1. Introduction

Long-wave infrared (8–14µm), also known as thermal infrared, is one of the most important atmosphere windows in infrared and has enormous potential applications from thermography to astronomy. Traditional light absorption is mainly due to the intrinsic absorption of materials and it’s rare to see a near unity absorption. In recent years, the emergence of perfect absorbers in the long-wave infrared has attracted much attention in various fields such as sensors [1], absorbers [2–4], detectors [5,6]. The absorption in natural materials mainly depends on the interaction length with photons or optical fields, and thus high-efficiency absorption generally indicates large size. This imposes inevitable restrictions on the device integrations. Surface plasmons is a kind of highly localized electromagnetic wave propagating at a metal-electrode or metal-air interface in near infrared or visible. Due to its outstanding ability to confine light at subwavelength scale, surface plasmons has been widely used in the enhancement of photodetectors [7], super imaging [8–10] and photonic integrated circuits [11]. Metasurfaces, which can almost arbitrarily control the phase, amplitude, and wavefront polarization of electromagnetic waves [12,13], have been conducted as an effective tool to manipulate light in subwavelength scale [14,15]. With compact configuration and flexible structure design many devices have been proposed, such as optical flat lens [16–18], polarizer [19] and controllable apparatus [20,21]. Phase gradient metasurfaces which are composed of gradual phase-change structures with constant gradient in a supercell provide a new route for the efficient free space light coupling [22–25]. However, the conventional plasmonic absorbers inherently operate within a broad bandwidth and are always arranged as cavities to increase the absorption efficiency. To some extent, the momentum mismatch prevents the free space light from coupling to the surface plasmons [26,27] and limits the absorbance. Based on a sandwich structure composed of “H” metal/dielectric layer/metal layers [23], researchers proposed a method to efficiently convert the incident light to surface waves through progressive phase-mutant structures in microwave. This platform operates at one single wavelength and absorption is a nuisance. Li et al. reported a novel design on the bidirectional perfect absorber by converting the free-space wave into evanescent wave at single wavelength. This way of eliminating the transmittance and reflectance is different from the method used by traditional absorbers with a sandwich configuration or coherent perfect absorption ways [28]. However, single-band absorbers have limitations on applications like spectroscopic detection of inflammable and explosive materials that have distinct absorption or “fingerprints” at multiple wavelengths. Traditional dual-band absorbers can be roughly categorized into plasmonic [29–32] and dielectric ones [33], in which electric/magnetic resonances are necessarily excited.

In this paper, different from the previously reported dual-band absorbers, our phase gradient design has narrower FWHMs. Besides, the number in the supercell can also be changed in our design as long as the phase could cover 2π. And compared with conventional dual-band absorbers configurations we propose a novel long-wave infrared dual-band absorbers based on the elaborately designed phase gradient metasurface. Incident lights are effectively coupled into the structure and two distinct absorption peaks of 0.365 and 0.986 are respectively observed at 8.095 µm and 14.121 µm. Eigen mode calculations are in well agreement with full wave simulations to confirm our phase gradient metasurface design. Besides, the role of phase gradient metasurface in the enhancement of absorption are separately and clearly demonstrated.

2. Results and discussion

As shown in Fig. 1(a), a reflection-type phase gradient metasurface is designed. It is composed of periodic supercells as indicated in Fig. 1(b). Each supercell consists of five individual nanoparticles with different lengths. The phase coverage of single unit cell through sweeping the lengths while fixing the width cannot realize 2π phase coverage. This is because the length sweeping direction is perpendicular to incident polarization. However, the proposed supercell successfully achieves the 2π phase coverage. An AlO_x spacer with refractive index of 1.5 [21] and thickness of 1.9 µm is placed between the top nanoparticles array and the reflection gold film. The candidate like NaCl can also be adopted which both have refractive index around 1.5 and are transparent within 1–15 µm [34]. Period of the phase change unit cell is L_x=1.2 µm and L_y=3.0 µm. The length of all nanoparticles is fixed with W_x=0.9 µm and the width of the five gold nanoparticles are W_y=0.5 µm, 1.07 µm, 1.27 µm, 1.5 µm and 2.6 µm, respectively. The periodic of supercell is P_x=6 µm and P_y=3 µm. The metasurface is normally illuminated with x-polarized incidence. Finite element method is employed to conduct the simulations. The scattering boundary condition is used as the excitation plane and periodic boundary conditions are applied along x and y directions. An inserted plane between the excitation and the structure is used to recording the reflected energy R. Therefore, the absorption can be calculated as A=1-R since no energy is leaked. To verify this, the energy integration of the whole structure is conducted. This is a more straightforward way to calculate the absorption and it is in excellent agreement with the previous method. There is no additional leaking channel.

 

Fig. 1. Schematic of single unit-cell phase gradient metasurface. (a) Schematic illustration of the proposed absorber. The supercell which are composed with five different phase change unit cells. The red wavy arrow represents the propagation of converted surface wave. (b) Schematic of the phase change unit cell. The thickness of gold nanoparticles is 320 nm. (c) phase coverage of the metasurface design at wavelengths λ=8.083 µm and 8.10 µm. (The horizontal coordinates X represents the length of a supercell period from left to right)

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With the metasurface design, each unit cell introduces an abrupt phase change while the overall effect of the periodic supercells leads to a constant phase gradient ξ=2π/P_x, P_x is the period of the supercell along x axis. The phase change of each unit cell in the super period is not evenly picked cover the whole 2π. However, it can still provide an average phase gradient and convert the incident light to surface waves. It will lower the absorption efficiency and this is why the two absorption peaks are not so high. The parallel wave vector of the reflected wave is k_x.=ξ, as shown in Fig. 1(c) the overall phase change is 2π around the wavelength of 8.1 µm. With normal incidence, the reflection angle θ can be derived as θ=arcsin(k_x/k₀), k₀=2π/λ is the vacuum wave vector. According to this equation there is a critical condition ξ ≥ k₀ for zero reflection. In other word, when the period of the supercell is smaller than the operating wavelength, the normal-incident propagating wave in the air will be converted to surface wave supported by the metasurface and finally absorbed.

As shown in Fig. 2(a), the phase gradient metasurface we have designed has a sharp absorption peak near 8.1 µm, and the full width at half maximum (FWHM) of absorption peak is 0.031 µm. With the inset figure, it has two absorption peaks, which locate at λ=8.083 µm with an absorption of 0.78 and λ=8.1 µm with an absorption of 0.9, respectively. From the phase change plot shown in Fig. 1(c), both wavelengths at λ=8.083 µm and λ=8.1 µm have a phase coverage of 2π over subwavelength period. The metasurface both provides an additional momentum to the incident light at two wavelengths and thus gives rise to the surface wave. Different from the phase coverage at λ=8.1 µm, at out-of-resonance wavelengths, 2π phase coverage is not achieved. Thus, the phase-gradient condition is not satisfied. The incident light would be reflected but not localized near the metasurface. From the electric field distribution in Fig. 2(b), the energy at the absorption peaks mainly localizes around the surface of the structure. The eigenfrequencies calculated are f₁=37.093 THz (8.087 µm) and f₂=37.006 THz (8.107 µm) which agree well with the absorption peaks positions in full wave simulations. The electric field distributions from eigenmode calculations as shown in Fig. 2(c) also confirm the simulation results in Fig. 2(b). To have a direct observation of surface wave propagation along the metasurface, in Fig. 2(d) the electric field distributions on x-y planes are also illustrated. It can be observed that the parallel wave vector k_x≈1.48k₀ which is in consistent with ξ. The normal incident plane wave is successfully converted into surface wave and travels along the structural interface.

 

Fig. 2. Realization of single absorption with phase gradient metasurface. (a) The absorption spectrum of phase gradient metasurface. The inset shows the details of around wavelength 8.1 µm. There are two peaks at λ=8.083 µm with 0.78 absorption and λ=8.1 µm with 90% absorption. (b) Electric field distributions on x-z plane at wavelengths 8.083 µm and 8.1 µm, respectively. (c) The electric filed distributions at f₁=37.093 THz (8.087 µm) and f₂=37.006 THz (8.107 µm) with eigenfrequency calculation, respectively. (d) Electric filed distributions on x-y plane near the metasurface at λ=8.083 µm and the λ=8.1 µm, respectively. The metasurface is illuminated with x-polarized normal incidence. (e. f) Phase coverage (X represents the length of a supercell period) and electric field distribution map from out-of resonant peak wavelength, respectively.

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As to the absorption peak splitting at λ=8.083 µm and 8.1 µm, we attribute this to interaction of the excited surface wave and the dipole-like resonance. To separately investigate the mechanism behind the two adjacent absorption peaks, we arranged the structures with double unit cells as shown in Fig. 3(a). The subwavelength property at λ=8.095 µm does not exist since the supercell period is 12 µm in this situation. The surface wave coupling condition is not satisfied for normal incidence. Therefore, at λ=8.095 µm the absorption is attributed to the dipole-like resonance. The absorption spectrum of double unit-cell metasurface in Fig. 3(b) confirms our analysis above. There is still an ultrathin narrowband absorption peak near 8.095 µm but with only 0.36 absorbance and FWHM=0.026 µm. Moreover, there is a near unity absorption peak around λ=14.121 µm, and its FWHM is 0.058 µm.

 

Fig. 3. Absorption of double unit-cell phase gradient metasurface. (a) Schematic of the double unit-cell phase gradient metasurface. P_x and P_y are the super period along the x-axis and y-axis, respectively. (b) The dual-band absorption of the phase gradient metasurface absorber. The absorption can be up to 98.6% at λ=14.12 µm and 36.5% at λ=8.095 µm, respectively. (c) Electric field distributions on the x-z plane at two absorption wavelengths. (The X represents the length of a supercell period) (d) The phase profiles of the overall metasurface at two absorption wavelengths.

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To demonstrate the difference of these two absorption peaks, the phase change of each unit cell for the two wavelengths are depicted in Fig. 3(c). For the wavelength at λ=8.095 µm the phase changes of unit cells cannot realize a constant gradient for the incident wave vector compensation. However, the phase change distributions at λ=14.121 µm satisfy the critical condition for the surface wave conversion. The super period of the metasurface is subwavelength and the phase changes arrangement realizes a constant gradient. Here, for the absorption peak at λ=14.121 µm we still attribute this to the hybrid mode that arises from the surface wave from the phase gradient and the dipole-like resonance from the unit cells. The electric field distributions for both absorption wavelengths in Fig. 3(d) further confirms the hybrid mode analysis.

To confirm the absorptions at two wavelengths, we calculated the eigenfrequencies of the double unit-cell metasurface in Fig. 4(a). Two frequencies are found: 37.063 THz (8.094 µm) and 21.237 THz (14.126 µm). They are very close to two absorption peaks in the simulations. In order to have a direct observation of the excited surface wave at 14.121 µm, the electric filed distributions on x-y plane are also illustrated in Fig. 4(b). The wavelength agrees well with that from the phase gradient compensation.

 

Fig. 4. Characterizations of dual-band absorptions. (a) The calculated eigenfrequencies’ electric field distributions of the double unit-cell metasurface. (b) E_x distribution of the metasurface at λ=14.121 µm. (c. d) The absorption dependence on the incident polarization states at the two absorption peaks. (e) The absorptions of each unit-cell periodic arrays at two wavelengths for comparison. (f) The absorption dependence on the angle of oblique incident.

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Moreover, in order to distinguish the absorption contributions of the phase gradient metasurface from the overall absorption of periodic arrays (in each array there is only one type of unit cell), the absorptions for each unit-cell array are calculated in Fig. 4(e) at two absorption wavelengths, respectively. It can be seen that for wavelength λ=8.10 µm the absorption efficiencies for all unit cells are below 0.01 and for wavelength λ=14.121 µm around 0.02, which are far less than those with phase gradient arrangement. The absorption dependence on the incident polarization states at wavelengths λ=8.100 µm and λ=14.121 µm are also illustrated in Fig. 4(c) and (d). As the incident polarization state changes from along x-axis to y-axis. The absorption at both wavelengths has a consistent and dramatic decrease, which further confirms the absorption enhancement role of the phase gradient metasurface in the dual-band absorber. In addition, we also have studied the absorption of the different incident angle, as show in Fig. 4(f), With the increase of incident angle, it is found that both absorption peaks shift toward the middle. Besides, the absorption peak on the left gradually increases and the other one decreases. It can attribute this to the coupling condition changing and resonances are satisfied at other wavelengths. For one hand, the dual band absorbers based on the phase gradient metasurface provides another efficient method to realize dual-band absorption in long-wave infrared. The phase gradient metasurface shows an effective role in enhancing the absorptions in comparison with those periodic arrays which consists of only one type of unit cells. On the other hand, most of reported broadband [35] or narrow-band absorbers [36] are based on plasmonic resonances. Due to the inherent broad dispersion of plasmons, the full width at half maximum is usually larger than 100 nm in long wavelength infrared region. However, the phase gradient metasurface we proposed realize an ultra-narrow bandwidth with FWHMs less than 60 nm.

3. Conclusion

In this paper, we propose a novel phase gradient metasurface design to achieve dual band absorption through exciting hybrid mode. Different from previously reported the metasurface absorber, surface wave together with the excitation of the dipole-like resonance is utilized to realize dual-band absorption at the long-wave infrared. Compared with the absorption properties of the unit-cell array, we confirm that the phase gradient metasurface plays a crucial role in enhancing the absorption efficiencies. Though the proposed device works in the long-wave infrared, this kind of absorber could also be extended to other wavelength bands such as microwave and terahertz through changing the structural parameters.