1. Introduction

Metamaterials have attracted extensive attention in recent years due to the ability to display exotic properties with extraordinary effective permittivity and conductivity that are unavailable in nature and enable negative refraction [1,2], invisibility cloaks [3], superlenses [4], etc. Especially, perfect absorbers with zero reflection and zero transmission are developing rapidly since the first propose by Landy in 2008 [5]. Different absorbers, including polarization insensitive/dependent absorbers [6,7], broad/narrowband absorbers [8–10], hyperbolic absorbers [11], plasmonic absorber [12,13], and van der Waals (vdW) absorbers [14,15] have been investigated from microwave range [16], through terahertz [17], infrared [18] and into the visible [19]. However, among them most of the reported absorbers are based on plasmonic resonances or lossy dielectrics and are short of tenability [5,6,13,20,21]. The absorption performance is fixed and cannot be tuned in a controllable way, such as voltage, external light, or temperature. Some absorbers based on the vdW materials (such as graphene) can be tuned but with limited working bandwidth. They always need external electric bias, which makes the absorbers are quite cumbersome [22–24]. With these restrictions, the absorbers that are compact and have tuned dual wavelength bands are much more desired. Recent researches show that the absorption can be manipulated by using specific materials rather than changing the geometry of the device for impedance match [25,26]. In this respect, phase change materials provide an effective way to introduce tunability since their optical properties change significantly with external stimuli. As a typical representative, vanadium dioxide (VO₂), exhibits many fascinating opportunities which originate from dielectric to metal transition occurring while switching from monoclinic phase to rutile phase across the critical temperature T_c(T_c=68°C) [27]. Its conductivity has a change of five orders in magnitude upon the phase transition within picosecond [28,29]. Compared with electrically controlled graphene absorbers which need external bias [22–24], the VO₂ based absorbers are much more flexible and compatible. Besides, the natural vdW material-hexagonal boron nitride (hBN), which provides an ultra-compact alternative-hyperbolic surface phonon polaritons(hSPPs) to steer the mid-infrared light, has emerged as an interesting topic to control the light–matter interactions [30–33]. It respectively supports two types of hSPPs in the lower (ε_⊥>0, ε_//<0) and upper (ε_⊥<0, ε_//> 0) reststrahlen bands [34] due to the out-of-plane and in-plane E phonon vibrations. Different from their plasmonic counterparts, the phonon polaritons offer a large light-momentum cutoff in mid-infrared introduced by the interatomic spacing in hBN lattices. Therefore, the combination of VO₂ and hBN opens a new possibility to control the absorption in a dynamical and very compact manner in the mid-infrared [35,36]. The pioneering work proposed a bi-functional and tunable metamaterial absorber in mid-infrared based on the hBN/graphene/hBN heterostructure [37]. However, the nearly perfect resonant absorption function is possible only with metallic VO₂. Another work based on graphene-hBN hyper crystal is reported with perfect absorption only possible at certain fixed wavenumber and incidence angle [38]. All the above mentioned mid-infrared absorbers are with restrictions on tunability and number of operating bands. It’s worth mentioning that absorbers based on traditional polaritonic materials (such as GaAs, SiC) are also proposed with one-way transparent manners [39–41]. With the above discussions, tunable dual band absorbers with compact configurations are very expected.

Here, taking advantage of the phase change property of VO₂ and the extremely tight field confinement of hSPPs in hBN, we propose a tunable polaritonic perfect absorber with stacked VO₂ and hBN layers in the mid-infrared. Two absorption peaks at 7.2µm and 12µm are observed with the dynamic control of temperature above and below the critical point. The plasmonic resonance at 12µm in VO₂ above critical temperature and polaritonic resonances at 7.2µm in hBN under critical temperature are alternatively demonstrated. The absorption dependencies on the polarization and incident angle are also investigated.

2. Structure and simulation method

As shown in Fig. 1(a), the metamaterial absorber consists of three functional layers: a 30nm-thick and 460nm-radius hBN disc, a 530nm-thick and 920nm-width active VO₂ square block and an optically thick(100 nm) Au slab. Dielectric layers of 130nm-thick and 220nm-thick CaF₂ are alternatively placed between the functional layers for impedance match purpose. The simulation is conducted with finite element method (COMSOL Multiphysics). Periodic boundary conditions are employed in x and y axes directions. The period of the device is P=1000 nm. In simulation, the permittivity of Au [42] in the mid-infrared is introduced by the Drude model ${{{\mathrm {\varepsilon}} }_{\textrm{Au}}} = 1 - \frac{{{{\mathrm{\omega}}}_\textrm{p}^2}}{{({{{{\mathrm{\omega}} }^2} + {{\textrm{i}}{\mathrm{\gamma}} {\mathrm{\omega}} }} )}}$, where ω_p=1.37×10¹⁶ Hz, and γ=4.07×10¹³ Hz. The refractive index of CaF₂ is 1.4 [43] . VO₂ has negative real part of permittivity and large optical loss when T > T_c while as a low loss dielectric when T < T_c [29] . The transmission coefficient S₁₂ and reflection coefficient S₁₁ are extracted from the simulations. The absorption A can be obtained by A=1-T-R, where transmissivity T=|S₁₂|² and reflectivity R=|S₁₁|²_.

 

Fig. 1. Schematic of the tunable polaritonic perfect absorber and absorption spectra. (a) Schematic view of the unit of designed absorber and the incident light polarization configuration. (b) Simulated absorption at T < Tc(black) and T > Tc (red), respectively. Numerical calculations of normalized optical impedance and reflection of the designed absorber at T < Tc (c) and T > Tc (d). The impedance is perfectly matched to the vacuum at resonant wavelengths both at 7.2µm and 12µm. The black solid lines, red dashed lines and blue triangle lines represent the real part of the impedance, imaginary part of the impedance and reflectance, respectively.

Download Full Size | PDF

In Fig. 1(b), two perfect absorption peaks occur at 7.2µm when T < T_c, and at 12µm when T > T_c. Similar to the pioneering works on perfect matching of input impedance for one-way quasiplanar [40] and broadband absorbers [44,45], the formation of perfect absorption can be interpreted by analyzing the optical impedance at absorption peaks. The impedance of our absorber can be calculated from the scattering parameter results by Z= [ (1+S₁₁)²-S₂₁²]/[(1-S₁₁)²-S₂₁²]^1/2 and can be simplified to Z=(1+S₁₁)/(1-S₁₁) due to the presence of the Au layer (S₂₁=0). The results of reflectance and the real and imaginary parts of the impedance are illustrated in Figs. 1(c) and 1(d). The impedance of the absorber is normalized to that of the free space Z₀, which is about 377Ω. The real part of normalized impedance is 1 and imaginary part is nearly 0 at resonant wavelengths of 7.2µm and 12µm corresponding to T < T_c and T > T_c, respectively. The impedance match at resonant wavelengths indicates the well design of our structure.

3. Results and discussions

Figures 2(a) and 2(b) show the electric field distributions of the xz cross sections of the absorber at the resonant wavelengths when T < T_c and T > T_c. Below the T = T_c, the VO₂ behaves as dielectric and the hyperbolic surface phonon polaritons are excited. As shown in the hBN slab, the excited phonon polaritons propagate in the hBN layer. The electric field is highly localized in the nearby of the hBN disc array. Through optimizing the parameters to satisfy the phase compensation the surface polaritonic resonance is generated in this area due to the constructive interference, leading to the perfect absorption at the resonant wavelength 7.2µm. For the other peak at 12µm, the perfect absorption originates from the plasmonic resonance around the VO₂, which shows a metallic property at temperature above T = T_c. The effective impedance of the designed metallic structure matches to that of the free space, thus minimized the reflections. The electric field is efficiently localized in the edge of the VO₂ square block. The electromagnetic mode in this situation is different from that at T < Tc. The hyperbolic surface phonon polaritons in the hBN are not excited due to the phase change of VO₂, leading to little absorption around 7.2µm. Here we want to emphasize that the wavelength of the phonon polariton is much shorter than the plasmon polariton. The detail of the phonon polariton pattern is depicted clearer than the plasmons.

 

Fig. 2. The physical mechanism behind the perfect absorber. Electric field distributions of xz cross sections at 7.2µm(a) and 12µm(b). The difference of field confinement corresponds to different absorption behaviors of the electromagnetic resonance. The absorption(A) for the designed structure at T < Tc (c), and T > Tc (d), where ‘all’ (black), ‘hBN’(red), ‘VO₂’ (blue) correspond to the calculated absorptions in the whole structure, in hBN layer and in VO₂ layer, respectively.

Download Full Size | PDF

The absorption mechanism can be further explained by the power consumption in each layer. Since the absorbed power is related to the divergence of the Poynting vector in the materials, it is calculated directly through P_abs=1/2ωɛ₀Im(ε)|E|² for non-magnetic materials [46,47], where ω is the frequency, Im(ε) is the imaginary part of the relative permittivity and |E| is the magnitude of electric field. The absorption in each layer of the structure is calculated through the division of the volume integral of the P_abs in each layer to the incident power with FEM method. As shown in Fig. 2(c), the absorption peaks at 7.2µm are much narrower than those at longer wavelength at T > T_c. Most energy is absorbed in the hBN layer (red line), which indicates the excitation of the hSPPs. Besides, a much lower absorption peak at 13µm arising from the 2nd polaritonic mode of hBN is observed. However, as shown in Fig. 2(d), most of the energy is absorbed by the metallic phase VO₂ layer due to the excitation of the surface plasmons. The broadband property of the absorption peak at 12µm agrees with the plasmonic resonance. Despite there is little absorption (∼4%) in hBN, it's negligible compared to the absorption of VO₂ layer.

Figure 3 shows the absorption with oblique incidences ranging from 0° to 60° for both transverse electric (TE) polarized and transverse magnetic (TM) polarized light at T < T_c and T > T_c. Under the condition of T < T_c in which VO₂ is dielectric, the strong absorption originates from the efficient hSPPs excitation with the in-plane incident electric field. For thin hBN discs, large optical absorption occurs when phonon polaritons are effectively excited and the hBN disc layer here forms an effective impedance-matched layer on the surface. The absorption maintains up to 85% at 60° incidence which behaves moderate in comparison with reported papers [47,48]. And the absorption peak gets wider since the enhanced absorption of VO₂ near 7µm for TE polarization with the angle of incidence increased.

 

Fig. 3. The absorption dependencies on wavelength and incidence angle. The simulated absorption of the proposed perfect absorber when incident angles θ ranging from 0° to 60° for TE polarization at T < T_c(a), T > T_c(c)), and TM polarization at T < T_c(b), T > T_c(d).

Download Full Size | PDF

Different from the situation of dielectric phase VO₂, the absorption sensitivity on the polarization state is much more obvious at T > T_c. As shown in Figs. 3(c) and 3(d), the plasmonic resonance is excited over a broad band and maintained high absorption within a wide range of incidence angles. Compared with the absorption in Fig. 3(c), there is a bending phenomenon in Fig. 3(d). It can be explained by the plasmonic resonance excitation condition. Compared with the wave vectors of hSPPs, the wave vector of surface plasmon polaritons (SPPs)- k_spp is much smaller and approximates that of free space k₀. This means the change of in-plane wave vector component k_0// from the incident light angle variation poses a much more significant effect on the plasmonic resonance excitation from the formula k_spp=k_0//+k_a, where k_a=2mπ/P (m=0, ±1, ±2…) is the additional vector from the periodic structure. As shown in Fig. 3(d), the resonant wavelength has a blue shift of 1.5µm with incident angle changing from 0° to 60° for TM polarization. Because there is no change of k_0// for TE incidence, the resonance is almost unchanged as shown in Fig. 3(c). Despite the absorption is polarization and incident angle dependent, the absorption still maintains at a high level due to the efficient excitation of hSPPs and SPPs for both dielectric phase and metallic phase of VO₂. Here we want to mention that the reason why the full width at half maximum(FWHM) of hBN supported hSPPs resonance is much narrower than that of SPPs resonance excited in VO₂ is due to the different dispersion relations of hBN and VO₂. The real part of the relative permittivity of VO₂ is negative from 5-15µm while for hBN the negative permittivity band only exists in the two narrow reststrahlen bands. Therefore, the excited peak at 7.2µm is much narrower than the peak at 12µm.

From the above discussion, the absorption peaks at 7.2µm and 12µm correspond to the resonances of the hSPPs in hBN and SPPs in VO₂, respectively. To have a direct look at the robustness of the absorber, the variations in the geometrical parameters of hBN and VO₂ are investigated. As shown in Figs. 4(a), 4(c), and 4(e), the absorption is more sensitive to the radius of hBN but has little dependence on the variation of d_v and l for T < T_c. This can be attributed to the hSPP excitation. Even if the radius has an ofset of 0.1µm, the absorption is still larger than 0.89 and the resonance shift is small. However, the situation is totally different for T > T_c (as shown in Figs. 4(b), 4(d), and 4(f). There is almost no absorption efficiency and resonance shift effect on the hBN radius change since the dominant absorption arises from the plasmonic resonance of metallic phase VO₂. Although the absorption has little change in Figs. 4(d) and 4(f), the plasmonic resonances suffer from large deviations when changing the VO₂ thickness and width. The maximum resonance shift reaches 4µm for VO₂ width changing 0.06µm. The geometrical parameters sweep results suggest that our polaritonic absorber is well tunable, compact and robust in the mid-infrared. According to the investigation of absorption dependence on the structural parameters, the absorber has high tolerance of fabrication errors. Since the linewidth is larger than 80 nm, the structure is possible to be implemented with current state of the art material deposition and fabrication methods. However, the absorption wavelength of the structure can still be substantially adjusted through dramatically changing the geometric parameters of the hBN and VO2 layers. It is also possible to tune the absorption by the thickness of the CaF2 layers.

 

Fig. 4. The absorption tolerance of the structural parameters. (a), (c) and (e) show the absorption spectra as functions of the hBN disk radius r, the VO₂ block thickness d_v, and the VO₂ block width l below T = T_c, respectively. (b), (d) and (f) accordingly show the absorptions as functions of the three parameters above T = T_c.

Download Full Size | PDF

4. Conclusion

In summary, we propose a novel tunable polaritonic perfect absorber in mid-infrared utilizing surface plasmon polaritons of metallic VO₂ and hyperbolic surface phonon polaritons of hBN. The spectral position of the absorption peaks can be dynamically switched by the temperature variations. The narrow perfect absorption peak occurs at 7.2µm due to the excitation of hSPPs in hBN layer at T < T_c. Most energy is confined and absorbed in the vicinity of hBN slab. For T > T_c, the broad absorption peak at 12µm is achieved through the SPPs excitation with metallic VO₂. More than 96% absorption are performed in the VO₂ layer. The incident electromagnetic wave energy is efficiently confined in the edge of VO₂ layers. Meanwhile, the absorber reveals an excellent absorption stability over a wide incidence angle range being about 60° for both TE and TM polarizations. The structural parameters sweep also suggests the robustness of the design. The method to excite two different polaritons offers another choice to design tunable nanophotonic devices for optical switching, filtering and sensing in the mid-infrared.