized in the waveguide strip. The optimized dimensions are Λ = 1.55 μm, w = 0.55 μm, h = 0.05 μm, d = 0.72 μm, and t = 0.16 μm, respectively.

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3. Results and discussion

Figure 2 shows the absorption spectra of our absorber for different polarization angles ranging from 0°(TM polarization) to 90°(TE polarization) at normal incidence. The absorption peaks for all polarization angles are at the same resonant wavelength of 5.25 μm, but with different spectral shape. For the TM polarization (polarization angle of 0°), the absorption spectra are a typical resonant peak with a symmetric line shape and a full width half maximum (FWHM) of 0.37 μm. For the TE polarization (polarization angle of 90°), the absorption spectra possess an asymmetric line shape with a narrower FWHM of 0.23 μm. The simulated absorptivity has a maximum value of 99.17% and 99.46% for the TM and TE polarization, respectively, and the off-resonance absorptions are low. As the polarization angle increases, the absorption peaks are always very high, whereas the bandwidths become slightly narrow due to the absorption mechanism changing from the MR to the GMR. Although, the proposed design is a 1D structure, this absorber is very robust to the polarization angle around the designed wavelength.

 

Fig. 2 Absorption spectra for different polarization angles ranging from 0°(TM polarization) to 90°(TE polarization) at normal incidence.

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To understand the origin of the system, we simulated the individual constituent parts of the 1D structure, as shown in Fig. 3. The red and blue curves represent the absorption spectra for the TM and TE polarization, respectively. Figure 3(a) shows the absorption spectra of the structure with metal and spacer strips on the metallic substrate. It can be seen that there exists an absorption peak for the TM polarization. However, the absorptivity is less than 2% indicating no absorption occurs for the TE polarization. The absorption spectra of the structure with metal, waveguide and metal strips on the metallic substrate are plotted in Figs. 3(b). There is a notable absorption peak for the TE polarization, while a relatively flat absorption curve is observed for the TM polarization. The calculation results reveal that the absorption peaks of the TM and TE polarization are contributed by different parts of 1D structure, respectively.

 

Fig. 3 Absorptivity as a function of wavelength for both TM and TE polarization of (a) the structure with metal and spacer strips on the metallic substrate, and (b) the structure with metal, waveguide and metal strips on the metallic substrate.

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In order to gain the physical mechanisms of the polarization independent absorption in the suggested absorption structure, we simulated the electromagnetic field distributions at the resonant wavelength of 5.25 um. It is observed that, for different polarizations, the electromagnetic fields are resonantly localized and then absorbed at different parts of the 1D structure. The distributions of the magnetic field and electric field at resonance for the TM polarization are shown in Fig. 4(a) and 4(b). It is found that there exists strong electric field on both sides of the spacer strip, especially near the corners of the lower metallic strip. The electric field vectors circulate around the spacer strip to form an induced eddy current [23]. The magnetic field with an order of magnitude larger than that of the incidence is confined in the spacer strip between the lower metallic strip and the substrate. The electromagnetic field distributions indicate a diamagnetic response, which is strong interaction between the magnetic field of the incident light and the magnetic moment resulting from the circulating currents. The excitation of the MR is responsible for the strongly resonant absorption. Further, the equivalent LC circuit model is used to explain and predict the absorption peak of MR [24]. According to the electromagnetic field distributions and the induced current loop, the two metallic surfaces behave as the inductive impedances [25], which include two components of the mutual inductance $L_m=0.\text{5}{\mu }_{0}wt$ and the kinetic inductance $L_e=w/({\epsilon }_0{\omega }_{\text{p}}^2\delta )$, where ${\epsilon }_0$ and ${\mu }_0$are the permittivity and permeability of vacuum, respectively, ω_p = 1.364 × 10¹⁶rad/s is the plasma frequency of silver and the penetration depth of silver δ is about 14 nm [26]. The spacer strip insulate the two metallic surfaces, which acts as a parallel-plate capacitive impedance$C_m=c_{\text{1}}{\epsilon }_d{\epsilon }_{0}w/t$, where ${\epsilon }_d$ is the spacing dielectric permittivity and c₁ = 0.2 is the coefficient that accounts for nonuniform charge distribution at the metal surfaces [17]. The gap capacitance between the neighboring Ag strips can be neglected due to the large slit width. The total impedance of the LC circuit can be expressed as:

 

Fig. 4 The normalized electromagnetic field distributions at the resonant wavelength of 5.25 μm.(a) Electric field and (b) Magnetic field for the TM polarization.(c) Electric field and (d) Magnetic field for the TE polarization.

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The distributions of the magnetic field and electric field at resonance for the TE polarization are shown in Fig. 4(c) and 4(d). The electric field is mostly concentrated in the waveguide strip, and leaks into the slits between the neighboring waveguide strips, which indicates that the resonance occurs at this layer. The magnetic field is localized at the upper and lower interfaces which are between waveguide strip and two metallic strips. The GMR effect occurs in the waveguide layer, and the TE polarized wave is absorbed by the two metallic strips. The eigen equation of the GMR in the waveguide structure is given as [28, 29]:

The wide-angle feature is very important for practical applications, thus we investigate the absorption spectra at various incident angles for both TM and TE polarizations, as shown in Fig. 5(a) and 5(b). The absorption peak for the TM polarization is not sensitive to the incident angle. Even for the incident angle of 60°, more than 82% absorption is still obtained while maintaining the center wavelength. For the TE polarization, the absorptivity is larger than 90% with the incident angle up to 23°. However, when incident angle continues to increase, both the absorptivity and resonant wavelength decrease, but the absorptivity remains above 50% for the incident angle as large as 42° at the fixed operating wavelength of 5.25 μm. The wide-angle property for the TM polarization results from that the magnetic field of the incident light is always perpendicular to the incident plane at different incident angles, thus the anti-parallel currents are efficiently excited. Conversely, for the TE polarization, the effective permittivity of the waveguide layer will gradually decreases with the increasing incident angle [33], thus the absorption peak moves towards shorter wavelength, which agrees well with the simulation results.

 

Fig. 5 The absorption spectra as a function of incident angle for the (a) TM and (b) TE polarization. The absorption spectra as a function of azimuthal angle at a fixed incident angle of 20° for the (c) TM and (d) TE polarization.

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We also present the absorption spectra as a function of azimuthal angle at a fixed incident angle of 20°, which are more normal cases representing the illumination from all directions, as shown in Fig. 5(c) and 5(d). For the TM polarization, the absorption peak remains very high for the azimuthal angle φ changes from 0° (the incident plane is perpendicular to the grating) to 90° (the incident plane is parallel to the grating) at the designed wavelength, and with a monotonic decrease of bandwidth. For the TE polarization, the absorption band has an extremely slight blueshift due to the inclined incidence. The absorption peak of 94.33% is obtained when the azimuthal angle φ is at 0°. As the azimuthal angle increases to 90°, the absorptivity remains up to 96.03% at the designed wavelength of 5.25 μm and the width of the absorption band becomes narrow. Therefore, the absorber can work well within a wide incident angular range for both polarizations at arbitrary azimuthal angle.

Compared with the 1D polarization independent MAs reported before [15–17], the current absorber is also superior in complexity and fabrication tolerance [34]. In contrast to the absorption by exciting the cavity mode in the grating groove [17], the filling of high refractive index medium into the groove is not necessary, and the resonances of both polarizations are excited in the vertically cascaded stack. Thus, we investigate the influences of slit width s (as shown in Fig. 1) on the absorption performances, as shown in Fig. 6. It can be seen that the absorption spectra are very insensitive to the spacing distance between neighboring stacks as long as the separation is large enough. Thus, the proposed 1D structure releases a degree of freedom in design, and greatly simplifies the fabrication process in practice.

 

Fig. 6 The influences of slit width s on the absorption performances for the (a) TM and (b) TE polarization.

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To further illustrate the fabrication-tolerance, we investigate the dependences of absorption spectra on the metallic strip thickness h (as shown in Fig. 1), as shown in Fig. 7. It is found that the resonant wavelength increases as the metallic strip thickness decreases, when the metallic strip thickness is smaller than a critical value. This effect arises because the charge distributions on the metallic strip’s surfaces are deteriorated as a result of the finite skin depth. However, the thickness of metallic strip has no influences on the absorption spectra as long as it is large enough.

 

Fig. 7 The influences of metallic strip thickness h on the absorption performances for the (a) TM and (b) TE polarization.

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4. Conclusion

In conclusion, we have proposed a wide-angle and polarization independent 1D perfect absorber based on a stacked array consisted of vertically cascaded two pairs of metal-dielectric bilayers. This absorber has absorption peaks at the wavelength 5.25 μm with the absorptivity above 99% for different polarization angles at normal incidence. The absorption mechanisms are attributed to the excitation of the MR (magnetic resonance) and the GMR (guided mode resonance) for the TM and TE polarization, and are further expounded by the LC circuit model and the eigen equation of the GMR, respectively. The absorptivity keeps above 82% even at the incident angle of 60° for the TM polarization, and remains above 50% when the incident angle is up to 42° for the TE polarization. Thus, the absorber can work well within a wide incident angular range for both polarizations at arbitrary azimuthal angle. More importantly, this 1D absorber is very robust to the spacing distance between the neighboring stacks and the metallic strip thickness, which releases degrees of freedom in design and makes the absorber extremely flexible and simple in fabrication.