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2 Laser & Photon. Rev. 3, No. 6, (2009) / DOI /lpor Abstract The explosive progress in nanoscience has led to uncovering and exploring numerous physical phenomena occurring at nanoscale, especially when metal nanostructures are involved so that optical fields and electronic oscillations can be resonantly coupled. The latter is the subject of (nano) plasmonics with implications extending from subwavelength waveguiding to localized field enhancements. In this review paper, we consider making use of various phenomena related to multiple scattering of surface plasmons (SPs) at periodically and randomly (nano) structured metal surfaces. After reviewing the SP waveguiding along channels in nanostructured areas exhibiting band-gap and localization effects, SP-driven field enhancement in random structures and plasmonic fractal drums is discussed in detail. SP manipulation and waveguiding using periodic nanostructures on the long-wavelength side of the band gap is also considered. A collage showing excitation and interaction of surface plasmons with fractal and waveguiding metallic nanostructures. Plasmonic metasurfaces for waveguiding and field enhancement Ilya P. Radko 1,*, Valentyn S. Volkov 1, Jonas Beermann 1, Andrey B. Evlyukhin 2, Thomas Søndergaard 3, Alexandra Boltasseva 4, and Sergey I. Bozhevolnyi 1 1 Institute of Sensors, Signals and Electrotechnics, University of Southern Denmark, 5230 Odense M, Denmark 2 Kama State Academy of Engineering and Economics, Naberezhnye Chelny, Russian Federation 3 Department of Physics and Nanotechnology, Aalborg University, 9220 Aalborg Øst, Denmark 4 School of Electrical and Computer Engineering, Purdue University, Birck Nanotechnology Center, West Lafayette, IN 47907, USA Received: 16 November 2008, Revised: 14 December 2008, Accepted: 18 December 2008 Published online: 16 January 2009 Key words: Surface plasmons, waveguides, field enhancement, band gap, random structures, localization, fractals, axicon, bessel beams. PACS: Qs, Pw, Mf, Bf, c 1. Introduction Surface plasmon polaritons, or surface plasmons (SPs) for breviety, are electromagnetic modes bound to a metaldielectric interface, comprising an electromagnetic field in dielectric (primarily transverse) coupled to coherent surface oscillations of free electrons in metal (driving a primarily longitudinal electromagnetic field). The existence of electromagnetic surface modes associated with the coherent electron oscillations at a metal surface has been demonstrated long time ago using electron energy-loss spectroscopy on metal films [1, 2]. However, it was not until the last decade that the interest to SPs greatly increased [3, 4] due to the development of nanofabrication techniques such as electron-beam lithography (EBL), ion-beam milling and self-assembly, together with modern nanocharacterization techniques such as dark-field and near-field optical microscopies and the emergence of quantitative electromagnetic simulation tools. There is a variety of techniques to excite SPs, for instance, using an electric current [5, 6] or thermal excitation [7], but the most widely used ones are based on a direct coupling of propagating electromagnetic waves into SP modes using various configurations and geometries for achieving the phase-matching between the corresponding fields [8]. For the long-wavelength part of the visible spec- * Corresponding author: ilr@sense.sdu.dk

3 576 I. P. Radko, V. S. Volkov, et al.: Plasmonic metasurfaces trum and the infrared, SPs are quite close to the light line, i.e., the SP wavelength is close to that of propagating (in dielectric) radiation. However, modifying the geometry of a metal surface one can slow down the corresponding SP mode and hence decrease its wavelength. This can be done by placing two or more metal-dielectric interfaces close to each other, which introduces the coupling between the SPs of individual interfaces and modifies the appropriate resulting SP mode [9 11]. Once achieved a large difference in the wavelengths of SP and radiation modes makes accessible two very attractive phenomena, namely subwavelength (relative to the radiation) waveguiding and (local) field enhancement in nm-sized volumes with obvious applications in nano-photonics and sensing [3, 12 16]. One of the main attractive features inherent to SP modes of a single metal-dielectric interface is their distinctive spatial distribution due to the fact that SP fields decay exponentially into both media and reach their maximum at the interface. This circumstance makes SP modes extremely sensitive to surface properties, in particular, to surface corrugations and heterogeneous structures. In this review we present various approaches to realization of SP waveguiding and field enhancement effects via multiple SP scattering at periodically and randomly nanostructured metal surfaces. The associated SP scattering phenomena, including bandgap and localization effects, can be related to variations in the effective refractive index (ERI) of SP induced within nanostructured areas, which thereby act as plasmonic metasurfaces. 2. Waveguiding in nanostructures exhibiting SP band-gap and localization effects There are two widely used designs to guide electromagnetic waves along a line: metallic pipe waveguides for microwaves and dielectric guides for infrared and visible light. Bends of conventional dielectric guides are restricted to moderate curvature by radiation losses, since their operation principle relies on total internal reflection. In fact, the radius of curvature must well exceed the wavelength of the light even for high dielectric contrasts to avoid large losses at the corners [17]. Dielectric structures consisting of regions of periodically modulated (in space) refractive index are called photonic crystals [18], and can modify and even eliminate the density of electromagnetic states inside the structure [19, 20], forming photonic band gap (PBG). It was shown that a linear defect in a PBG material can support a linearly localized mode when the mode frequency falls inside the gap [21]. Such a defect can act as a waveguide for electromagnetic waves, without relying on total internal reflection. As a consequence, a PBG waveguide can efficiently guide light around corners. The losses are very low for a wide range of frequencies, and vanish for specific frequencies, even if the radius of curvature of the bend is on the order of one wavelength [22]. Most of plasmonics waveguiding structures have predecessors in integrated optics and, in particular, among Figure 1 (online color at: Numerical results for electric field magnitude distributions of a Gaussian SP beam hitting (from the left) a ΓM-oriented triangular lattice (period = 475 nm) of nanoparticles (height = 60 nm, width = 136 nm) obtained at different wavelengths: a) 720 nm, b) 800 nm, c) 840 nm. Images show the surface area of μm 2. d) Wavelength dependence of the SP penetration depth into the structure estimated from the calculated field distributions. photonic-crystal components. After the demonstration of the complete band-gap effect for SPs [23], it was suggested (similarly to photonic crystals) to employ SP band-gap (SPBG) structures for plasmonic circuits and SP guiding along line defects in SPBG structures was shown experimentally [24]. Numerical simulations of a Gaussian SP beam hitting a set of metal cylindrical scatterers arranged in a 475-nm-period triangular lattice (ΓM orientation of the irreducible Brillouin zone) exhibit a band gap of the width 90 nm (Fig. 1) [25]. The SP penetration depth into the structure is more than three times suppressed for the wavelengths falling inside the band gap (Figs. 1b,d). This shows the efficiency of SPBG structures and their possible application for the purpose of waveguiding. However, the realization of plasmonic circuitry requires, no less importantly, the realization of bending of waveguids. There exist two solutions based on SPBG structures: bent line defect in a regular SPBG structure (Fig. 2a) and adiabatically rotated SPBG structure containing straight line defect (Fig. 2b). A random (disordered) medium can be viewed as an antipode of a periodic (ordered) medium. However, interference in multiple scattering of light in random nanostructured media can reveal strong (Anderson) localization, which has many features in common with SPBG effect. Both are transport phenomena that result in the inhibition of light propagation (in the absence of absorption)

4 Laser & Photon. Rev. 3, No. 6 (2009) 577 Figure 2 (online color at: a) Scanning electron microscope (SEM) image of a 2- μm-wide Y junction in a periodic triangular lattice of nanoparticles of ΓM orientation (for SP propagating from left to the right). The image is 30 tilted. b) Design of a 2-μm-wide line defect cut through a ΓMoriented triangular lattice of nanoparticles. The periodic lattice is 30 adiabatically rotated (along with the line defect). The radius of curvature of the bend is 32 μm. c,d) SEM images of areas filled with randomly located nanoparticles with a density of c) 50 μm 2 and d) 75 μm 2. manifesting itself as an exponential dependence of light transmission upon the medium thickness. The SPBG effect occurs in a limited wavelength interval, when the periodicity of dielectric constant modulation in a medium matches half of the light wavelength (at least for some directions), leading essentially to Bragg reflection of light incident on the medium. Strong localization of light happens due to recurrent multiple scattering in a random (nonabsorbing) medium and is expected when Ioffe-Regel criterion is satisfied, i.e., when kl =2πl/λ 1, where l is the (elastic) scattering mean free path and lambda is the light wavelength. The product kl diverges in the limit of both short (kl 1/λ) and long (kl λ 3 ) wavelengths [26] ending in the same feature, i.e., strong localization takes place in a limited wavelength interval. Furthermore, in both cases, variations of the medium dielectric constant should be large enough to realize sufficiently strong multiple scattering of light, i.e., both phenomena exhibit a threshold character with respect to the dielectric contrast. It should be noted that the threshold is noticeably higher for strong localization (since the interference effects are less effective in a random medium) making its direct observation quite a challenging task [27]. Given the similarities between the phenomenon of strong localization and the SPBG effect, one should be able to employ channels and cavities in (nonabsorbing) strongly scattering random media for essentially the same purposes as those in the SPBG structures. The fact that, in two dimensions, light is localized with any degree of disorder [28] makes the idea of using (quasi-) two-dimensional (2D) electromagnetic waves, e.g., planar waveguide modes or SPs, in random structures especially appealing. One might suggest that the localization can be realized in a broader wavelength range than the SPBG effect, since the former is not as directly governed by the geometrical characteristics of structured media as the latter. Furthermore, the absence of symmetry in random structures facilitates matching the modes propagating in differently oriented channels and, thereby, may reduce the associated bend loss. Two random media with the density of 50-nmwide scatterers of n 1 = 50 μm 1 (sample N1, Fig. 2c) and n 2 = 75 μm 1 (sample N2, Fig. 2d) are considered for the purpose of waveguiding. Since SPs are quasi-2d electromagnetic waves bound to the metal-dielectric interface [29], the most universal method for their investigation is scanning near-field optical microscopy (SNOM). A typical experimental setup (Fig. 3) consists of a SNOM probe scanned above the surface and an arrangement for SP excitation in Kretschmann configuration. The p polarized (the electric field is in the plane of incidence) light beam from a laser is weakly focused Figure 3 (online color at: Schematics of the scanning near-field optical microscope (SNOM) for investigation of SPs excited in Kretschmann configuration. An arrangement for far-field preliminary observation is also present.

5 578 I. P. Radko, V. S. Volkov, et al.: Plasmonic metasurfaces Figure 4 (online color at: Investigation of waveguiding along a 2-μm-wide Y-splitting line defect cut through a periodic structure. The structure is formed with nanoparticles arranged in a triangular lattice having ΓM orientation relative to the SP propagating upwards in the vertical direction. a c) SNOM topographical and d f) optical images of the structure. The half angle of the Y splitter is a,d) 10, b,e) 20, and c,f) 30. (spot size 300 μm) from below onto the sample attached with an immersion oil to the base of a glass prism. There is also an arrangement, which allows for far-field observation of the sample for the preliminary adjustment of the position and size of the focal spot from the laser. Fabrication of surface nanostructures involves EBL. The resist layer coating the gold film is exposed to an electron beam at the places where surface corrugations are needed. The resist development is then followed by evaporation of a second gold film and liftoff, resulting in gold protrusions (on top of the gold film) at the exposed places. nm-thick gold film. The period of the lattice is 410 nm, so that the fill factor is 0.3. The efficient SP guiding along the straight part of the line defect (before the Y junction) in the SPBG structure is observed in the wavelength range nm with the best near-field optical image obtained at λ = 737 nm (Figs. 4d f). It is seen that the SP intensity is strongly damped inside the SPBG structure, whereas the defect mode maintains its amplitude during the propagation in the structure. The first feature is explained by the fact that the SP propagation inside the periodically corrugated surface region is inhibited for light wavelengths corresponding to the SPBG. The second feature indicates that the propagation constant of the defect mode is close to that of the SP and, therefore, the mode power loss due to the damping and scattering can be compensated by the coupling from the incident laser beam (adjusted to excite the SP outside the SPBG structure). The confinement of the defect mode and SP damping inside the periodic structure gradually deteriorates with the decrease and increase of the light wavelength (not shown), thus providing clear and direct evidence of the SPBG effect in the structure. The intensity of the defect mode is damped after the first bend, as expected. Note, however, that after the second bend it is increased again. This is due to the fact that the defect mode running along the channel (after the double bend) that is parallel to the input one gains its power from the incident laser beam. Cross sections of the near-field optical images show that the mode profile is preserved during and after guiding around the bends (with the mode half width at the 1/e 2 level of intensity being 2 μm). This circumstance allows one to estimate the bend loss by simply relating the maximums of the mode intensity profiles made before and after the Y junction. Thus, the total (i.e. including the SP propagation and splitting) loss is found to increase with the increasing split angle from 3 db for 10 bend up to 8 db and 11 db for 20 and 30 bends, respectively. Note that for double bends (without splitting) these losses would be roughly two times smaller [30]. The attained loss level indicates that the waveguide circuits in the SPPBG structures having relatively large (tens of degrees) bend angles can be realized with relatively small (< 10 db) losses, allowing for a good integration level Regular SPBG structures The possibility of SP guiding along line bent defects (bent channels) in SPBG structures is investigated [30] with Y splitters cut through a periodic triangular lattice of metal scatterers deposited on top of a metal film. The fabricated surface structure has ΓM orientation of the irreducible Brillouin zone of the lattice with respect to the direction of the 2-μm-wide waveguide terminating with a Y junction (Fig. 2a). The half angle of the Y junction is 10,20, and 30 for three different waveguides (Figs. 4a c). The lattice of the SPBG structure is composed of 200-nm-wide and 45-nm-high gold nanoparticles deposited on top of a Adiabatically rotated SPBG structures Experimental [30, 31] and theoretical [32 34] studies of SPBG structures indicated that the main concern in the context of efficient SPBG waveguiding, in particular, low-loss bending for relatively large angles, is related to the problem of simultaneous realization of the full SPBG, i.e., the band gap for all in-plane directions of SP propagation, which turned out to be a challenging task [31, 34]. It appears that the main obstacle is the difference in the locations of the band gaps for two main orientations (i.e., ΓK and ΓM) of a SPBG structure: the band gap in ΓM direction is markedly shifted towards shorter wavelengths [31, 32]. It

6 Laser & Photon. Rev. 3, No. 6 (2009) 579 Figure 5 (online color at: Simulated electric field magnitude distributions of a Gaussian SP beam hitting (from the left) an adiabatically rotated ΓM-oriented triangular lattice (period = 475 nm) of nanoparticles (height = 60 nm, width = 172 nm) with a 2-μm-wide channel cut through the structure (as shown in Fig. 2b). Images show the surface area of μm 2 and are obtained at different wavelengths: a) 720 nm, b) 800 nm, c) 840 nm. d) Estimated transmission of the optical signal through the waveguide plotted versus the wavelength. should be noted though that their positions are expected to strongly depend on the dimensions of surface scatterers [32, 33], implying thereby the possibility for further improvement of SP guiding and bending by use of the SPBG structures. However, there is another way to deal with the problem of simultaneous realization of the full SPBG. One can adiabatically rotate the lattice of the periodic structure together with the bent channel in such a way that the orientation of the plasmonic crystal remains the same relative to the channel (Fig. 2b). This technique is applied to SPBG structures in the form of 475-nm-period triangular lattices arranged to have ΓM orientation relative to the 2-μm-wide line defect [25]. Numerical simulations (using Lippmann- Schwinger integral equation method [34]) of a Gaussian SP beam propagating through this structure demonstrate its guiding capability (Fig. 5). The size of the metal bumps forming the lattice is larger in these calculations than that used in simulations of the band-gap effect shown in Fig. 1. This gives broader band gap [34], and a reasonable waveguiding can be obtained already at the wavelength of 720 nm, which is supported experimentally below. However, the best guiding provided by this structure is expected at the wavelength of 840 nm, which roughly falls into the band-gap interval. The SP transmission through the bent waveguide (in percent) versus the wavelength (Fig. 5d) features a clear peak around this wavelength. The further increase in the transmission at longer wavelengths is due to the SP propagation (and scattering) directly through the structure for the wavelengths being on the long-wavelength side of the SPBG. It should be borne in mind that the transmission shown in Fig. 5d was estimated by averaging the field intensity in a small box placed at the exit of the bend and normalizing with the intensity of the incident SP, and reflects thereby not only the SP bend and propagation loss (in the channel) but also the coupling loss. The latter loss channel is difficult (though not impossible) to evaluate as it depends upon the overlap between the incident SP field and the SP mode field sustained by the channel [34]. Checking the above results experimentally, we fabricated two different lattices (samples A and B) formed by 133- and 166-nm-wide gold bumps of the height 60 nm, which are deposited on 60-nm-thick gold film. These two widths are chosen to emulate the shape and volume of the bumps used in simulations shown in Fig. 1 and Fig. 5, respectively. The SPBG structures are 30 adiabatically rotated with the radius of curvature being 32 μm. For a triangular lattice with square bumps, the filling factor is obtained by f = 2a2 p 2, where a is the side of the square 3 bump and p is the period of the lattice. This gives the filling factors of 0.1 and 0.14 for structures A and B, respectively. The interaction of SP with the periodic structure A is investigated in the wavelength range nm. The SP is excited globally at an area covering the structure completely, and propagates from left to the right in Fig. 6. By taking profiles in the near-field optical images (marked by the white bar in Fig. 6b) inside the SPBG structure, the dependence of the SP penetration depth on the wavelength is investigated (Fig. 6c). One can observe a clear band gap phenomenon at the wavelength around 770 nm. Note that the inhibition of SP propagation inside the structure is decreased after the bend. This is related to the change of the lattice orientation from ΓM to ΓK with respect to the SP (since the lattice is 30 rotated) and to the difference in the locations of the band gaps for these two orientations. One should note that the SNOM images are not directly comparable with Figs. 1 and 5 because the whole SPBG structure was illuminated from the side of the silica substrate (global illumination) in the experiment, resulting in the background radiation produced by scattered field components. Such a background sets a limit on the smallest SNOM signal measured at the SPBG structure influencing thereby the evaluation of the SP penetration depth, especially at the position of the SPBG. The filling factor of the structure A appears to be insufficient for the waveguiding of the defect mode around the bend. In fact, the signal drops down drastically with the lattice being rotated. Numerical simulations show that increasing the fill factor of the lattice should broaden the band gap while keeping its center approximately fixed [34]. Indeed, it is possible to observe efficient waveguiding of the defect mode around the bend for the structure B (Fig. 6d). It is important to note that the mode field sustained by the bent waveguide cannot be excited or replenished from below with the global illumination used here, because being directed perpendicular to the input interface of the SPBG structure, the laser illumination is parallel to the bent channel only at its input.

7 580 I. P. Radko, V. S. Volkov, et al.: Plasmonic metasurfaces Figure 6 (online color at: Investigation of the waveguiding along a 2-μm-wide line defect cut through a periodic SPBG structure adiabatically rotated. The rotation is accomplished so that the ΓM orientation of the triangular lattice (relative to the propagation direction of the defect mode) is preserved before and after the 30 bend. a c) Investigation of the band-gap effect: a) SNOM topographical and b) optical (λ = 825 nm) images of the structure, and c) experimental and numerical (same as in Fig. 1d) wavelength dependence of the SP penetration depth (from left to the right) into the structure filled with 133-nm-wide square bumps. No waveguiding was observed. d f) Demonstration of the waveguiding (from left to the right) in the structure filled with 166-nm-wide square bumps: d) SNOM optical image (λ = 713 nm) and profiles taken e) across (at different distances from the entrance) and f) along the waveguide. The positions of the transverse profiles shown in e) are denoted with the corresponding numbers in f). An increase in the longitudinal mode profile in f) can be related to the fact that, after the bend, the triangular lattice has ΓK orientation relative to the globally excited SP (since the grating is 30 rotated). Therefore, the inhibition of SP propagation into the array might be decreased, resulting in SP penetration into the channel. Several profiles taken across the channel (some of them are shown in Fig. 6e) show that the mode profile is preserved during the propagation. The maximums of the mode intensity profiles plotted versus the distance of the considered point from the entrance (along the waveguide) are found to decrease exponentially with the distance (Fig. 6f). The fitting results in the defect mode propagation length being equal to 4.4 μm, which is equivalent to the propagation loss of 1 db/μm. Note that the SP propagation length evaluated at the same wavelength (713 nm) for the same gold film thickness (60 nm) is 17 μm (for gold-air interface), which corresponds to loss of 0.26 db/μm. The measured propagation loss is substantial, but might be acceptable for some practical applications in which the main requirement is the small size of the components used rather than insertion losses. An opposite example could be long-rage SP stripe waveguides, which exhibit rather low bend loss but require very large (mm-sized) radii of curvature [35]. This precludes their usage in compact devices Random surface nanostructures As already mentioned earlier, random surface nanostructures might be a good alternative to SPBG structures, since the absence of symmetry in random structures facilitates matching the modes propagating in differently oriented channels [36, 37]. The pronounced effect of SP guiding along the corrugation-free channels was observed with sample N1 (Fig. 2c) in the wavelength range nm. The near-field optical image obtained at λ = 738 nm (Fig. 7b) shows a complete damping of the incident SP inside the random structures and unhindered SP propagation along the 4-μm-wide channel. The 2-μm-wide channel also supports SP propagation, even though its excitation efficiency (by the incident plane SP) is relatively small. Note that, if the propagation constant of a SP channel mode is sufficiently different from that of the (plane) SP, the channel mode cannot be excited with an incident laser beam adjusted to excite the SP outside the random structure. In this case, it will decay as a result of absorption and radiative damping, similarly to the SP defect modes observed in SPBG structures. If the propagation constant turns out to be close to that of the SP, one should expect the channel mode to maintain its amplitude while propagating in the region illuminated with the incident laser beam. One may suggest that (in the wavelength range nm) the channel mode for the 2-μm-wide channel is close to the former case, whereas that for the 4-μm-wide channel is close to the latter. SP guiding along the channels and attenuation inside the random structure gradually deteriorated with the increase in the light wavelength (Fig. 7c), and SP damping became

8 Laser & Photon. Rev. 3, No. 6 (2009) 581 rather weak at λ = 833 nm (Fig. 7d). Such wavelength dependence can be accounted for by the fact that the scattering mean free path l increases with the wavelength because of the decrease (for subwavelength-sized scatterers) in the scattering cross-section σ(λ) since l 1/(nσ). The increase in l leads in turn to an exponential increase in the penetration depth or localization length ξ, ξ l exp(2πl/λ). Implying the usual convention for the intensity attenuation, I(x) =I 0 exp( 2x/ξ) and taking average cross sections of optical images (obtained at different wavelengths), it is found that the localization length increases from 7 μm at the wavelength of 730 nm to 25 μm atλ = 850 nm. Note that the scattering mean free path (and therefore the localization length) can be decreased by increasing the density n of scatterers and, at least in the approximation of small scatterers, their sizes [38]. Similar investigations are carried out with the sample N2 whose scatterers are higher (70 vs. 45 nm) and their densities are larger (n 2 =1.5n 1 ) than those of the sample N1. The SNOM images obtained in the whole laser tunability range exhibit quite discernible effects of SP attenuation inside the random structures and the SP guiding along the 2-μm-wide channels, both effects being especially pronounced in the wavelength range nm (Figs. 8a f). The observed improvement of the SP guiding characteristics is explained by the increase in the scattering cross-section (due to the increase in the scatterers height and density) resulting in a decrease in the scattering mean free path and, thereby, in the localization length. The localization length for different light wavelengths is determined from the SNOM images using the procedure described above. The experimental dependence ξ(λ) is then fitted with the expected one for 2D scattering (σ λ 3 ) at short wavelengths, with the scattering mean free path l being the only fitting parameter (Fig. 8g). It is seen that in the experiment the localization length increases faster with the wavelength than it is expected. One of the reasons for that might be related to the increase of the SP propagation length changing (for a 55-nm-thick gold film on glass) from 16 μm at λ = 730 nm to 36 μm at λ = 830 nm. Evaluation of the propagation loss (over a distance of 10 μm) in the straight and 20 -bent channels of the sample N2 shows that a relatively low bend loss is expected in the wavelength interval nm (Fig. 8h). Note that, similar to the situation with sample N1, the seeming loss for the straight waveguide can be rather small if the propagation constant of the SP channel mode is sufficiently close to that of the (resonantly excited) plane SP. Direct evaluation of the propagation loss is possible only with the local excitation of the SP (see for instance [39]) or if the channel direction is sufficiently different from the direction of the excited SP, e.g. after the bend. Figure 8 (online color at: a) Random nanostructure consisting of 70-nm-high and 50-nm-wide gold bumps deposited (with the density of 75 μm -2 ) on top of a 55-nm-thick gold film. Three channels of 2-μm-wide (straight, 10 and 20 bends with radius of curvature of 15 μm) free of scatterers are left for waveguiding. Near-field optical images recorded at b) 713 nm, c) 750 nm, d) 785 nm, e) 815 nm, f) 855 nm. SPs are excited globally from below to propagate upwards in the vertical direction. g) Localization length inside the structure vs. wavelength. h) Propagation loss for straight and bent channels vs. wavelength.

9 582 I. P. Radko, V. S. Volkov, et al.: Plasmonic metasurfaces Figure 7 (online color at: a) SNOM topographical image of a random nanostructure consisting of 45-nmhigh and 50-nm-wide gold bumps deposited (with the density of 50 μm -2 ) on top of a 45-nm-thick gold film. Two channels of 2- and 4-μm-wide free of scatterers are left for waveguiding. Near-field optical images recorded at b) 738 nm, c) 785 nm, and d) 850 nm. SPs are excited globally from below to propagate upwards in the vertical direction. 3. Periodic nanostructures on the long-wavelength side of the band gap There are a number of elements to change the usual SP propagating behavior. The use of SPBG structures described earlier or Bragg-grating effect [40], although flexible and suitable for many applications, suffers from considerable out-of-plane scattering [34]. Another elegant method for controlling the SP propagation is borrowed from conventional optics. It consists in introducing dielectric elements of higher refractive index to define a spatial change in the optical path length [41]. The possibility of effective subwavelength SP waveguiding in such structures has recently been demonstrated at both near-infrared [42] and telecom [43] wavelengths. A 2D array of metal nanoparticles on a silicon membrane is able to sustain SP modes with an increased ERI (relative to the flat-surface SP mode) due to the modified dispersion property of the propagating plasmon [44]. This technique does not control the propagating behavior of the excited SP mode, but facilitates excitation of the mode with a silica fiber by matching their ERIs. Combining the two latter techniques, it is possible to create optical elements for SPs which would possess refracting, focusing and waveguiding properties. A 100-nmperiod square lattice of gold nanoparticles (height = 50 nm, width = 60 nm) on top of a gold film can be used to form variously shaped structures. The SP waves propagating along the surface inside the periodic arrays experience an increase in the ERI with respect to that of a flat-surface SP [45]. In this case, since the period is considerably smaller than the wavelength, the out-of-plane scattering is considerably weaker than for SPBG structures [46]. The refracting property of a nanoparticle array is demonstrated [47] with a triangular-shaped structure (Fig. 9a). One can see that passing through the triangular array of bumps, the SP beam is declined towards the base of that structure (Fig. 9c) as it happens with a light beam passing through a glass prism. Comparison with the propagation direction of the reference SP beam (not being Figure 9 (online color at: Investigation of periodic nanostructures on the long-wavelength side of the band gap. a) SEM image of a triangular-shaped 100-nm-period square lattice of 50-nm-high and 60-nm-wide gold bumps on top of a 50-nm-thick gold film. On the left there is a gold ridge for SP excitation. SP beam propagating b) along a smooth gold film and c) through the periodic structure shown in panel a) recorded at the wavelength of 800 nm. Focusing of SP beam by a 7.5-μm-diameter circular-shaped periodic structure [same parameters as in a)] recorded at the wavelength of d) 730 nm, e) 800 nm, and f) 860 nm.

10 Laser & Photon. Rev. 3, No. 6 (2009) 583 Figure 10 (online color at: Waveguiding using periodic nanostructures on the long-wavelength side of the band gap. a) Free-propagating SP beam, which was then used to couple into various funnel waveguides composed of periodic array of nanoparticles (same parameters as in Fig. 9a) and shown by the white contour line in b f). The funnel region is an equilateral triangle with the side length of 10 μm. The total length of each waveguide (including the funnel region) is 25 μm. Waveguiding through the b) 1-μm-wide, c) 3-μm-wide, and d f) 5-μm-wide funnel waveguides. e) and f) demonstrate that the 5-μm-wide waveguide is multimode: when the incident SP beam is coupled e) below or f) above the center of the funnel, the outgoing from the waveguide SP beam is deflected [compare with d)]. perturbed by any structure) (Fig. 9b) readily gives the deflection angle of 4.7, which corresponds to the value of ERI of the structure being equal to n Note that leakage radiation microscopy (LRM) was used to obtain the images shown here. This technique [48 50], in contrast to SNOM, gives classical resolution limited by a half of the light wavelength. The use of LRM is the reason why the SP beam is poorly visible inside the periodic structure. This is due to the array of bumps, which makes the average gold layer in that area thicker and thus the leakage of SPP power into the substrate (where it is collected by an objective) lower. Experiments with 7.5-μm-diameter circular-shaped array demonstrate the focusing property of the structure (Fig. 9d), as well as the wavelength dispersion with the highest ERI corresponding to the lowest wavelength (Figs. 9d f). The following values of ERI have been estimated from the analysis of the images [47]: n =1.10 at 730 nm, n =1.09 at 800 nm, and n =1.08 at 860 nm. This is sufficient to create functional waveguides with the periodic lattice being the core and the outer region (with smaller ERI, n =1) being the cladding of the waveguide. A simple estimation for this possibility can be given by determining the V -parameter (normalized frequency) of the planar waveguide and by comparing this parameter with the dispersion curves [51]. In our case of propagating SPs, the V -parameter is defined as follows: V = kd(n 2 1 n 2 2) 1/2 kd 2n 2 Δn, where k is the propagation constant of SP at a flat surface, d is the waveguide width, n 1 and n 2 are the effective refractive indices of the waveguide and the outer region, respectively. With n 2 being 1 and Δn being 0.08, one gets V =2.98 for a 1-μm-wide planar waveguide at the free-space wavelength λ = 860 nm, which is enough to have one guided mode [51] with about 83% of power concentrated inside the waveguide [52]. Three structures of one (Fig. 10b), three (Fig. 10c), and five microns width (Fig. 10d) prove the possibility of SP waveguiding evidenced by the SP beam coming out of the channel. The 25-μm-long structures start with a funnel region to facilitate coupling of a rather divergent plasmon signal (Fig. 10a). Note that though the 3- and 5-μm-wide structures are multimode, only the first mode is excited with the symmetrical illumination of the waveguide entrance, since the overlap integral with the second mode (and all the following ones) is zero. However, with asymmetric illumination one observes the excitation of higher order modes (Figs. 10e,f, cf. with Fig. 10d). Outcoupling of these modes at the exit of the waveguide produces SP beams propagating straight and slightly to the side. Qualitative comparison of Figs. 10a and 10d (adjusted to the same color contrast) reveals that the waveguides formed by periodic arrays of nanoparticles do not introduce substantial insertion losses into the SP signal. Further investigations of bent waveguides might show a promising potential of such structures. 4. Plasmonic fractal drums for field enhancement One of the research directions in nano-optics is the search for configurations that efficiently interconvert propagating (μm-sized) and strongly localized (nm-sized) optical fields resulting thereby in strongly enhanced local fields, which are indispensable for optical characterization, sensing and manipulation at nanoscale [53]. Resonant interactions in metal nanostructures involving both localized

11 584 I. P. Radko, V. S. Volkov, et al.: Plasmonic metasurfaces and propagating surface plasmons (SPs) have been intensively investigated using nanostructures of different shapes and configurations, ranging from individual pointed particles [54, 55] to their pairs [56 58] and periodic [59] and random [60, 61] ensembles. Insofar these structures represent either well-defined regular configurations exhibiting resonant field enhancements at one or several wavelengths [55 59] or irregular random nanostructures featuring (spatially separated) resonant excitations covering a wide spectrum range [60, 61]. The latter, although being very attractive for specific applications requiring resonant responses in a broad wavelength range, are difficult to reproduce due to their random nature. This is the situation where fractal-shaped periodic arrangements of nanoparticles can leverage the advantages of both configurations: the ease of reproduction guaranteed by the regularity of the structure and the randomness of the shape at any scale, the fundamental fractal property [62]. Investigation of such structures involves far-field nonlinear scanning optical microscopy, in which two-photon luminescence (TPL) from metal [63, 64] excited with a strongly focused laser beam is detected [59]. Spatially resolved TPL studies [65] and near-field imaging [66] have been lately used for characterization of local field enhancement. The structure chosen for investigation [67] is a small part of the Mandelbrot fractal [62] (Fig. 11a) filled with 60-nm-wide and 50-nm-high gold particles arranged in a 100-nm-period square lattice on top of a smooth 50-nmthick gold film (Fig. 11b). The whole structure is produced using EBL. Note the self-similarity of the fractal structure (cf. Figs. 11a and b) featuring nanoparticle clusters of practically all possible shapes within the available spatial range (from 100 nm to 100 μm). The fundamental harmonic (FH) image obtained in the cross-polarized configuration (Fig. 11c) replicates well (with the diffraction-limited resolution) the shape of fractal structure (Fig. 11a). The center fractal areas having the largest density of nanoparticles exhibit the strongest (depolarized) scattering and appear brighter in the FH image. On the other hand, the TPL image (Fig. 11d) only weakly indicates the fractal shape displaying instead several bright spots distributed inside the fractal structure. It should be noted that, for an incident power of less than 1.2 mw, the maximum TPL signal was measured being close to cps, which is one order of magnitude larger than that obtained with the random gold nanostructures [61, 68]. The use of TPL scanning optical microscopy for characterization of the local-field enhancement (for the incident FH radiation) in gold nanostructures can be considered well established [57 59]. Influence of the FH wavelength and polarization on the location of bright spots in the TPL images (Fig. 12) can be related to the occurrence of resonant (multiple) scattering of SPs within the structure boundaries. As was shown in Sect. 3, the SP waves (excited due to scattering of the tightly focused FH beam by nanoparticles) propagating along the surface inside a periodic array of nanoparticles experience an increase in the effective refractive index and, for the array periods considerably smaller than the wavelength, relatively weak out-of-plane scattering [46]. It is then reasonable to assume that fractalshaped boundaries of the structure would partially reflect and diffract incident SPs, forming thereby cavities that could be resonant at practically any wavelength. The corresponding physics is quite similar to that found with socalled fractal drums for which high-order modes localized to very small areas occur due to constructive interference of waves reflected and diffracted by a fractal-shaped boundary [69]. In our case, the bright TPL spots can be related to spatially localized eigenmodes at the FH frequency excited via incident radiation scattering off nanoparticles. Different wavelengths and/or polarizations of the incident FH radiation lead to the excitation of different FH eigenmodes (cf. Figs. 12a c and e). On the other hand, the TPL images obtained for different polarizations of the detected TPL radiation are, understandably, very similar (cf. Figs. 12c f). Small differences can be explained by the circumstance that the TPL radiation originating from the locations of FH field enhancements (bright spots) interacts also with the immediate scattering environment that can influence the process of TPL scattering in the reflection direction (toward its detection). Figure 11 (online color at: a) The entire geometry ( μm 2 ) of the Mandelbrot-fractal structure. The blue rectangle indicates the area shown in Fig. 12. The red square indicates the origin of b) a detailed SEM image of the corresponding area. The structure consists of 60-nm-wide gold bumps arranged in a 100-nm-period square lattice. The optical c) FH and d) TPL images of the structure obtained using 730 nm excitation wavelength and the polarization configurations indicated by a pair (incident FH, detection) of colored arrows on the images. The maximum TPL signal in d) was 12 kcps obtained at 1.2 mw of incident power.

12 Laser & Photon. Rev. 3, No. 6 (2009) Figure 12 (online color at: Merged TPL and SEM images of a μm2 area in the center of the fractal structure (indicated by the blue rectangle in Fig. 11a) exhibiting a c) wavelength dependence in the wavelength interval nm and c f) polarization dependence shown at 790 nm. The maximum TPL signal is a) 12, b) 4.6, c) 7.4, d) 3.0, e) 2.4, and f) 5.0 kcps. Quantitative evaluation of field intensity enhancements can be carried out by comparing TPL signals from bright spots within the nanostructure to that from a smooth gold film [57 59]. Following this approach the intensity enhancement factor χ from the fractal shape can be found using the relation 2 TPLfrac Pfilm Afilm χ2 =, (1) 2 TPLfilm Pfrac Afrac where TPL is the obtained TPL signal, P is the used average incident power, and A is the area producing the enhancement. Here Afilm is taken as the focus area estimated to at least π(0.4 μm)2, while we estimate Afrac by viewing the merged TPL and SEM images to find the number of gold nanoparticles located within each bright TPL spot. Using calibrated TPL signals obtained from smooth gold film regions, the TPL enhancement factors of up to 150 is estimated for various bright spots observed at different configurations of wavelength and polarization [67, 70]. However, it should be borne in mind that the (far-field) TPL images are diffraction limited so that, in fact, the TPL signal might possibly originate from much smaller areas Figure 13 (online color at: Simulated [a,c,e,g)] and experimental [b,d,f,h)] TPL images ( μm2 ) obtained at the outer part of the fractal structure seen in Fig. 11b and merged with either the designed geometry or the corresponding SEM images, respectively. The TPL images were obtained for the wavelengths and polarization combinations indicated on the images and show simulated TPL intensity enhancements of a,e,g) 220 and c) 45, compared to experimental values of b) 145, d) 30, f) 117, and h) 41. localized between only a few of the nanoparticles resulting in the significantly larger enhancement. At the less dense outer branches of the fractal shaped structure, where the periodic lattice is reduced to only a sparse distribution of fewer particles, it is possible to use a numerical approach to simulate TPL scanning optical microscopy from the exact configuration of particle positions as defined for the EBL fabrication (Fig. 13). We used total Green s tensor formalism with a dipole approximation for multiple SP scattering by nanoparticles [32, 71, 72], which proved previously to be reliable and giving a good agreement with experimental results [47]. Both numerical and experimental TPL bright spots exhibit a very strong wavelength and polarization dependence, although there seems to be no obvious connection between the geometry and obtained TPL spots [70]. However, it is still very interesting that nanostructures designed with a fixed lattice period and particle size do show multiple sharp resonances simply due to the lattice boundaries and internal particles missing with respect to the completely filled lattice. Note that, as observed, one should probably not expect the numerical and experimental results to resemble exactly the same distribution of TPL bright spots, since just minor defects in

13 586 I. P. Radko, V. S. Volkov, et al.: Plasmonic metasurfaces the EBL-fabricated sample can have a significant effect on the multiple scattering in the system of nanoparticles. With the use of a point-dipole approximation to simulate the field distribution at the particle locations, one of the possible ways of estimating the intensity enhancement factor obtained in the simulation could be by comparing the calculated maximum TPL intensity Ifractal TPL from the fractal-shaped structure to a reference TPL intensity Iparticle TPL obtained from a single individual particle, with all other parameters fixed, i.e., χ 2 = ITPL fractal Iparticle TPL. (2) In this way, the simulated bright spots appearing in Fig. 13 can be evaluated to intensity enhancements in the range χ 220, which turns out to be in good qualitative agreement with experimentally obtained enhancements levels. Note the strong polarization dependence of enhancement and locations of bright spots observed in both the simulated and experimental images (Figs. 13a and c versus Figs. 13b and d). Being able to qualitatively simulate the levels of TPL enhancement obtainable from asymmetric and less ordered structures (compared to previously FDTD investigated periodic square arrays [59]) can be very useful. 5. Plasmonic axicons for divergent-free SP beams In integrated optics (photonics, plasmonics), waveguiding implies transmission of a laterally confined optical signal, with an acceptable level of losses, preserving its original mode profile. This is only possible in a specially designed waveguides, because any field initially confined to a finite area in a transverse plane will be subject to diffractive spreading as it propagates outward from that plane in free space. Therefore propagation of a plane wave is not considered to be a waveguiding nor is propagation of a Gaussian beam, since the former is not confined and the latter is divergent. On the other hand, there is a class of diffraction-free mode solutions of the Helmholtz equation, which describe well defined beams with narrow beam radii [73, 74]. Those beams exist in free space in the absence of boundaries, guiding surfaces or nonlinear media. The central spot radius can be extremely narrow, on the order of one wavelength, without being subject to diffractive spreading. The simplest non-spreading beam has a transverse field-amplitude profile defined by the zeroth-order Bessel function of the first kind [74]. Of course, this field cannot be truly diffractionless unless unlimited in transverse extent. However, a comparison of equally confined Bessel and Gaussian beams having the same spot size in the origin plane gives a dramatic advantage of the former both in the on-axis intensity and in the beam diameter, at least within certain (reasonable) interval of propagation [74, 75]. The use of such beams showed already promising in optical micromanipulation of tiny particles [76,77]. Regarding Figure 14 (online color at: Numerical simulations illustrating the production of Bessel SP beams. a) and c) show Gaussian SP beams with a) 5-μm-radius and c) 15-μmradius waist. b) and d) show the refraction of the corresponding Gaussian beams with an isosceles-triangle prism (2D axicon) indicated by a gray area. the transmission of optical fields, Bessel beams might help, for instance, in delivery of a SP signal towards testing specimen (for Raman spectroscopy) without the use of waveguides. Fortunately, production of Bessel beams is relatively easy [74, 78]. One can use an axicon (conical lens) [79] illuminated with a plane wave. For the 2D analogy to be used in SP circuitry, a Bessel beam can be obtained by refracting a plane SP wave with an isosceles-triangle prism, which has its base oriented towards ongoing wavefront. It was demonstrated in Sect. 3 that periodic nanostructures on the long-wavelength side of the band gap possess increased ERI for SPs propagating through. This allows constructing SP prisms (axicons) by corrugating the metal surface (Figs. 9a,c). To illustrate the advantage of Bessel beams, we show here numerical simulations of SP waves refracted by an isosceles-triangle prism with the base angle of 1/6 radian. Parameters of the periodic structure are the same as those presented in Sect. 3. Instead of a plane SP wave, two Gaussian SP beams with the waist radius of 5 and 15 μm (feasible in the experiment) are used. As in Sect. 4, we employ here numerical simulations based on total Green s tensor formalism with a point-dipole approximation for multiple SP scattering by nanoparticles. Comparison of the Gaussian SP beam with the waist radius of 5 μm (Fig. 14a) and the same beam refracted with

14 Laser & Photon. Rev. 3, No. 6 (2009) 587 the axicon (Fig. 14b) shows that the Bessel beam is narrower: full width at half maximum is 4.9 μm at the distance of 40 μm from the origin plane versus 6.5 μm for the Gaussian beam. Unfortunately, with the numerical method used, the absolute values of intensity are not comparable between images (fitting with the experimental data is needed), but the relative distribution of that within one image is correct. Thus, the drop of intensity along the propagation distance of 40 μm is found to be 2.0 times for the Bessel beam versus 2.6 times for the Gaussian beam. The Gaussian beam with the waist radius of 5 μm is a very rough approximation of a plane wave, which is required to obtain the true Bessel beam. Therefore, similar comparison of the Gaussian beam with the waist radius of 15 μm (Fig. 14c) and that refracted with the axicon (Fig. 14d) is accomplished. In this case, the size of the axicon base (of 18 μm) seems insufficient, and hence the two side beams accompanying the central one appear (Fig. 14d). Nevertheless, there is an advantage in the drop of intensity (1.7 times for the Bessel beam versus 2.4 for the Gaussian beam along the propagation distance of 40 μm) and in the full width at 1/1.6 maximum of intensity (9.5 μm for the Bessel beam versus 14 μm for the Gaussian beam at the distance of 40 μm from the origin plane). The presented simulations are only preliminary and illustrative. They show that the advantage of using SP Bessel beams can be achieved. However, for striking effects similar to those demonstrated with light [74], a search of appropriate parameters of the axicon and the incident beam is required. 6. Conclusions By nanostructuring metal surfaces one can tailor their properties so that the SP multiple scattering occurring inside the structured areas would lead to various useful effects, among which are compact SP waveguiding and local field enhancements. Considering pure waveguiding characteristics, there is a general trade-off between the size of the components and losses that they introduce into the circuit. In this respect, plasmonic waveguides that can ensure the sub-wavelength waveguiding [39,80 86] are probably the most promising for future applications. However, it should be borne in mind that SP waveguiding nanostructures might be found useful in routing of SPs from the point of their efficient excitation towards field-enhancing structures or between any other plasmon-based devices in order to avoid multiple inter-conversions between light and SPs. Note that rather efficient approaches to the SP excitation [87] as well as to the SP out-coupling with subsequent tight (diffractionlimited) focusing [88] were very recently developed. At the same time, the use of nanostructured metal surfaces for field enhancement effects is one of the most promising applications in plasmonics. Combining localized SP resonances of individual metal nanoparticles [89] with the multiple SP scattering phenomena described in this paper, one can realize efficient SP resonances in a wide wavelength range, achieving highly localized (nm-sized) and strongly enhanced electromagnetic fields. Furthermore, the design of a complete surface structure can be complemented with introducing SP waveguiding, in- and outcoupling components, opening exciting perspectives for practical applications within bio- and molecular sensing, e.g. via the development of lab-on-chip concept. Acknowledgements The authors gratefully acknowledge financial support from the Danish Research Council (contract No ) and from the NABIIT project financed by the Danish Research Agency (contract No ). A. B. Evlyukhin is grateful to the Russian Foundation for Basic Research (project No ) for the support. Ilya P. Radko, born in 1981, is a postdoctoral researcher at the Institute of Sensors, Signals and Electrotechnics (SENSE), University of Southern Denmark. He received the M. Sc. degree (in applied mathematics and physics) from Moscow Institute of Physics and Technology in From 2005 to 2008 he was a Ph. D. student at the Department of Physics and Nanotechnology, Aalborg University (Denmark), where his research was focused on development of components for plasmonics and integrated optics using near-field scanning optical microscopy and leakage radiation microscopy. Valentyn S. Volkov, born in 1977, is an Assistant Professor at the Institute of Sensors, Signals and Electrotechnics (SENSE), University of Southern Denmark. He received the M. Sc. degree (in Physics) in 2000 from Moscow State University (Russia) and obtained his Ph. D. in 2003 from Aalborg University (Denmark). From 2003 to 2008 he was a postdoctoral researcher at the Department of Physics and Nanotechnology, Aalborg University (Denmark). His research is focused on the use and development of near-field scanning optical microscopy for integrated optics applications. Jonas Beermann, born in 1977, is an assistant professor at the Institute of Sensors, Signals and Electrotechnics (SENSE), University of Southern Denmark. He received the M. Sc. degree in Optics in 2001 and obtained his Ph. D. in Nonlinear Optical Characterization of Nanostructures in 2006, both from Aalborg University, Denmark. From 2005 to 2008 he was a postdoctoral

15 588 I. P. Radko, V. S. Volkov, et al.: Plasmonic metasurfaces researcher working on the European Network of Excellence (NoE), Plasmo-Nano-Devices project Field enhancement via multiple scattering of surface plasmon polaritons and the Danish Research Agency, program committee for Nanoscience and technology, Biotechnology and IT (NABIIT) project Plasmo-optical chip technology and spectroscopy. His research interests include nonlinear far- and near-field scanning optical microscopy, field enhancements in metal nanostructures, nano-optics, spectroscopy, and sensing. Andrey B. Evlyukhin, born in 1963, studied physics at the Moscow State University (Russia). He received his Ph. D. (1995) in physics of low temperatures from the same university. Recently he received D. Sc. (2008) degree again from Moscow State University in interaction of semiconductors and systems, containing nanoparticles, with electromagnetic field. Since 1995 until 2008 he had worked in Vladimir State University at the Department of Physics and Applied Mathematics. In 2008 he was appointed as Professor of the Kama State Academy of Engineering and Economics in Naberezhye Chelny (Russia). Currently he has scientific cooperation with groups from different European countries especially from Denmark, Germany, and Spain. Research interests include theory for near-field optical microscopy, theoretical study of surface plasmons in nanostructured surfaces, simulation of micro-optical elements for surface plasmons, diffraction problems of multiple scattering of light by nano-objects in complex geometry, non-equilibrium phenomena in semiconductors (recombination and ionization). Thomas Søndergaard received the M. Sc. and Ph. D. degrees from the Technical University of Denmark in 1999 and 2002, respectively. The Ph. D. involved theoretical work on photonic crystal structures and radiation from sources in a microstructured environment. He then joined the company Micro Managed Photons A/S, where he worked with modeling and design of metallic microstructures for integrated optics based on exploiting surface plasmon polaritons. In 2005 he started working at Aalborg University, Denmark, where he presently in a post. doc position works with Plasmonic nanostructures for biomolecular spectroscopy and microscopy. In 2006 Dr. Søndergaard received The Danish Independent Research Council s Young Researcher s Award. Alexandra Boltasseva is an Assistant Professor at the School of Electrical and Computer Engineering, Purdue University (USA). She received the M. Sc. degree (with highest honors) in applied physics and mathematics from Moscow Institute of Physics and Technology in In 2004 she obtained her Ph. D. in electrical engineering at the Research Center COM, Technical University of Denmark (DTU). From 2005 to 2007 she was a postdoctoral researcher working on fabrication and characterization of nanostructures for applications in plasmonics, integrated optics and sensing. In 2007 she obtained a position of Assistant Professor at the Research Center COM (DTU), followed by a position of Associate Professor at DTU Fotonik (DTU) in 2008, before she recently moved to Purdue University, Indiana. Sergey I. Bozhevolnyi received the M. Sc. degree in physics and the Ph. D. degree in quantum electronics, both from Moscow Institute of Physics and Technology, Moscow, Russia, in 1978 and 1981, respectively. He received the Dr. Sc. degree from Aarhus University, Aarhus, Denmark, in From 1990 to 1991, he was with the Institute of Microelectronics, Russian Academy of Sciences, as the Head of Optical Technologies after working as an Associate Professor at the Yaroslavl Technical University, Yaroslavl, Russia, from 1981 to Since 1991, he was with the Institute of Physics, Aalborg University (Denmark) doing research on near-field optics. In 2008, he became a Professor in nano-optics at the University of Southern Denmark (Odense). His current research interests include linear and nonlinear nano-optics and physics of surface plasmon polaritons, including plasmonic circuits and field enhancement effects for bio- and molecular sensing. References [1] R. H. Ritchie, Phys. Rev. 106, 874 (1957). [2] C. J. Powell and J. B. Swan, Phys. Rev. 118, 640 (1960). [3] W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature (UK) 424, 824 (2003). [4] S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 1 (2005). [5] J. Lambe and S. L. McCarthy, Phys. Rev. Lett. 37, 923 (1976). [6] K. Takeuchi, Y. Uehara, S. Ushioda, and S. Morita, J. Vac. Sci. Technol. B 9, 557 (1991). [7] Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.- A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, Nature (UK) 444, 740 (2006).