We design a new kind of metamaterial absorber in the form of an ultrathin silicon nanostructure capable of having wideband absorption of visible light. We show that our metamaterial can exhibit almost perfect absorption of incident light even though its thickness is several tens of times smaller than the optical wavelength. The combination of two resonant modes in a single nanostructure allows us to achieve absorptivities exceeding 80% in a wide band spanning from 437.9 to 578.3 nm. The physical origins of the two modes, elucidated via the analysis of current distribution inside the nanostructure, explain different metamaterial absorptivities for oblique incidence of TE- and TM-polarized waves. Our study opens a new prospect in designing ultrathin, yet wideband visible-light absorbers based on silicon.
© 2017 Optical Society of America
In the past decade, metamaterials have attracted considerable research interest from both scientific and engineering communities owing to their ability to challenge conventional limitations of natural materials and provide unique properties [1, 2]. Metamaterials are a kind of artificially structured media whose bulk electromagnetic properties are determined by the subwavelength-scale internal design rather than by chemical composition. The development of electromagnetic metamaterials enables a series of intriguing applications such as diffraction-free imaging , invisiblity cloaking , analogues of quantum phenomena in classical systems , wavefront modification , and perfect absorption . In particular, ultrathin metamaterial absorbers with broad absorption bands are urgently needed for applications in the fields of electromagnetism and optics.
Since their first demonstration by Landy et al.  at microwave frequencies, metamaterial absorbers have been extensively studied at microwave , terahertz , and optical frequencies . Usually, a metamaterial absorber is a sandwiched structure where two patterned metallic layers are separated by a dielectric spacer and whose absorption spectra is mainly determined by the layer patterns. Dielectric resonators, which can serve as building blocks of purely dielectric metamaterials, have also been recently studied with the aim of simultaneously achieving electric and magnetic resonances . Much like their metallic counterparts, dielectric metamaterials can be used to realize nontrivial optical functions, including perfect absorbers . Since the resonant nature of their response makes such absorbers suffer from relatively narrow bandwidths, quite a lot of ingenuity was required to design multi-band , wide-band , and tunable-band metamaterial absorbers . To effectively expand the bandwidth, one may combine several resonance bands through in-plane arrangement  or layer-by-layer stacking  of multiple resonant units, or using vertically standing nanowires instead of planar structures . These methods allow one to broaden the absorption band at the expense of increased thickness and/or complexity of the structure.
Another promising way of increasing both the absorption coefficient and bandwidth of metamaterial relies on the introduction of semiconductors (and, in particular, silicon) into the metamaterial design [20,21]. Silicon is compatible with the standard lithography and the complementary metal-oxide-semiconductor (CMOS) technology, so that it can be easily processed to produce complex patterns for achieving desired electromangnetic characteristics. Highly doped silicon has relatively low resistivity and behaves as a lossy dielectric at terahertz (THz) frequencies, which is beneficial for the realization of broadband THz absorption . Using a lossy patterned silicon substrate, Yin et al.  have already experimentally demonstrated a polarization-insensitive metamaterial with absorption band spanning from 0.9 to 2.5 THz. Most recently, Gorgulu et al.  reported on ultrabroadband all-silicon infrared absorbers made of periodically arranged silicon gratings. It is worth noting that most of studies on silicon-based metamaterial absorbers are carried out at THz or infrared frequencies. Using silicon for designing ultrathin metamaterial absorbers with wide absorption bands at visible frequencies is still highly demanded.
In this paper, we design and analyse a new ultrathin optical metamaterial absorber made of silicon nanostructure, silicon dioxide spacer, and metallic mirror. The nanostructure is a planar silicon layer with conical holes arranged in a square lattice and with thickness that is much smaller than the operation wavelength. We show that this metamaterial can feature almost perfect absorption over a wide frequency band due to the presence of two resonant modes of the nanostructure. We analyze current distributions of the two modes and the absorption properties of metamaterial under oblique incidence of TE- and TM-polarized waves.
2. Geometry and parameters of metamaterial absorber
Figure 1 shows the considered metamaterial absorber and its unit cell. The absorber consists of three functional layers: (i) a subwavelength silicon layer with a periodic array of truncated conical holes in it, (ii) a subwavelength silicon dioxide (SiO2) layer acting as a spacer, and (iii) a relatively thick gold substrate for reflecting the radiation. It is assumed that the silicon nanostructure is periodically extended in both the x and y directions and has geometric parameters listed in the caption of the figure. Such a silicon structure can be fabricated by electron-beam lithography . The electromagnetic performance of the metamaterial absorber is studied numerically with full-wave simulations using commercial software package, CST Microwave Studio. In our simulations we mimic light propagation through the infinite periodic nanostructure using unit boundary conditions in the x and y directions and open boundaries in the z direction.
The dispersion of the permittivity of silicon  is shown in Fig. 2. This permittivity has very large imaginary part for wavelengths below 400 nm, which explains the relatively high absorption coefficient of silicon at optical frequencies. Above 400 nm, silicon’s permittivity shows a high real component and relatively low imaginary component, which behaves similar to that of a high permittivity dielectric. In contrast to silicon, silicon dioxide has quite a flat dispersion and negligible dissipation , as can be seen from its permittivity plotted on the same figure. The optical permittivity of gold is taken from Johnson and Christy’s experimental work .
3. Absorptivity for normal incidence
Consider a y-polarized plane electromagnetic wave that is incident normally on the silicon-based nanostructure shown in Fig. 1(a). The frequency-dependent absorptivity A(ω) = 1 − |r|2 − |t|2 of the nanostructure is expressed through its reflection r(ω) and transmission coefficients t(ω), which are calculated numerically. We assume the gold layer to be so thick that no light could propagate through it, in which case t = 0. This assumption results in A(ω) = 1 − |r|2 for all the wavelengths of interest.
Figure 3 shows the absorptivity spectrum of the proposed silicon nanostructure for normally incident light. One can see that the nanostructure exhibits optical absorption over a wide band of visible wavelengths, with absorptivities exceeding 80% above 437.9 nm and below 578.3 nm. The primary absorption peak of 98.2 % at λ = 499.7 nm (mode I) is accompanied by the secondary peak with an absorptivity of 88.4% at λ = 567.1 nm (mode II). The relative bandwidth of the proposed metamaterial absorber is 27.6%, which is several times wider than that of common metamaterial absorbers with single resonance [8,10]. This result clearly demonstrates the viability of using silicon nanostructures for building wideband optical absorbers at visible wavelengths. At the resonance wavelengths, silicon behaves as a lossy dielectric and the resonance mechanism of the silicon-based metamaterial absorber is very similar to that of an all-dielectric metamaterial absorber. By varying the geometric parameters of the silicon nanostructure, one can realize optical absorption at other desired wavelengths.
To understand the reason of the absorption band widening, we examine silicon nanostructures with cylindrical holes (r1 = r2). The red (dashed) and blue (dotted) curves in Fig. 3 show the absorptivities of nanostructures with cylindrical holes of radii 100 and 140 nm. In both cases, there are two resonant modes, whose positions are seen to shift to shorter wavelengths with the radius of the holes. The nanostructure with large holes exhibits nearly uniform absorptivity for mode I and a relatively low absorptivity for mode II. On the other hand, for small holes the absorptivities of both modes are nearly equal, but comparatively low. By combing the useful features of nanostructures with small and large holes using holes in the form of truncated cones, one preserves a nearly uniform absorptivity for mode I while significantly increasing the absorptivity for mode II. This way the absorption bandwidth of the nanostructure is effectively extended.
The performance of the proposed metamaterial absorber is further illustrated by the distribution of the current density inside it. This current is induced by the oscillations of the local electric fields and has the dominating y component. Since the fused silica layer is assumed to be lossless, the current density inside it is zero. We therefore focus on currents inside the silicon and gold layers near the surface of the SiO2 spacer. Figure 4 shows distributions of these currents at the resonance wavelengths of 499.7 and 567.1 nm. The current density at λ = 499.7 nm shown in panel (a) is seen to concentrate along the x direction at the necks between the adjacent holes whereas the current density at λ = 567.1 nm in panel (c) concentrates both at the necks (negative current) and at the central region bounded by all four holes (positive current). One can also see that the currents in Fig. 4(a) are much stronger than in Fig. 4(c), implying a stronger resonance for mode I. This feature is consistent with the higher peak absorptivity evidenced by Fig. 3.
The current density inside the gold layer is similar to that inside silicon. Interestingly, these two densities oscillate nearly in phase with each other for both modes. This is uncommon for ordinary metamaterial absorbers, where current densities in two functional layers are often in antiphase [8–10]. The reason is that high absorptivities of ordinary metamaterials are contributed to the anti-symmetric coupling between the two functional layers (due to the strong magnetic resonance) whereas the behaviour of our silicon-based metamaterial absorber is dominated by the symmetric coupling between the structured silicon layer and the gold mirror (due to the strong electric resonance). It is also seen that the current densities in the gold layer are much stronger than those in the silicon layer for both modes, which implies that the majority of the incident energy is absorbed by the gold layer rather than by the silicon layer. In other words, the absorptivity is mainly contributed by the coupling between the structured silicon layer and the gold substrate.
4. Absorptivity for oblique incidence
We next study the performance of the proposed absorber under oblique incidence. Figure 5 shows absorptivity for various angles of oblique incidence of TE- and TM-polarized waves. The absorptivity of TE polarization is seen to exhibit moderate fluctuations for incident angles between 0 and 40°, with almost fixed wavelengths of the two resonant modes. This is due to the fact that the electric field driving these modes does not change with the incident angle. Still, the absorptivity decreases significantly when this angle exceeds 60° because of the decreased coupling between the structured silicon and the gold layer. Quite a different picture of the absorptivity spectrum modification is observed for TM polarization. As the angle of incidence is increased, the first resonant mode blueshifts from 499.7 to 457.2 nm while the peak absorptivity remains higher than 96%. At the same time, the second mode exhibits a noticeable redshift from 567.1 to 647.9 nm and its peak absorptivity decreases significantly. These specific behaviours of the two modes are due to the different physics of the underlying resonances.
We have designed an ultrathin and wideband metamaterial absorber for visible wavelengths. Based on a silicon nanostructure whose thickness is significantly smaller than the optical wavelength, our absorber was shown to be capable of possessing absorptivities as high as 98.2%. The combination of two resonant modes in a single nanostructure allowed us to make metamaterial absorptivity higher than 80% in a wide spectral region from 437.9 to 578.3 nm. Our study of metamaterial absorptivity also revealed significantly different behaviours of the two modes under the oblique incidence of the TE- and TM-polarized waves. The proposed silicon nanostructure may prove useful in solar photovoltaics and thermophotovoltaics.
National Natural Science Foundation of China (61675170, 61571298, and 61571289), Natural Science Foundation of Shanghai (17ZR1414300), Ministry of Education and Science of the Russian Federation (14.B25.31.0002), and Australian Research Council (DP140100883).
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