1. INTRODUCTION

The field of plasmonics has attracted a lot of attention because it enables light control at nanoscales [1,2]. In many cases, this relies on localized surface plasmon (LSP) resonances sustained by metal nanoparticles. When illuminated at the resonant frequency, the free electron gas of the metal strongly interacts with light, yielding a significative enhancement of the electromagnetic field in the vicinity of the nanoparticle [3]. This resonance frequency, $\omega$, critically depends on a number of parameters including the nature of the metal, the size and shape of the nanoparticle, and the refractive index of the surrounding medium [4,5]. As is the case with any resonant phenomenon, the width of the resonance peak is directly related to the associated losses, including scattering and absorption losses. The resonance width $\mathrm{\Delta }\omega$ is often described using the quality factor, $Q$, as a figure of merit, defined as $Q=\omega /\mathrm{\Delta }\omega$. Due to intrinsic losses in metals, the quality factor of LSP resonances is usually modest (in the 1–10 range) and mainly depends on the nature of the metal—noble metals such as silver and gold exhibiting better quality factors than the so-called “poor” metals in the visible and near-infrared spectrum. However, poor metals can be valuable plasmonic metals, especially outside the visible spectrum [6]. For instance, aluminum is currently being rediscovered as a relevant material for plasmonics, especially in the ultraviolet (UV) range (see [7] for a review). Actually, the main interest in aluminum as a plasmonic material lies in its broadband nature: apart from a relatively small region around $\lambda =800\mathrm{nm}$ (corresponding to interband transitions), aluminum can sustain LSP resonances from the deep-UV to the infrared [8,9]. Aluminum nanostructures have been used to date in both the UV, for instance to realize a UV-emitting plasmonic laser [10], and in the visible range—e.g., as a platform for color rendering [11,12], or for photodetection [13]. However, the amount of losses in the visible and IR regions is significantly higher than for noble metals, leading to relatively poor quality resonances.

The quality factor of LSP resonances can be improved in geometries where plasmonic particles are arranged in a periodic array, so that electromagnetic coupling between scatterers taking place due to diffractive effects leads to the emergence of so-called lattice modes (see Ref. [14] for a review). These diffracting lattice modes, sometimes called surface lattice resonances, are generally observed near a Rayleigh anomaly of the array. Rayleigh anomalies correspond to the appearance (or disappearance) of diffracted orders and are associated with a grazing wave propagating in the plane of the array [15]. Lattice modes can be described as a Fano-type process involving a broad resonance (the LSP resonance) and a discrete state associated with the light scattered in the plane of the array at the Rayleigh anomaly position [16]. This coupling yields two hybrid states sharing the properties of the contributing components. The lattice mode is one of these hybrid states, located close to the Rayleigh anomaly position, that offers an enhanced scattering cross section, based on the LSP contribution, while also demonstrating a high quality factor [16–18]. This effect was predicted as early as 1985 in the context of rough surfaces for surface-enhanced Raman scattering [19,20], before being rediscovered almost 20 years later for one-dimensional arrays of silver nanoparticles [21]. Later, lattice modes in two-dimensional gold nanoparticle arrays were shown to significantly improve the finesse of the resonance [18,22–28], finding applications in metal-enhanced fluorescence [29], nonlinear optics [30], and the realization of plasmon-based lasers [31]. Aluminum nanoparticle arrays have been shown to enhance and redirect the emission of nearby dye molecules, with potential applications in solid-state lighting [32,33], among others. Recently, a plasmonic sensor based on the lattice modes sustained by a one-dimensional aluminum grating has been demonstrated [34]. It should also be emphasized that lattice modes can be observed in different periodic systems, such as hole arrays [35,36], arrays of magnetic nanoparticles [37], and SiC nanocylinder arrays at mid-infrared wavelengths [38].

In this paper, we report a comprehensive and comparative study of the lattice modes supported by gold and aluminum gratings in the visible and UV regions. Dispersion plots are experimentally retrieved, allowing us to analyze the coupling between LSPs in the array. In the recent review [14], the critical role played by the periodicity was underlined to correctly position the Rayleigh anomalies in the spectrum with respect to the LSP to observe lattice modes. In the present work, we demonstrate the role of (i) the dielectric environment of the array and (ii) the polarization of the incident light, showing that the scattering pattern of the individual nanoparticles is the key parameter that controls the formation of the lattices modes. The paper is organized as follows: Section 2 is devoted to the design of our structures using numerical calculations. The role of the dielectric environment is unveiled by plotting the dispersion curves of the arrays. Then in Section 3, we present the experimental methods used to fabricate and characterize the nanoparticle arrays. Results obtained on gold and aluminum nanoparticle arrays are presented in Sections 4 and 5. Finally, in Section 6 we summarize our results and discuss conclusions.

2. LINEWIDTH ENGINEERING WITH LATTICE MODES

A. Design and Modeling

The structure under study is shown in Fig. 1(a). It consists of a square array of nanoparticles (nanodisks) deposited onto a dielectric substrate with refractive index $n_1$. The period of the array is denoted $D$, the diameter of the nanodisks is $d$, and the thickness is $h$. Two cases were considered, depending on the refractive index $n_2$ of the superstrate (upper medium). In the asymmetric configuration, the upper medium is simply air ($n_2=1$). In the symmetric case, a superstrate with a refractive index close to that of the substrate (e.g., a polymer layer) is added, so that the nanoparticles are effectively located inside a homogeneous environment.

 

Fig. 1. (a) Schematic of the considered geometry: an array of metal nanoparticles deposited onto a dielectric substrate of refractive index $n_1$. The superstrate can be air or a dielectric with refractive index $n_2$. (b) AFM image of a square array of gold nanodisks with $D=480\mathrm{nm}$, $d=160\mathrm{nm}$, and $h=50\mathrm{nm}$. (c) Scanning electron microscopy image of an array of aluminum nanodisks with $D=300\mathrm{nm}$, $d=120\mathrm{nm}$, and $h=50\mathrm{nm}$.

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To design the structures, we performed numerical modeling based on the finite difference time domain (FDTD) method [39]. 3D modeling was used, with perfectly matched layer (PML) as the boundary conditions on the top and bottom sides of the simulation box, while periodic boundary conditions were applied on the remaining four sides. An adaptive mesh was used to precisely model the shape of the nanoparticle. The refractive indices were taken from Refs. [40] and [41]. The incident light is a plane wave, impinging from the substrate side. Oblique incidence on the periodic structure was described using the approach presented in Ref. [42]. Due to the peculiar nature of the lattice modes, special attention must be paid to the PML bounding the simulation box. Lattice modes are high $Q$-factor (long-lived) resonances with a significant spatial extent that propagates in a direction that is parallel to the PML layers. This may yield undesired reflections on the PMLs, leading to overestimations of the resonance width. Here, we used the stretched coordinate PMLs, as implemented in [39], and performed extensive convergence tests.

B. Effect of the Dielectric Environment

We first focused our attention on gold nanoparticle arrays. Figure 2 shows a map of the normal incidence extinction cross section ${\sigma }_{\text{ext}}$ for a square array of gold nanodisks with diameter $D=80\mathrm{nm}$ and thickness $h=50\mathrm{nm}$ plotted for different lattice periods and wavelengths. Following Refs. [18,23], the extinction cross section is obtained through ${\sigma }_{\text{ext}}=D^2(1-T)$, where $T$ is the transmittance computed with FDTD. Here we consider a symmetric dielectric environment, as the refractive indices of the substrate and superstrate are set to $n_1=n_2=1.5$. Experimentally, this corresponds to a situation where the nanoparticles are deposited onto a substrate and subsequently covered with an index-matching superstrate. For shorter periods, the resonance position of the array, observed as a maximum in the extinction, is very close to the LSP resonance of an isolated particle (dotted horizontal line), but as the period increases, the resonance position red-shifts and simultaneously sharpens significantly. Moreover, the lineshape is also modified, from a relatively symmetric shape to a Fano-like lineshape (see the resonance near $\lambda =750\mathrm{nm}$ in Fig. 3, inset). To understand this behavior, we superimposed the theoretical position of the Rayleigh anomalies on the dispersion diagram. According to grating theory, in the most general case of a square grating with period $D$ sitting on the interface between two media with refractive indices $n_1$ and $n_2$, the position of the Rayleigh anomalies is given by

 

Fig. 2. Normal incidence extinction cross-section spectrum calculated with FDTD for a square array of gold nanodisks with diameter $d=80\mathrm{nm}$ and thickness $h=50\mathrm{nm}$ for different lattice periods (from 300 to 700 nm with a 10 nm step) in a homogeneous dielectric environment ($n_1=n_2=1.5$). Solid lines show the theoretical position of Rayleigh anomalies, and the dotted horizontal line is the position of the dipolar resonance from the isolated gold nanodisk.

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Fig. 3. Normalized electric field modulus maps for different lattice periods. The insets on the top of each of the columns are line cuts of Fig. 2, showing the extinction cross section ${\sigma }_{\text{ext}}$ versus wavelength for three different periods: $D=300$ (left column), $D=500\mathrm{nm}$ (center column), and $D=650\mathrm{nm}$ (right column). The arrows indicate the wavelengths where the field maps were calculated. (a) FDTD maps of the normalized electric field modulus computed in a plane located at mid-height of the metal nanoparticles for an array with $D=300\mathrm{nm}$ at $\lambda =620.3\mathrm{nm}$. The black arrow denotes the incident polarization. The same field maps were computed for (b) $D=500\mathrm{nm}$ and $\lambda =619.9\mathrm{nm}$; (c) $D=500\mathrm{nm}$ and $\lambda =754.8\mathrm{nm}$; (d) $D=650\mathrm{nm}$ and $\lambda =615.1\mathrm{nm}$; and (e) $D=650\mathrm{nm}$ and $\lambda =692.9\mathrm{nm}$.

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More insight on the nature of both hybrid modes can be gained by plotting the normalized electric field at the wavelength corresponding to each of the modes, for different periods. Let us start with a period $D=300\mathrm{nm}$, corresponding to the very left part of Fig. 2. The extinction spectrum shows only one relatively broad resonance around $\lambda =600\mathrm{nm}$. The field map associated with that resonance is shown in Fig. 3(a) and demonstrates that the electric field is mainly localized around the gold nanodisks, as expected for isolated particles. If the period is increased to $D=500\mathrm{nm}$, the extinction spectrum shows two resonances. The field map associated with the lower wavelength, broader resonance [Fig. 3(b)] shows field maxima that are localized in the vicinity of the gold nanodisks, similar to Fig. 3(a), and linked with the dipolar plasmonic resonance of the isolated nanodisk. Alternatively, the field map corresponding to the sharp resonance [Fig. 3(c)] demonstrates a simultaneous excitation of the metal nanoparticles along the polarization direction and a standing grazing wave (Rayleigh anomaly) in the perpendicular ($Oy$) direction. In other words, the coupling generates two hybrid modes, one with a more “photon-like,” delocalized nature, and the other one exhibiting a “plasmon-like,” localized nature. As the plasmon-like mode is more localized than the photon-like mode, it experiences more Joule losses, resulting in a much broader peak with a low quality factor. This is further confirmed by the field maps computed for an array exhibiting a period of 650 nm [Figs. 3(d) and 3(e)]. Figure 3(d) corresponds to the plasmonic mode, while Fig. 3(e) corresponds to the photonic mode, demonstrating coupling with the (1,1) Rayleigh anomaly at $\pm 45°$ for the axes of the array.

To emphasize the critical role played by the grating period, we computed the quality factor as a function of period for four different nanodisk diameters [Fig. 4(a), note the log scale on the vertical axis]. Note that in Fig. 4, the range of studied diameters and periods has been chosen to yield lattice modes in the visible and near-infrared spectrum. Extremely high values of $Q$ can be obtained ($Q>1000$) for high values of the lattice period, while an isolated gold nanodisk would exhibit $Q\sim 5–10$. Interestingly, the value of $Q$ seems to increase continuously with the period. Also, higher values of $Q$ are observed for smaller nanodisk diameters. The former effect can be understood as follows. When $D$ increases, the lattice mode gets closer to the position of Rayleigh anomaly (see Fig. 2). As a consequence, the hybrid mode becomes more and more photon-like in nature and exhibits reduced losses. The ultimate limitation on the value of the $Q$-factor is the size of the particles. As the period increases, the spectral position of the lattice mode red-shifts, hence the nanoparticles become smaller with respect to the resonance wavelength. This implies that the scattering efficiency, and thus the diffractive coupling strength between the LSP resonances near the Rayleigh anomaly, should decrease for higher values of the lattice period.

 

Fig. 4. Linewidth engineering using lattice modes. (a) Calculated quality factor of the lattice mode of arrays of gold nanodisks as a function of the lattice period for different disk diameters at normal incidence. The dielectric environment is symmetric ($n_1=n_2=1.5$). (b) Same, with air as the superstrate ($n_2=1$).

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To demonstrate the influence of the dielectric environment, we also computed the quality factor as a function of the period in the case of an asymmetric environment (glass substrate and air superstrate). The results are presented in Fig. 4(b) for different nanodisks diameters. Inside that range of periods, the observed behavior offers a striking difference with the symmetric case. Optimum values of the lattice period clearly appear for each diameter, and this optimum value increases with the diameter of the nanodisks. Moreover, the obtained values of $Q$ are more than one order of magnitude lower than in the symmetric geometry. Values in the range $Q\sim 10–13$ are obtained, which is roughly three times the value for an isolated nanodisk. We can also note that to obtain an efficient linewidth reduction, larger particles than those in the symmetric case have to be considered. In other words, if we set the grating period, the linewidth reduction will be efficient for different diameters in different dielectric environments. Altogether, from a “linewidth engineering” perspective, working in a homogeneous environment is clearly beneficial. However, a significant linewidth reduction can still be observed in an asymmetric environment, provided the grating is properly designed.

The role of the dielectric environment can be qualitatively understood as follows. With asymmetric geometry, the radiation pattern tends to be highly asymmetric with most of the light scattered inside the substrate [43]. This leads to a weak angular overlap with grazing diffracted orders. When the dielectric environment is symmetric, so is the radiation pattern—enabling a much higher coupling into in-plane scattered light. This is why setting an adapted period for the array is then a necessary, but not sufficient, condition to observe high-$Q$ lattice modes. Further evidence of the central role played by the radiative pattern of the nanoparticles will be given in Section 4.

It must be emphasized that while the symmetric configuration yields by far the sharpest resonances, such a configuration is not without drawbacks from an experimental perspective [27]. First, the nanoparticles are isolated from the environment, limiting potential interactions with emitters or analytes. But most importantly, as the effective refractive index around the nanoparticles is higher in this geometry, the lattice modes are red-shifted with respect to the asymmetric geometry. Obtaining high energy resonances with the symmetric geometry hence requires significantly smaller nanoparticles, whose reliable fabrication is more demanding.

In the following, we turn our attention to the experimental verification of our findings on gold and aluminum nanoparticle arrays.

3. EXPERIMENTAL METHODS

A. Sample Fabrication

Arrays of gold and aluminum nanoparticles were made using electron beam lithography, which enables the fabrication of nanostructures with well-controlled size, shape, and period [44]. The gold nanoparticles are 50 nm thick nanodisks that were deposited onto a glass substrate with a 3 nm thick ${\mathrm{TiO}}_2$ layer to ensure adhesion of gold onto glass. Two different aluminum nanoparticle samples were made: $d=120\mathrm{nm}$ nanodisks exhibiting a LSP resonance in the visible and $d=60\mathrm{nm}$ nanodisks with an LSP in the UV spectrum. The aluminum thickness was set to 50 nm in both cases. Both structures were deposited onto fused silica to ensure transparency in the UV. Note that for aluminum, no adhesion layer is required, as this metal firmly adheres onto glass [45]. The total size of the arrays is $50\times 50\mathrm{\mu m}$.

The quality of the fabricated structures was characterized with both atomic force and electron microscopy. Typical images are shown in Fig. 1(b) for gold nanodisks and Fig. 1(c) for $d=120\mathrm{nm}$ aluminum nanodisks. Regular arrays are observed in both cases, but clearly the gold nanoparticles exhibit a more defined shape than the aluminum ones. This is a well-known difference in the behavior of thermally evaporated layers of both metals, as it is much more difficult to obtain smooth surfaces of aluminum because it tends to nucleate in the early stages of deposition [46]. After measuring the dispersion curves of the arrays (see below), the nanostructures were spin-coated with poly(methyl methacrylate) (PMMA) to obtain the symmetric geometry. This ensures that the comparison between the asymmetric and symmetric geometries is made on the same arrays. The thickness of the deposited PMMA layer is $\sim 180\mathrm{nm}$. Let us emphasize that the refractive index of PMMA does not exactly match that of the glass substrate. However, as it is slightly lower, which ensures that no guided modes can propagate inside the PMMA layer and interact with the LSP.

B. Optical Characterization

The optical properties of all samples were measured using an angle-resolved extinction spectroscopy setup. This setup enabled the dispersion curves of the arrays to be retrieved, that is, the extinction was plotted as a function of the angle of incidence and the wavelength (or, equivalently, the wavevector and the energy). The setup works over a broad spectrum, from the UV to the near-infrared. Collimated light from a UV/visible lamp (Avalight-DHS, Avantes) is slightly focused onto the sample, which can be rotated by a controllable angle $\theta$ with regards to the incident beam. The light transmitted by the sample is collected using a microscope objective lens (MPlan UV $50\times$, Mitutoyo) confocally coupled to an optical fiber (solarization resistant fused silica fiber, core diameter 100 μm) to define a collection area corresponding to the sample size. Finally, the output of the fiber is sent toward a spectrometer (IsoPlane SCT320, Princeton Instruments) equipped with a cooled camera (ProEM ${1600}^2$, Princeton Instruments). The polarization of the incident light is controlled by a broadband polarizer placed in the illumination path. To obtain the dispersion curves shown below, we measured an extinction spectrum every 4°, from $\theta =0°$ to $\theta =48°$. Note that in the following, the arrays are illuminated from the glass substrate and the angle of incidence used as the horizontal axis is measured in air (i.e., before refraction inside the substrate).

4. GOLD NANOPARTICLE ARRAYS

Figure 5 presents the dispersion curves of an array of gold nanoparticles for $s$-polarization (electric field parallel to the $y$-axis) and $p$-polarization (electric field in the $xz$-plane) in the asymmetric geometry, that is, for gold nanoparticles in air on a glass substrate. In the left panels, the experimental results are plotted, while the right panels show the corresponding FDTD simulations. Figure 5 are shows the position of the Rayleigh anomalies, according to Eq. (1). The two polarizations exhibit slightly different behaviors. The $p$-polarization shows a broad and relatively flat dispersion branch corresponding to the plasmon resonance of this branch, while for $s$-polarization, an interaction with the (1,0) glass/air Rayleigh anomaly appears. The agreement with the numerical simulations is very good. The most important difference between $p$- and $s$-polarizations concerns the (1,0) glass/air anomaly (dotted white line in Fig. 5). In $s$-polarization, the anomaly has a detrimental effect on the plasmon branch, weakening the intensity for high angles [see Fig. 5(d)], while in $p$-polarization the anomaly seems to increase the absorbance. However, globally, the effect of the diffraction anomalies is weak, confirming what we observed in Section 2: to obtain significant hybridization, a symmetric dielectric environment is required.

 

Fig. 5. Experimental (a), (c) and simulated (b), (d) dispersion curves of the gold nanodisk arrays for $s$ (a), (b) and $p$ (c), (d) polarizations. The period of the array is $D=480\mathrm{nm}$, and the diameter of the nanodisks is $d=180\mathrm{nm}$. White lines represent the position of the Rayleigh anomalies computed using Eq. (1) with $n_1=1.52$ and $n_2=1.52$ (solid lines) or $n_2=1$ (dotted lines).

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Next, we considered the case of the “symmetric” dielectric environment, that is, after deposition of an $\sim 180\mathrm{nm}$ layer of PMMA onto the previously measured array. While such an environment cannot be considered rigorously homogeneous due to the slight refractive index difference between glass ($n=1.52$) and PMMA ($n=1.49$), this configuration is sufficiently close to that discussed in Section 2. Experimental results are reported in Fig. 6(a) for $p$-polarization and in Fig. 6(b) for $s$-polarization. Comparison with Fig. 5 shows a clear effect of the change in the dielectric environment. Notably, for $s$-polarization, a clear bending of the LSP branch is observed as it approaches the (1,0) symmetric Rayleigh anomaly. The resulting lattice mode has a sharper profile: the quality factor of the lattice mode is found to be $Q=15$ at normal incidence, increasing to $Q=28$ at $\theta =12°$. This is a clear demonstration of the beneficial influence of generating lattice modes inside a symmetric dielectric environment.

 

Fig. 6. Experimental (a), (b) and simulated (c)–(h) dispersion curves of the PMMA-covered gold nanodisk arrays for $s$ and $p$ polarizations. The period of the array is $D=480\mathrm{nm}$, and the diameter of the nanodisks is $d=180\mathrm{nm}$. White lines represent the position of the Rayleigh anomalies computed using Eq. (1) with $n_1=1.52$ and $n_2=1.52$ (solid lines) or $n_2=1$ (dotted lines). The simulations were performed using three different geometries as pictured in the insets: (c), (d) a semi-infinite PMMA superstrate; (e), (f) a 180 nm thick PMMA layer onto the top of the substrate, and (g), (h) a 180 nm thick PMMA standing onto the top of the nanoparticles.

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More insight can be gained by comparing the two polarizations. Considering Fig. 6(a), it is remarkable that the $(+\mathrm{1,0})$ anomaly (corresponding to a grazing wave propagating along the $x$ direction) crosses the main dispersion branch with limited perturbation. In contrast, in the other polarization, a strong interaction between the same anomaly and the LSP is demonstrated [Fig. 5(b)] with a bending of the band and the appearance of a Fano lineshape similar to those of Fig. 3. In other words, to be significantly active and therefore allow the creation of lattice modes with sensible coupling, an anomaly must be coupled in a direction perpendicular to the incident polarization. This effect can be explained qualitatively by considering how a single nanoparticle scatters light. If we assume the nanoparticle behaves as a dipole, then the far-field radiation will be perpendicular to the induced polarization, which is along the polarization of the incident electric field. In other words, as each nanoparticle scatters light in a direction perpendicular to the incident polarization, it will preferentially couple with grazing diffractive orders along that direction. This can be ascertained by looking again at Fig. 3(c), showing the electric field map at the wavelength corresponding to the excitation of a lattice mode. When the polarization is horizontal in the figure, it excites a grazing wave in the vertical direction. It is interesting to note that for non-square gratings, it implies that the position of the Rayleigh anomaly is governed by the period along the direction perpendicular to the incident polarization.

The bending of the plasmonic branch happens after interaction with the symmetric (1,0) Rayleigh anomaly. In principle, in a homogeneous dielectric environment, the asymmetric glass/air anomalies should not affect the LSP resonance. However, an effect can be observed on the experimental measurements for both polarizations [dotted line in Figs. 6(a) and 6(b)]. To understand this counterintuitive behavior, we performed additional numerical simulations. In Figs. 6(c) and 6(d) the simulated dispersion curves for a glass substrate ($n_1=1.52$) covered with a semi-infinite PMMA superstrate ($n_2=1.49$) are plotted. A number of discrepancies with the measurements are obvious: the position of the LSP branch is red-shifted, and the high-angle behavior is totally different, especially in $s$-polarization where the secondary branch, experimentally observed, is not predicted by the simulations. To better match the experimental geometry, we performed additional simulations by replacing the semi-infinite superstrate by a finite-thickness PMMA layer. The results are presented in Figs. 6(e) and 6(f). Now, in $s$-polarization, a branch around the (1,0) glass/air anomaly is visible. However, there is still a significant red-shift in the position of the resonance when compared to measurements. Such a shift could be explained if the nanoparticles are experiencing a lower effective refractive index in the experimental configuration, for example, in the case of the presence of air inclusions in the polymer film. To assess the validity of this hypothesis, we assumed that, the polymer did not perfectly fill the space between nanoparticles when spin-coated, but rather formed a film on top of the nanoparticles, with air between each nanoparticle. The results are shown on Figs. 6(g) and 6(h), demonstrating a good agreement with the experiments for both polarizations: the resonance position is close to the experimental one.

We summarize our results concerning the effects of both polarization and dielectric environment into the following rule of thumb: the coupling strength between LSPs near the Rayleigh anomalies is mainly governed by the radiation pattern of the single scatterers, and how it spatially and angularly overlaps with the grazing diffractive orders. More precisely, the Fano splitting (i.e., the coupling strength) is governed by three physical parameters: (i) spectral overlap between the initial modes, (ii) modal (i.e., spatial) overlap between the initial modes, and (iii) the initial linewidth.

5. ALUMINUM NANOPARTICLE ARRAYS

In this section, we apply our previous findings to the LSP sustained by aluminum nanoparticle arrays. As pointed out in the introduction, aluminum has a plasmonic response extending over a broad spectral region, but the losses, relative to gold, increase significantly for energies lower than the UV. Here, we discuss the possibility of using lattice resonances to reduce the amount of loss in two different spectral ranges: the first sample is designed to work in the visible range, while the second sample is designed for the blue-UV range.

A. Lattice Modes in the Visible

The first sample was designed to exhibit resonances in the visible spectrum. We fabricated arrays of aluminum nanodisks diameters of 120 nm and three different periods: $D=250$, 300 and 350 nm. Since a symmetric dielectric environment yields the sharpest resonances, the sample was covered with PMMA. The measured dispersion curves are presented in Fig. 7 for both polarizations. As the diameter of the metallic nanoparticles is kept constant while the period is changing, we are effectively moving the spectral position of the Rayleigh anomalies for a fixed LSP resonance. The effect is clearly observed for $s$-polarization by comparing Figs. 7(a)–7(c). In Fig. 7(a), the anomaly is located far from the LSP, and a weak interaction is observed with the broad LSP resonance. At normal incidence, the observed linewidth is quite similar to that of an isolated aluminum nanoparticle ($Q\simeq 2.5$). When the period is increased to $D=300\mathrm{nm}$, the position of the (1,0) Rayleigh anomaly shifts toward higher wavelengths, and a stronger coupling of the LSP resonances is observed as a bending of the plasmon branch and linewidth reduction when the angle of incidence is increased. At normal incidence, the linewidth is significantly lower than previously ($Q\simeq 5$), and the resonance further sharpens when the angle of incidence increases ($Q\simeq 9.5$ for $\theta =32°$). Finally, for $D=350\mathrm{nm}$, the anomaly is very close to the LSP resonance, leading to a stronger coupling and the apparition of a sharper lattice mode ($Q\simeq 9$ at normal incidence). For $p$-polarization [Figs. 7(d) and 7(e)], we clearly observe the same linewidth at normal incidence due to the symmetry of the nanoparticles, but the angular dependence is different, as no bending and linewidth reduction are observed when $\theta$ increases. This is due to the weak coupling efficiency between the LSPs excited in $p$-polarization near the (1,0) Rayleigh anomaly. We also note that, similar to the case with gold nanoparticle arrays, the glass/air Rayleigh anomaly influences the dispersion curve [see Fig. 7(e)], while it should be absent in a homogeneous environment. As was previously the case, this is likely due to the finite thickness of the PMMA layer and the presence of air inclusions.

 

Fig. 7. Experimental dispersion curves of PMMA-covered aluminum nanodisk arrays for (a)–(c) $s$-polarization and (d)–(f) $p$-polarization. The diameter of the nanoparticles is $d=120\mathrm{nm}$. The period of the array is (a), (d) $D=250\mathrm{nm}$; (b, e) $D=300\mathrm{nm}$; and (c), (f) $D=350\mathrm{nm}$. White lines represent the position of the glass/glass (solid lines) or glass/air (dotted lines), and Rayleigh anomalies were computed using Eq. (1).

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The obtained quality factors can be compared to the quality factor for isolated Al nanoparticles, which is generally $Q\approx 3–4$ in the visible range [9]. Hence, the linewidth engineering enabled by lattice modes enables $Q$-factors to be reached that are comparable to isolated gold nanoparticles in the visible. It is also interesting to compare Figs. 7(b) and 7(c). In the latter, the anomaly is very close to the LSP spectral position, leading to a sharp resonance at normal incidence where the intensity dramatically decreases when the angle of incidence increases. In contrast, in Fig. 7(b), the normal incidence linewidth is higher (due to the higher frequency mismatch between the LSP and the anomaly), but as the angle is increased, the resonance sharpens without being too detrimental to the lattice mode intensity. Consequently, if sharp lattice modes at normal incidence are sought then the Rayleigh anomaly should be designed to appear as close as possible from the LSP resonance. But if angular tolerance is required, then a minimal spectral mismatch should be introduced between the anomaly and the LSP.

B. Lattice Modes in the Blue-UV

Finally, we present results obtained on aluminum nanodisk arrays that were designed to exhibit a LSP resonance in the blue- and near-UV region. As explained in the introduction, aluminum can sustain LSP resonances down to deep-UV wavelengths; however, the particle diameter is a strong practical limitation. We made $d=60\mathrm{nm}$ diameter nanoparticles as a trade-off between exhibiting UV resonances and fabrication constraints. The period of the array is $D=260\mathrm{nm}$. We chose the superstrate to be air to avoid any red-shift of the plasmon resonance with the dielectric environment.

The experimental dispersion curve for $s$-polarization is presented in Fig. 8. A clear interaction between the LSP resonance around $\lambda =420\mathrm{nm}$ and the scattered light near the (1,0) Rayleigh anomaly is observed, leading to hybridization and the appearance of a sharper resonance. Under normal incidence, we obtain $Q\simeq 8$, a value that should be compared to $Q\approx 4–5$ obtained for isolated aluminum particles [9].

 

Fig. 8. Experimental dispersion curve of $d=60\mathrm{nm}$ aluminum nanodisk arrays in the ultraviolet for $s$-polarization. The period of the array is $D=260\mathrm{nm}$. White lines represent the position of the glass/glass (solid lines) or glass/air (dotted lines) Rayleigh anomalies were computed using Eq. (1).

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6. CONCLUSION

In summary, we have reported a study of the lattice modes, arising from diffractive coupling between localized plasmon modes sustained by individual nanoparticles near Rayleigh anomalies of the periodic array. Our results demonstrate the crucial role played by the dielectric environment and the incident polarization on the coupling strength and subsequent formation of lattice modes. The hybridization between the localized plasmon resonances and the formation of the lattice modes were mainly controlled by the radiation pattern of the individual metal scatterers forming the arrays. If carefully designed, nanoparticle arrays can exhibit lattice modes with remarkably high quality factors. For arrays of gold nanoparticles, it is possible to reach $Q$-factors on the order of several hundred. In the case of aluminum nanoparticles used in the visible spectrum, $Q$-factors of the same magnitude as those obtained for isolated gold nanoparticles were obtained, in spite of the relatively higher intrinsic losses of Al compared to gold. Moreover, it should be noted that the quality of the lithographed aluminum nanostructures was lower than that of the gold ones, which might have played a detrimental role on the $Q$-factor. As mentioned earlier, this is mainly due to the surface roughness of the evaporated Al film, which is difficult to master [46]. However, this limit can be overcome by using, for instance, the newly developed epitaxial aluminum films [47] to obtain high-quality Al nanostructures exhibiting low scattering and absorption losses. Altogether, we believe our results are a further demonstration of the potential of aluminum as a broadband plasmonic material. Among possible applications, aluminum nanoparticle arrays can be used to enhance the luminescence from wide bandgap semiconductors, such as ZnO [48]. The lattice mode can be finely tuned to match the exciton frequency (hence enhancing the emission rate), while the array can enhance light extraction from the active layer.