Broadband infrared absorbers with stacked double chromium ring resonators

A broadband absorber in the infrared wavelength range from 1 μm up to 5 μm is designed and demonstrated with stacked double chromium ring resonators on a reflective chromium mirror. The near-perfect broadband absorption is realized by combining the multilayer impedance match in the short wavelength range and the double plasmonic resonances in the long wavelength range, which is illustrated with an equivalent circuit model for the impedance analysis. The broadband absorber is proved to be angle-insensitive and polarization-independent due to the geometrical symmetry. The thermal analysis for heat generation and temperature distributions inside the absorber structure is also investigated. © 2017 Optical Society of America OCIS codes: (300.1030) Absorption; (260.5740) Resonance; (130.3060) Infrared; (160.3918) Metamaterials. References and links 1. Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. 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In this paper, a broadband infrared absorber made of stacked double chromium (Cr) ring resonators on a chromium mirror is designed based on the combination of multilayer impedance match in the short wavelength range and the double plasmonic resonances in the long wavelength range. The absorber structure is milled from two pairs of Cr-SiO 2 layers with overall thickness of 360 nm on a reflective substrate. Different from combining multiple resonators in the same horizontal plane, the proposed absorber has double Cr ring resonators stacked in the vertical direction. At the same time, the stacked double ring structure can be effectively regarded as one-dimensional metal-dielectric multilayer lattice for satisfying impedance match conditions in the short wavelength range. An equivalent circuit (EC) model is developed to analyze and optimize the broadband absorber according to the transmission line theory for the multilayer impedance in the short wavelength range and the coupled lumped-element LC resonators [22][23][24][25] for the resonance impedance in the long wavelength range. The absorption spectra predicted by the EC model agree with both the simulated and measured absorption spectra and can explain the two absorption mechanisms thoroughly. Further investigations on the oblique incidence under different polarizations, resonant mode fields, heat generation and temperature increase are also performed.

Absorber design and equivalent circuit model
The designed infrared absorber is based on a multilayer stack consisting of two pairs of Cr-SiO 2 layers with 30 nm thick Cr and 150 nm thick SiO 2 in each pair deposited on top of a 200 nm thick Cr mirror coated on a silicon wafer. There is an additional 30 nm thick SiO 2 protecting layer deposited on top of the multilayer stack to prevent the top Cr layer from oxidation. The multilayer stack is grown by RF sputtering. The Cr is grown in an Ar atmosphere at 5 mTorr pressure at a deposition rate of 0.5 Å / sec and the SiO 2 is grown in a 12:1 mixture of Ar:O 2 at a rate of 0.14 Å / sec . Figure 1(a) shows a scanning electron microscope (SEM) image of the deposited Cr-SiO 2 multilayer before milling where each layer can be clearly seen. The thick Cr mirror will block any transmission through the sample. At first, the absorption spectrum of the multilayer film is measured using Fourier transform infrared spectroscopy (FTIR). As shown in Fig. 1(b), the experimental absorption is below 50% in the range of 1~5 μm , which can be matched well with simulation (COMSOL The schematic of the designed absorber with stacked double ring resonators is illustrated in Fig. 2(a). The absorber structure is fabricated using Focused Ion Beam (FIB) milling in two steps. First, the top pair of Cr-SiO 2 layer is milled to form the top ring resonator; and then the bottom pair of Cr-SiO 2 layer is milled to form the bottom ring resonator. During the FIB milling, a SiO 2 layer with very thin thickness is remained on top of the second Cr layer to avoid oxidation. Due to the zero transmission from the absorber, the absorption A is merely determined by the reflection R and is equal to An equivalent circuit (EC) model is developed to evaluate the broadband absorption mechanism of the designed double-ring absorber by considering the combination of the multilayer impedance match in the short wavelength range and the double plasmonic resonances in the long wavelength range. The multilayer impedance mul Z can be regarded as a high-pass filter with no reflection at high frequencies and the resonance impedance res Z can be treated as a low-pass filter with no reflection at low frequencies. As shown in Fig. 2(b), the EC model is then built up by adding the two impedances together in series to estimate the total impedance of the absorber, tot mul res And the absorption can be calculated as ( ) where Z(1) represents the wave impedance of the whole multilayer structure seen from the top and can be calculated layer by layer starting from the bottom Cr mirror with the wave impedance of Z(6) up to the top SiO 2 protecting layer with the wave impedance of (1) Z , by considering the phase shift j δ and the characteristic impedance j Z for each layer j of the multilayer lattice.

Demonstration of broadband infrared absorber
The broadband absorption response of the double-ring absorber can be evaluated by combing the two impedances of mul Z and res Z together. As an example, for the absorber with period of P 700 nm = , Fig. 3(a) shows the absorption spectra calculated by the EC model and the simulation result (COMSOL Multiphysics software). In order to fit the simulated resonance peaks of two ring resonators and absorption amplitude, the coefficients used in the EC model for the double-ring absorber with P 700 nm = are set as the following: 0.8, 0.17, 0 .8, 0. for the coupling of two ring resonators. In the long wavelength range ( 2~5 μm ), the absorption is majorly due to the double ring resonances, and in the short wavelength range (1~2 μm ), the absorption is mainly due to the multilayer impedance match condition. To explain the combination of these two absorption mechanisms, mul Z , res Z and tot Z calculated by the EC model are plotted in Fig. 3  In order to show how the absorption spectrum change with the absorber structure size, three double-ring absorbers with different periods and ring sizes are fabricated. As shown in Figs. 4(a)-4(c), the solid curves are the measured absorption spectra for the double-ring absorbers with periods of P 600 nm = (in magenta), P 700 nm = (in blue) and P 800 nm = (in red), respectively, while the ring dimensions keep the same ratios as   The double-ring structure will change into double-square structure if the center hole has the zero width, which can make the fabrication process simpler. Similar to the double-ring structure, the double-square structure can also be regarded as two coupled plasmonic resonators. As shown in Fig. 5, the double-square absorbers with the periods of P 600 nm = , P 700 nm = and P 800 nm = can also achieve the broadband absorption spectra with absorption above 80% similar to the double-ring absorbers. The absorption spectrum of double-square absorber is not as flat as that of double-ring absorber, but it has a small absorption peak in the long wavelength range.
Oblique incidence is also considered to show if the designed absorber can work in different incident angles and collect more infrared light. Since the double-ring structure is symmetric, the absorption is the same for TE and TM polarizations (configurations as shown in Figs. 6(a) and 6(b)) under normal incidence. However, under oblique incidence, the absorption spectra varies differently for TE and TM polarizations when considering the incident angle from 0° to 85°, as shown in Figs. 6(c) and 6(d) for the absorber with P 700 nm = . It is shown that the absorption for TM polarization can be kept around 80% even at high incident angles, while the absorption for TE polarization is not as high as TM polarization but still remains around 70% at high incident angles. This is because the double ring resonances are magnetic resonances and the multilayer impedance match can be sustained better for TM polarization at oblique incidence. In consequence, the designed broadband infrared absorber is angle-insensitive and polarization-independent and thus it is practical for energy harvesting applications.  To further explore the two plasmonic resonances of the stacked double Cr ring resonators, optical field distributions are analyzed at the resonant wavelengths using COMSOL Multiphysics software. As shown in Fig. 7(a) operating temperature. In addition, chromium is significantly cheaper than gold or silver, making chromium a reasonable choice for high-volume production of infrared absorbers. In the broadband absorber, incident light will be eventually converted into heat because of the resistive loss ( m R ) of metal. In this way, the Cr ring resonators act as nanoscale heat sources resulting in the local temperature increase and eventually a thermal equilibrium will be reached since the heat is conducted away by air above the absorber structure and the Cr mirror below. To investigate the temperature distribution in the absorber, the heat transfer 2.92 10 W/m × located at the bottom ring. At thermal equilibrium, the temperature increase distribution is a result of the balance between the heat generation and the boundary conditions where heat is conducted away. In simulation, the top and bottom boundaries are set as the fixed temperature and the side boundaries are insulated since the structure is periodic. The temperature increase distributions are plotted in Fig. 7(c) at the two resonant wavelengths. According to the Fourier's law where heat transfer rate is proportional to the thermal conductivity of material and the temperature gradient as well, the highest temperature 51.3 ℃ is located in the top-ring for 2.15 μm λ = since heat is mostly generated in the top ring. However, for 3.75 μm λ = , temperature increase in the top ring is still high (reaching to 72.7 ℃ ) although heat is mainly generated in the bottom ring. This is because the bottom ring is close to the Cr mirror with high thermal conductivity, while dielectric layer and air has a much lower thermal conductivity.

Conclusion
A broadband infrared absorber consisting of stacked double Cr ring resonators on a Cr mirror has been designed and demonstrated with an average absorption more than 80% in 1 ~5 μm spectrum range. It is made of the refractory metal Cr based on the combination of two absorption mechanisms: the multilayer impedance match in the short wavelength range and the double plasmonic resonances in the long wavelength range. An equivalent circuit model has been constructed to analyze the impedance of the absorber. The designed absorber is proved to be angle-insensitive and polarization-independent under oblique incidence so that more light can be collected under different situations. The demonstrated Cr based absorber can work in high temperature environments due to the high melting point of Cr. The demonstrated broadband Cr double-ring absorber in infrared wavelength range will advance the relevant applications such as thermophotovoltaics, solar thermophotovoltaics, thermal detection, and thermal imaging.