We report on the focusing of surface plasmon polariton (SPP) beams with parabolic chains of gold nanoparticles fabricated on thin gold films. SPP focusing with different parabolic chains is investigated in the wavelength range of 700–860 nm, both experimentally and theoretically. Mapping of SPP fields is accomplished by making use of leakage radiation microscopy, demonstrating robust and efficient SPP focusing into submicron spots. Numerical simulations based on the Green’s tensor formalism show very good agreement with the experimental results, suggesting the usage of elliptical corrections for parabolic structures to improve their focusing of slightly divergent SPP beams.
© 2007 Optical Society of America
Plasmonic components operating with surface plasmon polaritons (SPPs), due to the hybrid nature of the latter, exhibit the potential of combining strong sides of electronic (nm-size confinement) and photonic (large bandwidth) components. The possibility for the electron charges on a metal boundary to perform coherent fluctuations has been demonstrated long ago [1, 2]. Nevertheless, it was not until the last decade that the interest to SPPs greatly increased [3, 4] due to the development of nanofabrication techniques, such as electron-beam lithography and ionbeam milling, and nano-optical characterization tools, such as near-field optical microscopy, as well as due to the emergence of accurate quantitative electromagnetic simulation methods.
In order to realize integrated plasmonic devices one has to first develop approaches for SPP launching [5, 6] and waveguiding [7–9], as well as to realize basic SPP components, such as interferometers [10–12], modulators and switches [13, 14]. One of the important functionalities that should be mastered in SPP micro-optics is the delivery of intense SPP fields to a particular point within an integrated circuit, a bio-sensor or a data storage device. Several configurations have been suggested for this purpose including SPP excitation on circular structures [15–17] and exploiting of elliptical corrals . For circular structures to perform efficiently, a very wide incident beam exciting converging SPPs should be used (in order to cover a large part of circumference) with only a small part of the beam contributing to the SPP excitation. In the elliptical configuration, SPP rays arrive to the focal point after propagating over considerable distances (much longer than the distance between the excitation and focusing points) and thereby being notably attenuated upon the propagation.
One can tackle the issue of SPP delivery to a particular surface point by separating the SPP excitation and focusing steps. Thus, local and efficient SPP coupling can be achieved with a metal ridge being illuminated at normal incidence, a process that results in slightly diverging SPP beams propagating away from the ridge . One can then further focus the excited SPP beams with parabolic chains of nanoparticles, utilizing the circumstance that nanoparticle chains represent efficient SPP reflectors for oblique angles of incidence . Here we present the results of experimental and theoretical investigations of SPP beam focusing by means of nanoparticles arranged in different parabolic structures having very small focal distances (from 63 to 250 nm). With these structures, we exploit the advantage of high SPP reflectivity at oblique angles while minimizing the SPP travelling path lengths and, thereby, the incurred propagation losses.
2. Experimental results
The structures we consider in this work were fabricated on a 50-nm-thick gold film deposited on a quartz substrate using electron-beam lithography, evaporation of another 50-nm-thick gold layer and subsequent lift-off. Thus fabricated parabolic chains consisted of 50-nm-high gold bumps having the lateral cross sections in the form of rounded squares [Fig. 1(a)] with the width varying from 160 to 250 nm for different structures. The centre-to-centre distance between bumps in the chains was also varying (from 250 to 320 nm) for different structures. It should be noted, that the fabricated structures included those in which the bump width of 250 nm was equal to their (centre-to-centre) separation, i.e. those representing continuous lines of 250 nm width. Five different parabolic structures corresponding to the focal distances of 250, 175, 125, 90 and 63 nm were fabricated and investigated. Hereafter we refer to these structures as parabola 1 through 5. Each parabola extended over 50 μm along the SPP propagation direction.
A 100-nm-wide straight (gold) ridge was fabricated perpendicular to each parabola’s axis of symmetry at the distance of 5 μm away from its entrance (i.e. 55 μm away from its apex) in order to facilitate the SPP excitation. The SPP excitation was achieved by direct illumination of the straight ridge with a tuneable (700-860 nm) laser beam focused to a ~ 3-μm-diameter spot and polarized perpendicular to the ridge. Figure 1(b) represents a free SPP mode (i.e. propagating along smooth gold surface without any parabolic structure on it) excited on the straight ridge. While investigating parabolic structures, the excitation spot was adjusted so that the excited SPP beam propagated from the ridge inside parabola’s branches towards its vertex [Fig. 1(c)].Mapping of SPP fields was accomplished by making use of leakage radiation microscopy (LRM) [20, 21], a technique which is well established and described in detail elsewhere . Note that all further experimental LRM images of the SPP intensity distributions are presented in the way that the left image border coincides with the excitation ridge position. Typical SPP intensity maps recorded for five different parabolic structures are displayed in Fig. 2. In this particular case, the laser excitation wavelength of 800 nm was used, and the parabolic chains consisted of 250-nm-wide bumps separated by the distance of 320 nm.
It is seen that all parabolas are rather efficient in reflecting the SPP beam with their branches and thereby confining the excited SPP waves (Fig. 2). The resulting SPP intensity distributions are however different for different parabolas. While parabolas 1–3 produce a bright spot close to the vertex, whose dimensions increase from parabola 1 to 3 [Figs. 2(a)–2(c), parabolas 4 and 5 do not form a clear spot at their vertices but rather split the incident SPP beam into two beams propagating further away [Figs. 2(d), 2(e)]. This effect is most pronounced with parabola 5.
In order to quantitatively characterize the focusing ability of parabolas 1–3 and the splitting ability of parabolas 4 and 5, we considered cross sections through the maximum intensity level of bright spots for parabolas 1–3 and 5 μm away from the parabola vertex for parabolas 4 and 5 (Fig. 3). To eliminate the influence of propagation losses, the signal was normalized with respect to the SPP beam propagation distance taking also into account the SPP beam divergence. The evolution of the SPP intensity distributions across the bright spots formed by parabolas 1–3 can be accounted for by the decrease in the effective aperture from parabola 1 to 3. The SPP splitting, which is especially pronounced with parabola 5, is a rather complicated phenomenon with both the SPP reflection by parabola branches and the SPP scattering along these branches (i.e., along the nanoparticle chains) contributing to the resultant splitting effect. Given the cross sections shown in Fig. 3, one can characterize the full-width-at-half-maximum (FWHM) of the central (parabolas 1–3) and side (parabolas 4 and 5) peaks (Table 1) along with the corresponding contrast levels determined as 10log(P max/P min), P max and P min being the maximum and minimum signal levels in the considered distributions (Fig. 3).
The SPP focusing by parabolic chains of nanoparticles is based on the SPP reflection and, therefore, expected to be stable and robust with respect to variations in both nanoparticle parameters and radiation wavelength. Indeed, the performance of parabolic structures characterized with 12 different combinations of bump width and separation was found quite similar and without clear influence of either of the parameters. The SPP intensity distributions imaged with the LRM remained similar also when changing the excitation wavelength from 700 to 860 nm, though the effect of increasing (with the wavelength) the SPP propagation length was clearly visible, resulting in the SPP intensity increase at parabola vertices (Fig. 4).
3. Numerical simulations
The SPP beam propagation inside parabolic structures has been numerically simulated by making use of the total Green’s tensor formalism and the dipole approximation for multiple SPP scattering by nanoparticles [19, 22, 23]. The bumps forming parabolic chains were approximated by spherical particles considered as point-dipole scatterers, which were characterized with isotropic free-space polarizability obtained in the long-wavelength approximation. First the dipole moments of particles illuminated with a Gaussian SPP beam were calculated self-consistently, and then the total electric field distribution was determined above the sample surface (using in both cases the total Green’s dyadic) . The radius of the particles was not a crucial parameter and chosen to be equal to 50 nm judging from the overall similarity between the simulated field intensity distributions and the experimental LRM images. Very good agreement between the LRM images and the intensity distributions was observed for all considered parabolic structures [cf. Figs. 5(a) and 5(b)]. Note that the simulated and experimental images have different contrasts due to the nonlinear sensitivity of a CCD camera used in our experiments and that otherwise all features are perfectly reproduced, confirming the validity of the developed numerical approach.
We have further used the developed modelling tool to get better insight in the underlying physics of the SPP focusing. In the approximation of geometrical optics, parabolic reflectors are ideal for the focusing parallel light beams. In our experiments, we have used a 3-μm-wide light spot for the SPP excitation resulting in slightly divergent SPP beams. We believe that this divergence constituted the main reason for the aforementioned complicated effects in the SPP focusing with different parabolas (Fig. 2). Indeed, our simulations of the SPP focusing of a 6-μm-wide SPP beam demonstrated a significant improvement in the quality of SPP focusing [cf. Figs. 5(b) and 5(c)]. In practice, however, an increase in the excitation spot size is not desirable since it would most probably result in a decrease of the SPP excitation efficiency (due to a decrease in the overlap between the excitation spot and a ridge). We would rather suggest to maintain the excitation spot size and to improve the SPP focusing by introducing elliptical corrections for parabolic structures, since elliptical structures are best suited for the focusing of divergent beams .
We have tested this idea by considering the SPP focusing with the elliptical structure corresponding to parabola 1 at the focusing end, i.e., with its first focus coinciding with that of the parabola, and having its second focus at the point of SPP excitation, i.e., 55 μm away from the vertex [Fig. 6(a)]. Modelling of the SPP focusing conducted for a 3- and 6-μm-wide SPP beam showed a significant improvement in the focusing quality for the 3-μm-wide beam (cf. 5(b) and 6(b)) and, somewhat surprisingly, a deterioration of the focusing for the 6-μm-wide beam (cf. 5(c) and 6(c)). Note that both considered beams are divergent (though with different rates) from the same focus point of the elliptical structure. The difference in their focusing can be explained by considering their waist lengths estimated as ~ 9 and 35 μm, respectively. The wide SPP beam remains therefore nearly parallel while propagating in the focusing structure and is therefore better focused with a parabolic chain. One should therefore use arguments of geometrical optics with care, when designing SPP focusing structures, and supplement such a design with accurate modelling.
Summarizing, we have realized the efficient SPP focusing with parabolic chains of gold nanoparticles. The influence of excitation wavelength and geometrical system parameters has been investigated with the help of LRM imaging, demonstrating good stability and robustness of the focusing effect. Numerical simulations based on the Green’s tensor formalism have shown very good agreement with the experimental results, suggesting the usage of elliptical corrections for parabolic structures to improve their focusing of slightly divergent SPP beams. The SPP splitting effect observed with narrow parabolic structures might also be found useful in SPP micro-optics.
Two of the authors (I.P.R. and S.I.B.) acknowledge financial support from the Danish Technical Research Council, Contract No. 26-04-0158, and from the European Network of Excellence, PLASMO-NANO-DEVICES (FP6-2002-IST-1-507879). A.B.E. is grateful to the Russian Foundation for Basic Research, Grant No. 06-02-16443 for the financial support. A.B. acknowledges support from the Danish Technical Research Council, “Talent project“ grant No. 26-04-0268.
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