1. Introduction

Light absorbers have attracted much attention because of their potential applications in photovoltaics [1,2], solar cells [3], sensors [4,5], thermal emitters [6–8]. A number of device configurations based on various working principles have been reported to achieve high absorption for a broad range of incident angles over broadband or multiband spectrum, such as plane film stack relied on Fabry-Perot cavity [9,10], metamaterial-based surfaces combined with noble metal nanoparticles [11–18] and metallic nanostructures employing surface plasmonic phenomenon [19–24]. Plane film stack can work as perfect absorber, however, its absorption response is always found sensitive to the incident angle [9]. Metamaterial absorbers have been investigated theoretically and experimentally because they can achieve perfect absorption with robust angle-independence over a certain bandwidth [11–16]. In order to enhance the trapping of electromagnetic field in small gaps and consequently intensify the absorption, the performance of this type of absorber involves building a highly dense nanocomposite with different size, shape, density, and distribution of the nanoparticles on a dielectric spacer layer which must be attached to a bulk metal block, but they are only suitable for black absorber in the whole visible spectrum Metallic nanostructures (such as perforated metallic film, strip metallic grating) appear as an inescapable solution for the design and realization of optical nano-antennas able to couple the selective incident optical power with high efficiency [25,26]. However, there are two obvious drawbacks in the above mentioned metallic nanostructures: one is that metallic substrate is usually required to enhance the absorption, the other is that it is fussy to fabricate discrete metallic gratings.

Here we demonstrate and characterize a light absorber with dielectric-based subwavelength metallic meanders, exhibiting angle-robust band absorption in visible regime. Metallic meanders have been investigated for subwavelength-imaging and selective reflection applications [27,28]. For the purpose of absorbance application, nevertheless, there are several distinct effects introduced by the meanders: (i) coupling of photons with the meander to evanescent wave, where the increased density of photon modes above the light line makes wide-angle coupling from incident light to trapped local cavity modes possible. (ii) light funneling effect, the fundamental transverse magnetic guided mode with non-existing cut-off frequency, which leads to squeezing light into air nano-groove much smaller than incident wavelength. (iii) with continuous ultra-thin metallic film (less than one-tenth of the incident wavelength), it is an outstanding candidate as high-efficiency absorber from both the structural geometry and the nanofabrication point of view. This paper is organized as follows. In part 2 we describe the configuration and present the optimized structure. In part 3, we analyze the simulation results in detail, including the dispersion relations, the excited photonic resonant modes and the influence of the geometrical parameters of the structure on the device performance. We demonstrate the important role played by the cavity mode for angle-robust behavior. In part 4, we summarize the paper.

2. Structures and simulation results

Figure 1(a) shows schematic configuration of the dielectric-based subwavelength metallic meanders, which consist of a substrate and dielectric grating covered by continuous thin Aluminum (Al) film. Air nano-grooves are formed between two neighboring meanders. The heights of the air nano-grooves are the same as that of the dielectric grating layer (h₁). The thickness of the Al layer is h₂. The pitch of the meander is p and its ridge width is w, respectively. The width of the air nano-groove is d, where d = p-w-2h₂. The transverse magnetic (TM) polarized light is incident from the top air side at an angle of $\theta$. The dielectric constants of Al [29,30] are fitted by the Drude-Lorentz model and the refractive index of the substrate and the dielectric grating is set to 1.5 with a negligibly small optical loss.

 

Fig. 1 (a) Schematic of the proposed dielectric-based subwavelength metallic meanders. (b) Absorption spectra of TM polarized light vary with the incident angle θ. The geometric parameters are chosen as p = 160 nm, d = 30 nm, h₁ = 220 nm, and h₂ = 30 nm.

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Figure 1(b) shows the absorption spectra versus the incident angle θ, where p = 160 nm, h₁ = 220 nm and d = 30 nm. The dielectric-based subwavelength metallic meander chain produces an absorption peak at the wavelength of 446 nm with full width at half maximum of 80 nm, which bandwidth is much wider than those based on hybrid guide-plasmon resonance [22,23]. The absorption approaches nearly 100% at normal incidence. It is obvious that the peak position does not change, even though the absorptive efficiency gradually decreases from unit to about 83% with respect to the incident angle θ increasing from 0° to 60°.

When light is incident on the meanders, several photonic modes, such as cavity resonant mode(CM), surface plasmonic mode (SPM) and Rayleigh-Wood anomalies (RWA), can be excited through the dielectric/metal composite nanostructure [21,27,28,31]. The physical origin of the wide-angle absorption of the meanders relies on the excitation of the localized evanescent field and CM through a waveguide funneling effect, which is controlled in a flexible fashion by the geometrical parameters over a large spectral range with continuous ultra-thin (less than one tenth of the incident wavelength) metallic film. Indeed, the coupling effect gives rise to omnidirectional absorption due to the excitation of the localized CM. However, absorbance enhancement through SPM and RWA at a given wavelength occurs only within very narrow angular range. The dielectric-based subwavelength metallic meanders give birth to spectacular effects allowing to manipulating light at nanometric scale.

3. Analysis and discussions

3.1 Angle-robust absorption in the dielectric-based subwavelength metallic meanders

Figure 2(a) presents the absorption as a function of the normalized wavelength and the normalized tangential wave vector k_x in the first Brillouin zone. The geometric parameters are chosen as the same as those in Fig. 1(b). There are several comprehensive optical responses occur for incident wave, such as CM, SPM and RWA. The solid lines represent the dispersion of the SPM obtained from $k_{SPM}/G$, where $(k_{SPM}=k_0\sqrt{\frac{{\epsilon }_m{\epsilon }_d}{{\epsilon }_m+{\epsilon }_d}})$, shifted by a multiple m, where G is the meander pitch vector with $G=2\pi /p$, m is an integer that defines diffraction order, ${\epsilon }_m$ and ${\epsilon }_d$ are the permittivity of the metal and dielectric materials, respectively. The dotted lines represent the dispersion of RWA obtained from $k_{RWA}/G$ shifted by a multiple m. The symbol ‘-‘ denotes the excited wave traveling in reverse x-axis direction. The strongly confined 1st and 2nd order CMs cause perfect absorption of incident photons for a broad range of incidences.

 

Fig. 2 (a) Absorption spectra as a function of the frequency and the wave vector k_x in the first Brillouin zone of the meander with a pitch of 160 nm. The solid lines and dotted lines represent the dispersions of SPM and RWA, respectively. (b) The colormap represents the amplitude of the time-averaged power loss density Q and the arrows represent Poynting vector at the incident wavelength of 446 nm at normal incidence. Contours of horizontal electric field E_x (c), vertical electric field E_z (d) and magnetic field H_y (e). The alignment of surface charges dipole is denoted by symbols “$\oplus$” and “$ⓛ$”. The surface currents are denoted by white arrows. (f) Phase of Ex and Hy along z-axis at the center of the cavity (x = 80 nm). Dotted-lines depict schematically the profile of Al film.

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The mechanism responsible for the angle-robust absorption of the dielectric-based subwavelength metallic meanders can be compared with that of nano-grooves etched on metallic surface [32]. The Poynting vector distribution at $p/\lambda$ = 0.358 ($\lambda$ = 446 nm) in Fig. 2(b) distinctly shows that the incident flow bends when reaching the meander surface, and propagates along the interface toward the air nano-groove, which can be attributed to the magnetoelectric interference of the incident wave with the scattered evanescent field. Stronger photo flux at the aperture of the groove and charge dipoles at the corner is observed, since the size of the arrows is proportional to the magnitude of the Poynting vector. The fundamental TM mode guided between two neighboring meander metallic sidewalls does not have a cut-off frequency, then the energy flow squeezes into the air groove which size is much smaller than the wavelength. Multiple reflection from the bottom metal layer yields standing wave patterns and they do not feature any dispersion as a function of the incident wave vector $k_x=\frac{\omega }{c_0}\sin \theta$. The time averaged resistive heating (Q) generated by the structure is also shown in Fig. 2(b), which is calculated using $Q=(1/2){\epsilon }_0\omega \mathrm{Im}\left\{{\epsilon }_{Al}(\omega )\right\}{\left|E\right|}^2$. Most of the loss energy is found to be absorbed by the Al sidewalls instead of its surface parts, which gives a solid proof that the CM plays a key role in the angle-robust absorptive behavior in the meanders. Such strong resonances effectively trap light and provide sufficient time to dissipate it by the Ohmic losses within metals.

Figures 2(c)-2(e) shows the field distribution of Ex, Ez and Hy at the resonant wavelength. The invariant field distribution of Ex and Hy along x-axis direction is observed and it is a solid proof that it is TM0 mode being excited in the air nano-groove. The Ez component is strongly localized around the metallic corners. The distribution of charges and currents induced on the metallic sidewalls, which are provided by $\sigma =\stackrel{\rightharpoonup }{E}•\stackrel{\rightharpoonup }{n}$ and$\stackrel{\rightharpoonup }{J}=\stackrel{\rightharpoonup }{H}\times \stackrel{\rightharpoonup }{n}$, with σ the sheet charge density, $\stackrel{\rightharpoonup }{J}$ the surface current density, and $\stackrel{\rightharpoonup }{n}$ the outgoing normal the metallic walls, indicated in Fig. 2(c) and Fig. 2 (e). It is noteworthy that there is a nearly π/2 phase difference between Ex and Hz along z-axis in the center of the air nano-groove, as shown in Fig. 2(f), which is characterized by the standing wave reflected from a perfect electronic conductor. At optical frequencies, however, metals have finite conductivity and their complex index is finite. Inside the cavity, there is a little variation from π/2 which helps to couple the incident wave into cavity mode and make the absorption possible. Dielectric-based subwavelength metallic meanders can provide an efficient way to couple in and out the radiation, which is also suitable for the oblique incidence case when the symmetry is broken.

3.2 Angle-sensitive absorption in the dielectric-based subwavelength metallic meanders

The wave vectors of RWA and SPM mode are governed by the well-known grating formula $k_{RWA}=k_{inc,x}\pm mG$ and the SPM excitation equation $k_{SP}=k_{inc,x}\pm mG$ respectively, where m is 0, 1, 2, …. Due to the above equations, both of these two modes are sensitive to incident angle in nature. However, the excitations of RWA and SPM are based on different mechanisms, by which RWA is a passing-off of a spectral diffraction and SPM is collective charge oscillations.

Figure 3(a) shows the absorption spectra as a function of the normalized wavelength and the normalized tangential wave vector k_x with a meander pitch of 300 nm. The thickness of the Al layer and the width of the air nano-groove between two Al sidewalls remain 30 nm. The reason that 300 nm pitch is chosen is based on the fact that the absorptive band can be in visible regime in this case. An absorption band is between the first order of the negative SPM and RWA. The absorption is 84% with the resonant wavelength 378 nm at incident angle 15° with full width at half maximum of 2 nm. The coupling effect is still allowed under oblique incidence, but a large portion of the incident electromagnetic energy is transferred to resistive heat on the top Al layer, as illustrated in Fig. 3(b). It is interesting to note that the net time average wave intensity is found greatly enhanced and almost parallel to the meander surface in the near-field region. It can be explained as following. RWA plays the key role in this case, however, the SPM is excited because of the very close dispersion relations of the first order of –RWA and –SPM. by scattering of the meanders. A large portion of the incident electromagnetic wave energy is disspitated on the top Al layer compared to that shown in Fig. 2(b). The field distributions of Ex, Ez and Hy are shown in Figs. 3(c)-3(e). The incident light excites opposite dipoles much weaker,and leaky wave funneling into the air nano-groove is much smaller. Inside the cavity, there are also localized CM occuring and a nearly phase difference of π/2 between Ex and Hy along z-axis direction at the center of the air nano-groove, as shown in Fig. 3(f).

 

Fig. 3 (a) Absorption spectra as a function of the frequency and wave vector k_x in the first Brillouin zone of the meander with a pitch of 300 nm. The square symbol represents the resonant wavelength 378 nm at incident angle 15°. The solid lines and dotted lines represent the dispersions of SPM and RWA, respectively. (b) The colormap represents the amplitude of the time-averaged power loss density Q and the arrows represent the Poynting vector. Contours of horizontal electric field E_x (c), vertical electric field E_z (d) and magnetic field H_y (e). The alignment of surface charges dipole is denoted by symbols “$\oplus$” and “$ⓛ$”. The surface currents are denoted by white arrows. (f) Phase of Ex and Hy along z-axis at the center of the cavity (x = 150 nm). Dotted-lines depict schematically the profile of the metallic Al film.

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The simulation results provide theoretical support that both SPM and RWA contribute to the enhanced absortpion of light in this case. We call it a hybrid mode of SPM and RWA. For the SPM, it can absorb light by collective excitation of electrons in the form of a plasmon, causing enhanced power flow near the surface and a loss of power in the remaining propagating orders. The surface plasmonic wave is bound to the surface and the electric field intensity decreases exponentially with distance from the meander surface (to the distance of a wavelength). For the RWA, a diffracted order becomes evanescent the energy associated with that order can be absorbed. The electric field in the RWA extends far from meander surface. Compared to the CM effect, the mechanism above can provide angular selectivity and polarization selectivity.

3.3 Geometry’s influence on the meander behavior

In order to obtain angle-insensitivity, one has to avoid relying on grating coupling for a hybrid mode of SPM and RWA excitation. In the dielectric-based subwavelength metallic meander, light funneling into nanoslits is exploited to generate strong CM resonance for the TM-polarized incident light. Funneling effect with narrow slits much smaller than the incident wavelength occurs and the light is trapped in the metal-dielectric-metal cavity Both effects possess plasmonic mode coupling with efficiency comparable to that of grating coupling. We studied the influences of the structural paramters of the meanders on absorption properties.

Figure 4 shows the absorption spectra as a function of incident wavelength, the air nano-groove (d = 30 nm, 60 nm), the meander pitch (p = 160 nm, 200 nm, 240 nm) and the incident angle (θ = 0°, 45°). Other geometric parameters are the same as those in Fig. 1(b). The plots clearly show that the meander pitch does not affect the position of the absorption peak as the pitch decreases. When d is decreased from 60 nm to 30 nm, there is redshift of peak position for the propagation constant of the metal-dielectric-metal waveguide is changed. The narrow absorptive peak in the d = 30 nm and p = 200 nm case is attributed to the excitation of the hybrid mode of SPM and RWA. A general conclusion from the above results is that in order to enhance angle-robustness, one needs to maintain a relatively small pitch and a narrow air nano-groove.

 

Fig. 4 Absorption spectra plotted as a function of incident wavelength, air nano-groove (d = 30nm, 60nm), meander pitch (p = 160 nm, 200 nm, 240 nm) and incident angle (θ = 0°, 45°). Other geometric parameters are the same as those in Fig. 1(b).

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Figures 5(a)-5(c) shows the absorption spectra as a function of the grating height h₁, which depicts that the angle-robust behavior is regardless of h₁. As h₁ is increased to 240 nm, shown in Fig. 5(c), two absorptive peaks are generated. They are the first and sencond order of the CM. Combining these structural parameters gives access to a range of interface reflection and band absorption that can be engineered by modification of the geometries.

 

Fig. 5 Absorption spectra with different dielectric grating height h₁. (a) 170 nm; (b) 220 nm; (c) 270 nm.

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4. Conclusion

In conclusions, dielectric-based subwavelength metallic meanders have been demonstratred as wide-angle band absorbers, in which there is no need for a bulk metallic substrate as in conventional absorbers. The meander can achieve perfect absorption and a good angular tolerance up to 60° for TM light incidence with continuous ultra-thin (less than one tenth of the incident wavelength) metallic film. It suggests that the angle-robust absorbance is due to collective efforts of the cavity mode resonances through the excited charge dipoles at the corner of the meander. Well-defined choices of the meander pitch, height and air nano-groove width allow us to control the properties of optical fields, which is a condition difficult to reach at the micro- and nanoscale owing to rather limited variations in the permittivity and permeability of conventional materials, thus the highly efficient visible light absorbers can be potential candidates for a range of passive and active photonic applications, including solar-energy harvesting as well as producing artificial colors on a large scale substrate.