pubs.acs.org/NanoLett
Resonant Plasmon Nanofocusing by Closed Tapered Gaps Thomas Søndergaard,† Sergey I. Bozhevolnyi,‡,* Jonas Beermann,‡ Sergey M. Novikov,‡ Eloı¨se Devaux,§ and Thomas W. Ebbesen§ †
Department of Physics and Nanotechnology, Aalborg University, Skjernvej 4A, DK-9220 Aalborg Øst, Denmark, Institute of Sensors, Signals and Electrotechnics (SENSE), University of Southern Denmark, Niels Bohrs Alle´ 1, DK-5230 Odense M, Denmark, and § ISIS, CNRS UMR 7006, Universite´ Louis Pasteur, 8 alle´e Monge, BP 70028, 67083 Strasbourg, France ‡
ABSTRACT We study radiation nanofocusing by closed tapered gaps, i.e. metal V-grooves, under normal illumination, and discover that the local field inside a groove can be resonantly enhanced due to interference of counter-propagating gap plasmons. Considering V-grooves milled in gold, we analyze this phenomenon theoretically, deriving an analytic expression for the resonance condition and predicting more than 550-fold intensity enhancements at resonance, and observe it experimentally with two-photon photoluminescence microscopy, demonstrating more than 100-fold intensity enhancements. KEYWORDS Surface plasmons, nanofocusing, field enhancement, nonlinear optics, plasmonics
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broad wavelength range and discover the phenomenon of resonant field enhancement occurring due to interference of counter-propagating gap SP (GSP) modes, bouncing between the groove bottom and opening. We study this phenomenon theoretically, deriving an analytic expression for the resonance condition, and experimentally with linear reflection spectroscopy and two-photon induced luminescence (TPL) microscopy,18 demonstrating more than 100fold intensity enhancements. Our analysis of resonant nanofocusing is based on simulations conducted for V-grooves milled in gold and illuminated from above (Figure 1a), by making use of the Green’s function surface integral equation method.19 In the following, only p-polarized (the magnetic field is parallel to the V-groove axis) light is considered, since s-polarized light experiences cutoff with respect to the groove width and cannot propagate until the groove bottom (and no significant local field enhancements was found in the considered parameter range). In the calculations, all corners are rounded with 2 nm radii to avoid field singularities and linear interpolation of experimental dielectric constants for gold20 is used. For all system parameters, the strongest local electric field was found close to the groove bottom, and we have chosen the height of 24 nm above the groove tip for the characterization of field enhancement effects. In general, the position of field maximum is gradually moving away from the groove tip for longer wavelengths with this height being a good compromise in the considered wavelength range. The wavelength dependencies of field enhancement calculated in a broad wavelength range (500-1500 nm) for subµm- and µm deep grooves with different angles reveal immediately their resonant behavior (Figures 1b,c). Careful inspection of these dependencies has shown that an increase
adiation nanofocusing, that is, concentrating electromagnetic fields well below the diffraction limit, is one of the most fundamental, yet rich with prospective applications, research directions in plasmonics. Nanofocusing can be realized by utilizing suitable surface plasmon (SP) modes supported by metal waveguides,1 that is, the SP modes persisting to exist even in the limit of infinitely small waveguide cross sections and scaling down in size linearly with that of the waveguide. Various configurations have been suggested for SP nanofocusing,2-7 all supporting progressively stronger confined SP modes when tapering down waveguides, and several experimental demonstrations of SP nanofocusing have been reported.8-11 While the choice of a particular nanofocusing configuration might be dictated by a specific application,12,13 tapered gaps2,5 were theoretically shown to be promising for realization of significant field enhancements.14 Recently, an appreciable field intensity enhancement (∼10) was experimentallyobtainedwithgoldV-groovessqueezingtheradiation at telecom wavelengths through a subwavelength (∼λ/40) slit at the groove bottom.10 In general, optimization of nanofocusing configuration requires dealing with rather complicated issues, such as balancing between SP propagation losses (that increase for smaller waveguide cross sections and longer tapers), SP reflections by taper walls (that increase for larger taper angles) and focusing effects.14-16 Here we consider radiation nanofocusing by relatively shallow V-grooves (which can be readily fabricated by focused ion beam milling17) under normal illumination in a
* To whom correspondence should be addressed. E-mail address: seib@sense. sdu.dk. Received for review: 10/24/2009 Published on Web: 12/22/2009 © 2010 American Chemical Society
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DOI: 10.1021/nl903563e | Nano Lett. 2010, 10, 291-295
FIGURE 2. Calculated normalized field magnitude distributions at resonant wavelengths (Figure 1b) as indicated on images for two 20° angle grooves with depths h ) (a,b) 200 and (c,e,f) 700 nm. The distributions show the resonant GSP standing-wave patterns of different orders, m ) (a) 1, (b,c) 2, (e) 3 and (f) 4. For comparison, a nonresonant field distribution is shown in (d) for h ) 700 nm.
wave patterns of various orders increasing for shorter wavelengths (Figure 2). The fact that the resonance order can be increased by decreasing the groove angle (Figure 1c) confirms directly the participation of GSPs, because the GSP propagation constant increases for smaller gaps. The standing-wave patterns bear close resemblance to resonant acoustic standing-wave patterns in closed pipes, with the fundamental difference being that GSP standing-wave patterns feature depth-dependent spatial periods due to the dependence of GSP propagation constant (and thereby the GSP wavelength) on the gap width. Away from resonance, an interference pattern formed by the incident and reflected GSPs is still observed but the resultant field magnitudes are weaker (Figure 2d). To get further insight in the phenomenon of resonant GSP nanofocusing, we have calculated the field enhancement spectra similar to those shown in Figure 1b for a wide range of depths h of V-grooves with the same groove angle θ ) 20°. The resulting (λ,h) distribution of the field enhancement displays resonance branches corresponding to the formation of GSP standing-wave patterns of different orders (Figure 3). The resonance branches being well separated for relatively shallow V-grooves decrease in contrast for deeper grooves indicating transition to the conventional regime of GSP nanofocusing2,5,14 with the GSP reflected at the groove opening becoming progressively weaker due to weaker reflection for wider gaps21 (since the reflectivity of uncoupled SPs is very low) and stronger attenuation (due to longer propagation). Assuming that the GSP reflection occurs very close to the groove bottom where variations in the GSP
FIGURE 1. (a) Geometry of the considered configuration. Field enhancement calculated at the groove bottom as a function of light wavelength for (b) various depths of 20° angle grooves and (c) various angles of 1500 nm deep grooves.
in the groove depth (see curves for depths of 1200, 1300, 1400, and 1500 nm in Figure 1b) and/or a decrease in the groove angle (see curves for angles of 20, 16, and 14° in Figure 1c) results in a gradual shift of resonant peaks toward longer wavelengths and, after a certain change, in an appearance of a new peak at g600 nm. The fact that the shortest resonant wavelength can be found only at the wavelengths close to 600 nm indicates that the occurrence of resonance is related to propagating SP modes, since their propagation loss (for gold-air interface) increases drastically for shorter (550. Even stronger resonant enhancement effects are expected to occur in silver V-grooves illuminated at shorter wavelengths (Figure 6). Finally, we believe that the phenomenon of resonant nanofocusing is not limited to the case of closed tapered gaps, that is, V-grooves, under normal illumination, but can also be found with other nanofocusing configurations (e.g., with tapered metal rods16) under realistic condi-
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DOI: 10.1021/nl903563e | Nano Lett. 2010, 10, 291-295
