pubs.acs.org/NanoLett
Cavity Plasmonics: Large Normal Mode Splitting of Electric and Magnetic Particle Plasmons Induced by a Photonic Microcavity Ralf Ameling and Harald Giessen* 4th Physics Institute, University of Stuttgart, Stuttgart, Germany ABSTRACT We couple localized plasmon modes in nanowire pairs with resonator modes of a microcavity. Depending on the position of the nanowire pair in the resonator, the electric (symmetric) or magnetic (antisymmetric) plasmon mode is coupled, manifested by a huge anticrossing in the dispersion diagram. We explain this behavior by taking the symmetry and spatial distribution of the electric fields in the resonator into account. Experimental spectra verify the predicted mode-splitting due to the resonant coupling and agree well with theory. Our work can serve as a model system for far-field plasmon-plasmon coupling and paves the way toward enhanced localized plasmon-plasmon interaction in photonically coupled three-dimensional Bragg structures. KEYWORDS Plasmonics, microcavity, strong coupling, magnetic coupling, normal mode splitting, metamaterial
M
icrocavities confine the electromagnetic field within a very small volume and allow large field enhancement.1-4 When combined with radiating species, such as atoms,5 molecules,6-9 or semiconductor excitons,10 strong coupling between the optical modes of the microcavity and resonant modes of the emitters can occur. This strong coupling has been utilized in the past to demonstrate enhancement and inhibition of spontaneous emission11,12 or to tailor the photon statistics.13 Even vacuum Rabi-splitting of excitons in quantum dots has been observed.14,15 An additional feature of microcavities is their ability to couple two radiating systems via the optical farfield over a larger distance.16,17 In this Letter, we show that strong coupling between localized plasmons in nanowire pairs and photonic microcavity modes can occur. Furthermore, we demonstrate that the field symmetry of the microcavity mode can excite electric (symmetric) and magnetic (antisymmetric) modes in a nanowire pair, depending on its position in the microcavity. Our design allows especially strong coupling of light to the generally weakly excited magnetic dipole and can serve as a model for far-field coupling of localized particle plasmons in individual layers of stacked metallic metamaterials.18,19 This work paves the road toward strong coupling of multiple localized plasmons in three-dimensional metamaterials.20,21 Isolated nanowires exhibit a well-defined localized plasmon resonance frequency which is determined by their geometrical parameters and the materials used. For an isolated gold nanowire with a length of 300 nm, a width of 100 nm, and a height of 30 nm (these geometrical parameters are used throughout this Letter for simulations and
experiments) embedded in a dielectric medium with the refractive index nd ) 1.4 µm the plasmon resonant wavelength is λNW ) 1.4 µm when illuminated from above with linearly polarized light (E-field along the nanowire). By placing another nanowire in the vicinity, the plasmons associated with the two nanowires are coupled and the resonances are significantly modified. The near-field interaction among plasmons can be well described by the principle of plasmon hybridization22,23 which is applicable to nanowires.24 By stacking two nanowires on top of each other, thus creating a nanowire pair,25,26 the plasmon resonance is split into two hybridized modes, namely, a symmetric and an antisymmetric mode (Figure 1). The antisymmetric mode (also often referred to as magnetic mode since it induces a magnetic dipole moment) occurs at the lower frequency (higher wavelength) because it is the energetically more favorable hybridized state. For a spacer thickness of s ) 40 nm between two nanowires, the resonant wavelengths are λvv ) 1.3 µm for the electric (symmetric) and λvV ) 1.75 µm for the magnetic (antisymmetric) plasmon mode. Resonator modes of different order can be excited between two gold mirrors forming a Fabry-Pe´rot microcavity (see Figure 1). When the propagation direction of the incident light is perpendicular to the resonator planes, the wavelength of the Nth mode can be calculated as
λN )
(1)
where nd is the real part of the refractive index of the dielectric coating and d denotes the thickness of the dielectric between the two gold mirrors. The apparent length increase δ of the cavity due to the reflection phase27,28 at the metal plates has been determined as approximately δ
* To whom correspondence should be addressed,
[email protected]. Received for review: 06/1/2010 Published on Web: 10/06/2010 © 2010 American Chemical Society
2nd(d + δ) N
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DOI: 10.1021/nl1019408 | Nano Lett. 2010, 10, 4394–4398
FIGURE 1. Nanowire pairs in a resonator. For a central position (sample A) the odd resonator modes excite the electric (symmetric) plasmon mode and the even resonator modes excite the magnetic (antisymmetric) plasmon mode. For noncentral positions (sample B) only those resonator modes with a field node between two individual nanowires of a pair can excite the magnetic plasmon mode.
) 96 nm. In Figure 2b the unperturbed resonant modes are depicted for resonator lengths from d ) 100 nm to d ) 3000 nm. These modes, as well as the localized plasmon modes in the metal nanostructure, are depicted as dashed lines in the dispersion diagrams of parts c-e of Figure 2. When a nanowire pair is placed into the resonator, the plasmonic nanowire modes can interact with the resonator modes. This interaction is evident through an anticrossing of the modes. A large anticrossing of the dispersion curves denotes a large strong coupling, a small anticrossing a smaller strong coupling. (The definition of strong coupling is g > κ,γ in the case of cavity QED. g is the coupling strength (polariton splitting), and κ and γ are the mirror losses and spontaneous emission (radiative coupling) losses, respectively. In our case, we are definitely in the strong coupling regime because the polariton splitting both for the electric as well as for the magnetic case is substantially larger than the coupled resonance line width.) The simulation of a nanowire pair placed in the center of a resonator shows a number of interactions (Figure 2c): The even resonator modes interact with the magnetic nanowire mode at a wavelength of λvV ) 1.75 µm, indicated by a small anticrossing, whereas the odd resonator modes are not affected by the magnetic plasmon mode. For lower wavelengths a large anticrossing can be observed for the odd resonator modes around λvv ) 1.3 µm, caused by a strong interaction of these resonator modes with the electric plasmon mode. The even resonator modes remain unaffected in this spectral region. By considering the positions of field nodes of standing waves in a resonator (Figure 1), this behavior can be © 2010 American Chemical Society
FIGURE 2. FDTD Simulations: (a) Hybridized plasmon resonances of an infinite nanowire pair (NWP) array (unit cell 500 nm ×500 nm), (b) unperturbed microcavity modes, and (c-e) nanowire pairs at different positions in a cavity. (c) Nanowire pair in a central position in a cavity. (d, e) Nanowire pair in noncentral positions. The dashed lines denote the unperturbed resonator and plasmon modes. The circles indicate the coupling area of the plasmonic modes and the resonator modes characterized by an anticrossing of the resonances. The vertical lines mark the fabricated samples A and B (see Figure 4). The sketches on the right side illustrate the considered structure in which the different colors identify the cavity modes.
explained. In the center of the resonator the electric field vectors of the odd modes point into the same direction for both nanowires of a pair, so only the electric (symmetric) mode can be excited. The field amplitude is close to the maximum for the odd modes near the nanowire spatial region; therefore also the coupling is strong. The even modes, however, possess an electric field node directly in between the two nanowires, resulting in opposite directions of the electric field vector for each nanowire, exciting only 4395
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FIGURE 3. Plots of the electric and magnetic field distributions (logarithmic color scale) at the various resonances. (a) and (b) show the x-component of the electric field in the y-z plane for the electric (symmetric) and the magnetic (antisymmetric) plasmon mode of nanowire pairs without a cavity. The modes split when the nanowire pairs are embedded in a microcavity (c-h). The third resonator mode (3) splits widely into two modes (3′ and 3′′) (c, d) due to strong coupling to the electric (symmetric) mode. The second resonator mode (2) splits into two modes close by (2′ and 2′′) (e, f) due to strong coupling to the magnetic (antisymmetric) plasmon mode (see Figure 2). The plots (g) and (h) show the y component of the magnetic field of the split magnetic (antisymmetric) plasmon modes in the x-z plane. The graphs below correspond to cross sections of panels a and c of Figure 2 (marked “A”). The dashed lines in the background denote the unperturbed resonances of an empty cavity corresponding to Figure 2b.
the magnetic (antisymmetric) mode. Since the field amplitude is low around the node, the strong coupling between the even modes and the plasmon is weaker. To verify this explanation, the nanowire pair is placed at different positions in the cavity. When placed at a node of the third mode, the magnetic mode can couple to the third resonator mode, and the other modes couple only to the electric mode (Figure 2d). Similar observations apply for the fourth mode (Figure 2e). The coupling manifests itself as a large spectral mode splitting. One might also look at the interaction from a magnetic viewpoint.29 The magnetic field in the microcavity is maximum at the nodes of the E-field. Hence the interaction with the magnetic nanowire pair modes is then strongest at such locations. The field plots in Figure 3 provide a deeper insight concerning the nature of the split modes. Panels a and b of Figure 3 illustrate the hybridization of plasmon modes into an electric (symmetric) mode at lower wavelength and an antisymmetric (magnetic) mode at higher wavelength. It is obvious that the electric fields inside the nanowires point in the same direction for the electric plasmon mode and in opposite directions for the magnetic plasmon mode. When the nanowire pairs are placed into a microcavity, normal mode splitting occurs. The coupling of the third resonator mode to the electric plasmon mode is illustrated in panels c and d of Figure 3. The electric field points in the same © 2010 American Chemical Society
direction in both nanowires, whereas it points in opposite directions for the coupling of the second resonator mode to the magnetic plasmon mode in panels e and f of Figure 3. Note that the two split resonances of one microcavity mode differ in such a way that the plasmon oscillation is in phase with the microcavity mode for the resonance at the lower wavelength and antiphase for the resonance at the higher wavelength. Panels g and h of Figure 3 finally show the corresponding strong magnetic dipoles that are exhibited by the magnetic (antisymmetric) plasmon modes. All simulations were performed with a commercial FDTD simulation program (CST Microwave Studio) and a Fourier model based Maxwell solver30,31 using linearly polarized light impinging perpendicularly on the resonator surface. The polarization direction is along the nanowire. Gold is described in the near-infrared region by a Drude model with the plasma frequency ωp ) 1.37 × 1016 Hz32 and the damping frequency ωc ) 8 × 1013 Hz. The refractive indices of the dielectric coating (spin-on glass), the spacer between two gold nanowires (MgF2), and the glass substrate (Infrasil) are taken as 1.40, 1.38, and 1.45, respectively. For the fabrication of the structures we use physical vapor deposition for the metals and the magnesium fluoride layers, spin-coating for the dielectric layers, and electron beam lithography for the nanostructuring. With these techniques the investigated structures can be manufactured in a layer4396
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FIGURE 4. (a, b) Sketches of the two fabricated samples A and B. SEM images of uncovered nanowire pairs (x- and y-period 500 nm) (c) and nanowire pairs embedded in a cavity (FIB cut) (d).
by-layer fashion. First a 20 nm thick gold layer serving as the lower mirror is evaporated on an Infrasil glass substrate that has been coated with 3 nm chromium for better adhesion of the gold. Thereafter the first dielectric spacer between the gold layer and the later nanowire is spin-coated. For the spacer we use a polysiloxane-based spin-on glass (IC1-200 Intermediate Coating from Futurrex) in different mixing ratios with butanol, resulting in different layer thicknesses. The spacer consists of one or more dielectric coating layers with different mixing ratios. Subsequently, the positive resist PMMA 950 K is spun onto the sample in which the nanowire pattern is written by electron beam lithography. After the exposure and the development, the sample is coated with 30 nm of Au, 40 nm of MgF2, and 30 nm of Au. By leaving the sample in acetone for several hours, the unexposed PMMA as well as the gold and magnesium fluoride layers thereon are removed (lift-off), and only the nanowire pairs on the dielectric coating remain. For planarization a 100 nm thick layer of IC1-200 and subsequently the upper dielectric spacer is spin-coated on the sample. Finally, 20 nm of gold is evaporated. Two samples (A and B) have been produced in the above explained manner (Figure 4) to confirm the simulated results experimentally. Each reflection spectrum of a fabricated sample (Figure 5) corresponds to one cross section in the 2D plots of Figure 2. Additional reflection spectra were recorded away from the structure to measure the unperturbed resonator modes and thus determine the resonator length. The reflection and transmission spectra have been measured with a Fourier transform infrared spectrometer (Vertex 80 from Bruker) using linearly polarized light. We detected the spectra with a Si diode and an MCT detector. © 2010 American Chemical Society
FIGURE 5. Comparison of measured and simulated reflection spectra. Sample A: Nanowire pair in a central position in the resonator (d1 ) d2 ) 550 nm). The graphs correspond to the cross sections A in Figure 2b and Figure 2c. The second resonator mode (2) splits into two modes close by (2′, 2′′) due to strong coupling to the magnetic (antisymmetric) plasmon mode. The third resonator mode (3) splits widely into two modes (3′, 3′′) due to strong coupling to the electric (symmetric) mode. Sample B: Nanowire pair in a noncentral position in the resonator (d1 ) 580 nm, d2 ) 1160 nm). The graphs correspond to the cross sections B in Figure 2b and Figure 2d. The second resonator mode (2) does not split up for this resonator length and is only slightly shifted. The third resonator mode (3) splits into two modes close by (3′, 3′′) due to strong coupling to the magnetic (antisymmetric) plasmon mode. The fourth resonator mode (4) splits widely into two modes (4′, 4′′) due to strong coupling to the electric (symmetric) mode.
One sample (A) has been produced with the nanowire pairs located in the center of the resonator. The resonator length of sample A is 1100 nm. This is approximately the length where the second resonator mode wavelength equals the magnetic plasmon mode wavelength. The measured spectrum is in good agreement with the simulation (Figure 5a). Around λvV ) 1.75 µm the splitting of the second mode into two peaks 2′ and 2′′ around the magnetic plasmon mode can be clearly observed. The splitting energy is 82 meV, which corresponds to 11% of the resonance energy itself. Additionally, the large splitting (354 meV) of the third mode due to its strong coupling to the electric plasmon mode is evident. (The splitting values are taken from simulations 4397
DOI: 10.1021/nl1019408 | Nano Lett. 2010, 10, 4394-–4398
REFERENCES AND NOTES
(Figure 2c and Figure 2d) at those points where the unperturbed plasmon and cavity modes would intersect.) Finally, the higher modes remain mostly unaffected for this resonator length. The relative difference in the strength of the modes in experiment and simulation can be explained by the fact that the thickness of the spacer layers between nanowire pair and metal mirror is subject to variations. Sample B has a resonator length of 1740 nm. Around this length the wavelength of the third resonator mode equals the magnetic plasmon mode wavelength. The nanowire is positioned in such a way that the ratio of the distances to the two gold cavity mirrors is d1:d2 ) 1:2. Hence, the third mode couples strongly to the magnetic plasmon mode and is split by 64 meV (see Figure 5b) since it is located at a position around an electric field node of the third resonator mode. The fourth mode couples strongly to the electric plasmon mode and is split into two well-separated peaks 4′ and 4′′ (splitting 235 meV). We have shown both experimentally and theoretically that hybridized nanowire pair plasmon modes can exhibit strong coupling to standing waves in a microcavity. Depending on the position of the nanowire pair, the resonator modes can couple either to the electric (symmetric) or to the magnetic (antisymmetric) plasmon mode. The behavior is explained by the direction of the electric field vectors of the resonator modes at the positions of the nanowires. The splitting can be as large as 82 meV for the magnetic and 354 meV for the electric mode. This is very large, as the splitting is 36% of the resonance energy. Our experimentally observed splitting-to-line-width ratio can be as large as 10 for the electric mode and 2.5 for the magnetic mode. The coupling might be further increased by using dielectric mirrors resulting in a high-Q cavity. The experiments can lead to new hybrid plasmon-light coupling schemes and shed light on plasmonic Bragg-coupling and hybrid photonic-plasmonic far-field interaction in three-dimensional nanostructures. Applications include coupling of multiple plasmonic elements, for example, nanorods or pairs of nanorods, inside of a microcavity. This concept can be expanded to multiple cavities or multiple elements at Braggor anti-Bragg spacing. Even more intriguing is the coupling to quantum emitters, such as J-aggregates or semiconductor quantum dots, which can be spaced a Bragg distance away from the metal. This avoids near-field quenching and should result in strongly coupled plexcitons.8 Quantum effects in combination with metamaterials33-37 could become better controlled using our microcavity scheme.
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Acknowledgment. We would like to thank R. Vogelgesang for useful comments, H. Gra¨beldinger for technical assistance, and B. Fenk from the MPI for Solid State Research for the FIB support. This work was financially supported by Deutsche Forschungsgemeinschaft (FOR557 and SPP1391) and Bundesministerium fu¨r Bildung und Forschung (13N10146).
© 2010 American Chemical Society
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DOI: 10.1021/nl1019408 | Nano Lett. 2010, 10, 4394-–4398
