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May 7, 2009 - unidirectional radiation pattern for emission wavelengths close to the antiphase hybridized plasmon. We analyze this unique effect in te...
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NANO LETTERS

Unidirectional Ultracompact Optical Nanoantennas

2009 Vol. 9, No. 6 2343-2349

Tavakol Pakizeh* and Mikael Ka¨ll Department of Applied Physics, Chalmers UniVersity of Technology, Go¨teborg 412 96, Sweden Received March 12, 2009; Revised Manuscript Received April 29, 2009

ABSTRACT We report on a dramatic directionality effect in a simple and ultracompact optical nanoantenna consisting of a pair of interacting plasmonic nanoparticles. We found that the emission from a dipole source positioned close to one of the particles in the pair exhibits an essentially unidirectional radiation pattern for emission wavelengths close to the antiphase hybridized plasmon. We analyze this unique effect in terms of radiation, reception, and reciprocity concepts using electrodynamics simulations and dipole analysis. A forward-backward directionality of ∼18 dB at 665 nm is obtained for a nanoantenna that consists of two 90 nm wide and 20 nm thick gold nanodisks separated by a 10 nm gap.

Metal nanostructures considerably enhance the electromagnetic (EM) emission of a local source, such as a fluorescent dye, a Raman scatterer, or a near-field microscope tip. This process can be thought of as an antenna effect in which the evanescent EM fields generated by the local source excite the collective electron oscillations of the nanostructure, which in turn scatter to the far-field.1-7 The antenna effect is strongest if the frequency of the source field coincides with a localized surface plasmon resonance (LSPR), as determined by the nanostructure shape, size, and composition. A variety of plasmonic nanoantennas, such as nanorods,1,8-12 particle dimers,13 bow-ties,14 and nanohole chains,15 have been described in the literature. Many of these studies have demonstrated enormous enhancement effects, but less attention has been devoted to directionality properties of nanoplasmonic antennas. In a recent study by Taminiau et al.,8 it was shown that the emission from a molecular fluorophore could be effectively redirected by a plasmonic nanorod in such a way that the fluorescence emission pattern was determined by the orientation of the nanorod rather than by the molecular source. Similar effects can be expected for a variety of nanoantennas dominated by localized dipolar plasmon modes, but such systems will always exhibit the typical omnidirectional emission pattern of a Hertzian dipole. The realization of highly directional nanooptical antennas has thus remained a challenging goal. One obvious route forward starts from classical antenna concepts developed for radio frequencies. It has, for example, been shown theoretically that Yagi-Uda antennas and dipole * To whom correspondence should be addressed. E-mail: Tavakol. [email protected]. Tel: +46(31)7725177. Fax: +46(31)7722090. 10.1021/nl900786u CCC: $40.75 Published on Web 05/07/2009

 2009 American Chemical Society

arrays based on appropriately spaced metal nanoparticles may yield very large directivities for selected wavelengths in the visible,9,16 and similar effects have been demonstrated also for bulls eye structures17 and arrays of nanoholes in thin metal films.15 However, such designs are typically rather large, as they are based on phase matching of several individual weakly coupled antenna elements separated by distances of the order λ/4-λ, where λ is the free space wavelength. In contrast, we here describe a simple optical nanoantenna design that results in essentially unidirectional emission for a nanoplasmonic structure of size less than λ/7. The high directionality is obtained due to strong coupling between dipolar plasmons of two close-by nanoparticles arranged in the end-fire configuration. Specifically, the nanoantenna supports a hybridized plasmon mode in which the elementary nanodisk plasmons oscillate in antiphase. If a local source, positioned close to the edge of one of the nanoparticles, oscillates with a frequency close to this antiphase mode, the system only radiates in one direction. Figure 1 illustrates the unidirectionality effect through electrodynamical simulations based on the three-dimensional dispersive finite-difference time-domain (D-FDTD) method (see ref 18 and Supporting Information). We start from a single Hertzian dipole that is oriented in the vertical (z-) direction and therefore has its familiar toroidal far-field pattern (Figure 1a) concentrated to the equatorial (xy-) plane. Next, we position a gold nanodisk (diameter D ) 90 nm, thickness T ) 20 nm) at a distance of 4 nm directly below the dipole source, as shown in Figure 1b. The nanodisk has a plasmon resonance that strongly enhances the emission by a factor of ∼50 at the λ ) 585 nm peak of the plasmon response, but the emission pattern is only slightly changed

Figure 1. Illustration of unidirectional emission by an ultracompact optical nanoantenna from D-FDTD simulations. (a) Coordinate system and emission pattern characterizing a Hertzian dipole oscillating in the z-direction. (b) Emission pattern resulting from coupling between the dipole source and a single Au nanodisk of diameter D ) 90 nm and thickness T ) 20 nm. The dipole is positioned at P (4 nm centrally above the nanodisk surface) and the emission wavelength (λ ) 590 nm) is selected to coincide with the long-axis LSPR of the nanodisk. Note the ∼50-fold enhancement compared to the isolated dipole. (c) Unidirectional emission pattern resulting from placing a second identical nanodisk at a distance of d ) 10 nm from the first one. The wavelength (λ ) 665 nm) is close to the antiphase dipolar plasmon of the coupled nanodisks system.

compared to the isolated dipole. We now place a second identical nanodisk just to the left of the first one (Figure 1c). The surface-to-surface distance, d ) 10 nm, is such that a strong near-field coupling and plasmon hybridization occurs.19 At a wavelength that corresponds to the antiphase plasmon mode of the nanoantenna, which occurs at λ ) 665 nm for the parameters in Figure 1, we now observe a drastic change of the emission pattern, that is, an almost complete cancellation of the radiation towards the left half plane (-y direction) and a further enhancement (up to a factor of ∼70) of the emission propagating to the right (+y direction). Naturally, these directions would be reversed if we had instead placed the second nanodisk just to the right of the first one. We should also mention that the effect summarized in Figure 1 would have been essentially identical if we had started from a randomly oriented dipole source. However, 2344

components of the source field originating from dipole oscillations perpendicular to a radial direction through the first nanodisk (x- and y- in Figure 1) do not couple to the main nanodisk plasmon and, hence, are not enhanced or contribute to the unidirectionality effect. Although the action of the second nanodisk superficially resembles that of the reflector in a basic Yagi-Uda antenna,9,11,16 we stress that the effect is due to a strong nearfield interaction and not to diffractive far-field interference, as in most classical antenna designs. To prove this point and to characterize the effect further, we have performed extensive D-FDTD simulations as well as model calculations using a coupled dipole approach. The latter provides a clear physical insight into the coupling effects that constitute the basis for the observed unidirectionality. Although qualitatively similar antenna effects are expected for a variety of dimer systems (for example, two nanorods, two nanospheres, etc.), we here entirely focus on gold disk “nanosandwiches” with size parameters (D, T, d) accessible by lithographic techniques.18,20,21 We note that this type of nanostructure has received recent attention in the metamaterials field because of interesting magnetic dipole effects associated to the antiphase plasmon mode.18,22-26 Figure 2 summarizes the spectral response of the nanoantenna structures in Figure 1. We first study the emission enhancement-factor S(θ,φ) (relative to the isolated dipole) in the forward direction (defined as θ ) 90°, φ ) 90°, or to the right in Figure 1). As seen in Figure 2a (dashed line), the single Au nanodisk exhibits a distinct peak reaching S ≈ 50 at λ ≈ 585 nm due to a dipolar LSPR polarized in the plane of the disk. The exact peak position is determined mainly by the nanodisk aspect ratio D/T; the peak would be further to the red if the nanodisk had been wider with constant thickness T or thinner with constant diameter D.27 The asymmetric shape of the peak originates mainly from the strongly wavelength dependent interband absorption in Au,28 which sets in rather abruptly at ∼530 nm (a silver nanodisk with the same dimensions would display a slightly stronger and more symmetric peak, because the interband threshold occurs further to the blue). In contrast, the nanoantenna (full line) exhibit two peaks at opposite sides of the single nanodisk plasmon: the aforementioned in-phase (short wavelength) and antiphase (long wavelength) hybridized dipolar modes of the strongly coupled nanodisk dimer.18,20,22,25 Because of the small surface-to-surface separation (d ) 10 nm), the interaction is in fact so strong that the in-phase mode has been partially pushed into the interband region, thus significantly reducing the strength of the enhancement. On the other hand, the antiphase mode produces a stronger enhancement than the single disk LSPR. This is primarily due to its small line-width, a feature that can linked to the dipole forbidden (subradiant) nature and reduced radiative damping of the antiphase mode.25,29,34 However, the most dramatic difference between the single nanodisk and the nanoantenna obviously concerns the unidirectionality effect. The directionality of an antenna, measured in dB, can be defined from Nano Lett., Vol. 9, No. 6, 2009

Figure 2. Spectral variation of emission enhancement and directionality from D-FDTD simulations. (a) Emission enhancement factor S(θ,φ) in the forward direction versus wavelength for a single Au nanodisk (dashed line, same parameters as in Figure 1b and a nanoantenna (full line, same parameters as in Figure 1c). (b) Forward-backward directionality GFB of the single disk (dashed line) and the nanoantenna (full line) versus wavelength. The directionality of the nanoantenna reaches ∼18 dB in a narrow spectral range around 665 nm, whereas the single nanodisk antenna radiates almost equally in the forward and backward directions.

D(θ, φ) ) 10 × log10[4πS(θ, φ)/

∫ ∫ S(θ, φ)sin(θ)∂θ∂φ], φ

θ

0 e θ e π,

0 e φ e 2π (1)

We are here primarily interested in the forward-backward (FB) ratio GFB ) DF - DB ) 10 × log 10(SF/SB), that is, the ratio between the power radiated in the forward (θ ) 90°, φ ) 90°) and backward (θ ) 90°, φ ) 270°) directions.30 As seen in Figure 2b, GFB for the nanoantenna reaches ∼18 dB at the position of the antiphase plasmon, whereas the single disk has GFB ≈ 0 across the whole spectral range. From the spectral dependence, it is also evident that the in-phase mode supported by the nanostructure does not contribute to the unidirectionality effect at all. This unique near-field interaction effect has not been observed in previously studied antenna designs for the optical range. In a conventional three-element Yagi-Uda antenna designed for an operating wavelength λ, the reflector and the director are typically ∼5-10% longer and shorter, respectively, than the length l ∼ 0.5λ of the driven half-wave dipole antenna element, whereas the separation between the elements are of the order ∼0.2-0.4λ. The resulting phase matching between elements typically yields GFB ∼ 6-8 dB for radio frequencies.30 In the case of a nanoplasmonic Nano Lett., Vol. 9, No. 6, 2009

antenna for the optical range, the lengths of the elements can be greatly reduced because the operating wavelength, given the LSPR resonance position, is primarily determined by the aspect ratio of the driven element. Similarly, the distance between the elements can be reduced because of strong near-field coupling and plasmon hybridization. Consequently, a variation of the aspect ratios and near-field coupling characterizing the nanoantenna can be expected to have a major impact on its directionality properties. Inspired by the Yagi-Uda design, we explored the tunability by varying the separation d between the two disks in the sandwich and by letting their diameters differ by an amount 2δD. Specifically, we make the front disk, which is fed by the dipole source and thus acts as the primary driver element, smaller (D1 ) D - δD) while the second disk (the “reflector”) is made larger (D2 ) D + δD). The thicknesses (T ) 20 nm) of the disks and the distance to the source dipole (4 nm) are kept the same as for the symmetric sandwich described in Figures 1 and 2. Figure 3 shows radiation patterns for several nanoantennas with varying d and δD values. Both parameters obviously alter the radiation pattern and strongly affect the resulting directionality. Figure 3a shows the effect of varying d between 6 and 40 nm while keeping D1,2 ) 90 nm constant. Each pattern is plotted for the particular wavelength that yields the highest directionality, which closely matches the antiphase plasmon resonance wavelength. The latter red-shifts continuously as d decreases, because of the increasing plasmon hybridization. Going from d ) 40 nm to d ) 10 nm, one notes a gradual increase in forward emission and a concomitant decrease for the backward direction, resulting in rapidly increasing GFB. However, the trend is obviously broken for the shortest distance, d ) 6 nm, demonstrating that a specific degree of field retardation is essential for the unidirectionalty effect. We should also mention that the case d ) 0, that is, representing a single but twice as thick disk, exhibits an essentially toroidal radiation distribution (similar to Figure 1d), because no antiphase plasmon mode is possible in this case. In Figure 3b, we instead keep d ) 10 nm and vary δD from 0 to 16 nm, thus breaking the symmetry of the nanoantenna. This obviously increases the emission in the forward direction, but the backward emission increases even more and the unidirectionality effect therefore diminishes. Additionally, we may note that the direction of the main radiation lobe is reversed if the source point is instead located on the larger nanodisk (not shown). However, the FB directionality is reduced and the design is clearly not ideal from an antenna point-of-view. Another parameter that is expected to play an important role in determining the radiation properties of the antenna is the location of the feed or, in our case, the position of the local point source. To investigate the influence on directionality and enhancement properties, we studied cases in which the position of the source dipole was displaced along the y-axis while keeping the same structure dimensions as in Figure 1c. Figure 4 shows the influence on the emission enhancement in the forward direction SFW and the FB directionality GFB for positions P - 4 nm and P + 4 nm, 2345

Figure 3. Tunability of emission pattern from D-FDTD simulations. (a) Emission enhancement patterns S(θ,φ) of symmetric nanoantennas with varying surface separation d ) 10, 20, 30, 40 nm. Except for d, the parameters are the same as in Figure 1c. (b) Emission enhancement patterns of asymmetric nanoantennas. The diameter of the front nanodisk has been decreased to D1 ) D - δD with δD ) 0, 8, 16 nm, while the diameter of the back nanodisk has been increased by the same amount.

Figure 4. Dependence of (a) the emission enhancement in forward direction SFW and (b) the FB directionality GFB of the nanoantenna on the position of the local point source from D-FDTD simulations. The position of the local point source is changed along y-axis. Two cases with P - 4 nm (dash-dot) and P + 4 nm (dash) are considered and compared with the case that P is located in the center above the front nanodisk (solid), seen in Figure 1c. The directionality is reduced when the local source is moved toward the center of coordinate.

where P refers to the central position (same as in Figure 1c) and the “-” sign means moving the source closer to the gap region. Interestingly, the latter case leads to increased enhancement but decreased directionality, while the reverse is true for the opposite displacement P + 4 nm. This indicates that the central position (P) gives a good representation of the averaged enhancement and directionality properties of a system for which local sources are distributed randomly around the perimeter of one of the disks. 2346

On the basis of the reciprocity theorem of electromagnetism,30 we expect that a nanoantenna should have very similar directionality properties in transmittance and in reception mode. To check whether this is actually the case, we compared the near-field distributions around nanoantennas illuminated by a plane wave incident from either the forward or the backward direction. This allows us to calculate a forward-backward ratio for reception as KFB ) 10 × 2 2 log10(|EP|forward /|EP|backward ), where EP is the total field at a particular point P, corresponding to the position of a virtual receiver. Figure 5a illustrates the field distribution generated by the two illumination configurations for a slightly asymmetric nanoantenna (δD ) 8 nm). The chosen wavelength (λ ) 665 nm) is close to the one yielding highest emission directionality and, as expected from the reciprocity theorem, one indeed notes a much higher local intensity close to the source point P for forward than for backward illumination. Figure 5b quantifies this observation for a set of nanoantennas with fixed δD ) 8 nm but varying separation d ) [10, 40 nm]. The figure thus compares the FB directionality GFB obtained for transmission mode (using a z-oriented dipole source 4 nm from the rightmost nanodisk, as in Figure 1-3) with the FB directionality KFB for reception calculated for the same position and orientation (i.e., z-component of EP) as for the Hertzian dipole source. From the data, it is clear that the spectral dependences of KFB and GFB are nearly identical, which thus confirms the validity of the reciprocity concept for the studied systems. This further implies that the intensity received at P will closely follow the nanoantenna patterns shown in Figures 1 and 3 if the angle of illumination (θ,φ) is varied. Figure 5b shows that the FB directionalities obtained for slightly asymmetric nanoantennas are in general smaller than for the symmetric case (Figure 3a) but follow the same general trend versus separation d. However, it is interesting to note that the highest directionality (GFB = KFB ≈ 15 dB) is obtained at twice as high separation (d ≈ 20 nm). It is thus possible to partially compensate for the decrease in directionality induced by an asymmetry δD by tuning separation d, and vice versa. Nano Lett., Vol. 9, No. 6, 2009

Figure 5. Reciprocity, tunability, and extinction of nanoantennas from D-FDTD simulations. (a) Spatial distribution of the z-component of the total E-field around a nanoantenna with δD ) 8 nm and d ) 10 at 665 nm for z-polarized illumination from the forward (upper plot) and backward (lower plot) directions. P denotes the source point for the emission calculations (Figure 1-3). (b) Forward-backward directionalities for emission GFB (lines) and reception KFB (points) of nanoantennas with δD ) 8 nm and varying separation: d ) 40 nm (solid-green), d ) 30 nm (dash-dot), 20 nm (dash), and 10 nm (solid-red). (c) Extinction spectra for the same nanoantennas as in (b).

For completeness, we show in Figure 5c the extinction efficiencies Qext for the slightly asymmetric nanoantennas discussed above. The extinction Qext is obtained from the calculated extinction cross-section by dividing with the geometrical area of the largest nanodisk in the structure. As discussed in ref 18, the extinction spectrum is nearly identical for forward and backward illumination. For the smallest distances, d ) 10-20 nm, the spectra clearly reveal two peaks, that is, the long-wavelength antiphase mode, which peaks at the same positions as the corresponding directionality spectra in Figure 4b, and the in-phase mode, which dominates the extinction but does contribute to the unidirectionality effect. In the previous discussion, we have entirely focused on results obtained through D-FDTD calculations. This method produces accurate solutions to Maxwell’s equations (to a degree primarily determined by discretization errors) but it gives limited insight into the basic physical processes behind the unidirectionality effect. To complement the D-FDTD results, we have previously utilized a coupled dipole approximation (CDA) model in which the gold nanodisks are approximated as oblate nanospheroids.22 As demonstrated in ref 18, the method can be used to calculate far-field properties, for example extinction and absorption spectra, and near-field effects, such as magnetic field enhancement, that are in good quantitative agreement with both D-FDTD and experimental results for various nanoantenna structures. We now use this method to further elucidate the unidirectionality effect (see Supporting Information and ref 18 for full details of the CDA model). We consider a nanoantenna that consists of two identical oblate nanospheroids with major axis D/2, minor axis T/2, and center-to-center separation d0 ) d + T. Referring to the schematic in Figure 1c, the nanoantenna is illuminated by a z-polarized plane wave incident from the right (forward direction) or from the left (backward direction). We now estimate KFB = GFB by comparing the strengths of the near-fields generated at P just above the rightmost nanospheroid (particle 1) for the two illumination Nano Lett., Vol. 9, No. 6, 2009

directions. These fields will be primarily determined by the z-, or long-axis, polarizability component of nanospheroid 1, and therefore |EPz |2forward/|EPz |2backward ≈ |R˜ zz,1|2forward/|R˜ zz,1|2backward. Further, due to the symmetry of the problem, we have that |R˜ zz,1|backward ) |R˜ zz,2|forward, that is, we can estimate the directionality by simply comparing the magnitudes of the renormalized particle polarizabilities for one incidence direction. In turn, these are obtained by solving the coupled dipole equation, which describes the interaction between the two nanospheroids. If only the near-field component of the induced field is considered, one obtains KFB ≈ 10 × log10[|R˜ zz,1 |forw /|R˜ zz,2 |forw] ) 10 × log10[ |d30 - Rzz,0eiψ | 2 /|d30 - Rzz,0 | 2]

(2)

where Rzz,0 is the frequency-dependent polarizability of a single nanospheroid and ψ ) 4πd0/λ is the phase retardation between nanospheroids 1 and 2.31 From eq 2, it is obvious that the distance between the nanoparticles plays a crucial role in determining the directionality. In particular, no directionality can be achieved without phase retardation ψ. However, if ψ > 0, then eq 2 indicates that the highest directionality will occur in a wavelength region for which Re [Rzz,0] ≈ d30, a condition that is satisfied at a wavelength slightly to the red of the single particle LSPR. Further analysis shows that the maximum amplitude of KFB almost coincides with the maximum amplitude of the antiphase dipole oscillation, which can be obtained by projecting the [R˜ zz,1 R˜ zz,2] on the antiphase normal mode [1 - 1] of the coupled system (see Supporting Information for further details). To demonstrate that the CDA approach yields results that are in good qualitative agreement with full D-FDTD simulations, we show in Figure 6 the variation in KFB and Qext with separation d0. The calculations include all components of the induced fields, utilize the same gold dielectric function as the D-FDTD simulations, and are based on the size-corrected27 polarizability of two nanospheroids with D ) 90 nm and T ) 20 nm. As can be seen in Figure 6a, the directionality peak red shifts continuously with decreasing separation and reaches a maximum amplitude at d0 ≈ 40 nm, corresponding to a surface-to-surface separation of d ) 2347

Figure 6. Directionality and optical extinction for nanoantennas approximated as coupled dipoles. (a) Directionality spectra in dB according to eq 2 for nanoantennas composed of two oblate gold nanospheroids (D ) 90, T ) 20) vs center-to-center distance d0 ) d + T. (b) Extinction efficiencies Qext for the same nanostructures as in (a) vs d0.

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