Observation of Near-Field Dipolar Interactions Involved in a Metal

Letter pubs.acs.org/NanoLett

Observation of Near-Field Dipolar Interactions Involved in a Metal Nanoparticle Chain Waveguide A. Apuzzo,*,† M. Février,† R. Salas-Montiel,† A. Bruyant,† A. Chelnokov,‡ G. Lérondel,† B. Dagens,§,∥ and S. Blaize*,† †

Laboratoire de Nanotechnologie et d’Instrumentation Optique, CNRS-UMR 6279, Université de Technologie de Troyes, 12 rue Marie Curie CS 42060, 10004 Troyes cedex, France ‡ CEA-LETI Minatec Campus, DOPT, 17 rue des Martyrs 38054 Grenoble cedex 9, France § Univ. Paris-Sud, Institut d’Electronique Fondamentale, UMR 8622, 91405 Orsay cedex, France ∥ CNRS, 91405 Orsay cedex, France ABSTRACT: We present near-field measurements of transverse plasmonic wave propagation in a chain of gold elliptical nanocylinders fed by a silicon refractive waveguide at optical telecommunication wavelengths. Eigenmode amplitude and phase imaging by apertureless scanning near-field optical microscopy allows us to measure the local out-of-plane electric field components and to reveal the exact nature of the excited localized surface plasmon resonances. Furthermore, the coupling mechanism between subsequent metal nanoparticles along the chain is experimentally analyzed by spatial Fourier transformation on the complex near-field cartography, giving a direct experimental proof of plasmonic Bloch mode propagation along array of localized surface plasmons. Our work demonstrates the possibility to characterize multielement plasmonic nanostructures coupled to a photonic waveguide with a spatial resolution of less than 30 nm. This experimental work constitutes a prerequisite for the development of integrated nanophotonic devices. KEYWORDS: Optical near field microscopy, surface plasmon polariton, localized surface plasmon, silicon photonics, plasmonics, integrated optics ptical fields confined to the nanometer scale have been used in applications such as surface enhanced Raman scattering,1,2 ultrasensitive molecular spectroscopy,3 and highresolution microscopy.4 More recently, a new class of subwavelength optical circuits5 has motivated the study of different types of plasmonic structures.6−10 Within this context, metal nanoparticle arrays have been proposed as a rather ideal platform for ultrasmall integrated optical devices, as they combine the ease of controlled nanofabrication with the possibility of localized enhancing and tailoring of the electric fields.11−15 Most of the work to date on metallic nanoparticle (MNP) chains has been done in free space,16−18 which allows for experimentally retrieving the dispersion relation of the localized surface plasmon (LSP) waveguide above the light line. Krenn et al. have demonstrated a squeezing of the optical near field due to plasmon coupling above a chain of metallic nanoparticles.19 Although the propagation of light and dipolar coupling between particles in a MNP chain has been demonstrated,20 only the dipolar behavior of MNPs at LSP resonance has been observed by optical near-field microscopy.21,22 Recently, Février23 and co-workers proposed to load with a high refractive index silicon waveguide (SOI) a LSP waveguide based on a linear array of gold elliptic nanocylinders. With this structure they demonstrated a complete energy

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transfer from the photonic to the plasmonic device with a record coupling length of only 560 nm. It was also shown that this hybrid photonic/plasmonic coupler could be used for efficient molecular detection. 24 However, the collective excitation of the MNP chain was numerically simulated by finite-difference time-domain (FDTD) methods and characterized mainly in terms of waveguide transmission and intensity sensitive near-field measurement. In this paper, the use of phase sensitive high spatial resolution optical near-field microscopy brings clear experimental evidence of the mechanisms involved in the propagation of light along MNP chains by dipolar coupling. This imaging method has been critical for drawing direct conclusions about the exact mode operation of plasmonic nanostructures, which may otherwise only be inferred from simulations mimicking experimental results.25−27 In situ phase measurements show the dipolar patterns of the MNPs in the near field, which is characterized by a 180° transversal phase shift at the center of each individual MNP with zero amplitude. Additionally, the phase profiles measured along the propagation Received: November 10, 2012 Revised: February 10, 2013 Published: February 15, 2013 1000

dx.doi.org/10.1021/nl304164y | Nano Lett. 2013, 13, 1000−1006

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Figure 1. (a) 3D artwork of the gold MNP chain integrated on top of a silicon waveguide. The incident field is the fundamental quasi-TE mode of the silicon waveguide. (b) Scanning electron micrograph of a gold MNP chain aligned with the center of the silicon waveguide. The major and minor axes of the MNP are 210 and 60 nm, respectively, and the period is 150 nm (inset). (c) Upper panel: Schematic representation of the coupling mechanism between the dielectric Si waveguide and the plasmonic MNP waveguide. In the coupling region, two hybrid modes of even and odd symmetries are excited, which arise from the hybridization of photonic and plasmonic modes of the isolated structures. Lower panel: Electric field intensity calculated in the (xz) plane at y = 0. A beating pattern is visible as a result of the coherent superposition of the even and odd modes. The orange arrow is a guide to the eye that highlights the energy transfer between the two coupled structures.

direction allow us to observe the propagation mechanism in the MNP chain. The structure consists of a silicon-on-insulator (SOI) ridge waveguide vertically coupled to a periodic chain of elliptical gold nanocylinders as shown in Figure 1a. The waveguide cross section is 220 nm high by 500 nm wide, and it supports the fundamental quasi-transverse electric (TE) mode between 1400 and 1650 nm. The MNPs have been fabricated by electronbeam lithography with PMMA and the lift-off process.23 The gold nanocylinders are 30 nm thick, have elliptic parameters D1 = 211 ± 5 nm and D2 = 66 ± 5 nm, and a center-to-center separation distance of d = 150 ± 5 nm (Figure 1b). These dimensions have been empirically tailored by using a combination of analytical calculation (chain in homogeneous medium) and 3D FDTD simulations of the complete structure (Figure 1c). The transmission spectrum of the structure presents a broadband minimum between 1260 and 1630 nm.23 It is due to LSP resonances that are excited by the quasiTE dielectric waveguide mode and propagate themselves through strongly interacting metallic dipole fields.12 The underlying principle is shown in Figure 1c. Basically, in the overlapping area, the SOI and MNPs waveguides merge together to form a new structure that supports two hybrid modes of even and odd symmetries. The chain mode is transverse in nature because electric dipole moments are oriented in the substrate plane, orthogonal to the chain axis (Figure 1a). It corresponds to the so-called T1 transverse mode as defined in ref 18. The energy transfer from one waveguide to the other is the result of the strong coupling between the two modes of the uncoupled waveguides when they are placed in close proximity. The strong coupling is evidenced by a spatial

beating (interferences) of the two hybrid modes of the coupler as they have different propagation constants (Figure 1c). The optical setup is depicted in Figure 2a. For the near-field measurements, an ultrasharp atomic force microscope (AFM) tip (super sharp enhanced/high density carbon tip by Nanotools) with a nominal terminal radius of 5 nm was used as an optical nanoprobe to scan the sample. The nanoprobe periodically scatters the local optical field at frequency fo, which can be then collected in the far field with a confocal microscope. The modulated, scattered signal is then mixed in a single mode fiber coupler with a reference signal shifted in frequency by Δf. The demodulation of this mixed signal is obtained with the use of a dual output lock-in amplifier at frequencies Δf − nfo, where n is harmonic of demodulation. This detection provides the amplitude as well as the local phase variation of the optical near field.28 The AFM topography and scattering scanning near-field optical microscope (s-NSOM) raw signals recorded at an incident wavelength of λ = 1.55 μm are plotted respectively in Figure 2b, c, and d. We observe a high intensity signal characterized by tightly confined hot spots, which are the near field signatures of the LSP oscillations supported by the MNPs. A longitudinal periodic energy transfer between the Si waveguide and the MNP chain is clearly seen with an exponential decrease along the direction of propagation due to the metal losses as already observed in ref 23 by intensity sensitive near-field measurements. As shown in Figure 1c, this energy transfer can also be viewed as a consequence of the coherent superposition of the two odd and even plasmonpolariton TE hybrid modes with respective wavenumber βo and βe of the coupler. They arise from the hybridization of the fundamental Si waveguide quasi-TE mode and the T1 chain 1001


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Figure 2. (a) Setup of the s-NSOM in heterodyne detection with an AFM nanoprobe showing an apex radius less than 5 nm. (b) AFM topography of the sample. (c) Scattering-NSOM raw data of the MNP chain: scanning atomic force micrograph; optical amplitude; optical phase images.

mode, and they coexist at the operating wavelength of 1.55 μm, close to the crossing point in the dispersion relation of the waveguides considered separately (i.e., the silicon refractive waveguide and the LSP waveguide). Interestingly we note on the amplitude image (Figure 2c) a lateral asymmetry of the electric field distribution relative to the center of each MNP. More precisely, a mean ratio of 4 can be estimated experimentally between the intensities of the MNP’s lateral hot spots. This effect was modeled with calculations based on the Green’s tensor volume integral equation method, which allows us to explain this asymmetry by the spatial variation of the angular emission pattern of the NSOM tip as induced by the close proximity to the MNPs. In these 3D calculations, the carbon tip is assimilated to a semiellipsoid with a major axis of 160 nm and a minor axis of 80 nm, giving a tip apex diameter of approximately 40 nm. Both the tip and a single nanoparticle are discretized with a total number of 1002 cubic elements of matter, giving an elementary cell volume of 10 nm3. To estimate the scattering cross sections of the tip apex, the system schematically drawn on Figure 3a is illuminated with an incident electric field inside the tip of the form: E0 x , y(r0) = Eoe−(x − xapex)/ d pex , y

direction. The value of 70 nm considered for dp ensures that the source field is reasonably confined at the tip apex. These optogeometric parameters are arbitrarily chosen as we aim at qualitatively understanding the origin of the asymmetry in the electric field distribution measured on each metallic nanoparticle. A quantitatively prediction is possible but complex because the modeling of a nanometric probe in near-field interaction is a thorny problem.29 The total scattered field in the far-field zone can then be calculated by the integral equation:30 Ex , y(r) = E0 x , y(r) +

∫V G(r, r′)k 02Δε(r′)E(r′) dr′

(2)

where G(r,r′) is the dyadic Green’s function associated to the background approximated here by a semi-infinite silicon substrate, that is to say the finite size of the silicon waveguide is neglected and Δε(r′) = ε(r′) − 1 is the dielectric contrast. This self-consistent integral equation is then discretized and numerically solved using an iterative solver.31 From the calculation of the scattered far field, the scattering cross sections σx,y of the probe can be evaluated using: σx , y ∝

(1)

where r0 is the position vector inside the tip, Eo is the amplitude of the incident field, dp = 70 nm is an arbitrary decay length of the field inside the tip, and ex,y is the unit vector in the x or y

∬ |Ex ,y(r)|2 /Eo2 dΩ

(3)

where dΩ is the elementary solid angle. Figure 3a schematically depicts the probe location in various positions along the y scan line. The microscope objective lens 1002


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Figure 3. Theoretical predictions of the angular radiation pattern of the carbon NSOM tip apex coupled to a single nanoparticle for an x- and ypolarized incident field and different relative probe positions. The numerical simulation is performed with the Green dyadic volume integral equation method. (a) Schematic illustration of the tip-to-sample relative position Δy during the scan. The kd wavevector (red arrow) is the direction of the farfield detection, which lies in the xy plane. (b) Calculated radiation patterns dσ (in arbitrary units) in the (x,y) plan for both polarizations as a function of Δy. In the sequence, from top to bottom, each yellow rectangle represents a gold nanoparticle in a well-defined y position. dσx and dσy for Δy = 0 are multiplied by a factor 8 for better comparison. (c) Scattering efficiency in the kd direction integrated over the objective numerical aperture.

Figure 4. (a) Topography of the first 10 MNPs and the corresponding optical amplitude and phase of the optical near field. (b) Corresponding FDTD simulations of electric field components (Ex and Ey). (c) Experimental phase profiles along the propagation direction extracted from the phase cartography in a. See text for details.

collects the scattered field through a numerical aperture of 0.4 in the kd direction that lies in the (xy) plane. As shown in Figure 3b, the tip-to-sample relative position influences the tip differential scattering cross section dσx,y α|Ex,y (r)|2 dΩ for both x,y polarization of the incident field Ex,y 0 on the tip. From this

calculation, we can infer two conclusions: (i) the contribution of dσy remains negligible compared to dσx above the MNP thus showing that the scattering NSOM is more sensitive to the x component of the MNP near field (this is not surprising due to the high polarizability of the sharp tips along their axis); (ii) 1003


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Since the electromagnetic field is strongly confined into the MNP array, the excitation of periodic nanometric hot spots involves spatial harmonics, which are directly described in the Bloch−Floquet expansions (eq 4) by high frequency harmonics of the fundamental propagation constants βm. From the retrieved experimental amplitude and phase signals, the complex electric field can be mathematically reconstructed. A complex fast Fourier transform (FFT) of the field profile along the hybrid waveguide is then performed in order to obtain the wavevector spectrum of the electromagnetic field.28,36 This method gives both the amplitude Hn,m and the wavenumbers kn,m = βm + n(2π/d) of the propagating light. The FFT power spectra along the full structure (Figure 2c) and on its first ten nanoparticles (Figure 4a) are plotted in Figure 5a and b, respectively. The blue curves correspond to the experimental data, whereas the red curves have been obtained from FDTD simulations.

since the angular redistribution shows a direct dependence on the position of the tip with respect to the probed zone, a clear asymmetry in the NSOM image is expected. This is emphasized in Figure 3c where σx,y integrated over the numerical aperture of the objective are plotted as a function of the tip-to-MNP relative position. A strong lateral asymmetry is obtained with a ratio of 6 between the two sides of the MNP that is in rather good agreement with the experimental value of 4. This result is consistent with former studies of the impact of the local variation of the optical density of states on the redistribution of angular radiation pattern from fluorescent nanoemitters.32,33 On the phase cartography in Figure 2c, we clearly see out-ofphase (180° transversal phase shift) dipolar oscillations along the MNP chain. To better understand the dipolar behavior of the MNPs and to gain physical insight into their evanescent coupling, we limited our study to the first 10 MNPs, and we measured their nanometric fields. The sample topography, amplitude, and phase cartographies are depicted in Figure 4a. As already observed in the larger images, strong amplitude hot spots along the MNP chain reveal multiple excitations of the LSP modes. Moreover, the field amplitude vanishes at the center of each nanocylinder, which goes along with the 180° phase shift in the transversal phase profile. This phase lag further validates the excitation of dipolar-like resonances, assuming that we mostly observe the out-of-plane (Ex) component of the local electric field since the scattering efficiency of the s-NSOM tip is dominated by dσx.34 This assumption is confirmed by comparing the experimental amplitude and phase maps with the calculated (3D FDTD by Lumerical) amplitude and phase maps of the Ex and Ey components of the electrical field (Figure 4b). At this end, we considered a uniform mesh of 3 nm × 3 nm × 3 nm, and we reproduced the experimental s-NSOM pattern exciting the metallic nanoparticles by the quasi-TE fundamental mode of the Si waveguide. The electric field scattered by the plasmonic nanoresonators is detected at 80 nm with respect to the Si waveguide top surface, which represents a realistic value for the average distance between the sample and the AFM tip set in tapping-mode. We note that, even if the probe inevitably perturbs the sample as they interact in the near field, however the remarkable matching between the measurements and the simulations results shows that the perturbation of the dielectric AFM tip on the plasmonic device remains unambiguously weak. Two important observations can be inferred from the longitudinal phase profiles (Figure 4c): (i) the lateral dipolar phase shift of 180° replicates itself at each MNP position showing multiple dipolar LSP oscillations along the chain; (ii) the longitudinal step-like phase shifts of 90° between two consecutive MNPs shows that the polarization surface charge distribution seems to replicate itself periodically after each block of four nanoparticles (with a period of 600 nm). Because light is channeling in a periodic medium (like in plasmonic crystals), the electrical field can be written in terms of a superposition of Bloch−Floquet guided modes:35 E (x , y , z ) =

Figure 5. (a) FFT spectra of the complex electric field profile along the MNP chain normalized to the longitudinal wavevector in the first two Brillouin zones. Bloch modes effective indices are reported in the upper axis. (b) FFT spectra in semilogarithm scale for the first 10 Brillouin zones. Bloch-mode harmonic numbers are reported in the upper axis. The experimental data are plotted in the blue curves, and the calculated data are plotted in red curves.

The FFT in blue on Figure 5a corresponds to an AFM scan window of 5 μm sampled with 256 points; thus, the first two Brillouin zones are reachable in the reciprocal space. For the spectrum plotted in Figure 5b, the scan size has been reduced to 1.8 μm with the same sampling rate to increase the number of reachable Brillouin zones up to 10. On both power spectra, the fundamental harmonics of the two odd and even plasmonpolariton hybrid modes (propagation constants βo and βe) are clearly recognizable at effective index values no = 2.48 and ne = 1.55, respectively. Moreover, lower harmonics located in the second Brillouin zone at wavenumbers βo/e − 2π/d are also clearly visible. Therefore, we have here direct experimental proof of Bloch-wave light propagation in a MNP chain waveguide. The Bloch nature of the MNP chain modes is not

2π

∑ ∑ Hn,m(x , y)e j(n d + β )z m

m

n

(4)

where the coefficient Hn,m(x,y) is the amplitude profile of the nth harmonic in the Fourier series (n ∈ ) related to the guided mode number m, with complex propagation constant βm, and d is the period of the MNP chain. 1004


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surprising since the nanoparticles are periodically arranged.37,38 However, to our knowledge, it was never experimentally observed in MNP systems with an optical resolution of tens of nanometers. Only such a high spatial resolution allows revealing the very confined nature of the LSP fields surrounding the nanoparticles. It is well-known that, in one-dimensional plasmonic crystals, Bloch waves can propagate thanks to evanescent near-field coupling between consecutive metallic surfaces.39 As observed in the phase profiles in Figure 4c, the propagation of such waves goes along with subsequent jumps of the LSP phase due to a positive global phase shift (forward wave) imposed by the eigenmodes Bloch factors ejβmd from one nanostructure to another. The step-like phase profile is characteristic of LSP resonances with a quasi-uniform phase signal on each nanoparticle hot spot as it is expected in the quasi-static electromagnetic limit. Another interesting result is that the main excited harmonic, H−1, positioned in the second Brillouin zone, is locally much more intense than other harmonics and comparable in magnitude with the fundamental one. We stress this in Figure 5b reporting the amplitude of the FFT of the complex field profile in semilogarithm scale as a function of the wavevector. We note that the H−1 is at least one order in magnitude higher than the other harmonics. Considering the excellent agreement between FDTD simulations and NSOM measurements, we can attribute the presence of the harmonic H−1 to a real phenomenon and not to a tip artifact as proposed in ref 40. In the broader spectrum of Figure 5b, additional higher and lower spatial harmonics emphasize the high optical confinement in the MNP chain. The highest detected harmonics corresponds to n = ± 10. At this point we would like to estimate the optical resolution achieved in our NSOM measurements. This is not a trivial issue, and it does not admit a unique answer.41 However, according to Abbe’s optical resolution criterion,42 the optical resolution is linked to the maximal spatial frequency detected (corresponding here to the harmonic n = +10). This leads in our case to a resolution of less than 30 nm. This result has to be considered with caution. Indeed, as it was demonstrated experimentally in ref 43. a NSOM image may contain a contribution reproducing the motion of the tip. It creates an artifact which can lead to a wrong interpretation of the optical image. Since our topographic and near-field cartographies are highly uncorrelated and simulated images reproduced very well the experimental ones, this effect should not be preponderant here.44 In conclusion, we succeeded in observing near-field light propagation along a chain of gold elliptical nanocylinders loaded on a silicon waveguide and put in resonance by the quasi-TE dielectric waveguide mode. We imaged a collective plasmonic oscillation along the resonant nanostructures characterized by two hybrid plasmon-polariton guided modes with a spatial resolution of a few tens of nanometers. The modeling of the scattered NSOM signal using the Green volume integral method confirmed that this kind of microscope more efficiently scatters the vertical field component. In addition, due to the lateral detection scheme, the near-field images exhibit an asymmetry which is well understood from the scattering diagram of the local emitter placed in close proximity to a nanoparticle. Experimental phase and amplitude near-field profiles measured by heterodyne detection let us to observe the dipolar behavior of the coupled MNPs that are collectively excited. Due to efficient phase matching between the dielectric and

plasmonic waveguides, there is efficient energy transfer between them that leads to a global MNP excitation as observed in the near field. The local dipolar behavior of each nanoparticle was experimentally evidenced and confirmed with FDTD simulations. In addition, the FFT of the complex field distribution shows that light propagation into the plasmonic chain T1 mode involves a rich combination of electrical field spatial harmonics. These spatial harmonics are the result of the excitation of Bloch plasmonic waves that contribute to the energy propagation along the MNP linear array. We anticipate that strong dephasing effects may be obtained in such hybrid waveguides by tuning the Bloch wave dispersion curves. This tuning could be assessed with fine adjustments of the structure geometry.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the “Région Champagne-Ardenne” and by “Agence Nationale de la Recherche” under contract PLACIDO No. ANR-08-BLAN-0285-01. The authors thank Laurent Arnaud and Renaud Bachelot for fruitful discussions and William T. Snider for helpful comments on the manuscript.

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REFERENCES

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Observation of Near-Field Dipolar Interactions Involved in a Metal

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