Letter pubs.acs.org/NanoLett
Controlling Spontaneous Emission with Plasmonic Optical Patch Antennas C. Belacel,†,‡,§ B. Habert,∥ F. Bigourdan,∥ F. Marquier,∥ J.-P. Hugonin,∥ S. Michaelis de Vasconcellos,† X. Lafosse,† L. Coolen,‡,§ C. Schwob,‡,§ C. Javaux,⊥ B. Dubertret,⊥ J.-J. Greffet,∥ P. Senellart,*,† and A. Maitre‡,§ †
Laboratoire de Photonique et de Nanostructures, CNRS, UPR20, Route de Nozay, 91460 Marcoussis, France Université Pierre et Marie Curie-Paris 6, UMR 7588, INSP, Campus Boucicaut, 140 rue de Lourmel, Paris, F-75015 France § CNRS, UMR7588, INSP, Paris, F-75015 France ∥ Laboratoire Charles Fabry, Institut d Optique, CNRS, Univ Paris-Sud, 2 avenue Fresnel, 91127 Palaiseau cedex ⊥ Laboratoire de Physique et d’Étude des Matériaux, CNRS, UMR8213, ESPCI, 10 rue Vauquelin, F-75231 Paris, France ‡
S Supporting Information *
ABSTRACT: We experimentally demonstrate the control of the spontaneous emission rate and the radiation pattern of colloidal quantum dots deterministically positioned in a plasmonic patch antenna. The antenna consists of a thin gold microdisk separated from a planar gold layer by a few tens of nanometers thick dielectric layer. The emitters are shown to radiate through the entire patch antenna in a highly directional and vertical radiation pattern. Strong acceleration of spontaneous emission is observed, depending on the antenna geometry. Considering the double dipole structure of the emitters, this corresponds to a Purcell factor up to 80 for dipoles perpendicular to the disk. KEYWORDS: Plasmonic antenna, quantum dot, Purcell effect, deterministic positioning
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subwavelength volumes.12,13 The quality factor of one mode in a plasmonic structure can be as small as 10 and provide broadband control of spontaneous emission while maintaining large spontaneous emission acceleration, an important point to increase the source operation rate. First works took advantage of hot spots of the optical field in metallic nanoparticules or at the end of metallic tips to demonstrate acceleration of spontaneous emission.14,15 More recently, either acceleration of spontaneous emission16,17 or directional emission18,19 have been demonstrated in plasmonic antennas designed by lithography. In the present work, we experimentally demonstrate control of both the radiation pattern and the emission dynamics of emitters coupled to plasmonic patch antennas. Small clusters of colloidal quantum dots (QDs) are deterministically positioned with 25 nm accuracy in the antenna using an in situ lithography technique.20 The emitters are shown to radiate through the whole patch antenna surface with a directional far field pattern. Time-resolved measurements show a strong acceleration of spontaneous emission. By fitting the experimental curves to account for the random orientation of the double dipole of the
ontrolling the spontaneous emission of a single quantum emitter is a powerful tool to implement an efficient single photon-single emitter interface. Indeed, in the case of a single mode cavity, a quantum emitter spatially located at the maximum of the optical field experiences an acceleration of spontaneous emission given by the Purcell factor Fp, proportional to Q/V where Q is the mode quality factor and V is the mode effective volume.1 When the radiative decay rate into a mode is larger than in any other modes, this property ensures that a large fraction of the emitter emission is funnelled into this given mode. The Purcell effect has widely been used in dielectric cavities to fabricate bright sources of quantum light.2,3 In micropillars,2 microdisks,4 or defects in photonic crystals,5 the electromagnetic field is confined on the wavelength scale. Values of Q larger than 103 are used to obtain large Purcell factors, ensuring a high coupling to the mode.6 Although well suited to extract quasi-monochromatic single photons generated by emitters like epitaxial semiconductor quantum dots, this approach is not appropriate for spectrally broad single photon emitters operating at room temperature like N−V centers in diamonds7 or colloidal quantum dots.8 To provide broadband single photon collection, dielectric antennas have recently been used.9−11 Here, we explore the possibility of controlling the spontaneous emission of quantum emitters using plasmonic antennas, which can confine the electromagnetic field on highly © XXXX American Chemical Society
Received: December 18, 2012 Revised: February 25, 2013
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dx.doi.org/10.1021/nl3046602 | Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. Plasmonic patch optical antenna. (a) Sketch of the patch-antenna structure. (b) Calculated Purcell factor for a point emitter centered in a patch antenna with dipole along z (black lines) or along x−y (red lines). (c) Purcell factor for a point emitter in the middle of a silica layer under a 20 nm thick infinite gold film. (d) Purcell factor as a function of the dipole position along z within an antenna with infinite diameter and for a silica spacer of 30 nm.
factor cannot be defined using a single mode quality factor and effective volume. As discussed in detail in the Supporting Information, the quantum emitter decays through two channels: spontaneous emission of an electromagnetic mode (photon or plasmonic antenna mode) or direct quenching. A large Purcell factor is useful only if it is not dominated by quenching. The quenching effect is related to the short-range nonradiative energy transfer between the quantum emitter and the metallic interface.26 In the case of the patch antenna, the 15 nm distance between the quantum emitter and both gold layers has been chosen to ensure that direct quenching effects are negligible.27 The Purcell factor F is thus a direct measure of the enhanced spontaneous emission into plasmonic antenna modes. Note that after excitation, the plasmonic antenna mode also decays through two channels: photon emission or Joule losses in the antenna so that a radiative efficiency can be defined.21 Figure 1b presents the theoretically expected Purcell factor for a single quantum emitter emitting at 630 nm as a function of the patch antenna disk diameter for a silica spacer thickness of 30 nm. The modification of spontaneous emission is calculated using a point emitter with a dipole along either z- or x-direction precisely positioned at the disk center and at equal distance along z between the two metallic layers. It is seen on Figure 1b that the Purcell factor oscillates around a mean value. This mean value corresponds to the Purcell factor for an infinite disk size and strongly depends on the silica spacer thickness as shown in Figure 1c. The oscillations are due to resonances in the disk that behaves as a cavity if the diameter is smaller than 1.5 μm. For a dipole oriented along z, the maximum Purcell values F⊥ range from 70 to 80 for micrometer size antennas and reach a peak value of 180 for 150 nm diameter antennas. For an emitter presenting a dipole in the x− y plane, the coupling to the antenna is much less efficient and Purcell factors F∥ between 4 and 5 are expected for the whole diameter range. Finally, Figure 1d presents the variation of the Purcell factor as a function of the dipole position along z within an antenna for an infinite diameter and a silica spacer of 30 nm.
emitters, we show that this corresponds to a decay rate enhancement up to 80 for dipoles perpendicular to the antenna. Plasmonic patch antennas were recently proposed as a highly promising system for efficient single photon sources.21 The antenna structure is illustrated in Figure 1a. It consists of a thin metallic microdisk separated from a metallic plane by a few tens of nanometers thick dielectric layer. Coupling of surface plasmons at both dielectric−metal interfaces as well as reflections of surface plasmons at the disk edges results in strongly confined optical modes below the disk area. Esteban and co-workers21 calculated that an emitter inserted in such a structure should experience spontaneous emission enhancements as large as a few hundreds and highly directional emission. Here, we insert colloidal QDs emitting at 630 nm in gold plasmonic patch antenna. A silica layer with refractive index 1.45 is used as dielectric spacer between the two gold layers presenting refractive index n = 0.1835 + 2.9831i at 630 nm.22 Hereafter, we define the Purcell factor as the decay rate of the quantum emitter in the plasmonic antenna normalized by its decay rate in silica. The decay rate can be derived using the imaginary part of Green’s dyadic in the structure.23 Thus only the electric field at the emitter’s position is needed to calculate Purcell’s factor. To numerically describe the device under investigation, we use the rigorous coupled wave analysis as implemented in ref 24. The field is expanded over a basis of modes eiKzf(kr)eiLθ characterized by the wavevector along the disk normal K, the integer L, and the complex eigenvalue k of the radial transverse wavevector; f(kr) is an incoming or outgoing cylindrical mode. The method is generalized to the study of nonperiodic objects by introducing perfectly matched layers (PML)25 at two planes above and below the antenna. The mode amplitudes are obtained by enforcing the boundary conditions at the interfaces. We do not include the θ dependence when the vertical dipole is located at the center of the disk. Note that a monochromatic dipole source in the patch antenna is coupled to a large number of modes with quality factors, on the order of 10.21 As a result, the Purcell B
dx.doi.org/10.1021/nl3046602 | Nano Lett. XXXX, XXX, XXX−XXX
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rate of 0.021 ns−1. Variation of this decay rate is observed from QD to QD, with a Gaussian statistic as shown in Figure 2f. The single QD emission pattern is similar to that of a pair of orthogonally polarized incoherent dipoles30 perpendicular to the QD c-axis. As shown in Figure 1b, the orientation of the QD is a crucial parameter for efficient coupling to the patch antenna. Rather than fabricating a very large number of devices to statistically find antennas embedding a well-oriented emitter, we choose to study small clusters of nanocrystals made of approximately 50 randomly oriented QDs. Figure 2b shows that the emission spectrum of a QD cluster is very similar to the spectrum of an isolated single QD. Figure 2e presents the temporal dependence of the emission of a QD cluster at an air glass interface, evidencing a non-monoexponential decay due to the dispersion of the decay rate of QDs within the cluster. The emission decay rate of a cluster is therefore modeled by a Gaussian distribution characterized by a mean decay rate Γc and a width wc. The decay curve is proportional to ∫ ΓQ+∞ = 0 π1(ΓQ)exp(−ΓQt)dΓQ where we introduce the probability density π1(ΓQ) = exp[−(ΓQ − Γc)2/2wc] and where ΓQ is the individual QD radiative rate. The experimental curve is well reproduced (green curve in Figure 2e) with Γc = 0.0259 ns−1 and wc = 0.004 ns−1. This Gaussian distribution, plotted in green in Figure 2f), presents only a small deviation (
