SUPPLEMENTARY INFORMATION Supplementary Information for generation of single optical plasmons in metallic nanowires coupled to quantum dots

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1 Supplementary Information for generation of single optical plasmons in metallic nanowires coupled to quantum dots A.V. Akimov 1,4, A. Mukherjee 1, C.L. Yu, D.E. Chang 1, A.S. Zibrov 1,4, P.R. Hemmer 3, H. Park 1,, M.D. Lukin 1 1 Department of Physics, Harvard University, Cambridge, Massachusetts, 0138 Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843, USA 4 P.N. Lebedev Physical Institute RAS, Leninskiy prospect 53, Moscow, , Russia Preparation of silver nanowires Surface plasmons propagate a much longer distance in silver nanowires (NWs) with good crystallinity than in poly-crystalline ones 1. For this reason, chemically-grown bi-crystalline silver NWs were chosen for this study. Silver NWs were synthesized using the solution-phase polyol method with some modifications. Stock solutions of Iron(III) acetylacetonate ( Fe(acac) 3 : Aldrich) and NaCl (Aldrich) were prepared by dissolving.4 mg of Fe(acac) 3 in 3 ml ethylene glycol (EG: Mallinckrodt Baker) and 40 mg of NaCl in 6 ml EG, respectively. Solutions of AgNO 3 (Aldrich) and poly(vinyl pyrrolidone) (PVP, Mw 55, 000 : Aldrich) were prepared by dissolving 56 mg of AgNO 3 in 3.5 ml EG and 78 mg of PVP in 3.5 ml EG. Then 3.5 L Fe(acac) 3 and L NaCl solutions were added to the PVP solution to make the Fe-PVP solution. The synthesis started by heating 5 ml of EG to 160ºC in a 50 ml round-bottom flask for 10 min under a light nitrogen flow and then 50 min in air. Using a syringe pump, solutions of AgNO 3 (3 ml) and Fe-PVP (3 ml) were injected into the hot EG with rigorous stirring at a rate of 0.33 ml/min. Thirty minutes after the injection, heat was removed and the flask was allowed to cool to room temperature. The crude product was filtered through a syringe filter (Pall Life Sciences) with pore size of 0.8 m. Nanoparticles passed through the pores due to their small sizes, while most of NWs were retained on the filter. These NWs were then washed thoroughly with distilled deionized (DDI) water. Finally NWs were recovered from the filter by pushing water back into the syringe. As-obtained suspension of NWs was diluted to an appropriate concentration. The suspension of NWs was dropped onto a plasma-cleaned polydimethylsiloxane (PDMS) stamp (face area 1 cm 1 cm) and dried in the 1

2 air. The surfaces of the silver NWs were modified by immersing the stamp in an ethanol solution of 1-hexadecanethiol (0.06 g, 50 ml) overnight 3. The stamp was taken out and washed with ethanol Figure S1 SEM image of silver NW extensively to remove the excess thiol. Afterwards, the stamp was dried and placed under vacuum for 1 min to remove the ethanol and water. Characterization of Silver Nanowires The silver NWs were stamped onto a glass slide covered with a thin layer of PMMA and were characterized using a scanning electron microscope (SEM). Typical SEM images of silver NWs are shown in Fig. S1. For the experiments described in the main text, NWs with 5m lengths were Figure S Histogram of wire sizes for 66 wires.

3 chosen. Control over wire length was achieved by using a shorter reaction time and smaller amount of NaCl (compared to Reference ). The distribution of wire diameters was found to be R 10 4 nm. Figure S shows the histogram of wire diameters measured with SEM for 66 wires. Transmission electron microscopy images of silver NWs show that these NWs exhibit a bi-crystalline structure 4. QD Solution preparation A stock solution (PH ~ 8) of Na B 4 O 7 was prepared by dissolving 1.5 mg of Na B 4 O 7 (Mallinckrodt) in 1. ml DDI water. In 600 L Na B 4 O 7 solution, 7.3 mg of cysteine (Aldrich) was dissolved. Here cysteine was added to suppress blinking of CdSe quantum dots (QDs) in ambient conditions 5. Then 6 mg Na B 4 O 7 was added and sonicated to readjust the PH to about 8. Finally, 0.8 L of the QD stock solution (Invitrogen: Catalog No. Q1011MP) was added. We note that the QDs used in our experiment are a water-soluble variant and do not dissolve in toluene (the solvent for PMMA spin coating), and as such, the QDs are not expected to be lifted during the spin-coating process. Indeed, we found experimentally that the arrangement of QDs on the surface Figure S3 Scheme of experimental setup. 1 excitation laser, single mode fiber, 3 mirror, 4 dichroic mirror, 5 lens, 6 mirror, mounted on galvanometer, 7 beamsplitter, 8 Nikon CFI Plan Fluor 100x oil immersion objective NA1.3, 9 CCD camera Starlight Xpress SXVF-H9, 10 red filter, 11 avalanche photodiode, 1 Computer with installed Becker & Hickl GmbH SPC-630 counter board. 3

4 was not changed during the spin-coating process, proving that QDs are unperturbed. This observation is in direct contrast to the case where water or alcohol (in which QDs can be dissolved) was used for spin-coating. In these cases, QDs were indeed lifted and could be washed away from the surface. Experimental details In the main text we discussed the three Figure S4 Propagation of SP in silver NW. Image is scanning channels. In addition our setup also taken with the CCD camera. The laser, which corresponds to the bright spot, includes a CCD Camera shown in Fig. S3 that can directly excites SP on the wire which travel be used to image the sample. A beam splitter to and scatter from the end, seen as the smaller spot. mounted on a flip mount (so that it can be removed during the main measurement) is used to direct light to the camera. The camera is used mainly to test the out-coupling efficiency of SPs from the ends of NWs. Similar to previous experiments 3, this is done by focusing a laser on one end of the wire and observing emission from the other end by imaging onto the camera. This can be seen in Fig S4, where the bright spot corresponds to the laser focused on one end, and the dim spot corresponds to the other end of the wire. In studying samples where the NWs had an average diameter of 50 nm, we found that only a few percent of the wires showed noticeable out-coupling. On the other hand, in the samples where the average diameter was 100 nm, the percentage of wires showing substantial out-coupling exceeded 80%. As discussed in the main text, this result is in good agreement with theoretical predictions. QDs are 8 nm (average diameter) colloidal nanocrystals of CdSe with ZnS coating and extra polymer over-coating (not specified by Invitrogen) 6. This polymer shell has been directly coupled to streptavidin making QDs soluble in a buffer solution. In solution, size of QD with streptavidin is about 15 0 nm. We excite Figure S5 Correlation function, measured these dots using 53 nm CW Coherent Compass 315Mfrom a single wire end. Red curve indicates best fit, as described in 100 laser system which is focused with Nikon CFI Plan Data Analysis. Fluor 100X 1.3NA objective (focal depth of about 4

5 Figure S6 Spectrum of coupled QD (a), wire end emission (b) and uncoupled dot(c). 0.3 m ) after appropriate attenuation with neutral density (ND) filters. Due to the high absorption and emission efficiencies of these QDs, we use only W of excitation power for most of the experiments. At these powers, the QDs demonstrate relatively low blinking rates and are stable for hours. In order to additionally confirm the presence of single SPs in the NW, we also measured the correlation function of photons scattered by the wire end. In order to do this, light collected by Ch. III was split into two channels with a multimode fiber beamsplitter. To compensate for the resulting decrease in count rate and the originally low count rates from the end, the power incident on the dot was increased considerably ( 10 W ). Due to imperfections in the correlation measurements (see () below), the observed contrast of G was considerably reduced, but the anti-bunching dip is still clearly visible (Fig. S5). Spectral analysis The spectrum of a single QD radiation in proximity to the wire was measured using an Action Research Corporation Spectra Pro 300 spectrometer (Fig. S6a,b). The spectra of direct fluorescence from the QD and of the wire end emission are identical, with linewidths of ~15 nm (mostly caused by spectral diffusion at room temperature). As expected, the spectra are not affected by the wire. This is additionally confirmed by spectral measurement of an uncoupled dot (Fig. S6c). The inhomogeneous linewidth of the Figure S7 AFM image of scratch border. 5

6 QDs is ~30 nm, as listed by the Invitrogen data sheet 6. PMMA thickness measurement The thickness of PMMA films for different concentrations was measured using an Asylum MFP-3DAFM atomic force microscope (CNS, Harvard University). The film of PMMA was spin coated on a clean glass side using the method Figure S8 Resolution of APD. Red curve indicates described in the main text. The film was scratched Gaussian fit of experimental data. with a wood stick and the step height along several scratches was measured (Fig. S7). The waviness of the PMMA layer was found to be within 5 nm. The roughness of the PMMA film was measured with the same AFM in areas far away from the scratch and was found to be less then, 1, 0.3 nm for 30, 60, 90 nm films respectively (1wt%, wt% and 3wt% PMMA solution). Imperfections in correlation function measurement The finite time resolution of avalanche photodiodes (APD) and background noise affects the width and depth of the correlation function. To measure the time resolution we used ultra-short pulses from a picosecond Coherent Mira 900 laser with a repetition rate of 80 MHz and pulse duration of Figure S9 Simulation of resulting correlation function (see Data Analysis), taking into account the finite detector resolution and background noise. The red, green, and blue curves correspond to ideal widths of 5, 15, and 5 ns, respectively. The ratio of noise over total signal was assumed to be 0.03 for the left figure and 0.1 for the right. 6

7 10 ps. The laser light was coupled to a fiber beamsplitter and sent to two APDs. The intensity of the laser beam was reduced with ND filters so that the count rate corresponded to that from QDs in the experiment. The corresponding correlation function was measured (Fig. S8) for different count rates. The shape of this resolution function was found to be Gaussian with 1 nanosecond half width at the 1/e level. No dependence of the width or shape of the correlation function was found in the relevant range of experimentally important count rates (10-300kHz). Convolution of this resolution function with theoretical correlation functions are shown in Fig. S9. We now determine the effect of noise on the offset of the correlation function. By definition: () ItIt () ( ) g ( ), (S1) It () It ( ) where It ( ) St ( ) Nt ( ) is overall intensity of light ( St ( ) is the signal, Nt ( ) is the noise). Nt () Nt () St () we can rewrite (S1) as Introducing noise to overall signal ratio g StSt () ( ) ( ) o( ) It () It ( ) () (S) The first term in (S) is zero at zero time delay. The depth of measured would then be g (0) o( ), 1 () g () ( ) at zero time delay In our experimental setup noise is mostly due to dark counts of the APD and fluorescence of the glass substrate. Typical values of are in range of (0.0, 0.1) depending on power used. The effects of resolution and signal/noise ratio on correlation function depth and shape is demonstrated in Fig. S9. These plots qualitatively agree with our observed results. Data Analysis To measure the lifetime enhancement of the QDs, the zero excitation power width of the secondorder correlation function was extracted from measured data. In our experiment, the correlation function was measured by monitoring counts from the same QD using two separate channels, II and III, and calculating coincidences as a function of time delay between the two channels. This was done using a Becker and Hickl GmbH SPC-630 counter board with a 100 ns delay line for channel III in order to center and symmetrize the anti-correlation curve. The resolution of our measurement is limited by the timing jitter of the avalanche photo diode discriminator, and is ~ 1 ns (see Imperfections in correlation function measurement). 7

8 Extracting the width of the anti-correlation function was done using a simple model described in detail in Reference 7. It makes use of an incoherent pumping model (see Fig. S10) to describe the statistics of the photon emission. Intuitively, what the counter board measures is the population of state, n, as a function of time, triggered by an initial photon emission by the QD and its subsequent projection into state 1. Solving the above model predicts that: R 1 Rtot t n e, R where R is the pumping rate (which is proportional to the light intensity) and level. tot tot is relaxation rate of Following this model and taking into account background counts and resolution of our system we use the function xt 1ns R tot x ft () a e 1e dxb to fit our correlation function data and extract the parameter R tot. Numerical Simulations The simulation of plasmon-dipole coupling (see Fig. 1C in main text) uses a boundary element Figure S10 Level scheme for incoherent pumping model. Here the gray non-radiative relaxation process is assumed to be very fast. method (BEM) to solve the full Maxwell vector equations for the electric and magnetic fields. Our method closely follows that derived in Reference 8 and is briefly described here. To calculate coupling efficiencies and relevant decay rates we solve for the electric and magnetic fields emitted by i t an oscillating point dipole p0e, situated in medium 1, and in proximity to a different medium (medium ), which we assume is a closed body (in our case, the NW) whose surface we denote by S. The oscillating dipole can be characterized by known time-harmonic, external charge and current distributions ext and j ext, respectively, while the surrounding material and the NW are described by electric permittivities 1,, respectively. It is assumed that neither of 8

9 them have significant magnetic permeabilities, so that 1, 0. In the absence of any boundaries or different materials, the fields could easily be obtained by applying the Green s function for a homogeneous system to find the scalar and vector potentials. For example, if the system was composed entirely of material j, j 1,, these potentials satisfy (in the Lorenz gauge) 1 r dr G ( r r ) ( r ), 0 j j ext 4 0 j 0 0 Aj r drgj( rr) jext( r), 4 where the homogeneous Green s function G j is defined by G j r i e jr/ c r. In the actual system of interest, however, these solutions cannot be correct because the necessary boundary conditions for the electric and magnetic fields are not satisfied. The key principle behind BEM is that one can obtain the correct forms of the potentials, satisfying all boundary conditions, in material j by adding contributions from effective surface charge and current distributions residing on S. In particular, the potentials can be expressed in the form 1 r r ds G ( rs) ( s), 0 j j j j 4 0 j S 0 0 A j ra j r ds Gj( rs) hj( s). 4 Here j ( s ) and hj ( s) are the effective charge and current distributions, respectively. We emphasize that these quantities are only defined on the two-dimensional surface S, and furthermore, that they are mathematical constructions and do not generally correspond to real charge or currents (for instance, it is not necessary that ( s ) 1, or h ( s ) 1, be equal). At this point the effective charges and currents are unknown, but enforcing boundary conditions for the fields at S yields a set of linear integral equations that they must satisfy. For example, enforcing the continuity of the scalar potential across S, 1, S yields S 1 S ds G( r s ) ( s ) G ( r s ) ( s ) ( r ) ( r ), r S. (S3) 9

10 An important point is that the right side of the equation is a function of the external sources and is thus known. The remaining boundary conditions that must be enforced are the continuity of A, the continuity of the normal component of the electric displacement D, and the continuity of the tangential component of H. In principle these equations can be inverted to solve for j ( s ) and hj ( s) in terms of the external sources and the shape of S. While these effective distributions are continuous in nature, we can also solve for them numerically by discretizing the surface S into a grid, which is small enough that the distributions can be approximated as constant over each grid point. The linear integral equations are then transformed into a large but finite set of linear equations in j, equations (e.g., Eq. (S3)) contain singularities resulting from the Green s functions ( ) j h j. Note that these G r near r 0 ; however, these singularities are integrable and their numerical integration are avoided in the simulation by approximating them in a small region around r 0 with expansions valid for small r. After one solves for the distributions, the scalar and vector potentials and thus the electromagnetic fields can be determined. Simulations of the system shown in Fig. 1C in the main text can be further simplified due to its axial symmetry the system is invariant under rotations around the z -axis (the dipole is chosen to be oriented along z ). The BEM computation, which is generally two-dimensional due to the fact that one must solve for distributions on the surface S, can then be effectively reduced to an efficient onedimensional calculation. The linear integral equations such as the one appearing in Eq. (S3) are readily adapted to treat systems of rotational symmetry. Good convergence of the simulation is typically reached when the spacing between grid points is several hundred times smaller than the plasmon wavelength/wire diameter. Additional theoretical calculations of spontaneous emission rates Figure S11 (a) Theoretical calculation of the spectral dependence of the Purcell factor P, for an emitter positioned 35 nm away from a NW of diameter 100 nm. (b) Rates of emission (normalized by free-space emission rate) into radiative modes, SPs, and non-radiative modes as a function of emitter position, for a 100 nm wire. 10

11 To emphasize the broadband nature of the strong coupling between an emitter and NW, we have calculated the theoretical dependence of the Purcell factor on the frequency of the emitter, using the model described in the main text. The value of P, over emission wavelengths ranging from m, is plotted in Fig. S11a, for an emitter positioned 35 nm away from a 100 nm diameter wire. It can be seen that there is 0% variation (and no resonant effect) over this large Figure S1 Expeperimental data on losses in NWs. Red curve indicates best linear frequency range. In fact coupling increases away from fit, yielding a 1/e absorption length given by m. plasmon resonance frequency. Fig. S11b shows the theoretical dependence of the decay rates on emitter position, for a wire of 100 nm diameter. Here we have explicitly separated out the contributions of the radiative, SP, and non-radiative decay channels. It should be noted, in particular, that for distances d 0 nm, the non-radiative contribution is completely negligible. Estimation of collection efficiency into SPs In order to estimate the fraction of the overall emission going into SP modes (i.e., the efficiency), we examined wires that displayed emission from both ends, such as that shown in Fig. C in the main text. Two definitions of efficiency were considered: I1 I m I I I dot 1 l l1 Ie Ie 1 l l1 dot 1 I I e Ie Here m is the apparent efficiency, which is determined by comparing the number of counts originating from the two wire ends (1 and ) with the total number of counts of the system (radiative plus wire ends), I 1, are the intensities (counts) emitted by the wire ends, and I dot is the intensity of emission into free space by the QD. In order to take blinking of the QD into account, the ratio of counts between the points of interest (wire end or QD in Ch III and QD in Ch II) was recorded over several minutes and averaged. Since losses in the NW were demonstrated to be exponential with distance 9, we also were able to estimate the actual efficiency, which takes into account the dissipation of SPs before they reach the end of the NW. Here is the absorption coefficient of the NWs.,. 11

12 We use the difference in intensity observed from both ends to determine an absorption coefficient for SPs propagating along the wire. Once this coefficient is known, the amount of SP intensity that was lost to dissipation before reaching the wire ends can be extrapolated, which then yields the total emission rate into SPs. For this model, we assume that the scattering from both ends is equivalent, and that propagative losses are uniform and can be described by an exponential law: I I e l 0, where is the absorption coefficient, I is the observed intensity (or count rate in the case of our experiment) of SPs at distance l away from the quantum dot, and I 0 is the SP intensity originating from the dot. The difference in intensities observed from the wire ends and the different path lengths between the dot and the ends are then related to the absorption coefficient by 1 I l l I 1 ln( ), 1 where the indices 1, correspond to the two ends of the wire. The absorption length 1/ is estimated to be.7 0.5(0.3) m (see Fig. S1). Here systematic error is uncertainty of calibration. The large error bar can be attributed to the large variation in wire diameters and wire ends, as well as uncertainty (about 10%) in our measurements of length. The measured absorption coefficient was then used to calculate the efficiency. To calculate, we have also assumed that the non-radiative emission rate 10 for the dot is negligible. In our setup this is reasonable since this effect is predicted to be substantial only at distances smaller than the minimum allowed distance between the dot and the wire (~35 nm) 10. Furthermore, the above model assumes unit scattering efficiency of SPs at the wire ends. For lower scattering efficiencies, the formula above simply provides a lower bound on the efficiency. Finally, we have assumed that the collection efficiency of our optics in capturing the fluorescence from the quantum dot and the scattered light from the wire ends is identical, which we believe is reasonable given the high numerical aperture of our apparatus. References 1. Ditlbacher, H., Hohenau, A., Wagner, D., Kreibig, U., Rogers, M., Hofer, F., Aussenegg, F. R., Krenn, J. R. Silver Nanowires as Surface Plasmon Resonators. Phys. Rev. Lett. 95, (005). 1

13 . Wiley, B., Sun, Y., Xia, Y. Polyol synthesis of silver nanostructures: control of product morphology with Fe(II) or Fe(III) species. Polyol Synthesis of Silver Nanostructures: Control of Product Morphology with Fe(II) or Fe(III) Species. Langmuir 1, (005). 3. Tao, A., Kim, F., Hess, C., Goldberger, J., He, R., Sun, Y., Xia, Y., Yang, P. Langmuir-Blogett silver nanowire monolayers for molecular sensing with high sensitivity and specifity. Nano Lett. 3, (003). 4. Sun, Y., Xia, Y. Large-scale synthesis of uniform silver nanowires trough a soft-seeding, Polyol process. Adv. Mater. 14(11), (00). 5. Hohng, S., Ha, T. Near-complete suppression of quantum dot blinking in ambient conditions. J. Am. Chem. Soc. 16, (004). 6. Invitrogen catalog 7. Lounis, B., Bechtel, H. A., Gerion, D., Alivisatos, P., Moerner, W. E. Photon antibunching in single CdSe/ZnS quantum dot fluorescence. Chem. Phys. Lett 39, ,(000). 8. Garcia de Abajo, F. J., Howie, A. Retarded field calculation of electron energy loss in inhomogeneous dielectrics. Phys. Rev. B 65, (00). 9. Sanders, A. W., Routenberg, D. A., Wiley, B. J., Xia, Y., Dufresne, E. R., Reed, M. A. Observation of Plasmon Propagation, Redirection, and Fan-Out in Silver Nanowires. Nano Letters 6(8), (006). 10. Chang, D. E., Sørensen, A. S., Hemmer, P. R., Lukin, M. D. Quantum Optics with Surface Plasmons. Phys. Rev. Lett. 97, (006). 13