1. Introduction

Perfect absorption of electromagnetic waves in different wavelength regions is important to applications such as solar energy harvesting [1], photodetection [2], chemical sensing [3] and radiative cooling [4]. Metamaterials, artificial material made up of periodic deep-subwavelength structures, the so-called meta-atoms, provide unconventional optical property relying on the subtle design and arrangement of meta-atoms [5]. Due to the flexibility in controlling electromagnetic waves, research on metamaterials has boomed in the past decade, and promising applications have been demonstrated including negative refraction [6], electromagnetic cloaking [7], super lensing [8] as well as perfect absorption of electromagnetic waves [9,10]. Since the first demonstration of metamaterial perfect absorber (MPA) by Landy et al. in 2008 [11], who achieved single narrowband near-perfect absorption in microwave region, various MPAs were proposed and demonstrated in microwave [12], terahertz [13], IR [14], visible [15] and even UV range [16].

With a comprehensive search in state-of-the-art literature, we list in Table 1 typical theoretical and experimental works in recent years on the topic of broadband MPAs and compare their key features such as device configuration, overall absorptance, operation bandwidth as well as their feasibility in fabrication (see Table 1 in Section 4. Appendices). On the one hand, MPAs adapting the seminal metal-dielectric-metal (MDM) tri-layer design [17–26], as well as its variations such as dielectric-metal-dielectric (DMD) tri-layer [27], MDM four-layer [26], MDM tri-layer with composite unit cells [17,19,24] and vertical stacking of few metal-dielectric layers [19,28,29], possess the advantage of being ultrathin and easy to fabricate, achieving however a limited operation bandwidth compared to another category of MPAs discussed below. Some of the works do not cover IR atmosphere windows [17,23,27], and some of the works cover only one IR atmosphere window [18,19,21,25,26,30]. In other words, although ultrathin MDM tri-layer MPAs can achieve broadband absorption, their typical absorption bandwidth is still not broad enough to cover two IR atmosphere windows simultaneously. On the other hand, another group of MPAs based on tapered metal-dielectric multilayer structures provide a broader operation bandwidth [31–40], relying on the concept of the so-called “trapped-rainbow effect” [41]. MPAs with ultra-broadband absorption has become easier to obtain ever since Cui et al. proposed a sawtooth-like anisotropic metamaterial that achieved ultra-broadband absorption from 3 to 6 µm [31]. However, for this type of MPA, fabrication difficulty may be an issue hindering its realization and application. Encouragingly, with the progress in micro-/nano-fabrication technology, we see some successful experimental demonstrations along this direction, utilizing methods such as nanoimprint lithography plus the size reduction effect during physical vapor deposition [33], magnetron sputtering plus focused ion beam (FIB) milling [34,37] as well as electron beam lithography (EBL) plus ion beam etching (IBE) [38,39], etc. Especially, the EBL + IBE method mentioned by Abdelatif et al [38] is promising and has been successfully demonstrated by Hu et al [39]. Thus, although fabrication of tapered metal-dielectric multilayer structure is challenging, it is already possible with state-of-the-art micro-/nano-fabrication techniques.

In the sense of maximizing the operation bandwidth of MPAs, the tapered metal-dielectric multilayer structures outperform others. Especially, Liang et al. proposed in 2013 a polarization insensitive pyramidal MPA based on Au/Ge multilayers, covering a continuous absorption range from 1 to 14 µm [32], the broadest one reported in the IR range as far as our knowledge goes. However, in this proposal, metal component Au is not CMOS-compatible which cannot be accepted by semiconductor foundries of IC industries, hampering its feasibility in large-scale applications. Moreover, the optical performance of the proposed absorber in shorter wavelength range is unexplored, i.e., wavelength below 1 µm. Since Au cannot support surface plasmon resonance below the wavelength of 500 nm due to interband transition [42], the operation bandwidth of the proposed Au/Ge pyramidal absorber can theoretically not cover the whole visible range, let alone UV. Since the visible and UV range is important to applications such as photovoltaic and photocatalysis, it is favorable for an ultra-broadband MPA to cover these wavelength ranges while maintaining high absorption in the IR region. Here in this work, after a careful review of the superior plasmonic property of Al from LWIR to UV range [43,44] and the extraordinary lossless character of ZnS as a typical infrared material [45], we propose a sawtooth-like and a pyramid-like structure based on Al and ZnS multilayers, which are both CMOS-compatible [46–48]. The proposed absorber can not only achieve high absorption (>90%) from LWIR all the way down to UV range (0.2-15 µm), but also holds the compatibility with CMOS fabrication technology and feasibility in large-scale production, facilitating its potential application in fields such as enhanced solar-energy harvesting, sub-ambient radiative cooling, multi-color infrared detection, etc.

2. Results and discussion

The proposed Al-ZnS sawtooth-like infrared absorber is schematically shown in Fig. 1(a), with a cross-sectional view of the structure unit shown as the right inset. The infrared absorber is composed of multiple layers of alternating Al and ZnS, which forms a periodic sawtooth-like structure with a trapezoidal cross-section, sitting atop a continuous Al film on silicon (Si) substrate. Main geometric parameters of the structure include total number of metal and dielectric layers N, period of structure P, bottom and top width of the trapezoid W_l and W_s, as well as the thickness of metal and dielectric layer t_m and t_d, respectively. Since the thickness of the bottom Al mirror is fixed as 200 nm, which is much thicker than the penetration depth of infrared light in Al, the Al mirror can be considered as infinitely thick. Thus, the electromagnetic field will not be able to perceive the Si substrate beneath the Al mirror, and the substrate can be ignored during the whole simulation process, which was carried out using commercial software COMSOL Multiphysics (see Appendices for details about simulation set-up). As can be seen from Fig. 1(b), after extensive parameter sweep and optimization of the geometric parameters of the structure (see Appendices for the data of parameter sweep), an ultra-broadband near-perfect absorption is obtained for TM-polarized light (black curve) with an average absorptance higher than 90% for 1-5 µm wavelength-range (short-wave infrared, SWIR, 1-2.5 µm and MWIR bands, shaded orange) and close to 100% for 8-14 µm wavelength-range (LWIR band, shaded green), completely covering the three main atmosphere windows of infrared radiation. For TE-polarized waves, the absorption performance drops obviously except for the 1-1.2 µm wavelength-range (red curve), indicating that optical behavior of the sawtooth-like infrared absorber is strongly polarization dependent. This is understandable because electric field of TE-polarized light is along Y-direction, i.e., along the direction of Al layer with infinite extension, which does not support surface plasmon resonance at finite wavelengths. For TM-polarized light, on the contrary, multiple surface plasmon resonances can be excited in the wavelength range of interest (1-15 µm), as is evident by the following analyses. Figures 1(c) and (d) display magnetic field distributions under TM polarization at typical wavelengths in the SWIR, MWIR and LWIR bands, respectively. The field distributions suggest that the LWIR absorption band corresponds to the fundamental plasmonic resonance mode of the structure, while the SWIR and MWIR absorption bands have contributions from both fundamental and higher-order modes. As is evident from Figs. 1(c) and (d), the spatial position of the fundamental mode moves gradually downward as the resonance wavelength increases, in general agreement with the dependence of surface plasmon resonance wavelength on structure size [49]. Specifically, shorter-wavelength light is absorbed by layers with smaller widths close to the top of the trapezoidal structure, while longer-wavelength light is absorbed by layers with larger widths around the bottom of the structure. The behavior of 3^rd order modes in the 1-5 µm region is similar to that of fundamental modes. So, at a first glance, an intuitive picture suggests that excitation of fundamental and higher-order plasmonic resonance modes leads to the observed ultra-broadband absorption.

 

Fig. 1. (a) Schematic of the proposed Al-ZnS multilayer sawtooth-like absorber. Inset on the right: a structure unit with geometric parameters labeled. (b) Absorption spectra of the Al-ZnS sawtooth absorber under TM (black) and TE (red) polarized light incidence, and that of the hyperbolic metamaterial (HMM) model based on effective medium theory (EMT) is displayed as the blue curve. (c) Magnetic field distributions (surface plot) and Poynting vectors (white arrows) of the Al-ZnS sawtooth absorber at typical wavelengths in the SWIR and MWIR bands. (d) The same as (c), but for wavelengths in the LWIR band. (c) and (d) share the same color bar on the right.

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A more physical picture can be obtained by considering the sawtooth-like absorber as a homogeneous effective medium, which is schematically shown in Fig. 2(a). Since the sawtooth-like absorber consists of alternating Al and ZnS layers whose thickness is much smaller than the wavelength of interest, effective medium theory can be applied to describe the sawtooth structure, under which the permittivity tensor of the effective medium can be written as

 

Fig. 2. (a) Schematic of the HMM model based on EMT theory. Inset on the right: a structure unit with dielectric constant and geometric parameters labeled. (b) Calculated dielectric constants ɛ_∥ and ɛ_⊥ based on EMT. (c) Magnetic field distributions (surface plot) and Poynting vectors (white arrows) of the HMM model absorber at typical wavelengths in the SWIR and MWIR bands. (d) The same as (c), but for wavelengths in the LWIR band. (c) and (d) share the same color bar on the right.

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Here ɛ_∥ and ɛ_⊥ refers to dielectric constants parallel and perpendicular to the interfaces of the Al-ZnS multilayers, respectively, and f = t_m / t_d is the filling ratio of the metal layer. Using dielectric function data of Al [50] and ZnS [45], we calculate and plot the real and imaginary parts of ɛ_∥ and ɛ_⊥ in Fig. 2(b). As can be seen from the black and red curves in Fig. 2(b), ɛ_∥ has a negative real part and a non-zero imaginary part over the whole wavelength-range of interest, meaning that the effective medium demonstrates lossy metal property in the transverse direction. Meanwhile, ɛ_⊥ possesses a positive real part (blue dashed curve) and a close-to-zero imaginary part (dashed green curve), denoting near-lossless dielectric property in the longitudinal direction. In this way, the homogeneous effective medium formed by Al-ZnS multilayers possesses dielectric constants with opposite signs in transverse and longitudinal directions, resulting in an anisotropic hyperbolic metamaterial (HMM). Based on this and performing numerical simulations of the effective HMM model with the same geometric parameters under TM polarization, we obtained its absorption spectrum shown as the blue curve in Fig. 1(b). Absorption curve of effective HMM model overlaps nearly completely with that of Al-ZnS multilayer sawtooth absorber, except for some minor discrepancies in the shorter wavelength region, validating the correctness of effective medium theory.

In addition, when we look at the magnetic field distributions at typical wavelengths of the HMM model in Figs. 2(c) and (d), we see again the main features of fundamental and higher-order plasmonic resonance modes similar to that of Al-ZnS multilayer sawtooth absorber at corresponding wavelengths (see Figs. 1(c) and (d) for comparison). Furthermore, if we look closely at the Poynting vectors shown as white arrows in Figs. 2(c) and (d), we can find that they travel downwards from the top, nearly unaffected by the absorber structure until they curl into it at certain positions along the longitudinal direction. At each such position, the Poynting vectors curl into the absorber structure, travel backwards inside it and form vortices on both sides of the absorber structure, and the propagation of light stops here. Such vortex features can be found for both fundamental and higher-order modes in all field plots, and the position where light stops and gets trapped moves gradually downwards with increasing wavelength, a typical signature of trapped rainbow effect (excitation of slow-light modes) [31,41].

Indeed, the effective HMM absorber structure can be abstracted into an air/HMM/air slab waveguide with varying core-width W, as shown in the inset of Fig. 3(a). If we denote the vacuum wavevector as ω_c ≡ ω / c, the propagation constant along the longitudinal direction as β, the transvers wavevector in HMM and air region as k_∥and k_air, respectively, and the dielectric constant of air as ɛ_d, then for TM-polarized guided mode, the dispersion relation between ω_c and β can be obtained by solving the following equations analytically [35,40,51]:

 

Fig. 3. Calculated dispersion curves (ω_c-β) for the (a) 1^st, (b) 3^rd, and (c) 5^th-order guided modes based on the air/HMM/air slab waveguide model, shown as the inset in (a). (d) Extracted wavelengths of the degeneracy points as a function of the waveguide core-width where corresponding slow-light mode is excited.

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Since the incident light can only excite odd modes inside the slab waveguide under normal incidence due to symmetry restrictions [49], only the odd modes part of Eq. (5) is used to calculate the dispersion relations, and the results are shown in Figs. 3(a), (b) and (c). Because ɛ_{∥, r} < 0, Poynting vector inside the waveguide core is in opposite direction of the wave vector component β [51]. Thus, as can be clearly seen in Fig. 3(a), with the increase of β, ω_c increases first, flattens gradually at certain position and then decreases with further increase of β. This behavior indicates that group velocity of the guided mode, i.e., v_g = dω_c /dβ switches from positive to negative and crosses zero at certain position as β increases. These crossing positions are called degeneracy points corresponding to v_g = 0, i.e., slow-light mode with extremely small group velocity [51]. Similar behaviors are found for 3^rd and 5^th order slow light modes, only except that their degeneracy points locate at positions with larger β and ω_c values compared to that of 1^st order (see Figs. 3(b) and (c)). Actually all the dispersion curves make a turn between positive and negative v_g, and most curves are truncated for 3^rd and 5^th order slow-light modes due to limited display range. Degeneracy point can be found for each dispersion curve with varying core-width W, and the corresponding wavelength at which slow-light mode is excited is extracted and displayed in Fig. 3(d). For the core-width range considered here (400-3400 nm), the 1^st order slow-light mode covers a wavelength-range of 2.02-17.16 µm, whereas the 3^rd and 5^th order covers a range 0.64-5.42 µm and 0.38-3.21 µm, respectively. So, consistent with the field plots in Figs. 1(c), (d) and Figs. 2(c), (d), the perfect absorption of the LWIR band can be attributed to the excitation of 1^st order (fundamental) slow-light mode alone, while that of the SWIR and MWIR bands can be attributed to the superposition of contributions from 1^st, 3^rd and 5^th order slow-light modes together (and small contributions from even higher orders, see Figs. 1(c) and 2(c) at λ = 2 µm). In addition, we see from Fig. 3(d) that wavelengths of 3^rd and 5^th order slow-light modes can extend, theoretically, well below 1 µm, i.e., into the visible and even UV range, which implies that the proposed absorber has the potential to work from LWIR all the way to the visible and even UV (<400 nm) wavelength-range, which will be discussed in the following.

Absorption performance of the proposed Al-ZnS multilayer sawtooth absorber in the short wavelength range was also examined, with absorption spectra in the 0.2-2 µm range shown in Fig. 4(a). Seen from the black curve, absorptance of the Al-ZnS multilayer absorber is close to 100% except for a narrow dip around 620 nm and some modulations in the 1.2-2 µm range, indicating good absorption performance in the UV, visible and near-infrared range. Absorption spectrum of the corresponding EMT model is displayed as red curve in Fig. 4(a), which is also close to 100% except for some small modulations in the 1.2-2.0 µm range. Interestingly, the EMT model does not reproduce the shallow absorption dip around 620 nm, demonstrating deviation of optical behavior between Al-ZnS multilayer absorber and effective medium model. Indeed, in the wavelength range considered here, especially for wavelengths below 0.8 µm, the presumption that the thickness of each alternating metal/dielectric layer is much smaller than the incident wavelength is not valid any more (note the optimized thickness of ZnS layer is 170 nm, which is comparable to the wavelength in this range). As a result, the EMT does not apply to wavelength range below certain value. While it is not straightforward to determine the wavelength below which the EMT fails, a look at the field distributions can provide some hints. Thus, we plot normalized magnetic field distribution at typical wavelengths in the 0.2-2.0 µm range for Al-ZnS multilayer and EMT model in Figs. 4(d) and (e), respectively.

 

Fig. 4. (a) Absorption spectrum of Al-ZnS multilayer sawtooth-like absorber (black) and EMT model (red) in the short wavelength range (0.2-2 µm), respectively. (b) Real (black) and imaginary (red) part of dielectric constants in the parallel direction calculated using the EMT. (c) Real (blue) and imaginary (green) part of dielectric constants in the perpendicular direction calculated using the EMT. (d) Magnetic field distributions of Al-ZnS multilayer sawtooth-like absorber at typical wavelength in the 0.2-2 µm range. (e) The same as (d), but for the EMT model. All sub-plots in (d) and (e) share the same color bar on the right.

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At a first glance, field distributions between Al-ZnS multilayer and EMT models are obviously different for wavelength smaller than 1.2 µm, especially at the wavelength of 0.62 µm corresponding to the small dip on the black curve. At this wavelength, magnetic field inside the Al-ZnS multilayer absorber shows multiple bright spots along Al layers, while magnetic field of the EMT model concentrates at the edges (especially at the bottom corners). If one checks charge distributions of the Al-ZnS multilayer structure at 0.62 µm, one finds that all Al layers demonstrate charge distributions with alternating signs around each bright spot of magnetic field (not shown), meaning that Al layers show obviously metallic property. The EMT model at the same wavelength, on the other hand, does not reproduce such spots inside the structure. Actually, if one checks the permittivity values of Al [50] and ZnS [45] (see Fig. 9 in the Appendix), it can be found that Al stays metallic, and ZnS is always dielectric for the entire wavelength range considered in this work (0.2-15 µm). However, if one calculates relative permittivity based on EMT anyway using dielectric constants of Al and ZnS, one obtains results shown in Figs. 4(b) and (c). From Fig. 4(b), it is found that the real part of relative permittivity in parallel direction changes sign around 1 µm, i.e., ɛ_{∥, r}< 0 for λ > 1 µm and ɛ_{∥, r}> 0 for λ < 1 µm. So, the EMT model behaves like a lossy dielectric below 1 µm and a lossy metal above 1 µm in the parallel direction, which explains the observed discrepancy at 0.62 µm. Indeed, seen from the field distributions at wavelengths of 0.62, 0.8 and 1 µm, the EMT model absorbs incident light around the surface region of the structure, demonstrating lossy dielectric property. On the contrary, magnetic field of the Al-ZnS multilayer absorber penetrates more inside the structure, and the Al layers always demonstrate metal property through checking charge distributions. Thus, it is inferred that EMT is not valid below the wavelength of 1 µm for the proposed absorber in this work. At λ = 0.4 µm, the EMT predicts a near-lossless dielectric with ɛ_{∥, i} ≈ 0 and ɛ_{⊥, i} ≈ 0 (see Figs. 4(b) and (c)), thus the trapezoid made from effective medium behaves like a dielectric cavity, which allows electromagnetic field to oscillate inside the structure (see Fig. 4(e) at λ = 0.4 µm). But the field distribution pattern inside EMT model is still different from that of Al-ZnS multilayer absorber at the same wavelength, due to the existence of metallic Al layers inside the Al-ZnS absorber. At λ = 0.2 µm, both Al-ZnS multilayer absorber and EMT model absorb incident light around the surface region of the structure, due to the rapidly increasing inter-band transition absorption of ZnS in the UV range [45]. For λ ≥ 1.2 µm, field distributions between the two kinds of models become somewhat similar, especially the excitation of high-order slow-light modes is seen in both models, providing a rough criterion for the EMT to become valid, i.e., the wavelength/thickness ratio needs to be greater than 7:1 at least. Nevertheless, although based on different absorption mechanisms for different wavelength regions (metal and dielectric loss for λ < 1 µm and slow-light effect for λ > 1 µm), the proposed Al-ZnS multilayer absorber demonstrates the potential to achieve ultra-broadband near-perfect absorption covering from LWIR all the way down to UV range.

In the following, we restrict ourselves in the 1-15 µm wavelength-range where EMT is valid for the proposed absorber. In practice, incident light does not always impinge the absorber at normal incidence. Therefore, it is necessary to study the dependence of absorber performance on incidence angle. Under TM polarization, we gradually increased the incidence angle from 0 to 85° by a step of 5°. Figures 5(a) and (b) display absorption maps under various incidence angles for Al-ZnS multilayer and effective HMM absorber, respectively, with a contour denoting the value of 90% absorptance. As can be seen in Fig. 5(a), absorptance keeps above 90% in the SWIR and MWIR bands and close to 100% in the LWIR band up to an incidence angle of 30°. From 40°, absorptance starts to drop below 90% at some wavelengths in the SWIR band, and a shallow absorption dip emerges around 9 µm in the LWIR band. As the incidence angle increases further to 60 and 70°, modulations in absorptance in the SWIR and MWIR bands become more obvious, and the absorption dip around 9 µm is widened, degrading the absorber performance. Nevertheless, average absorptance keeps above 90% and 80% when the incidence angle does not exceed 50 and 60°, respectively, proving good performance of the Al-ZnS multilayer sawtooth absorber under oblique incidence. Similar behaviors can be found for the EMT HMM model (Fig. 5(b)). Except for some minor difference in details, the effective HMM model reproduces most features of the absorption map of the Al-ZnS multilayer sawtooth absorber and performs a bit better in the sense of smoothness of absorption spectra.

 

Fig. 5. Absorption maps of (a) Al-ZnS multilayer and (b) EMT HMM model absorber with various incidence angles. The black contour in each plot indicates an absorptance value of 90%.

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A polarization-insensitive absorber is more desirable in practical applications, so we further designed a multilayer Al-ZnS absorber with a truncated pyramid-like shape (Fig. 6(a)). Since the structure unit has C₄ symmetry, its optical response should be polarization insensitive [32], which is also verified by our simulation results in the following. Based on previously obtained optimal geometric parameters of the sawtooth absorber (N = 20, P = W_l = 3500 nm, W_s = 400 nm, t_m = 10 nm and t_d = 170 nm), absorption spectra of the truncated pyramid structure under two orthogonal polarizations were simulated and displayed in Fig. 6(b). Under normal incidence, absorption spectra of TM (black curve) and TE (red curve) polarizations are basically the same, elucidating the insensitivity of the pyramid-like absorber to polarizations. The absorptance of the SWIR and MWIR bands are greater than 80%, while that of the LWIR band exceeds 95% for both cases. In addition, the same truncated pyramid structure is simulated using a homogeneous HMM model. As can be seen form the blue (TM) and green (TE) curves in Fig. 6(b), absorption spectra of the homogeneous HMM model overlap well those of the Al-ZnS multilayer absorber, validating once again the effectiveness of effective medium theory in the 3D case. Since the pyramid-like absorber has a square cross-section which can be regarded as a square waveguide core surrounded by air cladding, analysis of dispersion relations of such a square HMM core/air cladding waveguide with varying core size can in principle be conducted in a similar way as done previously for air/HMM/air slab waveguides. Magnetic field distributions at typical wavelengths of 4 and 12 µm under TM polarization, indicated by the blue diamond and blue circle on corresponding absorption spectrum, further confirm the contribution of 1^st and 3^rd order slow-light modes, similar to the case of sawtooth absorber (see insets of Fig. 6(b)). From the field distributions, it is found that the main contributing modes do not have nodes in Y-direction, i.e., no high-order oscillations in the direction perpendicular to the polarization direction. At 12 µm, there is only the fundamental slow light mode. At 4 µm, a closer look at the field maps at different depth of the pyramid-like structure reveals that there are indeed some higher-order modes in the direction perpendicular to polarization, but they are not well excited, and thus their contributions are neglectable. In this way, the physical mechanism of ultra-broadband absorption of the pyramid-like HMM can again be attributed to the excitation of multiple slow-light modes, similar to the case of air/HMM/air slab waveguides, so dispersion relation analysis will not be repeated for the pyramid-like structure here.

 

Fig. 6. (a) Schematic of the proposed Al-ZnS multilayer pyramid-like absorber. Inset on the right: a structure unit of HMM model based on EMT with dielectric constant labeled. (b) Absorption spectra of the Al-ZnS multilayer pyramid-like absorber under normal incidence for TM (black) and TE (red) polarizations. That of the HMM model is displayed as blue (TM, EMT) and green (TE, EMT) curve, respectively. Insets: slices of magnetic field distributions at 4 and 12 µm for HMM model under TM polarization. Absorption spectra of Al-ZnS multilayer pyramid-like absorber under various incidence angle for (c) TM and (d) TE polarized light. Insets show magnetic field distributions at the wavelength of 9 µm. (e) and (f), the same as (c) and (d), but for HMM model based on EMT.

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Then we studied absorption performance of the Al-ZnS multilayer pyramid-like structure at various oblique incidence angles under TM (Fig. 6(c)) and TE polarizations (Fig. 6(d)). Up to an incidence angle of 30° (black curves in Figs. 6(c) and (d)), the absorber performance is nearly the same as that under normal incidence for both TM and TE polarizations. When the incidence angle increases to 50°, the overall absorptance drops to around 90% in the LWIR band and 80% in the SWIR and MWIR bands, respectively. An absorption dip starts to appear around 9 µm wavelength for TM polarization (red curve in Fig. 6(c)), like the case of the sawtooth absorber (see Fig. 5(a)), whereas no such dip exists at the same wavelength region for TE polarization (red curve in Fig. 6(d)). This indicates the difference in optical behavior between TM and TE polarizations under oblique incidence. As the incidence angle continues to increase to 60 and 70°, absorptance drops further for both polarizations, and optical behavior over increasing incidence angle differs obviously for TM and TE polarizations. Absorption curves of TM polarization show more complicated evolutions (Fig. 6(c)), whereas those of TE polarization roughly keep their basic line-shapes and just drop in value as a whole with increasing incidence angle (Fig. 6(d)). This is understandable because a large angle forms between the electric field and Al-ZnS interfaces under TM polarizations at high incidence angles, while the electric field lies always parallel to the Al-ZnS interfaces for TE polarizations no matter how large the incidence angle is. Thus, dependence of optical behavior over incidence angle for TM and TE polarizations is different, which is further verified by the magnetic field distributions under TM and TE polarizations, shown as insets in Figs. 6(c) and (d), respectively. With the same wavelength of 9 µm and incidence angle of 60°, it is obvious that TM polarization excites both 1^st and 2^nd order slow-light modes (2^nd order becomes available due to oblique incidence) while TE polarization only excites the fundamental mode. Furthermore, Figs. 6(e) and (f) show absorption spectra of the EMT HMM model at oblique incidence for TM and TE polarizations, respectively. Except for some minor differences in details, the different optical behaviors for TM and TE polarizations under oblique incidence are well reproduced and are consistent with those of the Al-ZnS multilayer structures, including the excitation of different slow-light modes at the same wavelength under the same incidence angle (see insets of Figs. 6(e) and (f)). Despite the difference in line-shapes of absorption curves, the Al-ZnS multilayer pyramid-like structure retains an overall absorptance of 80% up to an incidence angle of 60°, demonstrating good absorption performance under large-angle oblique incidence.

3. Conclusion

In summary, based on a close examination of the unique material property of CMOS-compatible Al and ZnS in the wavelength range from UV to LWIR, we have proposed a sawtooth-like and a pyramid-like Al-ZnS multilayer absorber, whose near-perfect absorption covers all three main infrared atmosphere windows. The working principle of the Al-ZnS sawtooth-like absorber was explained with the excitation of multiple slow-light modes based on an effective air/HMM/air slab waveguide model. The sawtooth absorber keeps an overall absorptance above 90% up to an incidence angle of 50°. The pyramid-like structure demonstrates polarization insensitive absorption under normal incidence. While difference in optical behavior under TM and TE polarizations was observed for large incidence angle, the overall absorptance keeps above 80% up to an incident angle of 60°. Further analysis implies that the proposed Al-ZnS multilayer absorber has the potential to work from LWIR all the way down to UV range. With the progress in nano-fabrication technology and some successful experimental demonstrations of such pyramid-like structures [33,52], the proposed Al-ZnS multilayer absorbers may find applications in enhanced solar-energy harvesting, radiative cooling and multi-color infrared detection, etc.

4. Appendices

Comprehensive comparison of device proposed in this work and other representative works in recent years

Table 1. Comparison of representative theoretical and experimental works on the topic of broadband MPAs in recent years.

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Details of simulation set-up

The proposed sawtooth-like and pyramid-like Al-ZnS multilayer structures were simulated numerically using commercial software COMSOL Multiphysics based on finite element method. A 2D model is enough to simulate the sawtooth-like absorber due to symmetry of the structures. Since 2D models do not consume too much memory, thin metal layers (such as 10 nm-thick Al layers) were built as domains in the model, and very fine mesh sizes were assigned to the metal layers in the 2D case (maximal mesh size = 4 nm). As the 2D model is solved quite quickly, geometric parameter sweep is also done with 2D models to obtain the optimized absorber design (see the next section).

The pyramid-like structures, in contrary, have to be simulated with 3D models, which need more careful consideration and will be described with more details in the following. As shown in Fig. 7(a), (a) 3D model was set up, and a perfect matching layer (PML) was put at the top of the model to absorb any reflected waves from the structure. Below PML, a periodic port was set to lunch plane waves to the structure, and the same port is used to calculate absorptance of the structure. The incidence angle can be scanned from 0 to 89° at the port, while incident polarization can also be switched between TM and TE. Figure 7(b) shows one pair of periodic boundary conditions in y-direction, and another pair of periodic boundaries in x-direction were set similarly (not shown). Type of periodicity was set as Floquet periodicity, and k-vector for Floquet periodicity was from the periodic port.

 

Fig. 7. Simulation set-up showing (a) the periodic lunching and listening port, (b) periodic boundaries in y-direction, (c) thin Al layers modeled as boundaries using transition boundary conditions and (d) the meshes, where blue and red color represent smaller and larger mesh sizes, respectively. V_mesh, volume of meshes.

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A tricky point that needs to be figured out is that 10 nm-thick metal films are difficult to simulate directly in the 3D case based on finite element method, which discretizes the structure with small meshes. If one builds thin metal layers as domains, then the laterally large (∼3 µm) thin (∼10 nm) metal films require a huge number of mesh elements to resolve, resulting in so many degrees of freedom (DOF) that a desktop workstation cannot afford. Thus, we modeled thin Al layers as boundaries instead of domains with corresponding thickness and dielectric constants assigned to them using transition boundary condition (Fig. 7(c)) [53], which greatly reduces DOF of the 3D models. Finally, to ensure good convergence of the simulations, the mesh size in different regions was carefully assigned. Specifically, a maximal mesh size of λ₀/( λ₀×1 µm^-1 + 8) was assigned to the air region, so that the maximal mesh size varies from λ₀/9 to λ₀/23 when λ₀ sweeps from 1 to 15 µm, and the maximal mesh size of the pyramid structure is limited to 100 nm, ensuring good resolution of electromagnetic field distributions inside the structure (Fig. 7(d)). In general, the typical DOF of such pyramid structure model is around 6.5 million, and the memory consumption is around 200 GB, affordable with our workstation equipped with 256 GB of memory.

Extensive parameter sweep

Extensive sweep of geometric parameters was conducted to optimize the performance of the Al-ZnS multilayer sawtooth absorber. First, the influence of total number of layers N on the absorption spectra was studied. Here, we assumed a parameter combination of P = 4000 nm, W_l = 3000 nm, Ws = 500 nm, t_m = 10 nm and t_d = 170 nm. With all other structural parameters fixed, the total number of superimposed layers N was scanned, and the results are shown in Fig. 8(a). When the number of layers is small (e.g., N = 5), the device does not provide good absorption in the entire wavelength-range of interest, indicating the invalidity of effective medium theory with small number of layers. When N increases to 12 (white dashed line), the overall absorption performance improves significantly, and broadband absorption covering all three atmosphere windows is already established. As the number of layers further increases to 15, 20 and 30 layers, the absorptance in LWIR band becomes close to 100% and very smooth with increasing N. However, from the perspective of fabrication feasibility, a moderate number of total layers is selected, i.e., N = 20. In the following, all the structures consist of a total layer of 20. Second, we considered whether the bottom edge length W_l and the period P needs to be equal. We fixed W_l = 3000 nm and changed P. Since P can only be larger than W_l, we increased P from 3000 nm to 6000 nm in a step of 100 nm. As shown in Fig. 8(b), as P increases, although the maximum absorptance in the LWIR band remains very close to 100%, the absorption bandwidth gradually decreases. Moreover, the absorptance in the SWIR and MWIR bands gradually decreases with increasing P. Therefore, it can be concluded that the absorption performance is the best when P equals to W_l, i.e., the period of the structural unit should be equal to the bottom edge length of the cross-sectional trapezoid. Third, the optimal value of period P (equals to W_l) needs to be determined. We kept W_l and P identical and changed P from 2000 nm to 5000 nm in a step of 100 nm, with the results shown in Fig. 8(c). It is found that when P = W_l = 2800 ∼ 4200 nm (see white dashed lines in Fig. 8(c)), optimal absorption performance can be achieved. If P is too small or too large, the absorption bandwidth in the LWIR band becomes smaller. Therefore, a moderate value of W_l = P = 3500 nm is finally selected as the optimized parameter. Next, we investigated the influence of the top edge length of the cross-sectional trapezoid W_s on the absorption characteristics. We fixed the parameter W_l = P = 3500 nm and changed W_s from 0 to 1000 nm in a step of 50 nm and obtained results shown in Fig. 8(d). At a first glance, the absorptance in the SWIR and MWIR region has a relatively obvious decrease for W_s greater than 600 nm. However, for W_s in the range of 0 to 600 nm, the influence of W_s on the absorption characteristics is not significant. In order to select an optimal W_s value quantitatively, we conducted integration to calculate area under the curve for the wavelength region of three atmosphere windows (SWIR, MWIR and LWIR bands). Then, the optimal value of W_s = 400 nm can be selected from the integral values (not shown). As a matter of fact, the difference among cases of W_s in the range of 200 to 600 is neglectable, meaning that the tolerance to size deviation is good so long as the top edge length does not exceed 600 nm. Then, we investigated the effect of the thickness of metal layer t_m, in the range of 5∼50 nm, on the absorption spectra. As shown in Fig. 8(e), we found that the thinner the metal layer, the better the absorption performance. However, from experimental perspective, when the thickness of metal layer is too small (<10 nm), it will be difficult to obtain a continuous metal film using common deposition methods, leading to deviation from simulation result. So, we chose t_m = 10 nm as a compromise. Finally, we studied the effect of thickness of the dielectric layer t_d and found that when the dielectric thickness exceeds 100 nm, the difference among different t_d cases become not distinct. For example, for t_d values in the range of 150 to 300 nm, little difference is observed in the LWIR absorption band, whereas absorption characteristics of SWIR and MWIR bands demonstrate some fluctuations. Again, like what we did to select W_s quantitatively, we calculated area under curve for all t_d cases and picked t_d = 170 nm as the optimal dielectric thickness according to the integral values.

 

Fig. 8. Absorption maps under extensive parameter sweep of (a) total number of layers N, (b) period P, (c) bottom edge length of trapezoid W_l, (d) top edge length of trapezoid W_s, (e) thickness of metal layer t_m and (f) thickness of dielectric layer t_d, respectively, while keeping all other parameters the same.

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So far, a combination of optimized geometric parameter is obtained as following: N = 20, P = W_l = 3500 nm, W_s = 400 nm, t_m = 10 nm and t_d = 170 nm. Its corresponding device has an average absorptance greater than 90% in the SWIR and MWIR bands and close to 100% absorptance in the LWIR band (black curve in Fig. 1(b)).

Dielectric constants of Al and ZnS in the 0.2-15 µm range

 

Fig. 9. Dielectric constants of (a) Al and (b) ZnS in the 0.2-15 µm range.

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Funding

Beijing Municipal Science and Technology Commission (Beijing Nova Program of Science and Technology, Z191100001119058); National Natural Science Foundation of China (61905273).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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