Ordered Arrays of Metal Nanostrings as Broadband Super Absorbers

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Ordered Arrays of Metal Nanostrings as Broadband Super Absorbers Vassilios Yannopapas* and Ioannis E. Psarobas Department of Materials Science, University of Patras, GR-26504 Patras, Greece ABSTRACT: We study the absorption spectrum of ordered arrays of strings of gold nanoparticles within a nematic liquid crystal by a rigorous electrodynamic approach. We find, in particular, that, as the length of the strings increases, light absorbance can be very high over the entire visible regime. The ordinary modes of the nematic liquid crystal allow the nanoparticle strings to absorb light much more efficiently than the extraordinary modes. Overall, absorption does not depend on the lattice type of the string array due to the subwavelength functionality of the system. Such a structure operates as a gray body exhibiting an absorption efficiency of 79% within the entire visible regime, averaging over all angles of incidence and polarization modes.

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INTRODUCTION Metamaterials are man-made structures with electromagnetic (EM) properties that are not observed in naturally occurring materials, such as artificial magnetism,1 negative refractive index (NRI),2 near-field amplification,3 cloaking,4 and other optical illusions.5 In the early years of the metamaterials era, absorption had been only considered as an undesirable intrinsic feature in naturally abundant materials, which blurred the observation of exotic phenomena such as a perfect lens. As the scientific community started realizing the unprecedented control over EM radiation offered by metamaterials, absorption came to focus in spectral regions where natural materials are poor absorbers, e.g., metals in the terahertz regime. To this end, the concept of perfect absorption was put forward6 wherein the ability to manipulate the magnetic permeability enabled the design of micrometer-sized metasurfaces whose impedance can be matched ideally to the vacuum one, diminishing the metal reflectivity. The latter can find application in bolometric devices and cameras that capture the infrared thermal radiation. The above designs operate strictly within a very narrow spectral window since they rely on a resonant phenomenon (perfect absorption). In some cases, however, narrow-band absorption is the sought functionality as, for example, in photovoltaic cells where the efficiency of energy conversion is increased when, ideally, the spectrum of incident radiation is sharply peaked around the semiconductor band gap energy. Such a functionality has been infused to so-called metallo-dielectric photonic crystals wherein with proper photonic band gap engineering, absorption can be suppressed over a broad region except for a narrow band around a preselected frequency.7,8 On the other hand, broadband absorption is pursued in devices such as radiation coolers and incandescent bulbs.9 In the latter case, ideal device performance is achieved if, supposedly, the bulbs were made of a material emitting light exclusively in the optical regime (having a cutoff at the upper edge of the IR spectrum). Recently, broadband absorption over the visible © 2012 American Chemical Society

regime with 71% efficiency has been demonstrated in lithographically defined plasmonic metamaterials10 which were justifiably named as super absorbers. As a rule of a thumb, whenever a new functionality is demonstrated in a top-down lithographic metamaterial, bottom-up technology promptly brings out an alternative material design of lower cost, higher throughput, and smaller sensitivity to damage or fabrication errors. As noble metals are highly absorbent in the optical regime, any candidate metamaterial design based on self-assembly must comprise such type of nanoparticles (NPs). The latter exhibit strong scattering and absorption around the surface plasmon (SP) wavelength which, e.g., for spherical gold NPs in air is about 530 nm. Due to this narrow-band response of a single metal NP, it is widely believed that a bottom-up metamaterial based on metal NPs can not manifest a broadband-absorption functionality.10 However, this is true only for two-dimensional (2D) or thin three-dimensional (3D) metamaterials formed by arrays of metal NPs. In this work we demonstrate theoretically that submicrometer thick metamaterials of metal NPs can exhibit strong light absorption over a wide range of frequencies in the visible regime. Quite recently, such 3D metamaterial designs have been realized in the laboratory in the form of hexagonal arrays of micrometer-long metal-NP strings. The NPs are self-organized into ordered arrays of strings after being functionalized with properly designed liquid-crystal (LC) mesogens.11,12 We note that 3D superlattices of NPs have been realized in the past by various self-assembly methods13−17 without, however, yielding thick enough samples that can serve the purpose of strong broadband light absorption. Received: April 28, 2012 Revised: June 18, 2012 Published: June 20, 2012 15599

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However, to a first approximation, we neglect this phenomenon due to the small difference between the ordinary no and extraordinary ne refractive indices. The dielectric function of the gold NPs is taken from experimental data26

OUTLINE OF THE MODELING METHOD In Figure 1 we show 2D periodic lattices occupied by NP strings. In order to study the optical response of such systems,

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RESULTS AND DISCUSSION In Figure 2 we show the absorbance spectra of light incident at various angles on finite slabs of hexagonal arrays of strings of

Figure 1. Hexagonal (left) and square (right) lattice of strings of gold NPs. The red arrow denotes the incident wavevector.

we employ the layer-multiple scattering (LMS) method for EM waves.18,19 The method is ideally suited for the calculation of the transmission, reflection, and absorption coefficients of an EM wave incident on a composite slab consisting of a number of layers, which can be either planes of nonoverlapping particles with the same 2D periodicity or homogeneous plates. For each plane of particles, the method calculates the full multipole expansion of the total multiply scattered wave field and deduces the corresponding transmission and reflection matrices in the plane-wave basis. The transmission and reflection matrices of the composite slab are evaluated from those of the constituent layers. By imposing periodic boundary conditions, one can also obtain the (complex) frequency band structure of an infinite periodic crystal. Its main advantage over the other existing numerical methods lies in its efficient and reliable treatment of systems containing strongly dispersive materials such as noble metals. Comparison of theory and experiment has been known to be very good.20−24 As stated above, the fabrication (self-assembly) of ordered arrays of NP strings requires that the NPs are functionalized by LC mesogens.11,12 The presence of the liquid crystal means that the medium surrounding each NP string is generally anisotropic. In order to account for this particular property of the medium in the study of optical absorption by the array of NP strings, we consider the simplest type of anisotropy, namely uniaxial anisotropy, i.e., the NPs are surrounded by a nematic LC. We assume a typical nematic LC, namely, E7 LC with refractive index no = 1.53 for the ordinary modes and ne = 1.74 for the extraordinary modes. We further assume that the director field lies along one side of the hexagonal array, say the x-axis, forming an angle θ′ with an incident plane wave. In this case (oblique incidence), the refractive index for the extraordinary modes is given by neno ne = 2 ne cos θ′ + no sin 2 θ′ (1)

Figure 2. Absorbance spectra for the extraordinary modes calculated for hexagonal lattices (a = 10 nm) of 3 nm gold NP strings inside a nematic LC versus angle of incidence, for three different slab thickness (string lengths): (a) 2 planes, (b) 16 planes, and (c) 128 planes.

For the above incidence setup, the extraordinary modes are excited by s-polarized incident light, while the ordinary modes are excited with p-polarized incident light. It is worth noting that close enough to the NPs, the LC molecules tend to anchor at the NP surface, generating an inhomogeneous distribution of the director field of the nematic LC around each NP.25

gold NPs with 3 nm radius, as obtained by the LMS method. The lattice constant of the hexagonal arrays is a = 10 nm, and for the slabs presented in Figure 2 they comprise 2 (a), 16 (b) and 128 (c) NPs in each string. Along a certain string, the NPs are touching each other. The first thing that is obvious from Figure 2 is the fact that the shape of the absorbance spectrum 15600

dx.doi.org/10.1021/jp304101a | J. Phys. Chem. C 2012, 116, 15599−15603

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alters drastically as the number of NPs in the strings increases. For a two-NP string, the absorbance curve exhibits the typical peak around the SP wavelength of a single gold NP (around 530 nm). There is also an almost constant level of absorption below the SP wavelength, which increases with the angle of incidence. This trend, however, is reversed for the case of 16 and 128 NPs in the string, and the degree of absorption below the SP wavelength decreases with the angle of incidence. This can be understood as follows. For thin slabs, EM interaction and thus absorption takes place mostly among the NPs within the same plane of spheres. For large angles of incidence, most EM radiation energy is dedicated to the lateral (parallel to the array) oscillation of the EM wave than to the normal (along the strings) one. Thus most of the energy is transferred to the lateral interaction among the NPs (which is stronger than the normal interaction due to the small slab thickness) resulting in a higher degree of absorption for large angles. However, as the slab thickness increases, the interaction among particles along the string catches up very quickly to the corresponding lateral interaction since the NPs are very close within the same string. Another feature which is evident as the slab thickness (string length) increases is the fact that a double peak structure builds up. This is a well-known result coming from the fact that the SP resonances are different when a plane wave incident on a pair of NPs is polarized along and normal to the pair axis [splitting of the single-sphere plasmon resonance in a dimer of spheres (plasmon hybridization)].27,28 Therefore, the SP wavelengths resulting from NPs interacting along the string and normal to it are different, generating the double-peak structure of Figure 2b. It is also evident from Figure 2 that the double-peak structure depends strongly on the angle of incidence. The position of the absorption peak would have been independent of the angle of incidence if the absorption peak were a single-NP feature. In our case, however, we have a 3D array of NPs, which is an inhomogeneous medium and results in a k-dispersion of the resonance wavelength. For a periodic inhomogeneous medium such as the system considered here, the dispersion is demonstrated in the frequency (wavelength) band structure, which is essentially the dispersion lines along the symmetry lines of the surface Brillouin zone corresponding to a given lattice. More about SP dispersion lines can be found elsewhere.29 Finally, the most striking feature in Figure 2 is the sizable absorption plateau that sets in for long enough NP strings. The level of absorption starts from about 68% for 60° angle of incidence and reaches the value of 92% for normal incidence, whereas the absorption range spans from 350 nm up to 500 nm. Figure 3 elucidates more clearly the role of the string length in the absorption spectrum, for a given angle of incidence. We observe that as the number of planes of the NP metamaterial (string length) increases, the absorbance increases accordingly, whereas for small wavelengths (below the SP) it saturates above a certain string length (number of planes). Another interesting feature of Figure 3 is the fact that, as the number of NP planes increases, the SP peak shifts toward shorter wavelengths (blue shift), while it eventually breaks up into two distinct peaks for 16 planes and above. These are the same peaks that are discussed above and in relation to Figure 2. In reality, these two resonance peaks also exist for slabs of fewer than 16 planes. However, their spectral distance is smaller than their width, resulting in the appearance of a single (Lorentzian) peak for thin slabs. According to the discussion in the previous paragraph, these two distinct peaks result from the hybrid-

Figure 3. Absorbance spectra for the extraordinary modes calculated for hexagonal lattices (a = 10 nm) of 3 nm gold NP strings inside a nematic LC versus the number of NP planes (string length), for three angles of incidence:(a) θ′ = 0°, (b) θ′ = 30°, and (c) θ′ = 60°.

ization of the single-NP SPs of two neighboring spheres, which generates a red- and a blue-shifted SP peak.27,28 As more NP planes are added to the slab, the blue-shifted peak dominates the spectrum, while, at the same time, the interaction among NPs results in a further increase in the frequency splitting of the two (hybridized) SP peaks. This means that, initially, the two (hybridized) peaks (appearing as one for thin slabs) move toward shorter wavelengths as the number of increases before they split into two distinct spectral peaks for thick enough slabs. Figure 4 compares the absorbance curves when incident light excites the ordinary and the extraordinary waves of the nematic LC surrounding the NPs. Evidently, light is much more attenuated by the ordinary modes than by the extraordinary modes, e.g., the short-wavelength plateau for the ordinary modes is about 98%, while that for the extraordinary modes is 15601

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distance, a = 10 nm. As such, the choice of the lattice type of the NP string array should be critical for short rather than long wavelengths. However, the fringe structure in the long wavelength regime results from the size of the string. As the NP string size increases, the operating wavelength becomes comparable to the string, rendering the string an effective metallic wire supporting SP modes along its length. As a result, the incident wave multiply scatters off the first and last NP of the string, generating the oscillatory behavior at long wavelengths. As the system considered here can potentially found application in thermo-photovoltaic (TPV) devices, we are interested in the spectral hemispherical (SH) radiative properties of the structure. More specifically, we are interested in the SH absorbance a(ω), which is the ratio of the SH absorbing power of the structure IS to the SH absorbing power IBB of a perfect blackbody at the same temperature T. For a slab infinitely extended in two dimensions,

Figure 4. Absorbance spectra for extraordinary (solid line) and ordinary (dashed line) light incident at angle of 45° on an hexagonal array (a = 10 nm) of 3 nm gold NP strings each consisting of 64 NPs.

80%. This is due to the enhanced reflectance of s-polarized incident light. In order to assess the dependence of the absorption spectrum on the type of crystal lattice formed by the NP strings, in Figure 5 we compare the absorbance spectra of the

2π

a(ω)

=

∫0 dϕ ∫0 2π

π /2

∫0 dϕ ∫0 =

1 π

∫0

2π

dϕ

dθIS(ω , θ , ϕ , T ) cos θ sin θ

π /2

∫0

dθIBB(ω , T ) cos θ sin θ

π /2

dθ ((ω , θ , ϕ) cos θ sin θ (2)

Figure 5. Comparison of the absorption spectra for s-polarized light incident at 45° on an hexagonal lattice NP strings (lattice constant a = 10 nm, NP radius S = 3 nm, solid line) with the respective spectra of square lattices of NP strings with the same NP surface coverage, i.e., a square lattice with the same interparticle distance (lattice constant a = 10 nm, NP radius S = 3.22 nm, dashed line) and a square lattice with NPs of the same radius (lattice constant a = 9.3 nm, NP radius S = 3 nm, dotted line) as with the hexagonal lattice. In all cases, the slabs are 64 planes thick.

The above equation is valid for each polarization type of an incident plane wave that is incident at angle θ [which is complementary to the angle θ′ of eq 1, i.e., θ + θ′ = 90°; see Figure 1]. For the total SH absorbance, we have to take the average of the absorbance ( (ω,θ,ϕ) for both polarization modes of the incident wave. Figure 6 shows the SH absorbance spectra for extraordinary (E) and ordinary (O) modes for different number of planes (string lengths). It is evident that the SH absorbance depends on the thickness of the slab. For the thickest of the slabs, i.e., the one consisting of 256 NP planes, the average absorbance over the entire spectral region shown in Figure 6 is 91% for the ordinary modes, 66% for the extraordinary modes, and 79% the average absorbance for both modes. These figures suggest that the structure under study is essentially a gray body (super absorber) over the entire visible regime. We also note that any imperfections in the fabrication process are not expected to have an impact on the above absorbance efficiencies due to the subwavelength nature of the structure.

hexagonal array (solid line) studied above with that of square arrays of NPs strings with the same surface coverage of the spheres (area of the spheres belonging to a 2D unit cell divided by the area of the unit cell) so that the same amount of gold mass corresponds to each array. For the dashed curve of Figure 5 we have kept the interparticle distance the same (10 nm) but modified the NP radius (from 3 to 3.22 nm), while for the dotted curve we have kept the NP radius the same (3 nm) but modified the lattice constant of the square lattice (a = 9.3 nm). It is evident that the short-wavelength absorbance is more or less independent of the lattice type, whereas the longwavelength fringe structures differ significantly. This is, at first, a counterintuitive observation since the studied metamaterial structures are truly subwavelength: the mid operating wavelength, i.e., 500 nm, is 50 times larger than the interparticle

CONCLUSIONS By using a rigorous electrodynamic approach, we have shown that ordered arrays of long NP strings immersed in a dielectric host can operate as super absorbers in the visible regime. The absorption efficiency is significantly higher when external light matches the ordinary modes of the NLC. It also depends strongly on the number of NP planes, but after a certain slab thickness (NP string length) it saturates to constant level. The lattice type of the nanostrings is of no practical importance since the operating wavelength is much longer than the characteristic one (i.e., interstring distance). This suggests that possible fabrication imperfections will not affect the absorptive properties of the structure. Structures similar to the ones studied here have been realized in the laboratory11 and if characterized optically, they will look like almost black (say

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Figure 6. SH absorbance spectra for different string lengths and (a) for the extraordinary (E), (b) the ordinary (O), and (c) the average of both modes (E+O).

gray) bodies as they absorb light within the entire visible regime.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. 228455-NANOGOLD (Self-organized nanomaterials for tailored optical and electrical properties). 15603

dx.doi.org/10.1021/jp304101a | J. Phys. Chem. C 2012, 116, 15599−15603