ARTICLE pubs.acs.org/JPCC
Nanoantenna Arrays for Large-Area Emission Enhancement Giovanni Pellegrini,* Giovanni Mattei, and Paolo Mazzoldi CNISM, Department of Physics, University of Padova, Via Marzolo 8, 35131 Padova, Italy ABSTRACT: The electrodynamic modeling of linear arrays of noble metal nanoantennas reveals that plasmonic Bragg modes allow for long-range and large-area emission enhancement. Significant light extraction is possible at large antenna emitter separation (micrometer range) and unfavorable emitter dipole moment orientation. One order of magnitude average emission enhancement for randomly oriented emitters is possible over areas ≈20 times larger than a single nanoantenna geometrical cross section.
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anoantennas (NAs) are a key element to enhance the coupling between light emitters and free propagating optical radiation.13 In the past few years, this class of nanostructures is receiving increasing attention because of its peculiar light-tailoring properties. Different effects including local field and emission enhancement, polarization rotation, angular emission redistribution, and high-efficiency single-photon collection are obtained by employing a variety of configurations such as multiple-coupled clusters, regular arrays, bow-tie, patch, and YagiUda antennas.416 One major drawback inherent to the usual NA approach is that emitters need to be placed at nanometric distance from the NA surface if strong emitterantenna coupling is desired.1720 In order to overcome this limitation, it has been suggested that plasmonic Bragg modes (collective plasmonic lattice modes where all the particles in the plasmonic crystal oscillate coherently) supported by ordered arrays may be employed; nevertheless, no clear indication of this possibility has yet emerged.21,22 Here we employ generalized multiparticle Mie (GMM) theory to study the large-area emission enhancement properties of one-dimensional (1D) plasmonic NA arrays.2325 First, the array spectral properties are investigated for a discrete set of dipolar emitter positions, and the emerging plasmonic Bragg modes are examined by local field mapping. Then, the large-area emission enhancement properties are analyzed by emitter position and orientation mapping. Finally, average emission enhancement performances are systematically studied by performing a parametric sweep of the array geometrical and structural parameters. In this modeling framework, emitters are classical dipoles with quantum efficiency qo = γor /(γor + γonr), where γor and γonr are the radiative and nonradiative recombination rates. Dipoles are modeled as pure sources of the incident field; that is, they are not driven by the field of the other dipoles or by the field scattered by the antennas. This corresponds to an experimental setup where a Stokes shift between excitation and emission exists.21 Finally, randomly oriented emitter properties are modeled by performing analytical orientation averaging of the dipole moment orientation over the unit sphere. Nanoantenna coupling r 2011 American Chemical Society
effects are expressed in terms of power dissipated inside the NA and radiated by the antenna emitter ensemble. Normalized modified rates are expressed as γr/γor = Pr/Por and γabs/γor = Pabs/Por , γabs being the contribution from ohmic dissipation Pabs, Pr the power radiated by the emitterantenna system, and Por the power radiated by a classical dipole. Modified quantum efficiency is finally written as1719 q¼
γr =γor γr =γor þ γabs =γor þ ð1 qo Þ=qo
ð1Þ
where γnr = γonr + γabs is the overall nonradiative rate. We remark that emitters in each elementary cell are modeled as coherently oscillating dipoles: this assumption may be retained as reasonable, since it has been experimentally demonstrated that emitters couple directly to Bragg modes supported by plasmonic crystals and photonic crystal slabs.12,21 Furthermore, cooperative spontaneous emission has been predicted for linear arrays of two-state atoms and has been observed for quantum dots and ions ensembles.2628 In the following we focus our analysis on a 600 unit long silver spherical NA array, with R = 70 nm radius and a = 550 nm pitch. The structure is embedded in a n = 1.5 refractive index matrix with silver optical constants taken from the literature.29 Array length is fixed throughout the paper, since the only effect of a size variation is a change in resonance intensity and bandwidth.30 Figure 2a reports the extinction spectrum for a unitary amplitude plane wave illumination as sketched in Figure 1a. The sharp peak at λ = 829 nm agrees well with coupled dipole model Bragg modes emerging at λ = n 3 a, where the effective polarizability αeff = α/(1 αS) presents a resonance for Re[α1] ∼ Re[S], S being the retarded dipole sum and α the original antenna polarizability. The sharp resonance shape arises both from the singularities in Re[S] and from the partial cancellation between Im[S] and the radiative damping terms.31 Received: September 29, 2011 Revised: November 2, 2011 Published: November 18, 2011 24662
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Figure 1. (a) Sketch of typical NA array configuration. Array is x oriented, with pitch a. Emitter position and dipole moment orientation are highlighted by the colored cones, with one emitter per unit cell. Incident plane wave E and k are along the z and y axis, respectively. (b) Mapping planes correspond to the three principal Cartesian ones, with one additional plane in interparticle position at the unit cell boundary.
Figure 2. (a) [R = 70 nm, a = 550 nm] NA array extinction spectrum normalized to the number of NAs in the array. (b) [R = 70 nm, a = 550 nm] NA array quantum efficiency enhancement spectra for q0 = 0.01 emitters as represented in Figure 1a. Radiative (γr) and dissipative (γabs) recombination rate enhancements are reported in the insets.
Quantum efficiency enhancement spectra for q0 = 0.01 emitters are reported in Figure 2b. Emitter positions in the unit cell are ri = (0, 0, 80) nm, rii = (0, 0, 275) nm, and riii = (275, 0, 0) nm, respectively, with dipole moments along the z axis as sketched in Figure 1a. Large quantum efficiency enhancements are visible at the Bragg resonance with q/q0 = 40 in the case of position (i) emitters. Emission enhancement is still present for emitter in position (ii) and (iii), with q/q0 = 10 in the former case. Recombination rate spectra reported in Figure 2b insets show indeed negligible ohmic losses for emitters in the interparticle position, given that the large antenna emitter separation inhibits the coupling to high-order dissipative modes.17,32 On the other hand, radiative recombination rates are still enhanced
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Figure 3. Local field plots for [R = 70 nm, a = 550 nm] NA array with unitary amplitude plane wave illumination as in Figure 1a. Field mapping is performed on the four mapping planes sketched in Figure 1b at λ = 829 nm.
by an order of magnitude, which allows for a 10-fold quantum efficiency gain. Local field mappings at the Bragg resonance wavelength allow for a straightforward interpretation of the long-range emission enhancement results. Figure 3 reports local field mappings at λ = 829 nm over the four planes illustrated in Figure 1b. Local field hot spots (|E| = 25) attributed to localized surface plasmon resonances (LSPR) are visible at the NP surface, though their intensity and spatial extension is larger than in the single-particle case, given the enhanced effective polarizability αeff.31 A second class of local field hot spots, whose intensity |E| = 10 is comparable to the one of LSPR modes associated with isolated NP, is located in the interparticle spaces at the unit cell boundary and directly attributed to the presence of Bragg modes.33 With this picture in mind, it is easy to understand by reciprocity that emitters in position (ii) undergo significant emission enhancement since they are able to efficiently couple to the Bragg modes supported by the regular array.12,21,34 In order to better elucidate the coupling between emitters and NA arrays, we performed a quantum efficiency enhancement mapping by displacing the emitters over the four usual planes. Up to 55 multipoles are employed in the calculation in order to ensure convergence for small antenna emitter separations. Figure 4ad shows q/q0 mappings for emitters with fixed dipole moment orientation parallel to the z axis. Emission enhancement hot spots ascribable to LSPR and Bragg modes are clearly distinguishable in the figure. LSPR modes are able to provide q/q0 > 40 enhancements for emitter very close to antenna surface (d e R/5), while quenching is observed for separations smaller than 5 nm. Bragg modes contribute to enhancements of more than 1 order of magnitude at emitter antenna separation of about 200 nm. Figure 4eh reports an analogue q/q0 mapping for emitters with orientation-averaged dipole moments, so as to estimate nanoantenna array performances for randomly oriented emitters. Emission enhancement mappings closely resemble the fixed orientation ones with LSPR and Bragg mode features again clearly identifiable. Emission enhancement performances are lowered by the orientation-averaging procedure; nevertheless, the LSPR and Bragg modes behave differently in this respect, the latter ones being less negatively affected. A rough estimate indeed shows that z Ω z qΩ LSPR/qLSPR = 1/3 for the LSPR modes and qBragg/qBragg = 2/3 in 24663
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the recombination axis normal to the NA surface, while the remaining axes in the xy plane show negligible quantum efficiency enhancement.32 The emitter in position (ii) couples to the collective Bragg mode: minor emission is obtained for the recombination axis along the array, while maximum enhancement is achieved for dipole moments oriented along the degenerate axes lying in the yz plane.22 In this framework the different behavior of LSPR and Bragg modes under orientation averaging is nicely explained as the ratio between good axes versus bad axes, that is, 1/3 and 2/3 for LSPR and Bragg modes, respectively. For practical purposes and applications, it is interesting to investigate the average emission enhancement properties of NA arrays. Local field and quantum efficiency enhancement averaging is performed over an S = [a a] square domain in the xz plane as sketched in Figure 4b, in order to allow a straightforward generalization to planar crystals. Average qS,z is defined as qS, z ¼
1Z z q ðrÞ dS a2 S
ð2Þ
and corresponds to the spatial average for an emitter with a fixed dipole moment orientation along the z axis, while qS,Ω is qS, Ω ¼
Figure 4. Quantum efficiency enhancement position mapping for a [R = 70 nm, a = 550 nm] NA array over the mapping planes sketched in Figure 1b at λ = 829 nm. (ad) Fixed z dipole moment orientation. (eh) Orientation-averaged dipole moment. The dashed square in (b) represents the integration area for the averaging procedures. Insets: quantum efficiency enhancement in proximity of antenna surfaces.
Figure 5. Polar surface plots representing the dipole orientation quantum efficiency enhancement dependence in real space at λ = 829 nm. Emitter positions are as sketched in Figure 1a.
the Bragg case, where qz and qΩ are the fixed and random orientation enhanced efficiencies. Emission enhancement orientation mapping allows for an interpretation of the LSPR and Bragg mode behavior under orientation averaging. Figure 5 reports q/q0 polar surface plots for the three adopted emitter positions. Quantum efficiency enhancement surfaces show the typical dumbbell-like shapes, since Green’s dyadic symmetry properties allow the description of the recombination rate polar surface by three orthogonal recombination axes and a quadric over the unit sphere.35 Emitters in position (i) and (iii) mostly couple to the LSPR mode: maximum emission enhancement is obtained for dipole orientations along
1 Z 4πa2
Z S
Ω
qðr, ΩÞ dSdΩ
ð3Þ
and corresponds to the simultaneous spatial and orientation averaging. Embedding matrix and NA array material (Ag) and length (600) are kept fixed, while array pitch a and NA radius R are the swept geometrical parameters with a ∈ [420, 1000] nm and R ∈ [50, 100] nm. Each averaging is performed at the corresponding Bragg resonance; that is, the wavelength of maximum emission enhancement is calculated for each [R, a] pair, and then the averaging procedure is performed. Figure 6 reports the results of the parametric sweep. The wavelengths of the Bragg resonances (Figure 6a) follow the relation λ = n 3 a and are largely independent of the NA size, with the exception of [R, a] pairs with radius and array pitch of comparable size where the LSPR behavior dominates. Local field results illustrated in Figure 6b show that maximum average |E| = 5 enhancement may be obtained for a unitary amplitude z-polarized incident plane wave over the integration domain sketched in Figure 4b. The peak enhancement roughly follows a linear relationship in the [R, a] plane since a wavelength matching between the LSPR resonance (dependent on the particle size) and the Bragg one (dependent on the array pitch) is required for optimal performances.22 Figure 6c, d shows that the mapping of qS,z and qS,Ω follows a behavior qualitatively similar to the one of |E| as may be expected by applying reciprocity.12,21,34 Average quantum efficiency enhancements of more that 1 order of magnitude are obtained in the case of z-oriented emitters throughout the visible and nearinfrared range, and roughly 2/3 of the peak performances are preserved after the orientation-averaging procedure. In the nearinfrared range 1 order of magnitude enhancements are obtained over areas =20 times larger than the single NA geometrical cross section. Finally, quantum efficiency enhancement performances for isolated NA at the dipolar peak wavelength are reported in Figure 6e. It is immediately clear that isolated NAs are unable to provide significant enhancement for randomly oriented emitters over large areas and are routinely outperformed by linear arrays. Summarizing, we have demonstrated by GMM calculations that NA arrays allow for large-area emission enhancement, relaxing the principal constraints imposed by isolated nanostructures, that is, 24664
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Figure 6. Parametric [R, a] sweep for the investigation of NA array average emission enhancement properties: (a) λBragg peak wavelength; (b) NA array average local field enhancement; (c) z-oriented emitter quantum efficiency enhancement; (d) orientation-averaged quantum efficiency enhancement; (e) orientation-averaged single NA quantum efficiency enhancement. The integrating domain for the average mappings is as sketched in Figure 4a; the white dot indicates the [R = 70 nm, a = 550 nm] array.
careful positioning and orientation of the emitters. One order of magnitude emission enhancement over areas =20 times larger than a single NA geometrical cross section is possible, bringing about the important consequence that very small amounts of noble metals are needed in order to obtain large light extraction. All the aforementioned conclusions are of a general nature and remain valid for different NA materials or shapes, and for different array geometries,11 provided that the structure is able to support plasmonic Bragg modes. Bidimensional (2D) arrays are especially interesting in this respect for their wavelength multiplexing and polarization sensitive properties, and their analysis is foreseen as future work.11,36 The presented results might find important application in a broad range of sensing, high-efficiency lighting and photonic devices.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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’ NOTE ADDED AFTER ASAP PUBLICATION This article was published ASAP on November 18, 2011. In Figure 1, the wave vector and electric vector labels (k,E) have been corrected. The correct version was published on November 23, 2011. In addition, the axis labels of Figure 5 were corrected; the correct version was published on December 15, 2011. 24665
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