Letter pubs.acs.org/NanoLett
Fano Coil-Type Resonance for Magnetic Hot-Spot Generation A. Nazir,†,‡ S. Panaro,†,‡ R. Proietti Zaccaria,† C. Liberale,† F. De Angelis,† and A. Toma*,† †
Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genova, Italy Università degli Studi di Genova, 16145 Genova, Italy
‡
S Supporting Information *
ABSTRACT: The possibility to develop nanosystems with appreciable magnetic response at optical frequencies has been a matter of intense study in the past few years. This aim was strongly hindered by the saturation of the magnetic response of “natural” materials beyond the THz regime. Recently, in order to overcome such limitation, it has been considered to enhance the magnetic fields through the induction of displacement currents triggered by plasmonic resonances. Here we investigate a nanoassembly supporting the hybridization of an electric and magnetic plasmonic mode in Fano resonance conditions. Taking advantage of the enhancement properties owned by such interferential resonance, we have been able to generate an intense and localized magnetic hot-spot in the near-infrared spectral region. KEYWORDS: Localized surface plasmon, Fano resonance, dark mode, magnetic hot-spot, electron beam lithography
S
Results and Discussion. We initially designed three gold disks (160 nm diameter) in triangular arrangement and performed both near- and far-field simulations under normally incident plane wave excitation.17 In order to obtain an efficient coupling between radiation and nanostructures, the polarization of light has been chosen parallel to the line connecting the centers of two disks (sketch in the bottom of Figure 1a). In such optical configuration we calculated the extinction efficiency spectrum of the trimer system (black curve in Figure 1b), observing an intense peak at 1000 nm, labeled “e”, and a high order peak around 700 nm, labeled “q”. From the current density plot related to the main peak “e”, we could ascribe the resonance to an electric mode involving both the lower disk dimer and the upper disk (Figure 1c). In such system the free charges inside the disks oscillate in-phase, inducing a net electric dipole parallel to the substrate plane (indicated by the vector p⃗e in Figure 1c).18−21 Differently, the peak “q” is related to a multipolar11,22 behavior, verified from the current density plot of Figure 1e. The modes corresponding to “e” and “q” show well distinct peaks spectrally separated by a pronounced valley indicated with “s” in the black curve of Figure 1b. By considering the global arrangement of charge current densities, we can associate both “e” and “q” modes to localized surface plasmons (LSPs) of electric nature. In order to generate a resonant magnetic dipole inside the system, we induced a phase retardation between the LSPs supported by the trimer. For such a reason, we gradually increased the upper disk diameter (Figure 1a from bottom to top) reporting the
everal efforts have been recently spent in the investigation of “artificial magnetic” resonances, inducing negative refractive index in metamaterials.1−4 One attempt in such direction consisted in the fabrication of split ring resonators, which can support circulating currents up to few hundreds of terahertz.5 Nevertheless, the promotion of coil-type modes at optical frequencies is still challenging, due to the saturation of the magnetic response in “natural” materials.6 A way recently found for overcoming such difficulty consists in exchanging usual conduction currents, affected by strong ohmic losses, with displacement currents induced by plasmonic resonances.7,8 In fact, by arranging metallic nanostructures in close proximity to one another, it is possible to promote resonating displacement currents in the interparticle gap regions.9,10 Moreover, the introduction of symmetry breaking8,11,12 into these systems can induce the hybridization of bright electric and dark magnetic modes in Fano resonant conditions13−15 with consequent current intensification.4 Within this context, an essential point to be considered is the geometry of the involved plasmonic devices. In fact, it can be shown how the conventional electric field hot-spots do not present a comparable magnetic counterpart (magnetic field enhancement factor close to 1). The excitation of effective magnetic hot-spots requires dedicated plasmonic devices,14−16 able to support close circulating current modes instead of linearly oscillating plasmons. In order to obtain a coil-type mode, we conceived a planar disk trimer system supporting a close current resonance. We simulated and fabricated this nanoassembly, demonstrating how a morphological symmetry breaking can promote the hybridization of electric and magnetic modes. © XXXX American Chemical Society
Received: February 4, 2014 Revised: May 12, 2014
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dx.doi.org/10.1021/nl500452p | Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. (a) Sketches of the considered trimer geometries (the diameter of the small dimer disks is 160 nm and the diameters of the upper disks are 160, 210, 260, 310, and 350 nm, respectively). (b) Simulated extinction efficiency spectra of single trimers for different upper disk diameters. (c,d) Two-dimensional charge current density plots evaluated on a plane parallel to the substrate passing through the center of the structure: the plots identify an electric mode in the 160 nm trimer and a coil-type mode in the 350 nm trimer, respectively. (e−h) Two-dimensional charge current density plots showing the current distributions induced inside the trimer systems, respectively, in “q” and “s” position (see black curve in panel b) and in “e↑” and “e↓” position (see green curve in panel b). The plots represent electric-like modes. (i) Plot reporting both the extinction efficiency spectrum (green continuous line) of 350 nm diameter trimer and the H field (evaluated at the center of the cavity) generated by such trimer as a function of wavelength (red dot curve): the spectral matching between the Fano resonance and the maximum of H field is highlighted by the vertical purple band.
Figure 2. (a) Simulated extinction efficiency spectra of single disks for diameters 160, 210, 260, 310, and 350 nm, respectively, and extinction efficiency spectrum of 160 nm diameter disk dimer (dashed line). (b) Simulated extinction efficiency spectra of 350 nm diameter disk (green dashed line), of 160 nm diameter disk dimer (yellow dashed line), and of the corresponding trimer (green continuous line) (left/right inset: phase (θ) relationship between external electric field and charge current density in the high/low energy side of single disk/dimer structure). (c−f) Twodimensional plots of conduction current density (Jc⃗ ), electric field enhancement (local electric field E⃗ normalized to the incoming electric field E⃗ 0), total charge current density (conduction plus displacement current (Jc⃗ + Jd⃗ )), and magnetic field enhancement (local magnetic field H⃗ normalized to the incoming magnetic field H⃗ 0), respectively, generated on a plane parallel to the substrate, passing through the center of the structure, under Fano resonance conditions.
extinction curves, the spectrum corresponding to the 260 nm diameter configuration (blue trace) shows a particular lineshape evolution as illustrated by the appearance of a dip around 1000 nm. By further increasing the size of the upper disk, the
corresponding evolution of the extinction efficiency spectra in Figure 1b. The morphological modification induces a red-shift of the extinction spectrum, in accordance to the red-shift of the upper disk resonance.23 In addition to the general shift of the B
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“m” valley gradually deepened as shown by the pink and green curves in Figure 1b. In order to better understand this behavior, we calculated and compared the charge current density in correspondence to the “s” and “m” spectral positions for the minimum (160 nm) and maximum (350 nm) disk sizes, respectively. While in the “s” valley the charge distributions oscillate in phase, but in out-of-resonance condition (Figure 1f), we can notice how in the “m” case the system responds to a normal incident plane wave mainly by the excitation of a planar coil-type resonance, which can be associated with a magnetic dipole perpendicular to the substrate (indicated by the vector “p⃗m” in Figure 1d). Furthermore, by considering the charge arrangements induced immediately in the high and low energy sides of the “m” dip (extinction peaks labeled respectively “e↑” and “e↓” in the green curve of Figure 1b), we could notice how the currents inside the disks present a dominant electric response (Figures 1g,h), which recalls the behavior of the “e” mode (Figure 1c). Finally, in Figure 1i we plotted the spectral response of the magnetic field associated with Figure 1d, overlapped to the extinction efficiency spectrum of the corresponding system (green curve in Figure 1b). By observing how the maximum of H field enhancement (ratio between actual and the incoming magnetic fields) matches to the minimum of the extinction curve (see vertical purple band), it is possible to attribute the sharp dip (“m” mode) to a Fano resonance7,24 that results from the interference between the spectrally broad electric resonance (“e” mode) with a narrow magnetic mode, which is dark in this optical configuration. Such observations confirm that the coil-type mode induced in Fano condition is a resonant phenomenon characterized by a minimum in the extinction efficiency spectrum. In order to better understand how the “m” mode can be excited and to find a threshold for its activation, we analyzed the resonance of the upper disk as a function of its diameter. Choosing the dipolar resonance of the lower disk dimer as spectral reference (dashed curve in Figure 2a), we plotted the extinction resonance peaks related to the upper disk for increasing diameters (Figure 2a). Since the extinction dip “m” was found starting from the blue line spectrum of Figure 1b, we observed that the Fano interference arises when the LSP resonance of the upper disk is in the low energy side of the dimer resonance (see the blue, pink, and green curves in Figure 2a). Such observation defines a precise threshold for the size of the upper disk, beyond which the system starts to exhibit a coiltype mode (Figure 1d). The reason for such transition has to be searched in the phase relationship between the dipolar mode in the disk dimer and the LSP in the upper disk. We considered the case of the 350 nm diameter (Figure 2b), plotting both the lower dimer (yellow dashed trace) and the upper disk (green dashed trace) spectra. In the same graph we also plotted the extinction spectrum of the corresponding trimer assembly (green continuous trace). As we could appreciate, the Fano resonance occurs in the overlapping region between the low energy tail of the dimer peak (cyan area under the dimer curve) and the high energy tail of the single disk peak (red area under the single disk curve). In such region the charge current density J ⃗ inside the dimer is in-phase with the external electric field E⃗ 0 (right inset of Figure 2b), while the current in the single disk is out-ofphase with respect to the external field (left inset of Figure 2b). Hence, the currents in the two subunits are mutually out-ofphase, and the global charge configuration arranges into a close circulating mode (central sketch in Figure 2b) (for more details
on the threshold analysis see Supporting Information, section 1). Both the charge current density |Jc⃗ | (Figure 2c) and the electric field enhancement |E⃗ |/|E⃗ 0| (Figure 2d) distributions simulated inside the trimer have been plotted at the Fano resonance. Figure 2d is related to the displacement current density distribution |Jd⃗ |, strongly resonating in the gap regions (in harmonic approximation Jd⃗ ∝ ωFanoE⃗ ). By overlapping |Jc⃗ | and |Jd⃗ | distributions, we obtained a plot of the total charge current distribution (Figure 2e), which corresponds to a coiltype circulating mode inside the trimer. We finally simulated the enhancement of the magnetic field |H⃗ |/|H⃗ 0| induced at the Fano resonance, observing the generation of an intense magnetic hot-spot in the gap region (Figure 2f). The magnetic field enhancement generated by the trimer nanoassembly in the visible/near-infrared window consists in a remarkable result, considering the strong ohmic losses, which affect conduction currents at these spectral regimes. In fact, as shown by Grosjean et al.,25 by increasing the magnetic resonance wavelength from 1 μm to around 2 μm, it is possible to gain 1 order of magnitude in terms of field enhancement, due to the significant reduction of the plasmon internal damping. Because of measurement sensitivity constraints on the optical setup, we fabricated arrays of 50 nm high disk trimers on CaF2(100) substrates via electron beam lithography (EBL) and physical vapor deposition. We fixed the diameter of the lower disks at 160 nm, while the diameter of the upper disk assumed the values 160, 210, 260, 310, and 350 nm. In all cases an interparticle gap of 10 nm was chosen (see SEM images in Figure 3b). Furthermore, the spacing among adjacent trimers
Figure 3. (a,c) Respectively measured and simulated extinction efficiency spectra of trimer arrays for upper disk diameters equal to 160, 210, 260, 310, and 350 nm (from bottom to top). (b) SEM images of single trimer structures for different upper disk diameters (scale bar: 200 nm).
inside the arrays was around 150 nm in the x-direction and 300 nm in the y-direction. In the 350 nm upper disk diameter sample, in order to obtain a densely packed matrix, the spacing in both the directions of the substrate plane was set as 150 nm (see Supporting Information, section 2). The introduction of trimer arrays, with respect to the single trimer system shown in Figure 1b, involves two major implications: (i) the arising of diffractive features that modulate the far-field spectra of the C
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Figure 4. (a) Simulated and measured spectral position of the minima in the extinction efficiency of trimer system as a function of upper disk diameter: black dots are related to the position of the valley between “e” and “q” peaks (electric-like modes), while red dots are related to the position of Fano resonance (coil-type mode). (b) Simulated magnetic field enhancement inside the gap region as a function of the upper disk diameter: black empty dots are related to the local magnetic field evaluated around the valley between “e” and “q” peaks, while red empty dots correspond to the local magnetic field generated around the Fano coil-type resonance. (c,d) Plots of the magnetic field simulated on a plane parallel to the substrate and passing through the center of the system. The local magnetic field is evaluated respectively around the Fano resonance of the 350 nm upper disk diameter trimer (resonant condition) and around the “s” valley of the 160 nm upper disk diameter trimer (no-resonant condition).
single system26 and (ii) a reduction in the measured spectral sharpness due to the convolution among the spectral responses of each array element. This is clearly highlighted by the comparison between the measured and calculated extinction efficiency spectra reported in Figure 3. The samples have been characterized via optical transmission spectroscopy in far-field (normal incidence condition), reporting the associated extinction efficiency spectra in Figure 3a. The black trace spectrum, corresponding to the minimum upper disk diameter (160 nm), presents two clear peaks centered at 1000 nm (first order peak “e”) and 670 nm (high order peak “q”), respectively. By increasing the upper disk diameter we observed the appearance of a dip around 1040 nm, signature of the Fano interference induced by the near-field activation of the dark magnetic mode. A trace of the array diffraction effect can be noticed in the modulations of the purple and green spectra between 600 and 950 nm. We calculated the extinction efficiency spectra of the trimer arrays varying the upper disk diameter (Figure 3c) (for more details on the simulative study, see Supporting Information, section 3), noticing a good agreement with the corresponding experimental data (Figure 3a). By comparing the left and right spectra, we can observe how the convolution effects tend to smooth the modulations of the measured line-shapes with respect to the simulated ones. In order to further confirm the role exerted by the upper disk diameter in defining the threshold for the appearance of a Fano coil-type resonance, we experimentally investigated the minima observed in the spectra for trimer configurations before and after the threshold. Figure 4a shows the spectral positions of the minima extracted from the measured extinction curves of the trimer arrays as a function of the upper disk diameter. A comparison with simulations is also reported. We can notice a red-shift of the valley between “e” and “q” peaks (black dots) from around 800 nm (160 nm diameter) to around 850 nm (260 nm diameter), as a consequence of the increase of the
upper disk diameter (full dots correspond to experimental data and empty dots result from the corresponding simulations). Instead, for diameters larger than 260 nm, the Fano dip clearly appears inside the spectra (red dots), showing a red-shift from 1040 nm (310 nm diameter) to 1140 nm (350 nm diameter) in accordance with the further increase of the upper diameter. In order to provide a finer estimation of the threshold observed in the array spectra, we simulated the far-field response of trimers varying the diameter of the upper disk from 210 to 260 nm at steps of 10 nm. By analyzing the simulative data of Figure 4a, we evaluated the diameter threshold (indicated by the vertical purple band) around 250 nm with an accuracy of 10 nm, close to the reproducibility tolerance of our fabrication technique. The good accordance between experimental and simulative values in Figure 4a is a direct consequence of the agreement between the measured extinction spectra reported in Figure 3a and the corresponding simulated spectra in Figure 3c. In Figure 4b we report the simulated magnetic field enhancement associated with the gap region for the spectral positions considered in Figure 4a. As we can notice, the magnetic field enhancement is close to unity for trimers below the threshold. Instead, after the diameter threshold, the magnetic field enhancement experiences an abrupt increase of around 1 order of magnitude. Such trend denotes the arising of a plasmonic coil-type mode, which was not sustained below the threshold. In order to confirm such interpretation, we reported the simulated magnetic field Hloc inside the trimers with 350 and 160 nm upper disk diameters, in spectral minimum condition. As we observe in Figure 4c, trimers above the threshold present an intense amplification and concentration of magnetic field (resonant condition). Moreover, as shown in section 4 of the Supporting Information, the array effect observed in far-field spectra does not influence significantly the near-field response of the system, both from the spectral and the spatial point of view. Conversely, as shown in Figure 4d, when light impinges D
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trimers illuminated by the light spot, and a represents the area occupied by a single nanoassembly. For a clearer interpretation of the spectra acquired, the optical response of the systems has been simulated by means of a Finite Integration Technique software (CST Studio Suite 2010).
on a trimer with a configuration below the threshold, the only magnetic field observed corresponds to the component carried by the light source (nonresonant conditions). Summary and Conclusion. We were able to induce a Fano coil-type resonance in a planar disk trimer nanoassembly for the generation of intense magnetic hot-spots. Applying a morphological symmetry breaking on the system, we could switch from an electric to a coil-type mode by exploiting dephasing effects between the LSPs. Although the considered spectral range is strongly affected by ohmic dissipation, we could induce an intense magnetic hot-spot taking advantage of the Fano resonance conditions. Such results are particularly remarkable considering that we conducted our study for exciting radiation orthogonal to the substrate and therefore without external magnetic component aligned to the trimer magnetic moment. Finally, the EBL technique adopted for the trimer fabrication can be mainly addressed in order to reproducibly pattern large areas with arrays of metamaterials. By keeping a fine control on the morphological parameters of such nanoassemblies inside high density matrices, it is possible to open encouraging perspectives for several applications in nanophotonics such as superlensing, cloaking, spintronics, and nonlinear spectroscopy. Methods. Fabrication of Nanodisk Trimers. Arrays of nanodisk trimers have been fabricated recurring to EBL nanopatterning technique. After substrate-cleaning in an ultrasonic bath of acetone, polymethylmethacrylate (PMMA) electronic resist has been spin-coated on the CaF2(100) substrate at 1800 rpm. Hence, annealing has been performed at 180 °C for 7 min. An Al layer of 10 nm thickness has been thermally deposited on the PMMA surface. Therefore, EBL machine (electron energy 20 keV and beam current 45 pA), equipped with a pattern generator (Raith 150-Two), has been employed for the nanostructure patterning. Once such procedure was terminated, the Al layer was removed in a KOH solution and then the exposed resist was developed in a conventional solution of MIBK:IPA (1:3) for 30 s. Physical vapor deposition (evaporation rate 0.3 Å/s) respectively of 5 nm Cr as adhesion layer and 45 nm Au has been performed on the sample. Finally, the unexposed resist was removed in ultrasonic bath of acetone and the sample has been rinsed out in IPA. For removing organic residues, O2 plasma ashing at 200 W for 60 s was carried out. Device Modeling and Characterization. The optical properties of the trimer arrays have been analyzed through far-field transmission spectroscopy in a range between 600 and 1700 nm. In order to collect appreciable far-field signals from the plasmonic nanostructures, 50 μm × 50 μm size matrices of nanodisk trimers were patterned on the CaF2(100) substrate, employed for its high transparency in the visible and nearinfrared (vis−NIR) region. During the optical characterization, the samples have been illuminated at normal incidence with a linearly polarized vis−NIR (DH-2000-BAL lamp, Ocean Optics) light spot, performing optical spectroscopy (HR4000, Ocean Optics and Symphony InGaAs-1700 detector coupled to iHR320 spectrometer, Horiba Jobin Yvon). Once collected, each transmission spectrum has been converted into the corresponding extinction efficiency spectrum. Considering the geometrical cross-section of the single trimer defined by its planar area a, the equation that links the measured transmittance T to the extinction efficiency Qext reads Qext = σext/σgeo = A(1 − T)/Na where A parameter consists in the area of the light spot on the sample, N parameter quantifies the number of
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ASSOCIATED CONTENT
S Supporting Information *
Near-field response below the threshold; trimer arrays (SEM images); simulative analysis; local magnetic response in trimer arrays. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*(A.T.) E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Zheludev, N. I.; Kivshar, Y. S. Nat. Mater. 2012, 11, 917−924. (2) Yen, T. J.; Padilla, W. J.; Fang, N.; Vier, D. C.; Smith, D. R.; Pendry, J. B.; Basov, D. N.; Zhang, X. Science 2004, 303, 1494−1496. (3) Shalaev, V. M. Nat. Photonics 2007, 1, 41−48. (4) Luk’yanchuk, B.; Zheludev, N. I.; Maier, S. A.; Halas, N. J.; Nordlander, P.; Giessen, H.; Chong, C. T. Nat. Mater. 2010, 9, 707− 715. (5) Wang, J.; Fan, C.; He, J.; Ding, P.; Liang, E.; Xue, Q. Opt. Express 2013, 21, 2236−2244. (6) Zhou, J.; Koschny, T.; Kafesaki, M.; Economou, E. N.; Pendry, J. B.; Soukoulis, C. M. Phys. Rev. Lett. 2005, 95, 223902. (7) Shafiei, F.; Monticone, F.; Le, K. Q.; Liu, X.-X.; Hartsfield, T.; Alù, A.; Li, X. Nat. Nanotechnol. 2013, 8, 95−99. (8) Sheikholeslami, S. N.; García-Etxarri, A.; Dionne, J. A. Nano Lett. 2011, 11, 3927−3934. (9) Mastel, S.; Grefe, S. E.; Cross, G. B.; Taber, A.; Dhuey, S.; Cabrini, S.; Schuck, P. J.; Abate, Y. Appl. Phys. Lett. 2012, 101, 131102. (10) Das, G.; Patra, N.; Gopalakrishnan, A.; Zaccaria, R. P.; Toma, A.; Thorat, S.; Di Fabrizio, E.; Diaspro, A.; Salerno, M. Analyst 2012, 137, 1785−1792. (11) Habteyes, T. G.; Dhuey, S.; Cabrini, S.; Schuck, P. J.; Leone, S. R. Nano Lett. 2011, 11, 1819−1825. (12) Zaccaria, R. P.; De Angelis, F.; Toma, A.; Razzari, L.; Alabastri, A.; Das, G.; Liberale, C.; Di Fabrizio, E. Opt. Lett. 2012, 37, 545−547. (13) Fan, J. A.; Bao, K.; Wu, C.; Bao, J.; Bardhan, R.; Halas, N. J.; Manoharan, V. N.; Shvets, G.; Nordlander, P.; Capasso, F. Nano Lett. 2010, 10, 4680−4685. (14) Liu, N.; Mukherjee, S.; Bao, K.; Brown, L. V.; Dorfmüller, J.; Nordlander, P.; Halas, N. J. Nano Lett. 2011, 12, 364−369. (15) Liu, N.; Mukherjee, S.; Bao, K.; Li, Y.; Brown, L. V.; Nordlander, P.; Halas, N. J. ACS Nano 2012, 6, 5482−5488. (16) Wen, F.; Ye, J.; Liu, N.; Van Dorpe, P.; Nordlander, P.; Halas, N. J. Nano Lett. 2012, 12, 5020−5026. (17) CST. Computer Simulation Technology; Darmstadt, Germany, 2010. (18) Neubrech, F.; Weber, D.; Katzmann, J.; Huck, C.; Toma, A.; Di Fabrizio, E.; Pucci, A.; Hartling, T. ACS Nano 2012, 6, 7326−7332. (19) Razzari, L.; Toma, A.; Shalaby, M.; Clerici, M.; Zaccaria, R. P.; Liberale, C.; Marras, S.; Al-Naib, I. A. I.; Das, G.; De Angelis, F.; Peccianti, M.; Falqui, A.; Ozaki, T.; Morandotti, R.; Di Fabrizio, E. Opt. Express 2011, 19, 26088−26094. (20) Panaro, S.; Toma, A.; Proietti Zaccaria, R.; Chirumamilla, M.; Saeed, A.; Razzari, L.; Das, G.; Liberale, C.; De Angelis, F.; Di Fabrizio, E. Microelectron. Eng. 2013, 111, 91−95. (21) D’Andrea, C.; Bochterle, J.; Toma, A.; Huck, C.; Neubrech, F.; Messina, E.; Fazio, B.; Maragò, O. M.; Di Fabrizio, E.; Lamy de La E
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Chapelle, M.; Gucciardi, P. G.; Pucci, A. ACS Nano 2013, 7, 3522− 3531. (22) Bohren, C. F.; Huffman, D. R. Absorption and Scattering of Light by Small Particles; Wiley: New York, 1983. (23) Aizpurua, J.; Bryant, G. W.; Richter, L. J.; García de Abajo, F. J.; Kelley, B. K.; Mallouk, T. Phys. Rev. B 2005, 71, 235420. (24) Lassiter, J. B.; Sobhani, H.; Knight, M. W.; Mielczarek, W. S.; Nordlander, P.; Halas, N. J. Nano Lett. 2012, 12, 1058−1062. (25) Grosjean, T.; Mivelle, M.; Baida, F. I.; Burr, G. W.; Fischer, U. C. Nano Lett. 2011, 11, 1009−1013. (26) Auguié, B.; Barnes, W. L. Phys. Rev. Lett. 2008, 101, 143902.
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Fano Coil-Type Resonance for Magnetic Hot-Spot Generation A. Nazir,†,‡ S. Panaro,†,‡ R. Proietti Zaccaria,† C. Liberale,† F. De Angelis,† and A. Toma*,† †
Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genova, Italy Università degli Studi di Genova, 16145 Genova, Italy
‡
S Supporting Information *
ABSTRACT: The possibility to develop nanosystems with appreciable magnetic response at optical frequencies has been a matter of intense study in the past few years. This aim was strongly hindered by the saturation of the magnetic response of “natural” materials beyond the THz regime. Recently, in order to overcome such limitation, it has been considered to enhance the magnetic fields through the induction of displacement currents triggered by plasmonic resonances. Here we investigate a nanoassembly supporting the hybridization of an electric and magnetic plasmonic mode in Fano resonance conditions. Taking advantage of the enhancement properties owned by such interferential resonance, we have been able to generate an intense and localized magnetic hot-spot in the near-infrared spectral region. KEYWORDS: Localized surface plasmon, Fano resonance, dark mode, magnetic hot-spot, electron beam lithography
S
Results and Discussion. We initially designed three gold disks (160 nm diameter) in triangular arrangement and performed both near- and far-field simulations under normally incident plane wave excitation.17 In order to obtain an efficient coupling between radiation and nanostructures, the polarization of light has been chosen parallel to the line connecting the centers of two disks (sketch in the bottom of Figure 1a). In such optical configuration we calculated the extinction efficiency spectrum of the trimer system (black curve in Figure 1b), observing an intense peak at 1000 nm, labeled “e”, and a high order peak around 700 nm, labeled “q”. From the current density plot related to the main peak “e”, we could ascribe the resonance to an electric mode involving both the lower disk dimer and the upper disk (Figure 1c). In such system the free charges inside the disks oscillate in-phase, inducing a net electric dipole parallel to the substrate plane (indicated by the vector p⃗e in Figure 1c).18−21 Differently, the peak “q” is related to a multipolar11,22 behavior, verified from the current density plot of Figure 1e. The modes corresponding to “e” and “q” show well distinct peaks spectrally separated by a pronounced valley indicated with “s” in the black curve of Figure 1b. By considering the global arrangement of charge current densities, we can associate both “e” and “q” modes to localized surface plasmons (LSPs) of electric nature. In order to generate a resonant magnetic dipole inside the system, we induced a phase retardation between the LSPs supported by the trimer. For such a reason, we gradually increased the upper disk diameter (Figure 1a from bottom to top) reporting the
everal efforts have been recently spent in the investigation of “artificial magnetic” resonances, inducing negative refractive index in metamaterials.1−4 One attempt in such direction consisted in the fabrication of split ring resonators, which can support circulating currents up to few hundreds of terahertz.5 Nevertheless, the promotion of coil-type modes at optical frequencies is still challenging, due to the saturation of the magnetic response in “natural” materials.6 A way recently found for overcoming such difficulty consists in exchanging usual conduction currents, affected by strong ohmic losses, with displacement currents induced by plasmonic resonances.7,8 In fact, by arranging metallic nanostructures in close proximity to one another, it is possible to promote resonating displacement currents in the interparticle gap regions.9,10 Moreover, the introduction of symmetry breaking8,11,12 into these systems can induce the hybridization of bright electric and dark magnetic modes in Fano resonant conditions13−15 with consequent current intensification.4 Within this context, an essential point to be considered is the geometry of the involved plasmonic devices. In fact, it can be shown how the conventional electric field hot-spots do not present a comparable magnetic counterpart (magnetic field enhancement factor close to 1). The excitation of effective magnetic hot-spots requires dedicated plasmonic devices,14−16 able to support close circulating current modes instead of linearly oscillating plasmons. In order to obtain a coil-type mode, we conceived a planar disk trimer system supporting a close current resonance. We simulated and fabricated this nanoassembly, demonstrating how a morphological symmetry breaking can promote the hybridization of electric and magnetic modes. © XXXX American Chemical Society
Received: February 4, 2014 Revised: May 12, 2014
A
dx.doi.org/10.1021/nl500452p | Nano Lett. XXXX, XXX, XXX−XXX
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Letter
Figure 1. (a) Sketches of the considered trimer geometries (the diameter of the small dimer disks is 160 nm and the diameters of the upper disks are 160, 210, 260, 310, and 350 nm, respectively). (b) Simulated extinction efficiency spectra of single trimers for different upper disk diameters. (c,d) Two-dimensional charge current density plots evaluated on a plane parallel to the substrate passing through the center of the structure: the plots identify an electric mode in the 160 nm trimer and a coil-type mode in the 350 nm trimer, respectively. (e−h) Two-dimensional charge current density plots showing the current distributions induced inside the trimer systems, respectively, in “q” and “s” position (see black curve in panel b) and in “e↑” and “e↓” position (see green curve in panel b). The plots represent electric-like modes. (i) Plot reporting both the extinction efficiency spectrum (green continuous line) of 350 nm diameter trimer and the H field (evaluated at the center of the cavity) generated by such trimer as a function of wavelength (red dot curve): the spectral matching between the Fano resonance and the maximum of H field is highlighted by the vertical purple band.
Figure 2. (a) Simulated extinction efficiency spectra of single disks for diameters 160, 210, 260, 310, and 350 nm, respectively, and extinction efficiency spectrum of 160 nm diameter disk dimer (dashed line). (b) Simulated extinction efficiency spectra of 350 nm diameter disk (green dashed line), of 160 nm diameter disk dimer (yellow dashed line), and of the corresponding trimer (green continuous line) (left/right inset: phase (θ) relationship between external electric field and charge current density in the high/low energy side of single disk/dimer structure). (c−f) Twodimensional plots of conduction current density (Jc⃗ ), electric field enhancement (local electric field E⃗ normalized to the incoming electric field E⃗ 0), total charge current density (conduction plus displacement current (Jc⃗ + Jd⃗ )), and magnetic field enhancement (local magnetic field H⃗ normalized to the incoming magnetic field H⃗ 0), respectively, generated on a plane parallel to the substrate, passing through the center of the structure, under Fano resonance conditions.
extinction curves, the spectrum corresponding to the 260 nm diameter configuration (blue trace) shows a particular lineshape evolution as illustrated by the appearance of a dip around 1000 nm. By further increasing the size of the upper disk, the
corresponding evolution of the extinction efficiency spectra in Figure 1b. The morphological modification induces a red-shift of the extinction spectrum, in accordance to the red-shift of the upper disk resonance.23 In addition to the general shift of the B
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“m” valley gradually deepened as shown by the pink and green curves in Figure 1b. In order to better understand this behavior, we calculated and compared the charge current density in correspondence to the “s” and “m” spectral positions for the minimum (160 nm) and maximum (350 nm) disk sizes, respectively. While in the “s” valley the charge distributions oscillate in phase, but in out-of-resonance condition (Figure 1f), we can notice how in the “m” case the system responds to a normal incident plane wave mainly by the excitation of a planar coil-type resonance, which can be associated with a magnetic dipole perpendicular to the substrate (indicated by the vector “p⃗m” in Figure 1d). Furthermore, by considering the charge arrangements induced immediately in the high and low energy sides of the “m” dip (extinction peaks labeled respectively “e↑” and “e↓” in the green curve of Figure 1b), we could notice how the currents inside the disks present a dominant electric response (Figures 1g,h), which recalls the behavior of the “e” mode (Figure 1c). Finally, in Figure 1i we plotted the spectral response of the magnetic field associated with Figure 1d, overlapped to the extinction efficiency spectrum of the corresponding system (green curve in Figure 1b). By observing how the maximum of H field enhancement (ratio between actual and the incoming magnetic fields) matches to the minimum of the extinction curve (see vertical purple band), it is possible to attribute the sharp dip (“m” mode) to a Fano resonance7,24 that results from the interference between the spectrally broad electric resonance (“e” mode) with a narrow magnetic mode, which is dark in this optical configuration. Such observations confirm that the coil-type mode induced in Fano condition is a resonant phenomenon characterized by a minimum in the extinction efficiency spectrum. In order to better understand how the “m” mode can be excited and to find a threshold for its activation, we analyzed the resonance of the upper disk as a function of its diameter. Choosing the dipolar resonance of the lower disk dimer as spectral reference (dashed curve in Figure 2a), we plotted the extinction resonance peaks related to the upper disk for increasing diameters (Figure 2a). Since the extinction dip “m” was found starting from the blue line spectrum of Figure 1b, we observed that the Fano interference arises when the LSP resonance of the upper disk is in the low energy side of the dimer resonance (see the blue, pink, and green curves in Figure 2a). Such observation defines a precise threshold for the size of the upper disk, beyond which the system starts to exhibit a coiltype mode (Figure 1d). The reason for such transition has to be searched in the phase relationship between the dipolar mode in the disk dimer and the LSP in the upper disk. We considered the case of the 350 nm diameter (Figure 2b), plotting both the lower dimer (yellow dashed trace) and the upper disk (green dashed trace) spectra. In the same graph we also plotted the extinction spectrum of the corresponding trimer assembly (green continuous trace). As we could appreciate, the Fano resonance occurs in the overlapping region between the low energy tail of the dimer peak (cyan area under the dimer curve) and the high energy tail of the single disk peak (red area under the single disk curve). In such region the charge current density J ⃗ inside the dimer is in-phase with the external electric field E⃗ 0 (right inset of Figure 2b), while the current in the single disk is out-ofphase with respect to the external field (left inset of Figure 2b). Hence, the currents in the two subunits are mutually out-ofphase, and the global charge configuration arranges into a close circulating mode (central sketch in Figure 2b) (for more details
on the threshold analysis see Supporting Information, section 1). Both the charge current density |Jc⃗ | (Figure 2c) and the electric field enhancement |E⃗ |/|E⃗ 0| (Figure 2d) distributions simulated inside the trimer have been plotted at the Fano resonance. Figure 2d is related to the displacement current density distribution |Jd⃗ |, strongly resonating in the gap regions (in harmonic approximation Jd⃗ ∝ ωFanoE⃗ ). By overlapping |Jc⃗ | and |Jd⃗ | distributions, we obtained a plot of the total charge current distribution (Figure 2e), which corresponds to a coiltype circulating mode inside the trimer. We finally simulated the enhancement of the magnetic field |H⃗ |/|H⃗ 0| induced at the Fano resonance, observing the generation of an intense magnetic hot-spot in the gap region (Figure 2f). The magnetic field enhancement generated by the trimer nanoassembly in the visible/near-infrared window consists in a remarkable result, considering the strong ohmic losses, which affect conduction currents at these spectral regimes. In fact, as shown by Grosjean et al.,25 by increasing the magnetic resonance wavelength from 1 μm to around 2 μm, it is possible to gain 1 order of magnitude in terms of field enhancement, due to the significant reduction of the plasmon internal damping. Because of measurement sensitivity constraints on the optical setup, we fabricated arrays of 50 nm high disk trimers on CaF2(100) substrates via electron beam lithography (EBL) and physical vapor deposition. We fixed the diameter of the lower disks at 160 nm, while the diameter of the upper disk assumed the values 160, 210, 260, 310, and 350 nm. In all cases an interparticle gap of 10 nm was chosen (see SEM images in Figure 3b). Furthermore, the spacing among adjacent trimers
Figure 3. (a,c) Respectively measured and simulated extinction efficiency spectra of trimer arrays for upper disk diameters equal to 160, 210, 260, 310, and 350 nm (from bottom to top). (b) SEM images of single trimer structures for different upper disk diameters (scale bar: 200 nm).
inside the arrays was around 150 nm in the x-direction and 300 nm in the y-direction. In the 350 nm upper disk diameter sample, in order to obtain a densely packed matrix, the spacing in both the directions of the substrate plane was set as 150 nm (see Supporting Information, section 2). The introduction of trimer arrays, with respect to the single trimer system shown in Figure 1b, involves two major implications: (i) the arising of diffractive features that modulate the far-field spectra of the C
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Figure 4. (a) Simulated and measured spectral position of the minima in the extinction efficiency of trimer system as a function of upper disk diameter: black dots are related to the position of the valley between “e” and “q” peaks (electric-like modes), while red dots are related to the position of Fano resonance (coil-type mode). (b) Simulated magnetic field enhancement inside the gap region as a function of the upper disk diameter: black empty dots are related to the local magnetic field evaluated around the valley between “e” and “q” peaks, while red empty dots correspond to the local magnetic field generated around the Fano coil-type resonance. (c,d) Plots of the magnetic field simulated on a plane parallel to the substrate and passing through the center of the system. The local magnetic field is evaluated respectively around the Fano resonance of the 350 nm upper disk diameter trimer (resonant condition) and around the “s” valley of the 160 nm upper disk diameter trimer (no-resonant condition).
single system26 and (ii) a reduction in the measured spectral sharpness due to the convolution among the spectral responses of each array element. This is clearly highlighted by the comparison between the measured and calculated extinction efficiency spectra reported in Figure 3. The samples have been characterized via optical transmission spectroscopy in far-field (normal incidence condition), reporting the associated extinction efficiency spectra in Figure 3a. The black trace spectrum, corresponding to the minimum upper disk diameter (160 nm), presents two clear peaks centered at 1000 nm (first order peak “e”) and 670 nm (high order peak “q”), respectively. By increasing the upper disk diameter we observed the appearance of a dip around 1040 nm, signature of the Fano interference induced by the near-field activation of the dark magnetic mode. A trace of the array diffraction effect can be noticed in the modulations of the purple and green spectra between 600 and 950 nm. We calculated the extinction efficiency spectra of the trimer arrays varying the upper disk diameter (Figure 3c) (for more details on the simulative study, see Supporting Information, section 3), noticing a good agreement with the corresponding experimental data (Figure 3a). By comparing the left and right spectra, we can observe how the convolution effects tend to smooth the modulations of the measured line-shapes with respect to the simulated ones. In order to further confirm the role exerted by the upper disk diameter in defining the threshold for the appearance of a Fano coil-type resonance, we experimentally investigated the minima observed in the spectra for trimer configurations before and after the threshold. Figure 4a shows the spectral positions of the minima extracted from the measured extinction curves of the trimer arrays as a function of the upper disk diameter. A comparison with simulations is also reported. We can notice a red-shift of the valley between “e” and “q” peaks (black dots) from around 800 nm (160 nm diameter) to around 850 nm (260 nm diameter), as a consequence of the increase of the
upper disk diameter (full dots correspond to experimental data and empty dots result from the corresponding simulations). Instead, for diameters larger than 260 nm, the Fano dip clearly appears inside the spectra (red dots), showing a red-shift from 1040 nm (310 nm diameter) to 1140 nm (350 nm diameter) in accordance with the further increase of the upper diameter. In order to provide a finer estimation of the threshold observed in the array spectra, we simulated the far-field response of trimers varying the diameter of the upper disk from 210 to 260 nm at steps of 10 nm. By analyzing the simulative data of Figure 4a, we evaluated the diameter threshold (indicated by the vertical purple band) around 250 nm with an accuracy of 10 nm, close to the reproducibility tolerance of our fabrication technique. The good accordance between experimental and simulative values in Figure 4a is a direct consequence of the agreement between the measured extinction spectra reported in Figure 3a and the corresponding simulated spectra in Figure 3c. In Figure 4b we report the simulated magnetic field enhancement associated with the gap region for the spectral positions considered in Figure 4a. As we can notice, the magnetic field enhancement is close to unity for trimers below the threshold. Instead, after the diameter threshold, the magnetic field enhancement experiences an abrupt increase of around 1 order of magnitude. Such trend denotes the arising of a plasmonic coil-type mode, which was not sustained below the threshold. In order to confirm such interpretation, we reported the simulated magnetic field Hloc inside the trimers with 350 and 160 nm upper disk diameters, in spectral minimum condition. As we observe in Figure 4c, trimers above the threshold present an intense amplification and concentration of magnetic field (resonant condition). Moreover, as shown in section 4 of the Supporting Information, the array effect observed in far-field spectra does not influence significantly the near-field response of the system, both from the spectral and the spatial point of view. Conversely, as shown in Figure 4d, when light impinges D
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trimers illuminated by the light spot, and a represents the area occupied by a single nanoassembly. For a clearer interpretation of the spectra acquired, the optical response of the systems has been simulated by means of a Finite Integration Technique software (CST Studio Suite 2010).
on a trimer with a configuration below the threshold, the only magnetic field observed corresponds to the component carried by the light source (nonresonant conditions). Summary and Conclusion. We were able to induce a Fano coil-type resonance in a planar disk trimer nanoassembly for the generation of intense magnetic hot-spots. Applying a morphological symmetry breaking on the system, we could switch from an electric to a coil-type mode by exploiting dephasing effects between the LSPs. Although the considered spectral range is strongly affected by ohmic dissipation, we could induce an intense magnetic hot-spot taking advantage of the Fano resonance conditions. Such results are particularly remarkable considering that we conducted our study for exciting radiation orthogonal to the substrate and therefore without external magnetic component aligned to the trimer magnetic moment. Finally, the EBL technique adopted for the trimer fabrication can be mainly addressed in order to reproducibly pattern large areas with arrays of metamaterials. By keeping a fine control on the morphological parameters of such nanoassemblies inside high density matrices, it is possible to open encouraging perspectives for several applications in nanophotonics such as superlensing, cloaking, spintronics, and nonlinear spectroscopy. Methods. Fabrication of Nanodisk Trimers. Arrays of nanodisk trimers have been fabricated recurring to EBL nanopatterning technique. After substrate-cleaning in an ultrasonic bath of acetone, polymethylmethacrylate (PMMA) electronic resist has been spin-coated on the CaF2(100) substrate at 1800 rpm. Hence, annealing has been performed at 180 °C for 7 min. An Al layer of 10 nm thickness has been thermally deposited on the PMMA surface. Therefore, EBL machine (electron energy 20 keV and beam current 45 pA), equipped with a pattern generator (Raith 150-Two), has been employed for the nanostructure patterning. Once such procedure was terminated, the Al layer was removed in a KOH solution and then the exposed resist was developed in a conventional solution of MIBK:IPA (1:3) for 30 s. Physical vapor deposition (evaporation rate 0.3 Å/s) respectively of 5 nm Cr as adhesion layer and 45 nm Au has been performed on the sample. Finally, the unexposed resist was removed in ultrasonic bath of acetone and the sample has been rinsed out in IPA. For removing organic residues, O2 plasma ashing at 200 W for 60 s was carried out. Device Modeling and Characterization. The optical properties of the trimer arrays have been analyzed through far-field transmission spectroscopy in a range between 600 and 1700 nm. In order to collect appreciable far-field signals from the plasmonic nanostructures, 50 μm × 50 μm size matrices of nanodisk trimers were patterned on the CaF2(100) substrate, employed for its high transparency in the visible and nearinfrared (vis−NIR) region. During the optical characterization, the samples have been illuminated at normal incidence with a linearly polarized vis−NIR (DH-2000-BAL lamp, Ocean Optics) light spot, performing optical spectroscopy (HR4000, Ocean Optics and Symphony InGaAs-1700 detector coupled to iHR320 spectrometer, Horiba Jobin Yvon). Once collected, each transmission spectrum has been converted into the corresponding extinction efficiency spectrum. Considering the geometrical cross-section of the single trimer defined by its planar area a, the equation that links the measured transmittance T to the extinction efficiency Qext reads Qext = σext/σgeo = A(1 − T)/Na where A parameter consists in the area of the light spot on the sample, N parameter quantifies the number of
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ASSOCIATED CONTENT
S Supporting Information *
Near-field response below the threshold; trimer arrays (SEM images); simulative analysis; local magnetic response in trimer arrays. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*(A.T.) E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
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