Supplementary Information Beaming light from a quantum emitter with a planar optical antenna Simona Checcucci, 1,2,3,4 Pietro Lombardi, 1,2,3 Sahrish Rizvi, 1 Fabrizio Sgrignuoli, 1,3 Nico Gruhler, 5,6 Frederik B. C. Dieleman, 7 Francesco Saverio Cataliotti, 1,3,4 Wolfram H. P. Pernice, 6 Mario Agio, 1,2,4,8 and Costanza Toninelli 1,2,4 1 European Laboratory for Nonlinear Spectroscopy (LENS, 519 Sesto Fiorentino, Italy 2 National Institute of Optics (CNR-INO, 5125 Florence, Italy 3 Dipartimento di Fisica ed Astronomia, Università degli Studi di Firenze, 519 Sesto Fiorentino, Italy 4 Centre for Quantum Science and Technology in Arcetri (QSTAR, 5125 Florence, Italy 5 Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT, Eggenstein-Leopoldshafen 76344, Germany 6 Institute of Physics, University of Muenster, 48149 Muenster, Germany 7 The Blackett Laboratory, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom 8 Laboratory of Nano-Optics, University of Siegen, 5772 Siegen, Germany In the following Supplementary Information we discuss in more detail the dependence of the antenna properties on the geometrical parameters of the structure. Dipole position and total antenna length In Figure S1 we plot the angular emission pattern, i.e. the electric field intensity on a reference sphere in the far field as a function of the dipole distances to the reflector ( and director (d 2. Calculations are normalized to the maximum value of the emission in the case of a homogeneous medium with refractive index n = 1.5. In particular, we perform a scan around the optimal geometry reported in Figure 1b of the main text, i.e., reflector and director made of gold with thickness 1 nm and 2 nm respectively, spacer medium with n = 1.5 and air above the director. If the total distance between the metallic elements is kept constant, i.e. moving orthogonal to the diagonal of the 2D-plot matrix, there is only a weak dependence on the dipole position, confirming what presented in Figure 4c of the manuscript. 1
Figure S1 Emission pattern as a function of the dipole position and total antenna length. Angular emission pattern of a Hertzian dipole aligned horizontally with respect to the plane of a multilayer, consisting from bottom to top of a 1 nm gold reflector, followed by a spacer layer with n = 1.5 containing the dipole, and by a 2 nm gold director (top view. The antenna is surrounded by air, while d1 and d2 represent the distances of the dipole from the reflector and director respectively. The plots are normalized to the maximum emission of a Hertzian dipole in a homogeneous medium with n = 1.5. Focusing on a single raw or column of Figure S1 instead, one can appreciate the sensitivity of the antenna response to the total distance D = d1 + d2 between reflector and director. In particular we calculate the radiated power integrated over the azimuthal coordinate and report it in Figure S2 as a function of θ. Directional emission occurs already for a total thickness of 18 nm (blue solid curve, but with suppression of the total radiated power (Prad, represented by the area underlying the curve. Both directivity and Prad increase until the total thickness amounts to 2 nm (red solid curve. Even 1-nm-higher values give rise to lobes in the emission pattern, while Prad remains constant (e.g., purple solid curve. Interestingly, the beaming effect is recovered for a total thickness of 46 nm and approximately every λ/2n from the first optimal condition corresponding to D = 2 nm (see Figure S3. In particular we observe that the directivity improves with increasing antenna length. Prad however is not conserved. This is due to a small variation in the local density of states and to the onset of guided modes in the spacer layer. Although the coupling to surface plasmon polaritons decreases, when the dipole distance from the metal layers increases, overall the radiation efficiency η = Prad/Ptot, becomes smaller for larger values of D. In practice, 2
the antenna structure behaves as a metal-insulator-metal waveguide with the number of guided modes increasing with D. These contribute to the total emitted power P tot and not to P rad, as it can be observed in the wavevector distribution of the power density in Figure S4. For thicknesses higher than about 1.5 µm, the condition for constructive interference on the dipole position becomes more critical and the peaks at higher angles (already visible in Figure S3 start to dominate. P rad =13 nm; d 2 = 5 nm 6 nm 7 nm 8 nm 9 nm Figure S2 Performances against total antenna length. Radiated power (P rad integrated over the azimuthal coordinate as a function of the polar angle for different values of the antenna length around the optimal configuration. In particular the dipole position is kept constant at = 13 nm from the reflector surface, whereas the distance to the upper director is scanned from 5 to 9 nm. The curves are normalized to the maximum value of the same quantity for the emission of a Hertzian dipole in a homogeneous medium with n = 1.5. The other parameters are like in Figure S1. P rad 14 12 1 8 Beaming configurations, Efficiency η (% D (nm (nm 2 13 56 2 + λ/2n 13 36 2 + 2 λ/2n 13 24 2 + 3 λ/2n 13 + λ/2n 28 2 + 4 λ/2n 13 + 2 λ/2n 19 2 + 5 λ/2n 13 + 3 λ/2n 2 + 6 λ/2n 13 + 4 λ/2n 6 4 2 1 2 3 4 5 6 7 8 9 Polar angle (deg Figure S3 Optimal configurations for different values of the antenna length. Radiated power (P rad integrated over the azimuthal coordinate as a function of the polar angle and corresponding efficiency η (P rad /P tot for different configurations yielding beaming. By simply scaling the shortest antenna with λ/2n we restore the angular confinement of the radiation profile. The optimal dipole distance to the reflector ( is accordingly modified. The curves are 3
normalized to the maximum value of the same quantity for the emission of a Hertzian dipole in a homogeneous medium with n = 1.5. For large values of D the efficiency (not shown is compromised by the presence of guided modes in the metal-insulator-metal structure. The other parameters are like in Figure S1. 1 6 1 4 1 2 P tot P rad 1 1-2 1-4 1-6 =391 nm - D=985 nm =13 nm - D=2 nm 1-8.5 1 1.5 2 2.5 3 Figure S4 for metal-insulator-metal structure. Power densities (P tot and P rad as a function of the parallel wavevector k // for two antenna configurations shown in Figure S3, one with large (solid lines and one with small (dashed lines separation between reflector and director. The boundary between radiative and evanescent partial waves in the air semi-infinite medium, where collection takes place, correspond to k // = 1, where k is the wavevector in vacuo. Director thickness The antenna director is a weakly reflective element, which configures the structure as a broadband device. In the proposed cost-effective design the director is made out of gold. The optimal gold thickness is the result of a compromise, which takes into account losses due to absorption in the metal, the desired broad wavelength response and the amplitude of the reflected field at the interface. In Figure S5, we report calculations for different antenna thicknesses presented above, both yielding a beaming effect. We observe that reasonable values for the thickness of a gold director should be between 1 and 3 nm. Outside this range either the directivity or the radiation efficiency are reduced. Intensity distribution inside double-mirror antenna In order to analyze the cavity role in the beaming antenna configuration, we performed finite-elementdomain (FED simulations 1. The mesh resolution was set to have a high resolution around the source (horizontal electric dipole and around the two gold mirror elements. The simulation domain is (3. x 3. x 3.12 µm 3. Perfect matched layer conditions were assumed in all calculations. Figure S6 panel a and b show the emitted profile inside a glass-top-layer of a Hertzian dipole at 785 nm (beaming-wavelength and 4
at 73 nm (resonant-wavelength in a 2-nm-thick medium with refractive index n = 1.5 at a distance = λ/4n from the reflector element, respectively. The thickness of the reflector and director elements are 1 nm and 2 nm, respectively. The bottom air layer is 5 nm thick. At resonance no beaming effect is observed, while lobes appear at wide angles. At the same time, a large portion of the emitted field is trapped inside the active layer in the resonant configuration with respect to the beaming one. Figure S5 Influence of director thickness. Radiated power (P rad integrated over the azimuthal coordinate as a function of the polar angle and corresponding efficiency η (P rad /P tot for different values of the gold director thickness. The curves are normalized to the maximum value of the same quantity for the emission of a Hertzian dipole in a homogeneous medium with n = 1.5. The other parameters are like in Figure S1. Figure S6 Intensity distribution inside the double mirror antenna. Near field distribution of the field emitted by a horizontal electric dipole for the double mirror structure at the wavelength of beaming (a and at the resonant wavelength of the equivalent cavity (b. The position of the dipole is identified by the black point at the central edge 5
of the cut section-profile (at the origin of the figures. Figures show a quarter of the simulation domain. Images are normalized to 1. The power densities corresponding to P tot and P rad can be plotted as a function of the parallel wavevector k // instead of the polar angle to illustrate the role of evanescent waves in determining P tot and the coupling to guided modes and/or lossy waves 2. In Figure S7 we analyze the excitation of surface plasmon polaritons when the dipole distance from reflector and director varies, for the antenna configuration of Figure 4c of the manuscript. When the dipole is closer to the reflector ( = 1 nm, the power density for P tot exhibits a peak for k // slightly above 1.5, which corresponds to a surface plasmon polariton mode at a gold-glass interface. k is the wavevector in vacuo. When the distance increases, the peak decreases while a second peak appears near k // = 2. The latter corresponds to the lower surface plasmon polariton mode at a thin gold film in glass, which exhibits a larger wavevector due to mode hybridization 3. When the dipole gets closer to a gold layer, the power density shows a broad distribution for large wavevectors, which is the typical fingerprint of lossy waves 1. On the other hand, when the distance between reflector and director increases, the coupling to surface plasmon polaritons and to lossy waves decreases, but the onset of guided modes in the metal-insulator-waveguide increases the contribution of trapped modes to P tot, hence decreasing the overall efficiency of the antenna (not shown. The power density associated with P rad is zero for evanescent partial waves, as these do not contribute to the radiated power in the upper medium. For propagating partial waves (i.e., for k // < 1.5 k, the power densities for P rad and P tot follow the same beaming profile but they are slightly different to account for absorption in the metal layers. The integrated power densities, i.e. P rad and P tot, are displayed in Figure 4c of the manuscript as a function of. The densities are normalised such that the integrated powers are relative to emission in a homogeneous medium with refractive index n = 1.5. The radiation efficiency η = P rad /P tot is more than 7% for = 6-1 nm and decreases to 1% when the dipole is 1 nm from one of the gold layers. We did not systematically investigate the dependence of η on the antenna parameters. 6
35 35 3 25 2 15 P tot P rad =1 nm 3 25 2 15 =11 nm 1 1 5 5.5 1 1.5 2 2.5 3 35.5 1 1.5 2 2.5 3 35 3 25 2 15 =3 nm 3 25 2 15 =13 nm 1 1 5 5.5 1 1.5 2 2.5 3 35.5 1 1.5 2 2.5 3 35 3 3 25 2 15 =5 nm 25 2 15 =15 nm 1 1 5 5.5 1 1.5 2 2.5 3 35.5 1 1.5 2 2.5 3 35 3 25 2 15 =7 nm 3 25 2 15 =17 nm 1 1 5 5.5 1 1.5 2 2.5 3 35.5 1 1.5 2 2.5 3 35 3 25 2 15 =9 nm 3 25 2 15 =19 nm 1 1 5 5.5 1 1.5 2 2.5 3.5 1 1.5 2 2.5 3 7
Figure S7 Power densities. Power densities (P tot and P rad as a function of the parallel wavevector k // for the antenna configuration discussed in Figure 4c of the manuscript. Each panel corresponds to a different dipole distance from the reflector, while the separation between reflector and director is always D = 2 nm. The boundary between radiative and evanescent partial waves in the glass semi-infinite medium, where collection takes place, correspond to k // = 1.5, where k is the wavevector in vacuo. Back focal plane imaging In order to measure the radiation pattern of single molecules using the back-focal-plane (BFP imaging technique, we chose a high-na plan apochromat 1x objective to well reproduce the apodization function up to large angles and to image the emission pattern over a broad spectral range. The high magnification reduces the dimensions of the BFP image on the EM-CCD camera, which is useful for imaging the weak signal of a single molecule. Moreover, we used a single lens BFP imaging system, which makes the setup less sensitive to positioning errors in the optical elements. These aspects are thoroughly explained in Ref. 4. In addition, we have been able to perform a rough calibration of the response function for our objective (ZEISS Plan-APOCHROMAT 1x/1.4Oil. Figure S8 shows that for light at 785 nm transmission drops down to 5% already at a polar angle of 55 o and it is aroun% at 67 o. For light at 632 nm the transmission is instead around 5% at 6 o and 3% at 67 o. Additional smoothing of the transfer function might be due to the use of a simple lens for imaging in place of an achromatic doublet. This is consistent with the fact that the objective is meant for use in the visible and that the emission at 785 nm is at the edge of its working range. The two curves are obtained by illuminating the objective with an almost plane wave and by imaging the BFP while focusing the light on a flat mirror. The response function is evaluated as the square root of the experimental data, as in this case the light goes through the objective twice. Such estimate for the objective response function, although rough, justifies the drop of signal we experienced for angles higher than 5 o. The optimal way to measure the response function would require an isotropic point-like source positioned at the place of the sample, which is not obvious to make. We decided not to apply the correction related to the response function of the objective and only recall it in the main text, because the curve we obtained shows systematic coherence-induced ripples, which would affect the results in a not correct way. It was not possible to obtain such characteristic curve from Zeiss. 8
Figure S8 Objective transfer function. Transmission through the microscope objective as a function of the polar angle for light at 632 nm (red curve and at 785 nm (black curve. References 1 COMSOL. COMSOL Multiphysics. Version 5. Stockholm: Sweden. Available from: https://www.comsol.com/comsol-multiphysics. 2 Barnes WL, Fluorescence near interfaces: the role of photonic mode density. J Mod Opt 1998; 45: 661-699. 3 Raether H. Surface plasmons on smooth and rough surfaces and on gratings. Heidelberg: Springer- Verlag; 1988. 4 Kurvits JA, Jiang M, and Zia R, Comparative analysis of imaging configurations and objectives for Fourier microscopy. J Opt Soc Am. A 215; 32: 282-292. 9