Ultra-broadband, lithography-free, omnidirectional, and polarization-insensitive perfect absorber

Perfect absorbers (PAs) at near infrared allow various applications such as biosensors, nonlinear optics, color filters, thermal emitters and so on. These PAs, enabled by plasmonic resonance, are typically powerful and compact, but confront inherent challenges of narrow bandwidth, polarization dependence, and limited incident angles as well as requires using expensive lithographic process, which limit their practical applications and mass production. In this work, we demonstrate a non-resonant PA that is comprised of six continuous layers of magnesium fluoride (MgF2) and chromium (Cr) in turns. Our device absorbs more than 90% of light in a broad range of 900–1900 nm. In addition, such a planar design is lithography-free, certainly independent with polarization, and presents a further advantage of wide incidence up to 70°. The measured performance of our optimized PA agrees well with analytical calculations of transfer matrix method (TMM) and numerical simulations of finite element method, and can be readily implemented for practical applications.

www.nature.com/scientificreports/ As a consequence, in this work we presented a superior absorber in near-infrared regime, to meet the critical challenges aforementioned. The demonstrated absorber was a non-resonant design that is comprised of six continuous layers of magnesium fluoride (MgF 2 ) and chromium (Cr) in turns. The materials adopted here were economic, in contrast to the noble metals used in conventional PAs. As for the structural design and realization, firstly, we analytically employed the transfer matrix method (TMM) to design and to optimize the absorption spectra of the electromagnetic absorber, with respect to various layer thicknesses. Next, by using a commercial solver (Comsol Multiphysics 5.3a) to conduct numerical simulation 37 , we confirmed our device achieving great absorbance beyond 90% over a broad range of 900-1900 nm. Such great and ultra-broadband absorption was independent with polarization angles, and also validated with the wide oblique incidence up to 70°. In addition, we further scrutinized the mechanism and contribution of designed each layer. Finally, to fabricate this non-resonant PA, it only required a facile thin-film deposition process that was totally free from using costly and cumbersome lithography. The corresponding experimental results, analytical calculation and numerical simulation were all in good agreement. To the best of our knowledge, this non-resonant PA shows the broadest absorption range. In addition, the realization of this PA only requires one-step of deposition process, free from the use of lithography. With the advantages of superior performance and facile fabrication process, this nonresonant PA can be readily employed for a wide range of practical applications.

Analytical calculation and numerical calculation
The non-resonant PA at NIR regime is comprised of MgF 2 and Cr, six thin layers pile-stacking alternatively, as shown in Fig. 1. There appear two reasons to choose MgF 2 as a dielectric material. One is based its low real part of complex permittivity, which facilitates to suppress the reflectance to the air (see the Sect. 1 of Supplementary  Information). As for the reasons of selecting Cr as the metallic material, its imaginary part of complex permittivity is much higher than other metals, such that Cr can absorb light efficiently (see the Figure S2 in Sect. 2 of Supplementary Information). Note that an absorber converts electromagnetic energy into heat and thus, the materials used to construct the electromagnetic absorbers should withstand elevated temperatures. MgF 2 and Cr possess high melting points of 1263 and 1900 °C, respectively. These high melting points help avoid atomic interdiffusion between MgF 2 and Cr at moderate temperatures during device operation.
As for the design of this layered structure, there appear three key parameters to fundamentally govern the absorption behaviors-t t , t d as well as t c , denoting the thicknesses of the top MgF 2 , middle MgF 2 and Cr layers, respectively. We calculated the demanded absorption spectra by using the TMM, sweeping the thicknesses of each layer from 0 to 1000 nm, in particular for t t and t d . The optimal absorption was achieved with the layer thicknesses of 230 nm (t t ), 7 nm (t c ), and 180 nm (t d ). Besides, the bottom Cr layer was 100 nm thick, which is much thicker than the skin depth to block the transmittance. With this facile configuration, the absorption efficiency of this PA device was over 90% for both s-polarized and p-polarized light in the wavelength range of 900 to 1900 nm at normal incidence, as shown in Fig. 2. Note that the multilayered structure also presented an impressive tolerance for oblique incidence angles due to the non-resonant structure. The calculated absorbance contour plots for s-polarized and p-polarized light are shown in Fig. 2a,b, respectively. Clearly, we observed that for both polarizations, the absorbance was greater than 80% within wide incidence angles of − 70° to + 70°. Besides, the absorption spectrum in Fig. 2a,b show the blue-shifting of the "main" resonance peak, i.e., the "most red" portion, when the incidence angle increases. This shifting phenomenon can be explained by Fabry-Perot cavity modes in the multilayer structure, as illustrated in Fig. 3. According to the Fabry-Perot condition, one can predict the resonance wavelength by Eq. (1), where k is the wavevector of incidence wave, k y is the wavevector of incidence wave in y direction, θ is the incidence angle. Therefore, as θ increases (cos(θ) decreases), λ should be blue-shifted to maintain the constant. So, we can observe this blue shift phenomenon in Fig. 2a www.nature.com/scientificreports/ We scrutinized the contribution and mechanism of three respective layer thicknesses t t , t c and t d , by using a commercial software package Comsol 5.3a. The results are presented in Fig. 4. Firstly, varying t t (i.e., the thickness of the top MgF 2 layer) contributed to similar absorbance, in the wavelength range of 900-1900 nm at normal incidence, as displayed in Fig. 4a. Upon oblique incidences, yet, there appeared distinct absorption behaviors of p-and s-polarizations. For example, as the indecent angle was up to 70°, the absorbance of p-polarization remained insensitive to wavelengths, but that of s-polarization fluctuated between 90 and 30% (see the Figure S3a in the Sect. 3 of Supplementary Information). Therefore, we further simulated two extreme thicknesses of 10 and 500 nm, to check the corresponding absorbance spectra and electric amplitude distributions. The absorbance spectra about t t = 10 nm is shown in Figure S4b. Note that at 70° incidence angle, the absorbance of p-polarized light was still over 80%, but the absorbance of the s-polarized light dropped below 60%. Besides, the field amplitude distribution and absorbance energy in the direction of propagation are plotted as functions of the wavelength at 70° incidence angles for s-polarization in Figure S4c,d. A large portion of the electric field located outside the structure, because the field was blocked and reflected by the top Cr layer after the wave penetrated through a 10 nm thin top MgF 2 layer. Such strong reflection caused the PAs absorbing s-polarized light poorly. We then increased the thickness of the top MgF 2 layer to 500 nm (see the Figure S5 in the Sect. 3 of Supplementary Information). In this case, though the thickness of the top MgF 2 layer was much thicker than the skin wavelength, the reflection of the s-polarized light was significant because of impedance mismatched, leading to a decrease in absorption.
Next, we examined the thickness of the Cr layer, t c , from 0 to 100 nm. The effect of varying t c was straightforward. As manifested in Fig. 4b and S5, if t c was too thick, the electromagnetic wave was strongly reflected; on the other hand, if t c was too thin, the limited absorbing region tarnished the energy absorption efficiency. Finally, we probed the thickness of the interior MgF 2 layer, t d , and found out that t d contributed to the absorption most among three thicknesses. As shown in Fig. 4c and S6, the absorbance surpassed 90% as t d was between 100 and 250 nm. In particular, the absorbance even reached nearly perfect efficiency at a t d value of 180 nm. Beyond the range of 100-250 nm, the excellent absorption performance started to fade away. For instance, once  www.nature.com/scientificreports/ t d was below 100 nm, the adjacent Cr layers were too close to one another and then collectively interacted with the electromagnetic wave to function as one thick Cr layer, such that a significant amount of light was reflected, resulting in poor absorption (see the Figure S8 in the Sect. 5 of Supplementary Information). In contrast, as t d exceeded 250 nm, there formed a Fabry-Perot cavity in the middle dielectric layer, so that the maximum local field existed in the less lossy MgF 2 layer instead of the lossy Cr layer (see the Figure S9 in the Sect. 5 of Supplementary Information). As a consequence, the absorption remarkably degraded, which was clearly indicated by the black dashed lines in Fig. 4c. Based on the aforementioned contribution and mechanism, we conducted full factorial sweeping to optimize this multilayered structure. Three layer thicknesses of this optimized non-resonant perfect absorber are t t = 230 nm, t c = 7 nm, and t d = 180 nm, illustrated in Fig. 5a. In this case, we can achieve both higher than 90% absorbance under normal incidence and higher than 80% absorbance under up to 70° incidence angle within 900-1900 nm wavelength range. As evidenced in Fig. 5c, the top Cr layer did not block the electric field, so the incident wave can penetrate into the multilayered structure and then decreased gradually; besides, no Fabry-Perot cavity formed in the middle MgF 2 layer to deteriorate the absorption. The absorbed power in a broad band of 900-1900 nm was presented in Fig. 5d, which manifested that the absorption was vigorous and uniform in the top Cr layer within the entire working wavelength range. Notice that we also observed that our PA can substantially tolerate inaccurate fabrication of thicknesses in the range of t t (200-250 nm), t c (5-13 nm) and t d (160-190 nm). For example, our device still provided superior absorbance higher than 80%, within a broad wavelength range of 900 to 1900 nm for the normal and oblique incidences, as shown in Fig. 4 and Figure S3, S6, S7 in the Supplementary Information. Such thickness tolerance offers a further benefit for practical device implementation.

Sample fabrication and experimental verification
To fabricate the designed multilayered structure, a silicon (Si) wafer was first cut into small pieces. The samples were soaked in piranha solution for 15 min to remove the organic contamination, and then the native oxide layer on the Si was removed by using hydrofluoric acid. Next, Cr and MgF 2 layers with the desired thicknesses were deposited by using an electron beam (EB) evaporation process, in which the deposition rates of Cr and MgF 2 approximated 1 and 5 Å/s, respectively, and the chamber pressure was held below 4 × 10 −6 torr throughout the deposition process. First, we deposit 100-nm Cr and MgF 2 at a constant rate and measure the real thickness of the deposited thin film using atomic force microscope, which makes sure to deposit the desired thickness. The SEM image is shown in Fig. 1b. To measure the intensity of 900-2000-nm light reflected by the structure in the normal direction, we used a Hyperion 3000 Fourier-transform infrared (FTIR) microscope with a 15 × objective (Bruker, Billerica, MA, USA). The FTIR spectra were collected in reflection mode using a tungsten lamp as a light source and an InGaAs diode for detection. The angular response of the perfect absorber to p-and s-polarized light incident at angles of 40°, 60°, and 70° (θ) was evaluated using a commercially available Ellipsometer (see the Figure S10 in the Sect. 6 of Supplementary Information). All of the measured reflectance values were normalized to the reflectance of a thick Au-coated sample, which was near 100% reflectance in our desired frequency range. The measured absorbance results are shown in Fig. 6a,b. For the experimental results, the thickness of Cr is around 13 nm but not 7 nm due to the limitation of E-gun deposition process. For the normal incident cases, www.nature.com/scientificreports/ there are some noise around 1900 nm due to the limitation of FTIR detector. Note that to maximize the absorbance, we need to minimize both reflectance and transmittance, as depicted by the following equation, where A, R, and T represent absorbance, reflectance, and transmittance, respectively. The bottom Cr layer was 100 nm thick, which is much thicker than the skin depth to block the transmittance. So, absorbance is the complementary part of the reflectance. For conventional resonant PAs, the reflectance can be shut down by the resonance which will form antiparallel currents within upper and bottom metallic layer. However, such configuration only function at specific wavelength and small oblique incidence angle limitation. In contrast, here the fabricated non-resonance multilayer structure efficiently absorbed light by the intrinsic loss of the materials. Most importantly, the experimental results well agree with the calculated results, as shown in Fig. 6c,d. The experimental absorption is even higher than the calculation absorption in some certain cases. That is because the litter rough on the top MgF 2 layer which will decrease the amount of reflectance. For both experimental and calculated absorption approached or exceeded 80%, even when the oblique incidence angle up to 70°. To the best of our knowledge, this is the broadest absorption range reported for a multilayered device fabricated without the use of lithography. The performance of this absorber was not only with great efficiency, but also free from polarization, oblique incidence angles up to 70°, and lithographic process.

Conclusions
In this study, we presented a non-resonant perfect absorber (PA), which is composed of six pile-stacking layers of magnesium fluoride (MgF 2 ) and chromium (Cr). The key contributions and mechanisms of MgF 2 are to match the impedance for minimizing the reflectance and to act as spacers between metal layers; meanwhile, Cr, not only as a ground layer shuts own the transmittance, but also as middle layers play a key role of absorbing incident wave because of its great intrinsic loss. By optimizing the thickness of individual layers, we demonstrated excellent absorbance over 90% at normal incidence. Owing to its non-resonance nature, this PA possesses further advantages beyond conventional resonance-based perfect PAs: a broad operation range of 900-1900 nm, polarization insensitivity to both s-and p-lights, wide allowed incident angles up to 70°, cost-effective and inaccuracy-tolerate fabrication processes. In addition, comparing with non-resonance-type absorbers such as carbon nanotubes, our PA is ultrathin. These aforementioned features of our PA were consistently confirmed in experimental measurements, analytical calculation and numerical simulation, paving a way toward practical and instant applications.