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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 4 — Feb. 25, 2013
  • pp: 4578–4590
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Shaping single emitter emission with metallic hole arrays: strong focusing of dipolar radiation

Robert J. Moerland, Lur Eguiluz, and Matti Kaivola  »View Author Affiliations


Optics Express, Vol. 21, Issue 4, pp. 4578-4590 (2013)
http://dx.doi.org/10.1364/OE.21.004578


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Abstract

Nanoscale plasmonic structures allow for control of the emission of single emitters, such as fluorescent molecules and quantum dots, enabling phenomena such as lifetime reduction, emission redirection and color sorting of photons. We present single emitter emission tailored with arrays of holes of heterogeneous size, perforated in a gold film. With spatial control of the local amplitude and phase of the electromagnetic field radiated by the emitter, a desired near- or far-field distribution of the electromagnetic waves can be obtained. This control is established by varying the aspect ratio of the individual holes and the periodicity of the array surrounding the emitter. As an example showing the versatility of the technique, we present the strong focusing of the radiation of a highly divergent dipole source, for both p- and s-polarized waves.

© 2013 OSA

1. Introduction

Controlling the emission of light by (single) emitters on the nanoscale has been a subject of study for some decades already. With single fluorescent molecules imaged in the early 1990s [1

1. E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993). [CrossRef] [PubMed]

], new methods to control — instead of merely detect — the emission are being developed continuously [2

2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

5

5. R. J. Moerland, T. H. Taminiau, L. Novotny, N. F. van Hulst, and L. Kuipers, “Reversible polarization control of single photon emission,” Nano Lett. 8, 606–610 (2008). [CrossRef] [PubMed]

]. Also some long-established methods that have been applied at the radio-frequency regime are transformed into working concepts at optical frequencies [6

6. T. Taminiau, R. Moerland, F. Segerink, L. Kuipers, and N. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007). [CrossRef] [PubMed]

,7

7. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010). [CrossRef] [PubMed]

]. The driving force behind the research is the desire to achieve ever more sensitive detection of molecules, with applications in, for example, in vivo imaging of cells [8

8. X. H. Gao, Y. Y. Cui, R. M. Levenson, L. W. K. Chung, and S. M. Nie, “In vivo cancer targeting and imaging with semiconductor quantum dots,” Nat. Biotechnol. 22, 969–976 (2004). [CrossRef] [PubMed]

] and early detection of malignant agents [9

9. A. Friedrich, J. D. Hoheisel, N. Marme, and J. P. Knemeyer, “DNA-probes for the highly sensitive identification of single nucleotide polymorphism using single-molecule spectroscopy,” FEBS Lett. 581, 1644–1648 (2007). [CrossRef] [PubMed]

]. Among the properties of emitters that nowadays can be controlled on the nanoscale are the polarization [5

5. R. J. Moerland, T. H. Taminiau, L. Novotny, N. F. van Hulst, and L. Kuipers, “Reversible polarization control of single photon emission,” Nano Lett. 8, 606–610 (2008). [CrossRef] [PubMed]

, 10

10. R. M. Bakker, V. P. Drachev, Z. T. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008). [CrossRef]

], angular emission [11

11. H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000). [CrossRef]

, 12

12. H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011). [CrossRef] [PubMed]

], lifetime [13

13. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006). [CrossRef] [PubMed]

, 14

14. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006). [CrossRef] [PubMed]

] and emission wavelength [15

15. M. Ringler, A. Schwemer, M. Wunderlich, A. Nichtl, K. Kürzinger, T. A. Klar, and J. Feldmann, “Shaping emission spectra of fluorescent molecules with single plasmonic nanoresonators,” Phys. Rev. Lett. 100, 203002 (2008). [CrossRef] [PubMed]

, 16

16. R. J. Moerland, H. T. Rekola, G. Sharma, A.-P. Eskelinen, A. I. Väkeväinen, and P. Törmä, “Surface plasmon polariton-controlled tunable quantum-dot emission,” Appl. Phys. Lett. 100, 221111 (2012). [CrossRef]

].

Optical structures that have received a substantial amount of attention are comprised of thin metal films with thicknesses on the order of 200 nm, perforated with regular arrays of subwavelength-sized holes of identical shape. One of the reasons of the interest for these so-called hole arrays is their well-known property of providing extraordinary optical transmission (EOT) [17

17. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

]. In short, the hole arrays show a much larger transmission for specific wavelengths than what could be expected based simply on the total area of the holes in the film. This particular effect sparked off further research into the behavior of emitters near and in such hole arrays, and effects like enhanced fluorescence from molecules on hole arrays [18

18. Y. D. Liu and S. Blair, “Fluorescence enhancement from an array of subwavelength metal apertures,” Optics Lett. 28, 507–509 (2003). [CrossRef]

, 19

19. A. G. Brolo, S. C. Kwok, M. G. Moffitt, R. Gordon, J. Riordon, and K. L. Kavanagh, “Enhanced fluorescence from arrays of nanoholes in a gold film,” J. Am. Chem. Soc. 127, 14936–14941 (2005). [CrossRef] [PubMed]

], reduced luminescence lifetime [20

20. J. Y. Zhang, Y. H. Ye, X. Y. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005). [CrossRef]

, 21

21. A. G. Brolo, S. C. Kwok, M. D. Cooper, M. G. Moffitt, C. W. Wang, R. Gordon, J. Riordon, and K. L. Kavanagh, “Surface plasmon-quantum dot coupling from arrays of nanoholes,” J. Phys. Chem. B 110, 8307–8313 (2006). [CrossRef] [PubMed]

] and strongly polarized emission [20

20. J. Y. Zhang, Y. H. Ye, X. Y. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005). [CrossRef]

] have been reported.

Figure 1 contains a graphical representation of the simulation model, used throughout this work to study and shape the radiation of a single emitter embedded in an array of nanoscale holes. A substrate with a refractive index of 1.5 (glass) is coated with a 200 nm thick layer of gold. A matrix of N × N rectangular holes is removed from the gold layer. The index of refraction in the holes and in front of the gold is that of vacuum (n = 1). The periodicity of the holes in the x- and y-directions is px and py, respectively. In the most general case, the aspect ratio Δxy of each individual hole is allowed to vary from 0.3 to 3.4, resulting in hole sizes that can be manufactured with current lithography techniques. The central hole contains an emitting dipole, which is oriented in the y-direction.

Fig. 1 Graphical representation of the simulation model to study and shape the radiation of a single emitter embedded in an array of nanoscale holes. A substrate with a refractive index of 1.5 is coated with a 200 nm thick layer of gold. A matrix of N × N rectangular holes is removed from the gold layer. The index of refraction in the holes and in front of the gold is that of vacuum. The periodicity of the holes in the x-direction is px, in the y-direction it is py. The holes all have an area of 34 × 103 nm2, but the aspect ratio Δxy of each individual hole can be varied from 0.3 to 3.4, modifying the local amplitude and phase of the electromagnetic field in the hole. The central hole contains a dipole, 10 nm above the substrate, which is oriented in the y-direction. During optimization, the fraction of power that is emitted by the dipole and is directed through surface S is maximized by adjusting the aspect ratio of the individual holes and the periodicities px and py. The surface S has dimensions of 800 × 800 nm2.

To give an example of the strong influence that the hole shape can have on the local field in an array of sub-wavelength sized holes, two straightforward calculations, employing the finite-difference time-domain [29

29. A. Taflove and S. C. Hagness, Computational Electrodynamics: the finite-difference time-domain method, (Artech House, Norwood, MA, 2000), 2nd ed.

] (FDTD) method, were performed with the model shown in Fig. 1. The dipole is embedded 10 nm above the substrate in the central hole of an 11 × 11 array of holes. In both cases, the periodicities are px = py = 410 nm, and for each hole the area is Δx Δy = 34 × 103 nm2. For this demonstration, the aspect ratio of the holes is the only difference between the two calculations. For the first calculation, the holes all have an aspect ratio of 1.0. For the second calculation, the holes have an aspect ratio of 2.0. Here, the possibility of changing the aspect ratio on an individual per-hole basis was explicitly not used.

For these two distinct cases, Figs. 2(a) and 2(b) show the electric field amplitude (in dB, left halves) and phase (in degrees, right halves) of the Ey component, with the amplitude normalized to its maximum value. The maximum coincides with the location of the dipole in the central hole. The electric field was recorded on a plane 20 nm away from the hole array, on the vacuum side. From the visible difference in the amplitude distributions between Fig. 2(a) and 2(b) (left halves), it is evident that the aspect ratio has a strong influence on the set of holes that appear as brightest. Moreover, not only does the local amplitude distribution of the y-component of the electric field change with the aspect ratio, but also the phase distribution of Ey is significantly altered (right halves).

Fig. 2 Electric field strength (in dB, left half of (a) and (b)) and phase (in degrees, right half of (a) and (b)) of the Ey field component, recorded on a plane in vacuum, 20 nm away from a layer of gold which has 11 × 11 rectangular holes inscribed in it. The central hole contains a y-oriented dipole in the center of the hole, 10 nm above the glass substrate. The field amplitude has been normalized to the maximum of the Ey component, occurring at the central hole. In (a) the aspect ratio (Δxy) of the holes is 1.0, in (b) it is 2.0. The location, size and shape of the holes are shown for a few rows of the complete array in the bottom part of the Figs. The set of holes with the strongest Ey field in or near them depends strongly on the aspect ratio of the holes. Moreover, the phase of the Ey field component is also radically different. Thus, the local phase near each hole directly depends on the aspect ratio of the holes. Therefore, by tuning the aspect ratio, it is possible to tune the local amplitude and phase of the electromagnetic field local to the holes.

The holes with the largest field amplitudes, shown in Fig. 2, act as secondary sources with amplitudes and phases that differ from the primary source, the single emitter. Therefore, the evolution of the electromagnetic field as it propagates through space is a direct result of the coherent addition of the dipole and the secondary sources. Based on this notion, one can tailor the emission of a single emitter on the nanoscale by surrounding the emitter with an appropriately structured array of holes. Here, we rely on a numerical optimization technique to shape the emission of a single emitter to show the strong focusing of dipolar radiation.

2. Simulation and optimization methods

All simulations employ the finite-difference time-domain (FDTD) method. The particular implementation used is freely available as open source [32

32. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010). [CrossRef]

] (patched in order to remove a memory leak, see the listing in Fig. 7 in the appendix). The computational volume has dimensions of 8 × 8 × 3.4 μm. Additionally, 30 perfectly-matched layers are added to the computational grid at each face of the volume in order to absorb the outgoing waves emitted by the dipole, simulating an infinite substrate. The excitation source of the dipole is a broadband current pulse with a Gaussian spectral envelope ranging from 500 nm to 1000 nm. Due to the computational effort involved, the optimization uses a relatively coarse FDTD grid of 20 × 20 × 20 nm3 and a time step of 0.0334 fs. However, the convergence of the final solutions presented in this work has been established by simulating the optimal structure at progressively smaller grid sizes. We do leave the option open that better solutions to the optimization problem than shown here exist, which possibly are not found due to the relatively low resolution used during optimization. This possibility has not been investigated due to limited computing resources.

As the FDTD method is inherently a time-domain method, Fourier transforms of the electromagnetic fields are calculated during time stepping at the location of S and on the faces of a cube, placed around the dipole and having sides of 800 nm in length. From the Fourier-transformed fields, the power radiated by the dipole can be calculated, as well as the power that is flowing through the surface S. Fourier transforms are also obtained on the surfaces used for the cross sections shown in Fig. 3.

Fig. 3 Visualization of the electromagnetic field components, after optimizing an 11 × 11 array of nanoscale holes with the aspect ratio of each individual hole and the periodicity in the x- and y-direction as parameters. As a result of the optimization, the power emitted by a y-oriented dipole in the central hole is focused, at a distance of 2 wavelengths from the source, onto the surface marked with S. In (a), |Ey| is shown in the y = 0 plane in a cross-section through the central hole. The color scale has been clipped for viewing purposes. In (b), |Hx| is shown in the x = 0 plane. The plots indicate that the field strength is enhanced at the location of surface S, marked by the solid red line at z = 1.6 μm. More clearly, this can be seen in (c), where a cross-section of the power density I = 0|E|2/2 is shown, through the z = 1.6 μm plane at the location of surface S.

For the optimization of the structure, a two-step approach is employed to obtain a satisfactory solution. First, to find an initial set of adequately performing aspect ratios for the holes, an evolutionary optimization algorithm is used [33

33. T. P. Runarsson and X. Yao, “Search biases in constrained evolutionary optimization,” IEEE T. Syst. Man Cyb. 35, 233–243 (2005). [CrossRef]

]. The implementation of this algorithm is also freely available and open source [34

34. S. G. Johnson, “The nlopt nonlinear-optimization package,” http://ab-initio.mit.edu/nlopt.

]. Given the symmetry of the optimization goal, it is possible to reduce the computational volume by a factor of 4. Therefore, starting out with an array of 11 × 11 holes, the total number of holes with a freely variable aspect ratio is 36. The periodicities in the x- and y-directions, px and py, respectively, are additional parameters in the optimization procedure. Altogether, the total number of free parameters is 38. The lower bound for the aspect ratio of each hole is 0.3, and the upper bound is 3.4. The lower and upper bounds for the periodicities in each direction are 400 nm and 700 nm, respectively.

The initial size of the population in the evolutionary optimization run is 380. In other words, 380 simulations are run with random values for each parameter. Then, the evolutionary part of the optimization algorithm is started, and the most suitable candidates for further optimization are selected. As the second step, an optimization with a multi-level single-linkage (MLSL) [35

35. A. H. G. Rinnooy Kan and G. T. Timmer, “Stochastic global optimization methods part I: Clustering methods,” Math. Programming 39, 27–56 (1987). [CrossRef]

, 36

36. A. H. G. Rinnooy Kan and G. T. Timmer, “Stochastic global optimization methods part II: Multi level methods,” Math. Programming 39, 57–78 (1987). [CrossRef]

] algorithm is performed, itself employing a local optimization algorithm [37

37. M. J. D. Powell, “The BOBYQA algorithm for bound constrained optimization without derivatives,” Technical Report NA2009/06, Department of Applied Mathematics and Theoretical Physics, Cambridge England (2009). http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf.

] as part of the global algorithm. The best set of values for the free parameters, found by the evolutionary optimization, are used as the starting point.

3. Results

After 4689 simulations were run, the evolutionary optimization was stopped. At that point, the fraction of the power emitted by the dipole flowing through surface S was 4.5% for the most suitable generation. The associated values of the free parameters for that generation were used as the input for the second step with MLSL. After 409 additional simulations, the fraction of the total emitted power, flowing through surface S, rose to 6.5%. Each simulation that was part of the optimization loop took on average 10.8 minutes on a standard workstation with 8 GB of memory, making the total running time slightly more than 38 days for both optimization loops combined.

Graphs of the evolution of the fraction of power flowing through S versus optimization step are included in the appendix. Figure 8(a) shows the outcome of the evolutionary optimization process and Fig. 8(b) shows the evolution of the multi-level single-linkage optimization procedure. Halving the mesh size twice for the optimal solution showed that the fraction of power flowing through S was lowered by just 0.2%, indicating convergence.

The results obtained after the optimization procedure are summarized in Fig. 3, depicted by several cross sections through the calculation volume. For reasons of symmetry, it is sufficient to show only the Ey-component in the plane at y = 0 (Fig. 3(a)) and Hx in the plane at x = 0 (Fig. 3(b)). The color scale in the Figs. has been clipped such that the presence of the large electromagnetic field at the location of the dipole and in the holes does not dominate the graphs. These plots clearly show that the field strength is concentrated at the location of the surface labelled S in Fig. 1, the location of which is marked by the red dashed line at z = 1.6 μm in the graphs. In Fig. 3(c) the resulting power density I = 0|E|2/2 in the plane containing S is plotted, at z = 1.6 μm. Here, c is the speed of light and ε0 is the permittivity of free space. The power density shows a distinct focus, slightly elliptical in shape, with a full width at half the maximum (FWHM) of 620 nm in the y-direction and 960 nm in the x-direction. The fraction of the dissipated power flowing through S is 6.3%. The main lobe, defined as the distance between the first minima in the y-direction, contains 10.2% of the total dissipated power, which equals 23.2% of the power that is radiated into the vacuum. Furthermore, two weaker satellite spots are visible, each containing 2.6% of the power dissipated by the dipole.

Figure 4 shows cross sections of the power density I normalized by the power P dissipated by the dipole. By normalizing with P, the effect of emission redirection can be separated from variations in intensity due to changes in the local environment of the dipole. The lines in Fig. 4 are cross sections for the optimized structure, a reference calculation and the result of the optimization of a simplified model. The cross sections in Figs. 4(a) and 4(b) are taken along the x-and y-axis, respectively, at the plane of the focus (z = 1.6 μm). The optimal structure yields an intense focus at the required location and significantly increases the photon flux into the surface S compared to the reference calculation, which was performed for the same dipole-to-substrate distance (10 nm) and dipole orientation, but without a gold film present. At sub-wavelength distances from an interface between two semi-infinite dielectrics, dipoles radiate the largest fraction of power into the dielectric with the higher refractive index [38

38. W. Lukosz, “Light-emission by magnetic and electric dipoles close to a plane dielectric interface. III. radiation-patterns of dipoles with arbitrary orientation,” J. Opt. Soc. Am. 69, 1495–1503 (1979). [CrossRef]

]. Indeed, for the reference calculation, 82.3% of the dissipated power was radiated into the glass, and the remaining 17.7% into the vacuum. Only a fraction of 1.1% of the dissipated power goes through surface S, as also Figs. 4(a) and 4(b) confirm. In contrast, for the optimized structure the fractions of dissipated power radiated into the substrate and the vacuum are almost balanced, i.e., 44.4% and 43.9%, respectively. This leaves 11.7% of the power to be dissipated in the form of non-radiative decay by Ohmic losses in the metal. Naturally, the overall decay rate of the dipole is also affected by the presence of the metal structure. We found that for the optimized structure, the relative decay rate was increased by a factor of 6.5. The simplified structure contains a matrix of holes all having the same aspect ratio. This aspect ratio and the periodicities in both directions were parameters in a separate optimization run with the same goal (maximize the fraction of power through S). The simplified model (aspect ratio 3.0, px = 478 nm and py = 486 nm) does increase the fraction of power flowing through S, but does not attain the same efficiency nor quality of the focus, which underlines the importance of the individual hole shape on the outcome of the optimization. Table 1 in the appendix contains a list of the width Δx of each hole of the optimal structure, which combined with the area of the holes (34×103 nm2) gives the aspect ratio. Figure 9 is a graphical representation of this data. The particular amplitude and phase distributions of all the electric field components, leading to focusing at surface S, are shown in the appendix in Fig. 10.

Fig. 4 Cross sections of the power density I normalized to the power dissipated by the dipole P, taken at the plane containing surface S. A line section of I/P is shown for y = 0 and z = 1.6 μm in (a) and for x = 0 and z = 1.6 μm in (b). The graphs contain curves for the optimized structure, a reference calculation without the gold and a simplified structure which contains a matrix of holes all having the same aspect ratio which was obtained with a separate optimization run. The focusing action is purely the result of a redirection of the dipole’s emission.

Figure 5 shows cross sections of the intensity profile of the electromagnetic field components, normalized to their maximum value. The graphs display the field intensity for the optimized structure at the wavelength that was used for optimization (850 nm) and for wavelengths shifted up and down by 100 nm, i.e., 750 and 950 nm. In Fig. 5(a), a line section of |Ey|2 along the x-direction is displayed, taken at y = 0 for z = 1.6 μm. In Fig. 5(b), a line section of |Hx|2 is shown along the y-direction, taken at x = 0 for z = 1.6 μm. For the wavelength of 850 nm, a clear focusing action is seen. For the wavelengths of 750 nm and 950 nm, strong side lobes occur and the focusing action disappears, displaying the wavelength selectivity of the hole array structure.

Fig. 5 Cross sections of the electromagnetic field components, taken at the plane containing surface S. In (a) and (b), the field component intensity for several wavelengths for the optimized geometry are shown, normalized to their maximum value. In (a), a line section of |Ey|2 along the x-direction is displayed, taken at y = 0 for z = 1.6 μm. In (b), |Hx|2 is shown in a line section along the y-direction, taken at x = 0 for z = 1.6 μm. For the wavelength that was used for optimization (850 nm), a clear focusing action is seen to take place. The emission pattern at wavelengths of 750 nm and 950 nm in contrast show strong side lobes and the focusing action disappears.

Finally, we provide an intuitive explanation for the physical reason behind the focusing effect that the optimized structure provides. Since the contribution of the y-polarized electric field is dominant in the focus, we restrict the discussion to the amplitude and phase of the Ey-field in the holes. Furthermore, only the holes along the x- and y-axis are discussed. The amplitudes of the Ey-field in the holes are shown in Fig. 6(a), with the blue open circles denoting the holes on the x-axis and the filled red circles denoting the holes on the y-axis. Figure 6(b) shows the phase information, where the markers have the same meaning as in Fig. 6(a). The amplitudes and phases shown in Fig. 6 are compared to a simplified model that shows focusing, i.e., a scalar spherical wave which converges at the center of the focus as exp(−ikr)/r, with k = 2π/850 rad/nm being the wave vector in vacuum and r the distance from the focus. The solid curves in Fig. 6 are the amplitude (6(a)) and phase (6(b)) distributions of the scalar wave, evaluated at the location of the holes. The amplitude of the field in the central hole at x = y = 0 differs about one order of magnitude from the field amplitudes inside the remaining holes, and was excluded from the analysis for this reason. Naturally, the large amplitude at the central hole, due to the singular behavior of the dipole, will set a limit to the quality of the focus. It is interesting to see, though, that in general the amplitudes and phases as shown in Fig. 6 display the same trend as the simplified model. The amplitude of the Ey-field along the y-axis follows the scalar model more closely than along the x-axis. This is likely the reason why there is a more narrow focus in the y-direction than in the x-direction (620 nm vs. 960 nm). These results show that the optimal solution converges to a case where the amplitude and phase of the Ey-field in the holes have physically reasonable values, even though the objective function does not directly take the amplitude and phase into account in reaching the optimum.

Fig. 6 Relative amplitudes (a) and phases (b) of the y-polarized electric field in the center of the rows of holes on the x-axis (blue open circles) and y-axis (filled red circles), at 850 nm wavelength. The solid curve in both Figs. is the amplitude (a) and phase (b) distribution of a converging spherical scalar wave, evaluated at the location of the holes. In general, the amplitudes and phases of the Ey-field in the holes display the same trend as the simplified model.

4. Conclusion

Fig. 7 Patch for MEEP version 1.1.1, file “structure.cpp”. The patch is necessary to remove a memory leak preventing the iterative use of MEEP in an optimization loop.

In summary, we have presented a versatile method for single emitter emission design and control. The method relies on the resonances that regular arrays of nanoscale holes in a thin metal film show in the optical regime. The tuning of these resonances allows one to tailor the emission of the emitter for a specific task. Based on the interference of propagating waves, the method is applicable at any distance from the source where the non-radiative fields have sufficiently decayed, i.e., from approximately one wavelength to infinity. As an example showcasing the merits of the scheme, the emission of a single emitter was strongly focused at a distance of two wavelengths from the source. The optimization process of the structure resulted in a high-quality focus, even for waves that are essentially s-polarized and are unable to excite surface plasmon polariton-based surface waves. This would indicate that the main multiple-scattering mechanism in that particular plane is through all diffracted orders [22

22. F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Modern Phys. 82, 729–787 (2010). [CrossRef]

] and is strong enough to significantly alter the flow of light.

After optimizing the hole array structure for focusing the emission of a single dipole emitter, a 6.3% fraction of the total power emitted by the dipole was concentrated into a focus at 1.5 μm distance from the surface of the gold film, for a wavelength of 850 nm. A focus was obtained with a cross-sectional size of 620 nm in the y-direction and 960 nm in the x-direction. When translated to an effective NA of a positive lens, a similarly-sized focus occurs for an NA of 0.5–0.8, an especially excellent result if one keeps in mind that the input of the hole array ‘lens’ is not a parallel beam, but a highly divergent source. Furthermore, the additional degrees of freedom that come with changing the individual hole shape are highly important to obtain a quality focus: a simplified model of a hole array where all the holes are forced to have the same aspect ratio does not lead to a satisfactory result. It is also interesting to observe that the dipole emits about the same amount of power into the vacuum as into the substrate, instead of primarily into the substrate as is the case for a bare dipole on a dielectric interface. Despite some losses due to the metal, the fraction of power that is radiated into the vacuum is also larger than for a dipole on an interface, by about a factor of 2.5. Hence, this type of structure is potentially interesting also for light extraction purposes.

Having control over both s- and p-polarized radiation significantly broadens the use of metal nanostructures for photonics applications. We foresee that the method presented here can be especially useful for optimally coupling nanoscale sources to plasmonic elements and integrated circuits, where the potential of additional degrees of freedom can be used to, e.g., focus light of different wavelengths at different locations. In the far field, examples of possible applications are light extraction from solid state devices with beam shaping and angular color sorting of emission.

A. Appendix

Table 1. Δx sizes (widths) in nm of the holes in the top right quadrant of a 11 × 11 hole array. The optimal periodicity in the x-direction was px = 545 nm, in the y-direction it was py = 534 nm. The holes are graphically indicated by the red rectangle in Figure 9.

table-icon
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Fig. 8 In (a), the result of a genetic optimization run involving 4689 generations is shown, for the geometry as presented in Fig 1. The percentage of the total power emitted by the dipole that flows through surface S in Fig. 1 is displayed on the y-axis. For clarity, the results of the optimization run have been low-pass filtered and decimated, such that the average increase in efficiency versus generation is better visible. In (b), the best solution found with the genetic optimization is used as a starting point for a multi-level-single-linkage optimization run, further increasing the percentage of emitted power that flows through S.
Fig. 9 A graphical representation of the array of holes in the gold film is displayed, which shows the found optimal layout for the focusing optimization goal. The red dashed square indicates the area with holes that are listed in Table 1. The location of the hole and the location of its width in Table 1 have a one to one correspondence. The blue dotted lines indicate axes of symmetry.
Fig. 10 Field amplitudes (a,c,e) and phases (b,d,f) of the electric field components Ex, Ey and Ez, respectively. The field amplitudes have been normalized to the maximum of |Ey|, occurring at the central hole. The field amplitudes have been clipped to −200 dB when the actual value was lower, e.g., zero.

References and links

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E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993). [CrossRef] [PubMed]

2.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

3.

H. Mertens, J. Biteen, H. Atwater, and A. Polman, “Polarization-selective plasmon-enhanced silicon quantum-dot luminescence,” Nano Lett. 6, 2622–2625 (2006). [CrossRef] [PubMed]

4.

O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. G. Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007). [CrossRef] [PubMed]

5.

R. J. Moerland, T. H. Taminiau, L. Novotny, N. F. van Hulst, and L. Kuipers, “Reversible polarization control of single photon emission,” Nano Lett. 8, 606–610 (2008). [CrossRef] [PubMed]

6.

T. Taminiau, R. Moerland, F. Segerink, L. Kuipers, and N. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007). [CrossRef] [PubMed]

7.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010). [CrossRef] [PubMed]

8.

X. H. Gao, Y. Y. Cui, R. M. Levenson, L. W. K. Chung, and S. M. Nie, “In vivo cancer targeting and imaging with semiconductor quantum dots,” Nat. Biotechnol. 22, 969–976 (2004). [CrossRef] [PubMed]

9.

A. Friedrich, J. D. Hoheisel, N. Marme, and J. P. Knemeyer, “DNA-probes for the highly sensitive identification of single nucleotide polymorphism using single-molecule spectroscopy,” FEBS Lett. 581, 1644–1648 (2007). [CrossRef] [PubMed]

10.

R. M. Bakker, V. P. Drachev, Z. T. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008). [CrossRef]

11.

H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000). [CrossRef]

12.

H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011). [CrossRef] [PubMed]

13.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006). [CrossRef] [PubMed]

14.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006). [CrossRef] [PubMed]

15.

M. Ringler, A. Schwemer, M. Wunderlich, A. Nichtl, K. Kürzinger, T. A. Klar, and J. Feldmann, “Shaping emission spectra of fluorescent molecules with single plasmonic nanoresonators,” Phys. Rev. Lett. 100, 203002 (2008). [CrossRef] [PubMed]

16.

R. J. Moerland, H. T. Rekola, G. Sharma, A.-P. Eskelinen, A. I. Väkeväinen, and P. Törmä, “Surface plasmon polariton-controlled tunable quantum-dot emission,” Appl. Phys. Lett. 100, 221111 (2012). [CrossRef]

17.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

18.

Y. D. Liu and S. Blair, “Fluorescence enhancement from an array of subwavelength metal apertures,” Optics Lett. 28, 507–509 (2003). [CrossRef]

19.

A. G. Brolo, S. C. Kwok, M. G. Moffitt, R. Gordon, J. Riordon, and K. L. Kavanagh, “Enhanced fluorescence from arrays of nanoholes in a gold film,” J. Am. Chem. Soc. 127, 14936–14941 (2005). [CrossRef] [PubMed]

20.

J. Y. Zhang, Y. H. Ye, X. Y. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005). [CrossRef]

21.

A. G. Brolo, S. C. Kwok, M. D. Cooper, M. G. Moffitt, C. W. Wang, R. Gordon, J. Riordon, and K. L. Kavanagh, “Surface plasmon-quantum dot coupling from arrays of nanoholes,” J. Phys. Chem. B 110, 8307–8313 (2006). [CrossRef] [PubMed]

22.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Modern Phys. 82, 729–787 (2010). [CrossRef]

23.

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92, 037401 (2004). [CrossRef] [PubMed]

24.

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004). [CrossRef]

25.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72, 045421 (2005). [CrossRef]

26.

J. C. Prangsma, D. van Oosten, R. J. Moerland, and L. Kuipers, “Increase of group delay and nonlinear effects with hole shape in subwavelength hole arrays,” New J. Phys. 12, 013005 (2010). [CrossRef]

27.

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003). [CrossRef]

28.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2008). [CrossRef] [PubMed]

29.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the finite-difference time-domain method, (Artech House, Norwood, MA, 2000), 2nd ed.

30.

R. X. Bian, R. C. Dunn, X. S. Xie, and P. T. Leung, “Single molecule emission characteristics in near-field microscopy,” Phys. Rev. Lett. 75, 4772–4775 (1995). [CrossRef] [PubMed]

31.

L. Novotny, “Single molecule fluorescence in inhomogeneous environments,” Appl. Phys. Lett. 69, 3806–3808 (1996). [CrossRef]

32.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010). [CrossRef]

33.

T. P. Runarsson and X. Yao, “Search biases in constrained evolutionary optimization,” IEEE T. Syst. Man Cyb. 35, 233–243 (2005). [CrossRef]

34.

S. G. Johnson, “The nlopt nonlinear-optimization package,” http://ab-initio.mit.edu/nlopt.

35.

A. H. G. Rinnooy Kan and G. T. Timmer, “Stochastic global optimization methods part I: Clustering methods,” Math. Programming 39, 27–56 (1987). [CrossRef]

36.

A. H. G. Rinnooy Kan and G. T. Timmer, “Stochastic global optimization methods part II: Multi level methods,” Math. Programming 39, 57–78 (1987). [CrossRef]

37.

M. J. D. Powell, “The BOBYQA algorithm for bound constrained optimization without derivatives,” Technical Report NA2009/06, Department of Applied Mathematics and Theoretical Physics, Cambridge England (2009). http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf.

38.

W. Lukosz, “Light-emission by magnetic and electric dipoles close to a plane dielectric interface. III. radiation-patterns of dipoles with arbitrary orientation,” J. Opt. Soc. Am. 69, 1495–1503 (1979). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.2110) Physical optics : Electromagnetic optics
(260.2510) Physical optics : Fluorescence
(260.3910) Physical optics : Metal optics

ToC Category:
Optics at Surfaces

History
Original Manuscript: December 11, 2012
Revised Manuscript: January 25, 2013
Manuscript Accepted: February 5, 2013
Published: February 14, 2013

Citation
Robert J. Moerland, Lur Eguiluz, and Matti Kaivola, "Shaping single emitter emission with metallic hole arrays: strong focusing of dipolar radiation," Opt. Express 21, 4578-4590 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4578


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References

  1. E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science262, 1422–1425 (1993). [CrossRef] [PubMed]
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58, 2059–2062 (1987). [CrossRef] [PubMed]
  3. H. Mertens, J. Biteen, H. Atwater, and A. Polman, “Polarization-selective plasmon-enhanced silicon quantum-dot luminescence,” Nano Lett.6, 2622–2625 (2006). [CrossRef] [PubMed]
  4. O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. G. Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett.7, 2871–2875 (2007). [CrossRef] [PubMed]
  5. R. J. Moerland, T. H. Taminiau, L. Novotny, N. F. van Hulst, and L. Kuipers, “Reversible polarization control of single photon emission,” Nano Lett.8, 606–610 (2008). [CrossRef] [PubMed]
  6. T. Taminiau, R. Moerland, F. Segerink, L. Kuipers, and N. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett.7, 28–33 (2007). [CrossRef] [PubMed]
  7. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science329, 930–933 (2010). [CrossRef] [PubMed]
  8. X. H. Gao, Y. Y. Cui, R. M. Levenson, L. W. K. Chung, and S. M. Nie, “In vivo cancer targeting and imaging with semiconductor quantum dots,” Nat. Biotechnol.22, 969–976 (2004). [CrossRef] [PubMed]
  9. A. Friedrich, J. D. Hoheisel, N. Marme, and J. P. Knemeyer, “DNA-probes for the highly sensitive identification of single nucleotide polymorphism using single-molecule spectroscopy,” FEBS Lett.581, 1644–1648 (2007). [CrossRef] [PubMed]
  10. R. M. Bakker, V. P. Drachev, Z. T. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys.10, 125022 (2008). [CrossRef]
  11. H. Gersen, M. F. Garcia-Parajo, L. Novotny, J. A. Veerman, L. Kuipers, and N. F. van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett.85, 5312–5315 (2000). [CrossRef]
  12. H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett.11, 2400–2406 (2011). [CrossRef] [PubMed]
  13. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett.97, 017402 (2006). [CrossRef] [PubMed]
  14. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett.96, 113002 (2006). [CrossRef] [PubMed]
  15. M. Ringler, A. Schwemer, M. Wunderlich, A. Nichtl, K. Kürzinger, T. A. Klar, and J. Feldmann, “Shaping emission spectra of fluorescent molecules with single plasmonic nanoresonators,” Phys. Rev. Lett.100, 203002 (2008). [CrossRef] [PubMed]
  16. R. J. Moerland, H. T. Rekola, G. Sharma, A.-P. Eskelinen, A. I. Väkeväinen, and P. Törmä, “Surface plasmon polariton-controlled tunable quantum-dot emission,” Appl. Phys. Lett.100, 221111 (2012). [CrossRef]
  17. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391, 667–669 (1998). [CrossRef]
  18. Y. D. Liu and S. Blair, “Fluorescence enhancement from an array of subwavelength metal apertures,” Optics Lett.28, 507–509 (2003). [CrossRef]
  19. A. G. Brolo, S. C. Kwok, M. G. Moffitt, R. Gordon, J. Riordon, and K. L. Kavanagh, “Enhanced fluorescence from arrays of nanoholes in a gold film,” J. Am. Chem. Soc.127, 14936–14941 (2005). [CrossRef] [PubMed]
  20. J. Y. Zhang, Y. H. Ye, X. Y. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B72, 201306 (2005). [CrossRef]
  21. A. G. Brolo, S. C. Kwok, M. D. Cooper, M. G. Moffitt, C. W. Wang, R. Gordon, J. Riordon, and K. L. Kavanagh, “Surface plasmon-quantum dot coupling from arrays of nanoholes,” J. Phys. Chem. B110, 8307–8313 (2006). [CrossRef] [PubMed]
  22. F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Modern Phys.82, 729–787 (2010). [CrossRef]
  23. R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett.92, 037401 (2004). [CrossRef] [PubMed]
  24. K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett.92, 183901 (2004). [CrossRef]
  25. K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B72, 045421 (2005). [CrossRef]
  26. J. C. Prangsma, D. van Oosten, R. J. Moerland, and L. Kuipers, “Increase of group delay and nonlinear effects with hole shape in subwavelength hole arrays,” New J. Phys.12, 013005 (2010). [CrossRef]
  27. F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett.83, 4500–4502 (2003). [CrossRef]
  28. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett.9, 235–238 (2008). [CrossRef] [PubMed]
  29. A. Taflove and S. C. Hagness, Computational Electrodynamics: the finite-difference time-domain method, (Artech House, Norwood, MA, 2000), 2nd ed.
  30. R. X. Bian, R. C. Dunn, X. S. Xie, and P. T. Leung, “Single molecule emission characteristics in near-field microscopy,” Phys. Rev. Lett.75, 4772–4775 (1995). [CrossRef] [PubMed]
  31. L. Novotny, “Single molecule fluorescence in inhomogeneous environments,” Appl. Phys. Lett.69, 3806–3808 (1996). [CrossRef]
  32. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun.181, 687–702 (2010). [CrossRef]
  33. T. P. Runarsson and X. Yao, “Search biases in constrained evolutionary optimization,” IEEE T. Syst. Man Cyb.35, 233–243 (2005). [CrossRef]
  34. S. G. Johnson, “The nlopt nonlinear-optimization package,” http://ab-initio.mit.edu/nlopt .
  35. A. H. G. Rinnooy Kan and G. T. Timmer, “Stochastic global optimization methods part I: Clustering methods,” Math. Programming39, 27–56 (1987). [CrossRef]
  36. A. H. G. Rinnooy Kan and G. T. Timmer, “Stochastic global optimization methods part II: Multi level methods,” Math. Programming39, 57–78 (1987). [CrossRef]
  37. M. J. D. Powell, “The BOBYQA algorithm for bound constrained optimization without derivatives,” Technical Report NA2009/06, Department of Applied Mathematics and Theoretical Physics, Cambridge England (2009). http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf .
  38. W. Lukosz, “Light-emission by magnetic and electric dipoles close to a plane dielectric interface. III. radiation-patterns of dipoles with arbitrary orientation,” J. Opt. Soc. Am.69, 1495–1503 (1979). [CrossRef]

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