1. Introduction

Highly efficient light absorption by a nanoscale structure has been developed and discussed intensively for the past ten years [1–3]. How to reduce the thickness of a light absorber has been an important issue. Intuitively, the surface of a strong light absorber must have low reflection and the bulk must have a high energy dissipation rate inside when it interacts with light. The optical property of a non-magnetic material is described by its refractive index. The real and imaginary parts of the refractive index are the index of refraction and the extinction coefficient, respectively. Low reflection requires the refractive index to be close to that of incident medium to enable the incident light to couple into the absorber efficiently. However, high energy dissipation in a thin material requires a high extinction coefficient, which is at odds with the need for low reflection. Although a high extinction coefficient ensures efficient dissipation of energy, it also results in strong reflection when a light wave hits the surface. One study developed a super dark array of carbon nanotubes with a refractive index of 1.026 + i0.0006 and an ultra-low reflectance of 0.045% but it was 300μm thick [4]. Some other light absorbers are developed to perform antireflection and energy dissipation separately with two different parts of structure. Jing-qun Xi et al. [5] applied oblique-angle deposition to deposit a five-layered structure on an aluminum nitride substrate. They obliquely deposited TiO₂ and SiO₂ to form a five-layered structure with a refractive index that varied from 2.03 to 1.05. The grade index profiles satisfied a perfectly antireflective design whose reflectance was 0.1%. After the light passed through the antireflective structure with a thickness of 0.6μm, the energy of the light was absorbed by the aluminum nitride substrate with a refractive index of approximately 2.05 + i0.00002. An average thickness of 10mm was required to absorb 95% of the energy of the incident light.

The trade-off between low reflection and high dissipation was made successfully by the development of subwavelength metallic nanostructures. Artificially nano-sculptured structures with unusual and favorable optical properties that are not found in nature are called metamaterials [6]. Electromagnetic waves that propagate through a subwavelength structure of a composite induce local plasmonic resonance, which changes the equivalent permittivity and permeability from the intrinsic values of the constituent materials. Their permittivity and permeability can be tailored to be positive or negative, yielding many extraordinary optical phenomena, including negative refraction and negative index of refraction [7, 8]. Using metamaterials as light absorbers can be reached via local plasmonic resonance within nano-metallic structures [1, 2]. Metamaterials with impedance matching to the incident medium perform antireflection in the infrared [9] and terahertz [10] frequency regime. One previous work applied a periodic and regular distribution of metal wires to absorb light at some specific frequencies [11, 12]. The structure is similar to Fakir's bed of nails and its fraction of metal is so small that the magnetic fields induced between wires were ignored. In 2011, Aydin et al. [13] developed the metallic trapezoid fishnet structure, which was 160nm-thick on a 100 nm-thick silver mirror that was covered with a 60nm-thick SiO₂ film. Its average absorptance was around 65.14% in the wavelength range from 400nm to 750nm.

Recent research has shown that the optical property of a typical metamaterial film should take the bianisotropy into account [14, 15], and an equivalent bianisotropic parameter should be added to equivalent relative permittivity and equivalent relative permeability to represent the associated optical parameters, which are equivalent refractive index and the two equivalent impedances that are associated with forward and backward propagations. The equivalent refractive index and equivalent impedances determine the fundamental optical properties of a metamaterial, such as reflectance, transmittance and aborptance. The tailored impedance dominates the reflection/transmission at the surface and the refractive index dominates the propagation and dissipation of waves in the thin film. The equivalent refractive index and equivalent impedance are mutually independent, providing strong absorption of light in a very thin film. Therefore, light can be coupled into a film that is impedance-matched to the incident medium and dissipated with high imaginary part of the refractive index.

The authors’ previous work demonstrated that a tilt silver nanorod array is a kind of metamaterial thin film with non-unity permeability [16]. At visible wavelengths, the real part of the refractive index is negative when an electromagnetic wave with polarization along the rods propagates through the film. In this work, an upright aluminum nanorod array (Al NRA) is grown using glancing angle deposition (GLAD) [17]. The extraordinary absorption of light over visible wavelengths makes the film look dark. This new light absorber has impedance that is close to that of the incident medium, air, so it exhibits very weakly reflection. Owing to its considerable extinction coefficient, the film can efficiently absorb light energy. The near-unity impedance does not affect the extinction property of the film. To reduce the thickness of the light absorber, a semicontinuous thin-film (SCF) [18] is arranged between the Al NRA and a glass substrate. The SCF reduces the transmittance of light at the bottom interface and absorbs light energy with thickness of only 15nm. Therefore, the Al NRA arranged upon Al SCF/glass can be thinner than that upon bare glass to achieve the similar absorption.

2. Single Al NRA on glass

Fabrication by GLAD involves tilting the substrate at an angle ${\theta }_v$ with respect to the deposition flux in the electron-beam evaporation system, as shown in Fig. 1(a). In the initial deposition, nucleation centers form randomly on the substrate and the deposited flux causes the preferential growth of nanorods towards the direction of deposition owing to the shadowing effect. To grow upright aluminum pillar arrays, the substrate was spun rapidly during deposition. Films were deposited on the substrate of BK7 glass. Prior to deposition, the chamber that contained the substrate and the solid silver was pumped to a base pressure of 4×10^-6 Torr. The deposition rate was maintained at 1 nm/s and the deposition angle was maintained at θ=89°. During deposition, the substrate was rotated about the substrate normal at a constant speed of dϕ/dt = 10rpm. The lengths of the pillars were controlled using a quartz thickness monitor that was placed next to the substrate.

 

Fig. 1 The Schematic diagram of Al NRA array fabricated by GLAD with rotating the substrate rapidly during deposition.

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Three films with thicknesses d = 350nm, 520nm and 750nm were fabricated. Figure 2 shows their top-view and cross-section scanning electron microscopic (SEM) images. The diameter w of the pillars in the films with thicknesses 350nm, 520 nm and 750 nm, are approximately 162 nm, 211 nm and 283 nm, respectively.

 

Fig. 2 Top-view and cross-sectional scanning electron microscopic images for the three Al NRAs with thicknesses of (a) 350nm, (b) 520nm and (c) 750nm.

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Figure 3 shows the spectra of the transmittance $T_j$, reflectance $R_j$ and absorptance $A_j$, $j\in \{x,y\}$ measured by using a spectrometer (Jobin Yvon iHR320). The three Al NRAs were illuminated under normally incident light. Both x-polarized and y-polarized spectra were obtained in orthogonal polarization directions. The difference of transmittance between x-polarized and y-polarized spectra is less than 0.0511, indicating that the NRA is polarization-independent when the light is normally incident. The low reflectances of the 350nm-thick, 520nm-thick and 750nm-thick films are less than 0.0134, 0.0119 and 0.0068, respectively. The transmittance (absorptance) increases (decreases) as the wavelength increases from 400m to 700nm. The high absorption extends to higher wavelengths as the thickness of the Al NRA increases. The average absorptance is proportional to the thickness of the film. The 750nm-thick film exhibits absorptance from 0.96388 at 400nm to 0.80804 at 700nm.

 

Fig. 3 Measured spectra of T_j, R_j, and A_j, $j\in \{x,y\}$of three NRAs. Light was normally incident when transmittance measurements were made but obliquely incident at 5 deg to the normal when reflectance measurements were made.

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To understand the propagation of waves through the film, the refractive index, forward impedance, and backward impedance were derived using a walk-off interferometer [19] to measure the reflection and transmission coefficients of the air/film/glass structure and the reverse configuration, glass/film/air. The 520nm-thick film was adopted to make measurements because its transmission was enough to be detected. Figure 4 shows the equivalent refractive index $n_j,$ forward impedance $Z_{+,j},$ and backward impedance$Z_{-,j}$. The forward impedance $Z_{+,j}$ and backward impedance $Z_{-,j}$ are 1.01779 and −0.02288, respectively, so the reflection remains low when light interacts with the surface of the film and the light is coupled into the film efficiently. The near-unity impedance of the metamaterial film does not result in a near-unity refractive index, as it does in a nonmagnetic material, which has a reciprocal relationship between impedance and refractive index. The real part of the tailored refractive index $n\text{'}$ is 1.07671. The extinction coefficient $n"$ falls from 0.13771 to 0.10125 as the wavelength increases from 405nm to 690 nm, reflecting the decay of absorptance with increasing wavelength.

 

Fig. 4 Measured spectra of refractive index $n_j$, forward impedance $Z_{+,j}$, and backward impedance $Z_{-,j}$, $j\in \{x,y\}$_.

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From the equivalent parameters $n\text{'}$, $n"$ and $Z$, the propagation of light through the film can be understood. As shown in Fig. 5, when the 520nm-thick film is illuminated by light with an electric field amplitude of unity and a wavelength of 690 nm, the wave penetrates the upper interface of the film with transmission coefficient 0.9413$\angle -{1.1395}^{\circ }$. From the upper interface to the bottom interface, the wave propagates with a phase change of −50.77^。 and the field amplitude decays to be 0.5828. The reflection coefficient and transmission coefficient at the bottom interface are 0.1031$\angle {171.9876}^{\circ }$ and 0.8980$\angle {0.9174}^{\circ }$, respectively. The electric field amplitude of the transmitted wave is 0.5233. The reflected wave from the bottom interface is backward-propagating with an initial field amplitude of 0.0601. When the reflected wave returns to the upper interface, the transmitted wave with an amplitude of 0.0515 interferes with first-order reflected wave destructively. The initial amplitude of the reflected wave from the upper interface is 0.0143, and it decays to be 0.0089 when the wave again reaches the bottom interface. The first-order transmitted wave and the first two orders of reflected waves contribute most to the transmittance and reflectance from the film, respectively.

 

Fig. 5 The wave tracing of the Al NRA normally illuminated by light with an electric field amplitude of unity at wavelength of 690 nm.

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The relative electromagnetic parameters-permittivity ${\epsilon }_j$, permeability ${\mu }_j$ and equivalent bianisotropic parameter ${\xi }_j,$ $j\in \{x,y\}$-can be derived from equivalent refractive index $n_j$ and equivalent impedances $Z_{+,j}$ and $Z_{-,j}$ equivalently via the relationships: ${\epsilon }_j=(n_j+i{\xi }_j)/Z_{+,j},$ ${\mu }_j=(n_j-i{\xi }_j)Z_{+,j}$ and ${\xi }_j=i{n}_j(Z_{-,j}+Z_{+,j})/(Z_{-,j}-Z_{+,j}),$ as shown in Fig. 5. The real parts of both relative permittivi ty and relative permeability are positive. The real part and the imaginary part of the equivalent bianisotropic parameter are within the ranges (−0.0212, 0.21869) and (−0.4827, 0.2696), respectively. The real parts of $\epsilon$ and $\mu$ are within the ranges (1.0926, 1.6772) and (0.5195, 1.0421), respectively. The imaginary parts of $\epsilon$ and $\mu$ are within the ranges (0.0767, 0.2904) and (−0.0867, 0.1523), respectively. The relative permittivity and relative permeability vary in a manner similar to the variations in Figs. 6(a) and 6(b) because, when the equivalent bianisotropic parameter is negligible, ${\epsilon }_j$ and ${\mu }_j$ are equal, yielding unity impedance.

 

Fig. 6 Measured spectra of permittivity ${\epsilon }_j$, permeability ${\mu }_j$ and bianisotropic parameter ${\xi }_j,$$j\in \{x,y\}$_.

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The absorptance spectra of Al NRAs that are coated on a BK7 glass substrate were examined. The substrate is opaque in the visible regime from 400 nm to 700nm at angle of incidence $\theta \in [5^{\circ },{60}^{\circ }]$ with respect to the z axis with linear polarization (p- or s-polarization). Figure 7 plots shows the absorptances, $A_p$ and $A_s$, versus $\lambda \in [400,700]$ nm and $\theta \in [5^{\circ },{60}^{\circ }]$, for the 350nm-thick, 520nm-thick and 750nm-thick Al NRAs. The absorptance $A_p$ and $A_s$ have similar angular and wavelength spectra for each sample. As plotted in Figs. 7(a) and 7(b), the $A_p$ and $A_s$ of the 350nm-thick film increase with angle of incidence from $\theta ={20}^{\circ }$ to $\theta ={60}^{\circ }$. The absorptance decreases with increasing wavelength. As plotted in Figs. 7(c) and (d), the $A_p$ and $A_s$ of the 520nm-thick film over 0.80 continuously distribute at $\lambda \in [400,554]$ nm and $\theta \in [5^{\circ },{60}^{\circ }]$. The $A_p$ is larger than $A_s$ at each wavelength and angle of incidence. The $A_p$ and $A_s$ of the 750nm-thick film present absorptance exceed 0.85 and 0.82 over the whole wavelength and angular ranges, respectively, as shown in Figs. 7(e) and (f). The minimum absorptance $A_s$ occurs at the wavelength of 700nm and angle of incidence$\theta ={60}^{\circ }$. For a given incident angle and wavelength, the absorptance increases with thickness from 350 nm to 750 nm because the dissipation is proportional to thickness.

 

Fig. 7 P-polarized and s-polarized absorptances versus wavelength $\lambda \in [400,700]$nm and angle of incidence $\theta \in [5^{\circ },{60}^{\circ }]$ for three Al NRAs with thicknesses of (a) (b) 350nm, (c) (d) 520nm and (e) (f) 750nm.

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The Al NRA overcomes the problem of ultra-low reflectance with high absorption for a thin structure. Comparing the above results with those for a nonmagnetic optical thin film reveals that at a wavelength of 405nm, the forward impedance of Al NRA with a thickness of 520nm that yields a low R = 0.5% is 1.184 + i0.013. For a nonmagnetic thin film, such low reflection requires the equivalent refractive index to be 0.8449 + i0.0092. However, with such a refractive index, the film must be 9285nm-thick to yield an absorptance of 90.7%.

3. Al NRA/Al SCF/glass system

It has been demonstrated that semi-continuous metal films exhibit anomalous absorption and moderate reflection [20–22]. The localized surface plasmons and localization of strongly enhanced electromagnetic fields alone the boundaries of the voids lead to broadband absorption. Such an ultra-thin film can be applied under the Al NRA to promote absorption. In the fabrication of Al SCFs, the deposition rate was maintained at 0.2 nm/s and the deposition angle was kept at ${\theta }_v=0°$. Six Al SCFs with thicknesses of 5 nm to 30 nm were grown to observe their performance as buffer layers between NRA and glass substrate.

The transmittance, reflectance and absorptance of Al SCFs with difference thickness were measured at wavelengths from 400nm to 700nm. Figure 8 plots the average transmittance, reflectance and absorptance spectra of Al SCFs that were illuminated by normally incident x-polarized and y-polarized in the visible regime. The average reflectance increases from 0.2028 to 0.5614 as the thickness of the Al SCFs increases from 5 nm to 30nm, while the average transmittance decreases from 0.4446 to 0.1406. The average absoptance is within the range 0.2980 to 0.4242. Therefore, the 15nm-thick Al SCF was utilized as the bottom layer of Al NRA to improve absorption.

 

Fig. 8 Measured spectra of T_j, R_j, and A_j, $j\in \{x,y\}$ , of Al SCFs.

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Al NRAs with thicknesses of 245nm and 340nm were separately grown on a 15nm-thick SCF. Figure 9 shows the transmittance, reflectance and absorptance spectra of the Air/Al NRA(245nm)/SCF/BK7 system that was illuminated by normally incident x-polarized and y-polarized light. The average reflectance is less than 0.1591 and the average transmittance is 0.1304. The absorptance decreases from 0.8620 at λ = 350nm to 0.6893 at λ = 1000nm. Figure 10 shows the measured transmittance, reflectance and absorptance spectra of the other system, Air/Al NRA(340nm)/SCF/BK7. The average reflectance is less than 0.0680 and the average transmittance is 0.2232. Both reflectance and transmittance increases with wavelength. The absorptance decreases from 0.8914 at λ = 350nm to 0.5679 at λ = 1000nm. Figure 11 plots the absorptances $A_x$and $A_y$ versus $\lambda \in [350,1000]$ nm and $\theta \in [5^{\circ },{60}^{\circ }]$ for system Air/Al NRA(245nm)/SCF/BK7. Both$A_x$ and $A_y$exceed 0.60 over the whole wavelength range, and the average value of $A_x$ and $A_y$over the whole wavelength and angle ranges are 0.7613 and 0.7600, respectively. Based on the measurement results of the two Al NRAs, the absorptance of the Air/Al NRA(245nm)/SCF/BK7 is considerably extended throughout the violet-to-infrared regime.

 

Fig. 9 Measured spectra of T_j, R_j, and A_j, $j\in \{x,y\}$ of Air/Al NRA(245nm)/SCF/BK7.

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Fig. 10 Measured spectra of T_j, R_j, and A_j, $j\in \{x,y\}$ of Air/Al NRA(340nm)/SCF/BK7

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Fig. 11 Absorptance spectra $A_x$and $A_y$ of the compound film composited with Al SCF and Al NRA as functions of wavelength from 350nm to 1000nm and incident of angle from 5° to 60° for the Air/Al NRA(245nm)/SCF/BK7 system.

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Figure 12 compares absorptance of Air/Al NRA(245nm)/SCF/BK7 with that of the aforementioned trapezoid fishnet structure that was developed by Aydin et al. [13]. The Al NRA on SCF has an average absorptance of approximately 70.98%, which exceeds that of the fishnet structure. Our structure has a higher absorption than the trapezoid fishnet structure at wavelengths shorter than 450nm and longer than 650nm. The thicknesses of the two structures are almost equal.

 

Fig. 12 Absorptance spectra of $A=(A_x+A_y)/2$ for trapezoid fishnet structure [13] and Al NRA(245nm)/SCF coating on BK7 substrate.

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4. Conclusion

In conclusion, this work presents a method for fabricating a thin film that comprises an upright aluminum nanorod array. This nanoscaled aluminum semicontinuous film can effectively absorb a broad range of wavelengths over wide range of incident angles. The Al NRAs exhibits near-unity impedance, which dominates the low reflection at the interface between air and the film, and the energy dissipation represented by the extinction coefficient reduces the transmittance to an extent. Proper Al SCFs under the Al NRA can further enhance absorbance of light and reduce the thickness of the structure. This result reveals that the mutual independence of refractive index and impedance enables a tailored metamaterial to combine two kinds of optical property within an ultra-thin film. Based on the new concept of light absorber, a broadband and wide-angle impendence matching condition and relatively high extinction coefficient will be developed next to reach the requirement of perfect light absorber with a very compact structure. Such a structure can be fabricated using not only nano-lithography but also general coating technique.