Propagation and interaction of surface plasmon polaritons (SPPs) excited in the wavelength range 700–860 nm with periodic triangular arrays of gold bumps placed on gold film surfaces are investigated using a collection near-field microscope. We observe the inhibition of SPP propagation into the arrays within a certain wavelength range, i.e., the band gap (BG) effect. We demonstrate also the SPP propagation along a 30° bent channel obtained by an adiabatic rotation of the periodic array of scatterers. Numerical simulations using the Lippmann-Schwinger integral equation method are presented and found in reasonable agreement with the experimental results.
©2006 Optical Society of America
Surface plasmon polaritons (SPPs) are quasi-two-dimensional waves propagating along a metal-dielectric interface . SPP fields decay exponentially into both media and reach maximum at the interface, a circumstance that makes SPPs extremely sensitive to surface properties. SPP guiding structures are basic elements of most plasmonic components needed to route optical signals in photonic devices and optical interconnects . Many fundamental properties of SPPs have been studied, and a number of SPP guiding structures have been suggested, including SPP guiding along metal stripes [3–5] and their edges , as well as along channels in periodic arrays of scatterers (bumps) placed on metal surfaces . In the latter case, the main principle is similar to that known for photonic crystals , i.e., the inhibition of SPP propagation within a certain wavelength range in periodic scattering arrays. The possibility to fabricate periodically corrugated metal surfaces exhibiting a full band gap (BG) for SPPs was first demonstrated 10 years ago . Such a BG effect for SPPs excited in the wavelength range of 780–820 nm has been shown to result in efficient SPP guiding, bending and splitting (albeit for relatively small angles) by line defects in periodic scattering arrays . There has been shown also the possibility of the SPP propagation in and scattering by such periodic structures at telecom wavelengths .
The experimental [10, 11] and theoretical [12, 13] studies of SPPBG structures indicated that the main concern in the context of efficient SPPBG waveguiding is related to the problem of simultaneous realization of the full SPPBG, i.e., the BG for all in-plane directions of SPP propagation. In particular, low-loss bending (for relatively large angles) seems to depend crucially on the realization of full SPPBG, which turned out to be a challenging problem [11, 13]. One can try to circumvent this problem by using adiabatic bends for stripe SPPs  or long-range SPPs [14–16]. In both cases, SPP modes supported by thin metal stripes are only weakly guided implying that the bend radii should be relatively large in order to keep the bend loss at an acceptable level. Usage of SPPBG structures might be less restrictive in this respect because the SPP propagation outside a bent channel (into the periodic structure) is prohibited for the wavelengths in the BG [9, 10]. For this reason, we have decided to explore the potential of gradually bent SPPBG structures containing straight channels for low-loss guiding around large-angle bends. Similarly bent (curved) channels have been successfully used in low-loss silicon-on-insulator photonic crystal waveguides . Here we demonstrate the SPP propagation in the periodic array of scatterers along a 30° bent channel obtained by an adiabatic rotation of the triangular lattice. Using a scanning near-field optical microscopy (SNOM) arrangement operating in collection mode , we consider the SPP excitation in the wavelength range 700–860 nm along gold films covered with periodic arrays of gold bumps, and demonstrate the inhibition of SPP propagation into the arrays within a certain wavelength range as well as the SPP propagation along the bent channel.
2. Experimental setup
The experimental setup used in this work is shown in Fig. 1. It consists of a collection SNOM  in which the near-field radiation scattered by an uncoated sharp fiber tip into fiber modes is detected, and an arrangement for SPP excitation in the Kretschmann configuration . The p-polarized (electric field is parallel to the plane of incidence) light beam from a tunable Ti:sapphire laser (λ = 700–860 nm, P ~ 100 mW) is weakly focused (spot size ~ 300 μm) onto the sample attached with immersion oil to the hypotenuse side of a right-angle BK7 glass prism. The SPP excitation is usually recognized as a minimum in the angular dependence of the reflected light power (attenuated total reflection) . In our case, the SPP excitation is manifested by a dark stripe in the reflected beam spot. A sharp tip, obtained by a standard chemical etching technique in 40% hydrofluoric acid, is scanned over the surface at a constant distance maintained by shear-force feedback. The optical signal picked up by the fiber tip is then converted by a photomultiplier tube and amplified in a lock-in amplifier. The setup used allows us to make far-field observations of the sample for preliminary adjustment of the position and the size of a focal spot from the laser. Once the adjustment is accomplished, the far-field arrangement is removed and the near-field scanning head is placed instead.
The SPPBG structures we consider in this work consist of 60-nm-thick gold films deposited on silica substrate and covered with gold bumps having height ~ 60 nm and square profile of ~ 133 nm or ~ 166 nm on the side. This patterning was microfabricated by electron-beam lithography on a resist layer on the thin film, evaporation of a second gold layer and lift-off. The reason for choosing parallelepiped-shaped bumps instead of cylinders is the ease of fabrication, which is also less time consuming. The gold bumps have been arranged to form a 30° adiabatic bend of a triangular lattice with period 475 nm and ΓM orientation of the irreducible Brillouin zone of the lattice . Figure 2 represents the design of two bends investigated. Structure A (Fig. 2(a)) is designed to have the radius of curvature of the bend being 16 μm and combined of square bumps being 133 nm on the side. Structure B (Fig. 2(b)) has the radius of curvature equal to 32 μm and square bumps being 166 nm on the side. In both of the structures a channel has been cut through the array by removing 4 lines of scatterers.
3. Experimental results
The first task was to observe the SPPBG effect with these structures. This has been accomplished with structure A (Fig. 2(a)). Typical topographical and near-field optical images obtained with the SPP interaction with the structure are shown in Fig. 3. The SPP propagates from left to the right in the figure and it is excited globally at an area covering the structure completely, for the spot size from the Ti:sapphire laser is ~ 300 μm whereas the size of the structure is about 25 × 15 μm. For this reason the field of the incident SPP can be considered as a plane wave. Due to the interaction of the SPP and the surface microstructure, the inhibition of SPP propagation into the array can be observed. In order to estimate the penetration depth an averaged cross section has been made inside the structure as shown by the white bar on Fig. 3(b). Fitting obtained exponentially decaying SPP intensity profiles yields us wavelength dependent penetration depth, which is shown on Fig. 3(e). One can clearly notice a BG near 770 nm wavelength. With the structure A we, however, did not succeed in obtaining effective SPP guiding through the bent channel: the signal drops down drastically after the bend.
Structure B differs from A by larger radius of curvature (which is 32 μm against 16 μm in the case of structure A) and by larger bump side length (166 nm against 133 nm). While the former leads to more effective SPP guiding after the bend, resulting in a lower bend loss of the structure, the SPPBG is expected to broaden due to the larger bumps in the latter . The filling factor is defined as the ratio of the area occupied by the bump forming one lattice cell to the area of that. For a triangular lattice with square bumps, the filling factor is obtained by , where a and p are the side of the square bump and the period of the lattice, respectively. In our case we get filling factor 0.09 for structure A and 0.14 for structure B. According to the theoretical considerations , the SPPBG effect and waveguiding in structure B (having a larger filling factor) should be more pronounced and efficient than those in structure A.
With the conditions of SPP excitation being the same as with the structure A, we observed efficient SPP guiding along the bent channel in the structure B (Figs. 4(a) and 4(b)) at the light wavelength of 713 nm. In order to track the signal inside the channel fifteen perpendicular cross-sections have been taken along the channel. A maximum value in each cross-section, corresponding to the signal at a point positioned inside the channel, has been plotted versus its distance from the entrance to the waveguide along the channel (Fig. 4(c)). The maximum signal was found decreasing exponentially along the bent channel, with the fitting resulting in the SPP propagation length (inside the bent channel) equal to 4.4 μm, which is equivalent to a propagation loss of 1 dB/μm. Note that the SPP propagation length and loss evaluated at the same wavelength (713 nm) for a flat air-gold interface are ~ 32 μm and 0.14 dB/μm, respectively . The measured propagation loss is substantial, but might still be acceptable for some practical applications in which main requirements are to the size of components used rather than insertion losses. On the other hand, long-rage SPP stripe waveguides exhibit rather low bend loss with very large (mm-sized) radii of curvature  that preclude their usage in compact devices.
One should explain the origin of an increase of the signal in the interval between 15 and 20 μm from the entrance to the waveguide (Fig. 4(c)). This can be related to the fact that the triangular lattice has ΓM orientation before the bend and ΓK orientation after the bend (since the lattice is 30-degree rotated) relative to the incident SPP beam (Fig. 2). While there is an inhibition of SPP propagation into the array for ΓM orientation, this is not the case to the same extent for ΓK orientation, resulting in the SPP penetration through the array and up to the channel.
Finally, to give an idea of SPP field confinement in the channel and signal levels, four from a series of fifteen cross-sections are plotted in Fig. 4(d) (namely, 2nd, 4th, 6th, and 13th, which are also marked by numbers in Fig. 4(c)). It should also be noted that the SPP field sustained by the bent channel cannot be excited or replenished from below (from the side of the silica substrate) with the global illumination used here, because being directed perpendicular to the input face of the SPPBG structure it is parallel to the bent channel only at its input .
4. Numerical simulations
Following the experiment, we also calculated the electric field magnitude 300 nm above the air-gold interface for a SPP Gaussian beam incident on structures similar to A and B. The calculations are accomplished by making use of the Lippmann-Schwinger integral equation method and details can be found in ref. 13.
The first structure we analyzed was a set of 26×34 cylindrical scatterers (height h = 60 nm and radius r = 68 nm) arranged in ΓM-oriented triangular lattice with 475-nm period. The dimensions of the bumps have been chosen in a way to make their shape and volume similar to those composing structure A (Section 2). The calculations have been made for the wavelength range 700–900 nm. Figures 5(a)–(d) show results obtained for four different wavelengths. The dependence of the (theoretically estimated) intensity penetration depth on the wavelength is shown on Fig. 5(e) together with the experimental data, being the same as in Fig. 3(e). It is seen that there is overall agreement between the two dependencies as far as the SPPBG location is concerned, but the penetration depth observed experimentally is considerably larger than the theoretical one. The latter discrepancy can be accounted for by the circumstance that, in the experiment, the whole SPPBG structure was illuminated from the side of the silica substrate (global illumination) resulting in the background radiation produced by scattered field components. Such a background sets a limit on the smallest SNOM signal measured at the SPPBG structure influencing thereby the evaluation of the SPP penetration depth, especially at the position of the SPPBG.
The second structure is an adiabatically 30-degree rotated ΓM triangular lattice with a channel formed by removing four lines of scatterers. The structure has the same size and the radius of curvature of the bend as in the experiment and is composed of cylindrical scatterers (height h=60 nm and radius r =86 nm), whose dimensions have been chosen to emulate the shape and volume of the bumps of structure B (Section 2). Figures 6(a)–(d) show the electric field magnitude distributions obtained with this structure at four wavelengths, particularly Fig. 6(a) is produced at the wavelength of 720 nm, which is closest to that used in the experiment (713 nm). One should note that the figures obtained are not directly comparable with Fig. 4(b) because we used the global SPP excitation in the experiment (Section 3). One can, however, compare the guiding capability of that kind of structure and it is clearly seen on Fig. 6(a) that at the wavelength of 720 nm a reasonable result can be obtained, which has been also observed in the experiment. It appears, nevertheless, that the best guiding should be provided by this structure at the wavelength of 840 nm, which roughly corresponds to the SPPBG wavelength that we would expect for this size of cylindrical scatterers (which is larger than that used in the simulations shown in Fig. 5). We have evaluated the SPP transmission through the bent waveguide (in percent) versus wavelength (Fig. 6(e)) and found the existence of a clear peak around the wavelength of 840 nm. The further increase in the transmission at longer wavelengths is due to the SPP propagation (and scattering) directly through the structure for the wavelengths being on the long-wavelength side of the SPPBG. It should be borne in mind that the transmission shown in Fig. 6(e) 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 SPP, and reflects thereby not only the SPP 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 SPP field and the SPP mode field sustained by the channel .
To summarize, we have investigated the SPP excitation and interaction with periodic triangular arrays of gold bumps within the wavelength range of 700–860 nm. We have characterized the inhibition of SPP propagation into the periodic structures due to the SPPBG effect. The SPP propagation along a 30° bent channel obtained by an adiabatic rotation of the triangular lattice of scatterers was observed at the wavelength 713 nm, showing a propagation loss at the level ~ 1 dB/μm. We have also presented the corresponding numerical simulations of SPP propagation in and scattering by periodic arrays of cylindrical scatterers similar to those used in the experiment, which are in reasonable agreement with the experimental observations. We believe that the presented results are useful, in general, for the further understanding of various SPPBG phenomena and, in particular, for finding the optimum parameters of a given adiabatic bend to minimize the loss incurred. Finally, we would like to remark that, similar to recent developments within conventional photonic crystal structures [19, 20], one might expect very interesting applications of the SPPBG structures to be found apart from compact bending and splitting, e.g., in the areas of slow light control and super-prism-based filtering, utilizing thereby very strong dispersion present in BG structures.
The authors acknowledge the help of K. Leosson (University of Iceland) in fabrication of periodic gold nanostructures investigated in this work. This work was partially supported by the European Network of Excellence, PLASMO-NANO-DEVICES (FP6-2002-IST-1-507879).
References and links
1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature (London) 424, 824–830 (2003). [CrossRef]
3. J. R. Krenn and J.-C. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Phil. Trans. R. Soc. Lond. A 362, 739–756 (2004). [CrossRef]
4. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13, 977–984 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-977. [CrossRef] [PubMed]
5. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833–5836 (2004). [CrossRef]
6. M. Hochberg, T. Baehr-Jones, C. Walker, and A. Scherer, “Integrated plasmon and dielectric waveguides,” Opt. Express 12, 5481–5486 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5481. [CrossRef] [PubMed]
7. S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in Surface Plasmon Polariton Band Gap Structures,” Phys. Rev. Lett. 86, 3008–3011 (2001). [CrossRef] [PubMed]
8. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, NJ, 1995).
10. S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, “Bend loss in surface plasmon polariton band-gap structures,” Appl. Phys. Lett. 79, 1076–1078 (2001). [CrossRef]
11. C. Marquart, S. I. Bozhevolnyi, and K. Leosson, “Near-field imaging of surface plasmon-polariton guiding in band gap structures at telecom wavelengths,” Opt. Express 13, 3303–3309 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=OPEX-13-9-3303. [CrossRef] [PubMed]
12. M. Kretschmann, “Phase diagrams of surface plasmon polaritonic crystals,” Phys. Rev. B 68, 125419 (2003). [CrossRef]
13. T. Søndergaard and S. I. Bozhevolnyi, “Theoretical analysis of finite-size surface plasmon polariton band-gap structures,” Phys. Rev. B 71, 125429 (2005). [CrossRef]
14. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23, 413–422 (2005). [CrossRef]
15. A. Degiron and D. Smith, “Numerical simulations of long-range plasmons,” Opt. Express 14, 1611–1625 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-4-1611. [CrossRef] [PubMed]
16. P. Berini and J. Lu, “Curved long-range surface plasmon-polariton waveguides,” Opt. Express 14, 2365–2371 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-6-2365. [CrossRef] [PubMed]
17. J. Arentoft, T. Søndergaard, M. Kristensen, A. Boltasseva, M. Thorhauge, and L. Frandsen, “Low-loss silicon-on-insulator photonic crystal waveguides,” Electron. Lett. 38, 274–275 (2002). [CrossRef]
18. TM, Herlev, Denmark.
19. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature (London) 438, 65–69 (2005). [CrossRef]
20. A. Jugessur, L. Wu, A. Bakhtazad, A. Kirk, T. Krauss, and R. De La Rue, “Compact and integrated 2-D photonic crystal super-prism filter-device for wavelength demultiplexing applications,” Opt. Express 14, 1632–1642 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=OPEX-14-4-1632. [CrossRef] [PubMed]