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Abstract
We proposed a metamaterial absorber composed of an array of trapezoid multilayered grating Au and InP on top of an opaque substrate, which covers two atmosphere-transparent-window bands with appropriate modulation of geometric parameters. The absorption higher than 0.8 is from 3.5 to 4.8 µm and 7 to 14.3 µm. From the effective medium theory and dispersion relation, the reason of the broad-band absorption is the first and third order slow light effect respectively, which is verified by the electromagnetic and thermal loss distribution further. This absorber may greatly promote the practical application of absorbers in double-color infrared imaging, detecting, infrared stealth and sub-ambient passive radiative cooling by thermal emitting.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Artificial functional subwavelength materials termed metamaterials (MMs) have gained essential attentions in a variety of applications with fascinating electromagnetic properties, such as superlens [1], cloaks [2], highly sensitive sensors [3], and so on. The inherent large optical loss in MMs degrades the property of most applications. However, the loss in MMs is useful for absorbers and significantly enhances the absorber’s performance by proper designs.
The main infrared transparency windows of the atmosphere are MWIR (middle wave infrared) in the wavelength range from 3 to 5 µm, and LWIR (long wave infrared) in the wavelength range from 8 to 13 µm [4]. With near-unity absorption in the infrared transparency windows and near-zero absorption in the other wavelength range, infrared absorbers can be optimized as imaging and detectors [5–7] because of the low background noise, facilitating the applications of absorbers in military reconnaissance, environmental monitoring, fire alarm, night vision, etc. Besides, indicated by the Kirchhoff’s law, a good absorber is also a good emitter, which makes the near-unity infrared absorbers can be used in passive radiation cooling by radiating heat through the infrared atmosphere transparency windows into the cold sink of outer space [8–11]. Zhai et al. embedded resonant polar dielectric microspheres randomly in a polymeric matrix, resulting in a metamaterial that is fully transparent to the solar spectrum while having an infrared absorption greater than 0.93 in the atmospheric window 8-13 µm and around 0.7 in the atmospheric window 3-5 µm [11]. For sub-ambient night passive radiative cooling, gaining selective absorption with broadband near unit absorption in atmospheric windows and high reflection out of atmospheric windows is the key [8–12]. Therefore, broadening the selective bands of absorbers to cover the two transparent windows and having high reflection out of atmospheric windows is significant to promote the applications in these areas.
Landy first obtained the near-perfect absorber; however, the absorption is restricted to a narrow resonant wavelength by the structure [5]. To broaden the bandwidth of absorbers, a variety of approaches are proposed such as combining several resonators per unit cell horizontally [13–16] or vertically [17,18], using tapered anisotropic MMs [19–23], designs of aperiodic or disordered structures [24–26], using phase transition materials [27,28], functional metasurface structures [29,30], and so on. Since Cui et al. first adopted sawtoothed anisotropic metamaterial to realize ultra-broadband absorption in 2-6 µm [19], many kinds of research adopted similar structure to realize ultra-broadband absorber, which can controllably broaden the bandwidth of absorbers and has been demonstrated theoretically and experimentally in optical [31–33], infrared [19], microwave [34,35] and terahertz [36] frequencies. Liang et al. [37] proposed a pyramid metamaterial absorber to realize an absorption of nearly 100% in 1-14 µm. In 2014, a tapered, multilayered metal-dielectric structure was fabricated by using a nanoimprint-PVD method, which is easily scalable to large areas by taking advantage of linewidth reduction that occurs naturally in evaporation processes through a patterned template [31]. Another group also realized the fabrication of the tapered multilayered metal-dielectric structure [32,33]. He et al. [33] realized ultra-broadband absorbers through integrating multi-sized tapered metal-dielectric structures in one cell horizontally, which ensures polarization-insensitive light absorption between 500 nm and 2500 nm. Lin et al. [22] proposed an array of tungsten/germanium anisotropic nano-cones placed on top of a reflective substrate to absorb light at the wavelength range in 0.3-9 µm theoretically. Abdelatif et al. [38] proposed a funnel-shaped anisotropic MM absorber consists of conical and cylindrical units to achieve superior broadband optical absorption in 0.2-9 µm, which used two sub-cells vertically to realize one broadband absorption. Guo et al. proposed 4×4 cascaded metal-dielectric pairs to realize an ultra-broadband metamaterial absorber in the terahertz regime to reduce the demand for fabrication precision [39]. The previous works [13,16–20,22,23,25–30,32–39] devoted to realizing only one ultra-broadband absorption. Some of the works [13,16,18,20,23,25–30,32–36,39] don’t cover the atmospheric windows, and some of the works [19,22,37,38] cover one of the atmospheric windows, whereas having high absorption out atmospheric windows at the same time. This may affect the performances of the absorber in some areas, such as increasing the noise of imaging or detector, decreasing the cool power of sub-ambient passive radiative cooler at night and so on. Zhai et al. [11] realized two broadband absorption in the two atmospheric windows and acquired excellent performance for daytime passive radiative cooling. However, the polymeric matrix is easy to age. Li et al proposed a hybrid structure composed of trapezoid multilayered grating and trapezoid SiO2 hybrid structures to realize high absorption in MWIR and LWIR simultaneously, which is complex and difficult to fabricate. To the best of our knowledge, simultaneously acquiring high absorption in LWIR and MWIR atmospheric windows and high reflectivity out of atmospheric windows is relatively unexplored, which is very valuable to optimize the absorber’s performances in the areas of infrared imaging, detectors and sub-ambient passive radiative cooling
In this work, we broadened the bands of absorbers selectively to cover the two atmospheric windows in LWIR and MWIR used one unit, which is much simpler than the hybrid structure [21] and more stable than the polymeric matrix embedded by polar dielectric microspheres [11]. The absorber is composed of a trapezoid multilayered grating array, with one unit consist of alternating metal Au and dielectric InP plates on top of an opaque substrate. With parameter manipulation, the absorber can selectively absorb the light at atmosphere transparent windows with absorption higher than 0.8 from 3.5 to 4.8 µm in MWIR, and 7 µm to 14.3 µm in LWIR. The two broad absorption bands in the MWIR and LWIR are due to third order slow light mode and first order fundamental slow light mode, respectively. The absorption property can be tuned by changing the filling factor of Au as well as the geometry of trapezoid multilayered array, but with at least ± 50 nm imperfection tolerance. The designed absorber may greatly promote the practical application of absorbers in double-color infrared imaging, bolometers, sub-ambient passive radiative cooling by thermal emitting as well as military defense systems.
2. Design and simulation
The 3D schematic diagram of the metamaterial absorber and the cross-section of a unit in the x-z plane is presented in Fig. 1(a). It shows one unit of the trapezoid multilayered grating array consists of flat metal Au (yellow) and dielectric plate InP (blue). A gold film with a thickness (100 nm) larger than skin depth was added under the unit cell to block all transmission.
Fig. 1. (a) The 3D schematic diagram of the metamaterial absorber and its cross-section of one unit in the x-z plane. The yellow region represents gold, and the blue is for InP. The thicknesses of InP and Au are denoted as l1 and l2, respectively. The number of the layers of Au and InP is denoted as n. The top and bottom width of the multilayered trapezoid grating are denoted by p and w, respectively. The lattice constant is assumed to be a. A plane wave light source is used for illumination with its propagation direction and polarization along the negative z-axis and x-axis, respectively. (b) The absorption spectra of the metamaterial absorber simulated by 2D or 3D methods in FDTD, which are shown in blue squares and red circles, respectively.
The spectral characteristics of the metamaterials absorbers were calculated by performing electromagnetic wave finite difference time domain method (FDTD, available from the Lumerical software package [40]), which agreed with the experiment results [32,33]. A plane wave light source is used for illumination with its propagation direction and polarization along the negative z-axis and x-axis, respectively. For 3D simulation, a unit cell of the trapezoid grating was simulated using periodic boundary conditions along the x and y-axis, and perfectly matched layers boundary condition along the z-axis with 32 layers. In FDTD, if your grating has an identical cross-section in one direction, you can run 2D simulations instead [40]. For 2D simulation, a unit cell of the trapezoid was simulated using periodic boundary conditions along the x-axis and perfectly matched layers boundary condition along the z-axis with 32 layers. For both 2D and 3D simulations, the window size of the simulation area in the x-axis was set as the period a of the absorber, while the boundary of windows in the z-axis was about 8 µm above the structure and 1 µm below the structure. The auto shutoff min was set as 1e-8. The permittivity of Au and InP is extracted from Palik’s work in 1991 [41]. The permittivity of InP can be set as 9 for simplicity. All materials are assumed to be nonmagnetic (i.e., µ = µ0). The absorption spectrum (A) of the device is retrieved from scattering parameters as follows: A = 1 – T - R, where A, R and T denote the absorption, reflection and transmission, respectively. In this work, the optically thick (100 nm) bottom gold film prevents the light transmission (T = 0) and therefore the absorption is A = 1 - R.
As depicted in Fig. 1(b), there are two broad absorption bands with the maximum absorption over 96% in the MWIR and LMIR, where the atmosphere is transparent. The optimal performance of the absorber occurs at the parameters as follows: l1=55 nm, l2=25 nm, n = 16, a = 2.4 µm, w = 1.84 µm, and p = 0.8 µm. The first broad absorption band is in the MWIR, with the absorption higher than 0.8 in the wavelength region between 3.5 and 4.8 µm, almost covering the full MWIR atmosphere transparent window. The second broad absorption band is in the LWIR, with the absorption higher than 0.8 in the region between 7 and 14.3 µm, covering the full LWIR atmosphere transparent window. This grating structure has an identical cross-section in the y-direction, so we can run 2D simulations instead for simpler [40], which is verified by the comparison of 2D and 3D simulation results, as shown in Fig. 1(b).
3. Results and analyses
According effective medium theory (EMT), when the thickness of the alternating Au metal layer and InP dielectric layer is much smaller than the wavelength of the incident wave, the layered medium consisting of the multilayered array can be regarded as an anisotropic homogeneous effective medium, which is independent of the length and width of the multilayered array when they are very big. As the thickness of the multilayer structure is much smaller than the incident wavelength and the length and width are large, the multilayer structure can be regarded as an anisotropic homogeneous effective medium and its permittivity tensor can be given as
The effective anisotropic medium is consistes of alternating Au and InP films with a thickness of 25 nm and 55 nm, respectively. We extracted the parameters of Au by sampled data from [28, 41] as well as index data form FDTD fitting from the software FDTD. Figures 2(a) and (b) show the wavelength-dependent relative permittivity of the effective anisotropic medium. Fig. 2(a) indicates the sampled data and the index data are almost identical. The real part of the parallel component of the relative permittivity ɛ‖ is negative, which is opposite and several times greater than its imaginary part. Thus the effective medium layer consisting of alternating Au metal layer and InP dielectric layer shows metal property in x and y directions. Fig. 2(b) indicates the real part and imaginary part of relative permittivity ɛ⊥ are both positive and almost unchanged in the wavelength range from 3 to 16 µm. The relative permittivity ɛ⊥ is about 13.2 and the imaginary part is about 0.025, near to zero. Therefore, the effective medium layer consisting of alternating Au metal layer and InP dielectric layer shows dielectric property in the atmosphere transparent windows in the z-direction. In Figs. 2(a) and (b), the effect dielectric function ɛx = ɛy <0, ɛz>0 means the effective medium layer is a hyperbolic material.
Figure 2(c) shows the equivalent 3D schematic diagram of the metamaterial absorber and its cross-section of one unit in the x-z plane after the deal with EMT. The yellow region is Au substrate and the blue region is the effective medium with the complex relative permittivity shown in Figs. 2(a) and (b). We simulated the absorption of the structure in Fig. 2(c) with the same p, w, a, n, l1 and l2 parameters in Fig. 1(a) by 3D FDTD, which is shown in Fig. 2(d) in the green triangles. The blue and red symbols are the results in Fig. 1(b), which are the absorption spectra of the real structure. They are the same, except for a little difference in the wavelength around 14 µm, which indicates the validity of EMT.
Fig. 2. (a) The parallel component ɛx and (b) perpendicular component ɛz of the complex relative permittivity of the anisotropic homogeneous effective medium composed of the Au and InP based multiplayer film. The real parts of relative permittivity extracted from FDTD index and sampled data are shown in green and black symbols, respectively. The imaginary parts are shown in blue and red symbols, respectively. (c) The equivalent 3D schematic diagram of the metamaterial absorber and its cross-section of one unit in the x-z plane after the deal with EMT. The yellow region is the Au substrate and the blue region is the anisotropic homogeneous effective medium, with the complex relative permittivity shown in (a) and (b). (d) The absorption spectrum of structure (c) simulated by 3D FDTD, which is shown in the green triangle. The blue and red symbols are the results in Fig. 1(b), which are the absorption spectra of the real structure.
Then we analytically solved the eigenequation based on the effective medium theory in an air/HMM (hyperbolic metamaterial) /air planar (showing in the inset of Fig. 3(a)) with a fixed middle width d. The air/HMM/air planar is consisted of an air cladding layer (ɛd = 1) and an anisotropic core layer HMM. For transverse magnetic modes, the propagation constant in the z-direction marked as β, the propagation constant in the x-direction in the air marked as k and the propagation constant in the x-direction in HMM marked as kx can be obtained by solving the following equations [43,44]
Fig. 3. (a) First order fundamental slowlight waveguide mode’s dispersion curve when the width of the waveguide core d is tuned from 800 nm to 1800nm. (b) Third order dispersion curves when d is tuned from 800 nm to 1800nm. (c) For different orders of waveguide modes, the degeneracy wavelength where the slowlight is excited and the group velocity approaches zero, i.e., vg = 0 with tuned core width d. The first and third order curves are shown in blue squares and red circles, respectively.
To verify our conclusion, we simulated the field distribution maps. The electric, magnetic fields, Poynting vector and thermal loss distribution were extracted from the simulated results at 3.5 µm, 4 µm, 4.5 µm in the MWIR and 8 µm, 10 µm, 12 µm in the LWIR. The distribution in the x-z plane are shown in Fig. 4 in MWIR, and Fig. 5 in LWIR.
Fig. 4. The electric, magnetic field intensity, Poynting vector and thermal loss distribution at three wavelengths in the MWIR on the x-z plane of the absorber. (a), (b), (c) and (d) are the electric, magnetic intensity, Poynting vector and thermal loss distribution extracted from wavelength 3.5 µm, respectively. (e), (f), (g) and (h) are the electric, magnetic intensity, Poynting vector and thermal loss distribution extracted from wavelength 4 µm respectively. (i), (j), (k) and (l) were extracted from wavelength 4.5 µm.
Fig. 5. The electric, magnetic field intensity, Poynting vector and thermal loss distribution at three wavelengths in the MWIR on the x-z plane of the absorber. (a), (b), (c) and (d) are the electric, magnetic intensity, Poynting vector and thermal loss distribution extracted from wavelength 8 µm, respectively. (e), (f), (g) and (h) are the electric and magnetic intensity, Poynting vector and thermal loss distribution extracted from wavelength 10 µm respectively. (i), (j), (k) and (l) were extracted from wavelength 12 µm.
Figure 4 indicates the electric, magnetic fields, Poynting vector and thermal loss distribution, which are focused at the top-half of the structure at the wavelength 3.5 µm, focused at the middle at the wavelength 4 µm, and focused at the bottom of the trapezoid multilayered grating at the wavelength 4.5 µm. The figures of thermal loss quantify the conversion efficiency of the electromagnetic field into heat by calculating the differential form of ohm rule, which is the Joule dissipation of the structure. In the MWIR high absorption region, the electric, magnetic fields, Poynting vector and thermal loss resonant positions go deep into trapezoid multilayered grating of the absorber as the incident light wavelength increases, which is in good agreement with the red circles in Fig. 3(c). The only difference is the wavelength of simulation is smaller than the theoretical prediction in Fig. 3(c), which is due to the incomplete absorption resulted from the quickly changed core width d. Besides, it can be seen that for each wavelength, there are three electric and magnetic resonant spots at different waveguide width d. Therefore, we concluded the broadband absorption in the MWIR is due to the third order slow-light waveguide mode.
Figure 5 reveals the similar phenomenon. The electric, magnetic fields, Poynting vector and thermal loss resonant positions go deep into trapezoid multilayered grating of the absorber, as the incident light wavelength increases from 7 µm to 14 µm, which is consistent with the blue squares in Fig. 3(c). However, they match better than in MWIR because the light is absorbed more completely, which proves our inference from Fig. 3. Moreover, the number of the magnetic resonant spot is just one, which further confirms the broadband absorption in the LWIR is due to the first order fundamental slow-light waveguide mode.
Up to now, we used effective medium theory to design and explain an absorber with two broad perfect absorption bands in atmosphere transparent windows. But if the layers number n of trapezoid multilayered grating altering Au and InP is too small, the effective medium approximation is no longer valid, resulting in the two absorption bands vanish (as shown in Fig. 6(a)). When layers number n is bigger than 12, the absorption spectrum changes negligibly. As derived from Eq. (3) to (5), the resonant wavelength of fundamental and three order slow light waveguide modes are approximately proportional to the refractive index n⊥ and the middle medium layer width d [19]. Consequently, we tuned the structure parameter carefully to acquire the two broad absorption bands in atmosphere transparent windows by changing l1, l2, p, w and a, displayed in Fig. 6, respectively. As shown in Figs. 6(b) and (c), when l1 decreases or l2 increases, i.e., the filling factor t = l1 / l2 decreases, the degeneracy wavelength redshifts a little but still has a stable result with at least ± 50 nm fabrication error. That’s due to the effect medium permittivity function is decided by the permittivity function of Au, the permittivity function of InP and their filling factor t. Smaller t means effective medium layer shows more metal property. As shown in Figs. 6(d) and (e), as the up width p of trapezoid multilayered array increases, the absorption band in MWIR changes negligibly while the absorption band in LWIR changes much quicker. As the bottom width w of trapezoid multilayered array increases, the absorption wavelength in MWIR and LWIR becomes more linearly because of the complete absorption. That is consistent with the conclusion from Fig. 3(c). When the period a increases, the air gap width between the trapezoid multilayered gratings increases. Bigger the air gap width is more incident light is reflected by the metal substrate through the air gap, especially in the MWIR because of the incomplete absorption of the incident light. Though influenced by these parameters, the absorption property changes slowly with at least ± 50 nm imperfection tolerance, which makes the fabrication easier.
Fig. 6. The absorption spectra of the absorber for changes of the geometry parameters of the anisotropic trapezoid array. (a) The number of the layer n. (b) The thickness of InP l1. (c) The thickness of Au l2. (d) The top width of trapezoid anisotropic array p. (e) The bottom width of trapezoid anisotropic array w. (f) The period of trapezoid anisotropic array a is varied while the other structural parameters are set as given in Fig. 1.
4. Conclusion
In conclusion, we have designed an absorber of trapezoid multilayered array based on metal Au and dielectric InP plates, which has perfect absorptions of two broadband. With adaptive parameters, the spectral absorption range covers the atmosphere transparent windows of MWIR (3.5∼4.8 µm) and LWIR (7∼14.3 µm). The near-perfect absorption bands in LWIR and MWIR attribute to the first order and third order slow light modes respectively, which are verified by the dispersion relation, electromagnetic power and thermal loss distribution maps. The absorption property can be manipulated by the filling factor of Au and the geometry of trapezoid multilayered array with at least ± 50 nm imperfection tolerance, making the fabrication easier. This multilayered trapezoid period grating structure is polarization-dependent. If we change the units to multilayered pyramidal or conical units, it is polarization independent because of symmetry and the absorption keeps unchanged [32–34]. The design may greatly promote the practical application of absorbers in double-color IR imaging, bolometers, sub-ambient passive radiative cooling by thermal emitting as well as military defense systems.
Funding
National Natural Science Foundation of China (61504078); China Postdoctoral Science Foundation (2015M571545).
Acknowledgments
The authors thank Jun Yin for technical supporting.
Disclosures
The authors declare no conflicts of interest.
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