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Plasmonic Metastructures and Nanocomposites with a Narrow Transparency Window in a Broad Extinction Spectrum

We propose and describe plasmonic nanomaterials with unique optical properties. These nanostructured materials strongly attenuate light in a broad wavelength interval ranged from 400 nm to 5 um but exhibit a narrow transparency window centered at a given wavelength. The main elements are nanorods and nano-crosses of variable sizes. The nanomaterial can be designed as a solution, nanocomposite film, metastructure or aerosol. The principle of the formation of the transparency window in the abroad extinction spectrum is based on the narrow lines of longitudinal plasmons of single nanorods and nanorod complexes. To realize the spectrum with a transmission window, we design a nanocomposite material as a mixture of nanorods of different sizes. Simultaneously, we exclude nanorods of certain length from the nanorod ensemble. The width of the plasmonic transparency window is determined by the intrinsic and radiative broadenings of the nanocrystal plasmons. We also describe the effect of narrowing of the transparency window with increasing the concentration of nanocrystals. Two well-established technologies can be used to fabricate such nano- and metamaterials, the colloidal synthesis and lithography. Nanocomposites proposed here can be used as optical materials and coatings for shielding of electromagnetic radiation in a wide spectral interval with a simultaneous possibility of communication using a narrow transparency window.


Introduction
Metal nanocrystals and metamaterials with strong plasmonic resonances in the visible and infrared spectral intervals often exhibit very unique and unusual optical properties. 1,2 In single nanocrystals with specially-designed shapes, plasmonic resonance can efficiently be tuned with the geometry and can become very strong and narrow. 3,4,5 Especially there propoertyies are characteristic for the plasmonic nanorods that exhibit strong and narrow longitudinal resonances. 4 Whereas nanospheres, nanorods and nanocubes with small sizes can be grown with the colloidal synthesis in solution 3 , larger-size nanostructures are conveniently fabricated by the lithographic methods. 6 Lithographically-made 2D and 3D metamaterials employ the electromagnetic interactions between building blocks to create interesting optical responses. One of the prominent effects coming from the interactions between single nanocrystals is the Fano effect. This effect can occur in purely plasmonic system 7,8,9,10 or in hybrid exciton-plasmon nanostructures. 11,12,13,14 The Fano effect typically comes from an interaction between a broad and narrow resonances in a system composed of two or several elements. Another phenomenon, which is relevant to the plasmonic Fano effect, is the plasmon-induced transparency in planar metamaterials composed of a few interacting nanocrystals. 15,16,17 Here we propose another approach to the effect of transparency window in nanostructured systems. Our approach is to construct a nanomaterial as a composition of single nanocrystals and nanocrystal complexes with narrow and tunable absorption lines.
Here we describe plasmonic media with very unusual optical properties. The idea is to design a medium or metamaterial that should attenuate light in a very broad spectral interval but exhibit a narrow transparency window at a given wavelength. Such optical materials can be used for the electromagnetic shielding that simultaneously permits communications via the transparency window. Looking at the available materials and media, we can see that the optical materials found around us may exhibit narrow absorption lines or absorption bands. For example, dye molecules have typically narrow absorption lines in the visible, or water molecules exhibit a set of narrow absorption lines in the infrared. Or, another material system widely available is amorphous carbon and carbon particles that strongly absorbs and scatter light in a wide spectral interval without any transparency intervals. A medium with the needed properties, i.e. with a broad extinction spectrum and a narrow transmission window, seems to be challenging to realize. Nevertheless, we identify theoretically the materials and designs that may lead to a realization of such media. Importantly, the media proposed in this paper are based on the real materials and realistic technologies. A narrow transparency window in a very broad extinction spectrum can exist in nanocomposites and metamaterials incorporating nanorods, nanoparticles and nano-crosses (Fig. 1). The components and composition of these optical media should be carefully designed. The elements of the nanocomposite can be simple, such as single nanorods and nanoparticles (Figs 1a and b), or more complex such as nano-crosses and multi-bar nanocrosses (Fig. 1c). The main building block of the proposed systems is a nanorod with strong, narrow and tunable extinction lines of longitudinal plasmons. The media with these unique optical spectra can be fabricated as solutions, films, coatings, planar metamaterials, etc. Nanocrystals in such media can be either randomly-oriented (Fig. 1b) or arranged in the parallel layers ( Fig. 1a and c). Below we will describe the principles to design such materials as well as their optical properties.
The paper is organized in the following way. The discussion develops from the simple to the complex. The first sections concern composite media made from single plasmonic nanorods of small sizes, whereas the following sections describe media incorporating large nanorods, nano-crosses and metastructures. . c) Planar metamaterial composed of nanorods, nano-crosses and nanodisks. This metastructure is designed to exhibit the transparency window effect.

Optical properties of small NRs.
We start with the small plasmonic Au nanorods exhibiting narrow plasmon resonances. Optical properties of these nanocrystals are described by the analytical theory. 18,19 The extinction cross section of a small anisotropic NC is given by its absorption rate: where Q α and 0 I are the absorption rate and the incident photon flux, respectively; 0 E is the amplitude of incident electromagnetic field and 0 ε is the dielectric constant of matrix; α is index describes the direction of the electric field in the incident wave and , , x y z α = (Figure 2).
where Au ε and 0 ε are the dielectric constants of nanocrystal and matrix, respectively, and is the NR volume. In a 3D medium incorporating randomly-oriented NRs, the cross section should be averaged over the orientations, Sometimes it is more convenient to use, instead of the extinction cross section, a molar extinction coefficient defined as The extinction spectrum of a single NR exhibits a strong resonance related to the longitudinal plasmon at a long wavelength and a relatively weak peak for the transverse plasmon at a shorted wavelength (Fig. 2a). To realize a material with a narrow transparency window, we will utilize the strong L-plasmon resonance. We therefore look now at the function ( ) z σ ω and investigate the position and broadening of L-plasmon as a function of the NR aspect ratio  This can be done numerically using the empirical dielectric function. 20 Or we can use the Drude model, Equation 2 was derived for the limit 1 A >> . In particular, we see from Eq. 2 that the plasmon resonance broadening of NR stays the same in the long-wavelength spectral interval and is given by the intrinsic losses in the metal. While the plasmon-peak broadening of the cross section ( ) z σ ω stays constant as a function of the NR length, the width of the L-plasmon resonance ( , where , 2 Drude p ω Γ Γ = is the broadening of the L-plasmon coming from Eq. 2, , p L λ is the L-plasmon wavelength which is an increasing function of the aspect ratio. These properties of the L-plasmon peak are summarized in Fig. 2b. Numerically, the L-plasmon wavelength , ( ) p L A λ for the gold NRs can be approximated as a simple linear function for the aspect ratios 1 A > :

Collections of NRs.
Our first model is a composite medium that incorporates small plasmonic NRs with random positions and orientations. We assume that the ensemble of NRs is diluted and Coulomb and electromagnetic interactions between NRs are weak and can be neglected. We now construct a medium from a mixture of NRs of various sizes according to simple rules outlined below.
Designing collection of NRs, we do not include nanocrystals with a certain length and, therefore, the transmission spectrum of such composite material acquires a window centered at a certain wavelength. The best transmission windows can be made from an infinite collection of small NRs of various sizes and this collection of NRs should be represented by a continuous sizedistribution function. However, practical implementations of this simple idea will require a discrete sequence of NRs and we will give below related examples.

Continuous collection of NRs.
We The corresponding gap in the distribution of NR length is in the interval 50 70 nm c nm < < . In  The NR collection can be supplemented with spherical nanoparticles that create strong absorption in the interval 300-700nm.

Discrete collection of NRs.
From the above model case, we now move to a more realistic case of mixture of NRs with a discrete distribution of sizes. Namely we take a composite of 12 kinds of NRs and 2 kinds of NPs ( Figure 5). This composite gives an optical window at ~ 900nm. Spherical nanoparticles are used to "close" the absorption spectrum in the interval 400-600nm. One NP size is small,

Electromagnetic properties of single NRs.
Large NRs can be fabricated on a substrate using the lithography. Then, optical properties of NRs can be measured directly on a substrate, or NRs can be released to a liquid solvent 24,25,26 where the optical absorption can be recorded. As another processing step, NRs in solution can be deposited on a polymer film and then covered with another polymer layer using the standard layer-by-layer technology.
NRs with sizes comparable to the wavelength of light exhibit strong retardation effects.
Such nanorods should be calculated numerically. In Figures S4 and 6 we plot the extinctions of nanorods computed numerically by the Final Elements Method (COMSOL). We choose the geometry and sizes accessible for the lithographical nano-fabrications and, therefore, the NR dimensions are taken larger than those for the colloidal NRs. Simultaneously, since we aim at the transparency window effect we choose relatively small sizes to avoid strong radiative broadening of the L-plasmon peaks. Namely, we take the NR width and height as 40 w nm = and 50 h nm = . The NR length, L , is a variable parameter. First of all, we see that the extinction now has a strong component of scattering and this scattering contribution starts to dominate for large sizes (Fig. S4). Another important effect is the radiative broadening. With increase of NR size, the plasmon peak becomes much broader (Fig. 6). This is the effect of radiational decay of plasmon. The broadening of the plasmon peak is now composed of two terms: The contribution inter-band ∆Γ can be neglected since we deal with the L-plasmons with 600 p nm λ > . Another observation is that the NR geometry creates typically narrower plasmon peaks compared to the nano-disks (Fig. 6b). Therefore, to realize the optical transparency window effect, we prefer to use the NRs.

Discrete collection of large NRs.
Large plasmonic NRs, which can be fabricated lithographically, allow us to construct plasmonic media with a narrow transparency window in a much wider wavelength interval. In principle, one can construct a material with a transparency window located in the interval from 700nm to 1mm. We now describe one realization of the NR composition with the optical window around 1500nm. For this, we choose NRs in the interval 125-900nm and again create a gap in the size distribution. In this case, the gap is taken between 250 and 420nm. It means that the NRs with the L-plasmon wavelengths around 1500nm are not present in the collection. As before, we supplement the NR collection with large spherical Au NPs that create strong absorption for 600nm λ ≤ . Figures 7 and S5 show the calculated spectra.
One interesting observation in the calculated transmission spectra is that the transparency window becomes narrower with an increase of optical path because of the non-linear property of the exponential function (Figures 7 and S5). The same effect can be achieved if we increase the concentration of particles. Therefore, the window effect can be enhanced either with an increase of concentration of nanocrystals or by making an optical path longer.

Interactions between single NRs.
The NR composites discussed above were random collections of NRs and NPs suspended in a solution or built into a polymer matrix. The optical density of such composites was calculated as a linear superposition of extinctions of individual components. This approach assumes that the elements, NRs and NPs, are weakly interacting.
We have shown numerically that the interactions can be neglected if the inter-nanocrystal distance in a composite is about or larger than the sizes of components. Supporting information gives a few examples of interactions between nanocrystals. If however the inter-nanocrystal distance is smaller than the lengths of components, the electromagnetic interactions become strong and most likely destroy the window effect. In Figure S6, we show such case. In the model used in Figure S6, we arrange 17 NRs in an array with a relatively small inter-NR distance. Then, we calculate the total extinction and compare it with the case of linear superposition. Whereas the linear superposition has a transparency window at ~ 1500nm, the metamaterial structure, which looks like a pipe organ, does not exhibit the optical window at all. In this structure, strong inter-NR electromagnetic interactions modify the whole spectrum and completely destroy the window effect.
Another interesting question is whether the interactions between single nanocrystals can help to create a more narrow transparency window. In a nanostructure composed of two NRs, we expect the appearance of the splitting and the related double-peak spectral structure. The question is whether such double peak structure can be used for the transparency window effect. Figure 8 shows that the simple NR-NR interaction does not improve the window effect. The window effect of the two interacting NRs is almost identical to the effect created by two independent NRs with appropriately-chosen sizes. We should note that this is just one particular case of inter-nanocrystal interaction and there may be other cases when the interactions can be helpful for the transparency window effects.

Metastructures and metamaterials.
We now look at more complex structures. The idea is to find more complex elementary blocks that can be more compact and convenient. Such nanocomposite material can occupy less space and also have fewer elements which may simplify a fabrication. We could already see that two interacting NRs do not give much advantage since the window effect is similar to the case of two non-interacting nanocrystals (Fig. 8). Additionally, the structure with two perpendicular NRs exhibits an asymmetric double peak spectrum whereas, for a material with a transparency window, we better have elements with symmetric double-peak spectra. For this, we will try now simple and multi-bar nano-crosses.

Nano-crosses.
We aim to find an element that has a symmetric double-peak structure which can be used for a metamaterial with a transparency window. However, simple nano-crosses give typically asymmetric windows (Fig. 9). Therefore we can try a cross with two perpendicular bars. After the optimization of the parameters, we show that the two-bar cross can produce a symmetric window. A symmetric window effect appears only for certain, specially-chosen geometrical parameters. For example, the two-bar cross with a large inter-bar distance in Fig. 10 produces an asymmetric window since the long-wavelength peak becomes enhanced. The next step is to use nano-crosses as elements in a metastructure.

Composition of nano-crosses, nanorods and nano-disks.
We now involve three crosses, two NRs, and two nano-disks (NDs). Figure 11   The optical medium with the transparency window can also be fabricated as a planar meta-material on a substrate. Fig. 12 shows this case. The distances between the nanocrystals in this metastructure are long enough to avoid interference between the elements. The distances can be found in Figure S9. In addition, in this metastructure, we like to suppress the interference effects by orienting the nanocrystals. To do this, we arrange the elements in the way to avoid quasi-resonant interactions between the elements. For example, we orient the two-bar and three- these rules is to reduce the interference effects in a metastructure using the geometrical approach.
We also should make a few final comments on fabrication methods for the described metastructures. Thin substrates (glass or polymer) with metastructures can be randomly dispersed in a medium (liquid, polymer or air) or oriented as parallel multi-layers in a polymer matrix (Fig. 12). The resulting transmission spectrum of such system shows a strong transparency window effect (Fig. 12). This is another possibility to realize an optical material with both a strong broadband extinction spectrum and a narrow transmission window. Since the lithography allows us to fabricate nanorods and nanowires with an almost arbitrary length (of course, within the reasonable limits ), the proposed optical metamaterials may have transparency windows in the wavelength interval from 600nm to 1mm.       We see that effect of the interaction becomes small when the inter-NR distance is about the length of NR. In additional, the mutual orientation of NRs is very important and can be used to minimize the interaction. For two perpendicular NRs (right panel), the interaction is very weak, while for two parallel NRs (left panel) the interaction remains noticeable at relatively large distances. Figure S8: This graph shows the distances between the elements in the metastructure investigated in the main text and shown in Fig. 12.
. Figure S9: Interactions between nanocrystals in the metastructure. We assume the geometry and the inter-nanocrystal distances shown in Figures 12 and S8. We see that the electromagnetic interactions between the nanocrystals do not change noticeably the window effect in the metastructure. We designed this metastructure intentionally to reduce the interactions between the units since these interactions can disturb or even destroy the window effect. The simple rules to construct the structures with weak interactions are discussed in the main text.