NANO LETTERS
Fano Resonances in Individual Coherent Plasmonic Nanocavities
2009 Vol. 9, No. 4 1663-1667
Niels Verellen,†,†,⊥ Yannick Sonnefraud,§,⊥ Heidar Sobhani,| Feng Hao,| Victor V. Moshchalkov,† Pol Van Dorpe,† Peter Nordlander,| and Stefan A. Maier*,§ IMEC, Kapeldreef 75, 3001 LeuVen, Belgium, INPAC-Institute for Nanoscale Physics and Chemistry, Nanoscale SuperconductiVity and Magnetism and Pulsed Fields Group, K. U. LeuVen Celestijnenlaan 200 D, B-3001 LeuVen, Belgium, Experimental Solid State Group, Physics Department, Imperial College, London SW7 2AZ, U.K., and Laboratory for Nanophotonics, Department of Physics and Astronomy, M.S. 61, Rice UniVersity, Houston, Texas 77005-1892 Received January 19, 2009; Revised Manuscript Received February 28, 2009
ABSTRACT We observe the appearance of Fano resonances in the optical response of plasmonic nanocavities due to the coherent coupling between their superradiant and subradiant plasmon modes. Two reduced-symmetry nanostructures probed via confocal spectroscopy, a dolmen-style slab arrangement and a ring/disk dimer, clearly exhibit the strong polarization and geometry dependence expected for this behavior at the individual nanostructure level, confirmed by full-field electrodynamic analysis of each structure. In each case, multiple Fano resonances occur as structure size is increased.
Metallic nanostructures with their geometry-dependent localized plasmon resonances are an ideal system for realizing classical oscillators at the nanoscale.1-3 Simple geometries, such as disks, triangles, rods, and rings, support pronounced dipolar plasmon modes tunable over the visible and nearinfrared regions of the spectrum through variations in nanostructure size and geometry.4-6 For more complex structures, a rich resonance spectrum emerges, due to the hybridization of the parent plasmons of individual nanostructure components into bonding and antibonding combinations of plasmon modes.7 The subwavelength effective mode volumes and associated electromagnetic field enhancements8,9 of localized plasmon resonances have already found promising applications ranging from surface-enhanced spectroscopies10-12 to nanoshell-based cancer therapies.13 Complex plasmonic nanostructures can serve as model systems for a variety of fascinating coherent phenomena arising from the physics of coupled oscillators. Symmetrybreaking provides a crucial mechanism for enhancing the coupling of plasmon modes, allowing modes that only couple weakly to the radiation continuum to couple * To whom correspondence should be addressed. E-mail: S.Maier@ imperial.ac.uk. † IMEC. † INPAC-Institute for Nanoscale Physics and Chemistry. § Imperial College. | Rice University. ⊥ These authors contributed equally to this work. 10.1021/nl9001876 CCC: $40.75 Published on Web 03/12/2009
2009 American Chemical Society
directly to incident electromagnetic radiation.14 Recently, subradiant modes and higher-order resonances have attracted significant attention, particularly in the context of generating plasmon modes with reduced radiative damping, which might facilitate the development of plasmonic nanolasers.15,16 These concepts have been recently exploited for creating metamaterials with high-quality-factor resonances17-19 and for the creation of highly tunable subradiant ring/disk plasmon cavities.20 In structures with broken symmetry, Fano resonances can arise due to the interaction of narrow dark modes with broad bright modes. This phenomenon has been theoretically investigated for a variety of structures ranging from particle lattices and split-ring type structures to nanowire arrays and particle dimers.17,19,21-25 Nonconcentric ring/disk cavities have been identified as a system with a highly tunable Fano resonance, exceptionally large refractive index sensitivity, and localized surface plasmon resonance figure of merit.26 Using numerical electromagnetic simulations, Zhang and coworkers have shown that for a strongly coupled system with near-degenerate levels consisting of a side-by-side arrangement of a slab dimer and a slab monomer, the asymmetric Fano line shape can evolve into a full plasmonic-induced optical transparency for optimized geometries.27 This constitutes a classical analogue28,29 to the well-known phenomenon of electromagnetically induced transparency (EIT) of atomic physics.
Ti) between the glass substrate and the Au film. Prior to SEM imaging, a 20 nm thick layer of a conductive polymer is spun on the samples to avoid charging problems. The conductive layer was removed afterward in deionized water. Electromagnetic modeling was conducted using the finitedifference time-domain (FDTD) method. For this, the dielectric response of the metal was fitted using a combination of Drude and Lorentz oscillator terms to the experimentally determined dielectric permittivity.30 This fit has an excellent agreement with the dielectric permittivity of the particular Au films obtained in our fabrication process, as confirmed via ellipsometry. The effect of the glass substrate (refractive index between 1.4 and 1.5) on the resonances has been taken into account in the simulations, and simply leads to a red-shift with respect to extinction calculations in vacuum. Figure 1. Cavity structures studied and experimental setup. (a,b) Geometry and labeling convention for dolmen-type resonators (panel a) and ring-near-disk cavities (panel b), respectively. Insets: SEM images of individual resonators, scale bars: 200 nm. (c) Sketch of the confocal spectroscopy setup. FS: Fianium supercontinuum white light source, MM Fiber: multimode fiber.
Here, using confocal spectroscopy of individual structures, we present an experimental demonstration of Fano resonances in two plasmonic systems: the dimer/monomer slab structure proposed by Zhang et al.,27 and a side-by-side arrangement of a ring and a disk. We examine the dependence of the Fano lineshapes on the polarization of incident light, and the strength of this spectral feature on the separation between individual nanoscale subunits in each structure. We show that for larger structures with sufficiently broad dipolar modes, multiple Fano resonances can arise. The nature of the parent plasmon modes taking part in the interactions is clearly determined using numerical calculations of the associated surface charge distributions. Our study demonstrates that complex plasmonic spectra can be engineered in individual nanostructures in practical, realizable geometries, opening up new opportunities for optical nanocavities and nanosensors. The geometries of the two resonator structures investigated are shown in Figure 1, panels a and b, respectively. Because of its resemblance with the widely familiar neolithic stone structures (rotated by 90°), we suggest the term dolmen for the dimer/monomer slab arrangement. The ring/disk dimer will be called ring-near-disk cavity (RNDC) in the following. Insets show scanning electron microscopy (SEM) images of representative individual cavities fabricated on standard thin microscope glass slides via electron beam lithography and ion milling of a sputtered 60 nm Au/2 nm Ag film. The Ag film serves as an adhesion layer for the etch mask, which is obtained by electron-beam lithography on a negative hydrogen silsesquioxane (HSQ) resist coating and subsequent development. The final structures are etched into the Au film by means of Xe ion milling. As a consequence of the etching process, the particle sidewalls are slanted with an angle of approximately 20 degrees. This fabrication procedure allows for reproducible sub-20 nm gaps between particles and avoids the use of metal adhesion layers of poor optical quality (Cr, 1664
The confocal measurement setup is depicted in Figure 1c. The attenuated beam from a supercontinuum fiber laser (Fianium SC450-4), after passing through a linear polarizer, is focused on the surface of the sample by a 100 × IR-corrected microscope objective. A 50× IR-corrected microscope objective collects the light transmitted through the sample, which is subsequently spatially filtered by the 50 µm core of a multimode fiber guiding the light to a grating spectrometer equipped with Si and InGaAs CCD arrays. Confocal images obtained via raster scanning and avalanche photo diode detection further ensure the correct alignment/ focusing of the microscope objectives. All the optics used for beam shaping and routing are efficient in the near IR region. Focusing of the supercontinuum beam to a near diffraction-limited spot size ensures that measurements of single resonators, arranged on a regular square lattice with a lattice constant of 4 µm, were taken. We point out that as both the strength and line shape of the Fano resonances are expected to strongly depend on the size of the nanoscale gaps between individual elements, extinction measurements on individual units rather than ensemble averages are crucial for obtaining clear spectra. This further ensures that inhomogeneous broadening does not affect our measurements, and facilitates comparisons with electromagnetic simulations. The spectra display a sharp dip at 1064 nm due to detector saturation at the pump wavelength of the supercontinuum source. Figure 2 presents the extinction properties of a single Au dolmen cavity, which is shown in the SEM image in panel d, and has geometric dimensions as indicated in the figure caption. Panel a shows experimentally obtained extinction spectra for two distinct polarizations, as indicated by the red and blue arrows in panel d, and panel b numerical results obtained using FDTD. Excellent agreement between experiment and theory is apparent. In panel c, we further show how the experimentally obtained extinction spectra for both polarizations highlighted in panel a evolve into each other for changes of the in-plane polarization direction in 10° steps. The individual spectra can be clearly associated with coherent superpositions of the eigenmodes excited for polarizations along the fundamental symmetry directions of the structure, namely the spectra shown in panels a and b. To reveal the Nano Lett., Vol. 9, No. 4, 2009
Figure 2. Fano resonance of an individual dolmen structure (d) (scale bar: 100 nm) with the following parameters: L1 ) 160 nm, w1 ) 110 nm, L2 ) 135 nm, w2 ) 100 nm, S ) 55 nm, G ) 20 nm, height H ) 60 nm. (a,b) Experimentally and numerically obtained extinction spectra, respectively, with polarization as defined by the arrows in panel d. (c) The evolution of the experimentally measured extinction as the polarization direction is changed in regular 10° steps. (e,f) Calculated surface charge distributions of the dipolar mode and the Fano extinction dip, respectively.
Figure 3. RNDC with two dark modes of the ring interacting with the broad disk dipole. Structural dimensions: D ) 230 nm, d2 ) 425 nm, T ) 70 nm, G ) 114 nm, H ) 60 nm with SEM picture shown in the inset (scale bar 200 nm). (a,b) Experimentally and numerically obtained spectra, respectively. (c) Experimental extinction spectra for increasing polarization in steps of 20°. (d, respectively e) Surface charge distribution associated with the dip at 680 nm (respectively dip at 770 nm) for polarization along the dimer axis. (f) Surface charge distribution associated with the peak at 950 nm for polarization perpendicular to the dimer axis.
nature of these eigenmodes, we numerically calculate the surface charge distributions at the peak of the dipolar mode and the Fano dip around λ ) 780 nm, shown in panels e and f, respectively. For the electric field vector parallel to the symmetry axis of the dolmen (red curve), a broad dipolar mode of the whole structure is excited, due to the setup of copropagating surface currents in the individual dimer slabs (panel e). However, for perpendicular polarization (blue curve), along the direction of the long axis of the monomer, the excitation of counterpropagating currents in the two parallel slabs constituting the dimer leads to the establishment of a dark bonding mode with an overall quadrupolar charge distribution (panel f). While for individual dimers under normal illumination this mode would only very weakly couple to the radiation continuum, the presence of the monomer allows for dispersive coupling between the sharp bonding and broad dipolar modes. The resulting asymmetric Fano line shape with the central dip at about λ ) 780 nm is clearly resolved. Computed spectra of the individual modes of the constituents of the hybridized nanocavities are presented in the Supporting Information. We point out that the structure presented here is not optimized in terms of obtaining a maximum sharpness for the dip in extinction, as would be required for EIT. The strength of the EIT phenomenon depends both on the spectral overlap of the sharp and broad resonances and their coupling strength mediated by the separation between dimer and monomer.
Ultimately, the sharpness of the dip is limited by the dielectric losses of the metal.24 We now turn our attention to Fano interferences in a RNDC, presented in Figure 3. As for Figure 2, panels a and b show experimentally and numerically obtained extinction spectra for the particular cavity shown in the inset, with dimensions indicated in the figure caption. Panel c demonstrates how the experimentally obtained spectra change with polarization rotation. While not as pronounced as for the dolmen presented above, minima in extinction are observed experimentally (panel a) in the spectral regions around λ ) 750 and 850 nm for polarization along the dimer axis (red curve), which correspond to analogous features in the numerically obtained spectrum at 680 and 770 nm (b, red curve). The red shift and somewhat less pronounced extinction observed in the experiment, both here and for the further spectroscopic measurements on RNDCs presented below, are most likely due to the fact that our illumination spot is smaller than the full spatial extent of the RNDC, leading to a direct excitation of multipolar modes and hence weakening the asymmetry of the Fano line shape.26 A detailed discussion of the influence of illumination conditions on spectroscopy of plasmon cavities will be presented in a subsequent publication. An inspection of the associated surface charge distributions (panels d and e) reveals that these depressions are due to the coupling of higher order ring modes with a broad dipolar disk mode. For the high-energy dip, the
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Figure 4. Larger dolmen cavity exhibiting multiple Fano resonances. Dolmen dimensions: L1 ) 260 nm, w1 ) 115 nm, L2 ) 230 nm, w2 ) 100 nm, S ) 50 nm, G ) 13 nm, H ) 60 nm. (a-c) The layout is identical to Figure 2. (d, respectively f) Surface charge distribution for the mode corresponding to the high-energy (respectively low-energy) dip in the extinction spectrum for perpendicular polarization, and (e) for the mode at the extinction peak for parallel polarization.
associated ring mode is a fourth order multipole, and for the lower energy one it is an octupole. For polarization perpendicular to the dimer axis, the mutual coupling is very weak and the extinction spectrum (blue curve) approximates the sum spectrum of an individual disk and ring (spectrally shifted due to the effect of the finite illumination spot), as was experimentally verified (not shown). Panel f shows the surface charge distribution associated with the extinction peak at λ ) 950 nm for this polarization configuration. The appearance of multiple Fano lineshapes is caused by the larger linear size of this structure compared to the dolmen presented in Figure 2, resulting in a broader dipolar continuum. Multiple Fano resonances should therefore also appear for larger dolmen structures, as we will now show. For the cavity shown in the inset of Figure 4a with geometric dimensions as indicated in the caption, Fano interferences are clearly visible respectively at wavelengths of 850 and 1100 nm in the experimentally obtained extinction spectrum for polarization perpendicular to the pair axis (blue curve, Figure 4a). This result is in good agreement with the spectra obtained from the FDTD simulations shown in panel b. From the surface charge distributions, presented in panels d and f, it is apparent that the monomer dipole and quadrupole modes are mixed with each other, which makes the identification of the individual modes somewhat more difficult. However we can conclude that for this bigger dolmen the extinction dip at λ ) 850 nm results from the dispersive coupling of the dimer dipole mode with a quadrupole in the monomer 1666
Figure 5. Experimental (a,b) and calculated (c,d) extinction spectra of structures with decreasing gap size G showing an increased coupling. Left panel: dolmen with dimensions L1 ) 260 nm, w1 ) 115 nm, L2 ) 230 nm, w2 ) 100 nm, S ) 50 nm, H ) 60 nm. The gap sizes are G ) 28 nm (red), 18 nm (orange), 13 nm (green), 5 nm (blue), and G ) 0 nm (black). Right panel: RNDC with dimensions D ) 325 nm, d2) 425 nm, T ) 80 nm, H ) 30 nm. The gap sizes are G ) 20 nm (red), 10 nm (green) and G ) 0 nm (black). All spectra are for the polarizations exciting the Fano resonances. The SEM pictures show close-ups of the gap regions for selected gap sizes.
slab. The λ ) 1100 nm depression on the other hand, mainly results from a coupling between the monomer dipole mode and dimer bonding mode. Because of the strong near-field coupling the latter can couple back to higher order modes in the monomer, hence resulting in the observed mode mixing (panel f). For an incident polarization along the pair axis the extinction spectrum is again the sum of the individual dimer and monomer spectra (red curve Figure 4a and corresponding charge distribution panel e). Panel c outlines the experimental polarization dependence. Lastly, we turn our attention to a discussion of the variation of the strength of the Fano interferences on the separation between the units sustaining the dark and bright oscillator modes. Representative spectra for different gaps are presented in Figure 5 for both cavity geometries. Figure 5a shows experimentally obtained spectra for dolmens with different separations (colored lines) between the monomers and the dimers, while Figure 5b shows similar spectra for an RNDC with the magnitude of the separations indicated in the caption. For both geometries, the depths of the dip increases with decreasing gap size due to increasing coupling between dipolar and quadrupolar modes. For the dolmens, the polarization of the incident light is perpendicular to the long axis of the dimer and for the RNDC parallel to the dimer axis in order to maximize the Fano interferences. The black curves in Figure 5a,b show the spectra for touching particles. In this case, the coupling becomes conductive instead of Nano Lett., Vol. 9, No. 4, 2009
capacitive resulting in a strongly enhanced interaction and large shifts of the Fano features. This can most clearly be seen from the associated numerical simulations, presented in panels c and d, respectively, where the extinction dip at λ ) 1000 nm for the RNDC with finite gap experiences a shift of 150 nm upon closing of the gap. For the dolmen, closing the gap results in a split-ring-like structure31 with an even larger shift to λ ) 1500 nm in extinction minimum associated with it (not shown). Clearly, a large parameter space for tuning and optimization of the Fano features exists. It will be particularly interesting to see if the reduction in extinction can be optimized to the limit of being determined solely by Ohmic losses. To conclude, we have presented an experimental investigation of Fano interference phenomena in individual plasmonic nanocavities. For the particular dolmens and disknear-ring cavities analyzed, the Fano resonances are due to the coupling of dark quadrupolar and higher order modes with bright dipolar modes. As both the spectral position and the width of these Fano lineshapes depend very sensitively on the dielectric gap between the individual resonators sustaining the dark and bright modes, respectively, a high sensitivity for the sensing of molecular species within the gap region can be anticipated. This constitutes a promising application potential of such resonator structures. Acknowledgment. S.A.M. and Y.S. acknowledge support by the U.K. Engineering and Physical Sciences Research Council. P.V.D. acknowledges financial support from the F.W.O. (Flanders). H.S., F.H., and P.N. acknowledge support from the U.S. Army Research Laboratory and the U.S. Army Research Office under Grant W911NF-04-1-0203, the Robert A. Welch Foundation under Grant C-1222, and NSF under Grant CNS-0421109. N.V. acknowledges support from IMEC and the Methusalem funding by the Flemish Government. We thank Jos Moonens for e-beam assistance. Supporting Information Available: Computed spectra of the individual modes of the constituents of the hybridized nanocavities. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Maier, S. A.; Atwater, H. A. J. Appl. Phys. 2005, 98, 011101. (2) Lal, S.; Link, S.; Halas, N. J. Nat. Photon. 2007, 1, 641–648.
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(3) Maier, S. A. Plasmonics - Fundamentals and Applications, 1st ed.; Springer: New York, 2007. (4) Mock, J. J.; Barbic, M.; Smith, D. R.; Schultz, D. A.; Schultz, S. J. Chem. Phys. 2002, 116, 6755–6759. (5) Kuwata, H.; Tamaru, H.; Esumi, K.; Miyano, K. Appl. Phys. Lett. 2003, 83, 4625–2627. (6) Aizpurua, J.; Hanarp, P.; Sutherland, D. S.; Ka¨ll, M.; Bryant, G. W.; de Abajo, F. J. G. Phys. ReV. Lett. 2003, 90, 057401. (7) Prodan, E.; Radloff, C.; Halas, N. J.; Nordlander, P. Science 2003, 203, 419–422. (8) Maier, S. A. Opt. Express 2006, 14, 1957–1964. (9) Miyazaki, H. T.; Kurokawa, Y. Phys. ReV. Lett. 2006, 96, 097401. (10) Kneipp, K.; Kneipp, H.; Itzkan, I.; Dasari, R. R.; Feld, M. S. J. Phys.: Condens. Matter 2002, 14, R597-R624. (11) Xu, H.; Aizpurua, J.; Kaell, M.; Apell, P. Phys. ReV. E 2000, 62, 4318– 4324. (12) Anker, J. N.; Hall, W. P.; Lyandres, O.; Shah, N. C.; Zhao, J.; Duyne, R. P. V. Nat. Mater. 2008, 7, 442–453. (13) Lal, S.; Clare, S. E.; Halas, N. J. Acc. Chem. Res. 2008, 41, 1842– 1851. (14) Wang, H.; Wu, Y.; Lassiter, B.; Nehl, C. L.; Hafner, J. H.; Nordlander, P.; Halas, N. J. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 10856. (15) Bergman, D. J.; Stockman, M. I. Phys. ReV. Lett. 2003, 90, 027402. (16) Zheludev, N. I.; Prosvirnin, S. L.; Papasimakis, N.; Fedotov, V. A. Nat. Photon. 2008, 2, 358. (17) Fedotov, V. A.; Rose, M.; Prosvirnin, S. L.; Papasimakis, N.; Zheludev, N. I. Phys. ReV. Lett. 2007, 99, 147401. (18) Liu, N.; Guo, H.; Kaiser, S.; Schweizer, H.; Giessen, H. AdV. Mater. 2007, 19, 3628. (19) Christ, A.; Martin, O. J. F.; Ekinei, Y.; Gippius, N. A.; Tikhodeev, S. G. Nano Lett. 2008, 8, 2171–2175. (20) Hao, F.; Nordlander, P.; Burnett, M. T.; Maier, S. A. Phys. ReV. B 2007, 76, 245417. (21) Le, F.; Brandl, D. W.; Urzhumov, Y. A.; Wang, H.; Kundu, J.; Halas, N. J.; Aizpurua, J.; Nordlander, P. ACS Nano 2008, 2, 707–718. (22) Liu, N.; Kaiser, S.; Pfau, T.; Giessen, H. Cleo Qels Postdeadline paper QPDB5, CLEO/QELS2008, San Jose, USA. (23) Christ, A.; Ekinei, Y.; Solak, H. H.; Gippius, N. A.; Tikhodeev, S. G.; Martin, O. F. J. Phys. ReV. B 2007, 76, 201405R. (24) Liu, N. A.; Kaiser, S.; Giessen, H. AdV. Mater. 2008, 20, 4521–4525. (25) Bachelier, G.; Russier-Antoine, I.; Benichou, E.; Jonin, C.; del Fatti, N.; Valee, F.; Brevet, P.-F. Phys. ReV. Lett. 2008, 101, 197401. (26) Hao, F.; Sonnefraud, Y.; Van Dorpe, P.; Maier, S. A.; Halas, N. J.; Nordlander, P. Nano Lett. 2008, 8, 3983–3988. (27) Zhang, S.; Genov, D. A.; Wang, Y.; Liu, M.; Zhang, X. Phys. ReV. Lett. 2008, 101, 047401. (28) Alzar, C. L. G.; Martinez, M. A. G.; Nussenzveig, P. Am. J. Phys 2002, 70, 37–41. (29) Shvets, G.; Wurtele, J. S. Phys. ReV. Lett. 2002, 89, 115003. (30) Hao, F.; Nordlander, P. Chem. Phys. Lett. 2007, 446, 115–118. (31) Enkrich, C.; Wegener, M.; Linden, S.; Burger, S.; Zschiedrich, L.; Schmidt, F.; Zhou, J. F.; Koschny, T.; Soukoulis, C. M. Phys. ReV. Lett. 2005, 95, 203901.
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