Surface Plasmon Resonance in Metallic Nanocylinder Array

Journal of the Korean Physical Society, Vol. 47, August 2005, pp. S194 S199 Surface Plasmon Resonance in Metallic Nanocylinder Array Tai Chi Chu and Din Ping Tsai Center for Nanostorage Research, National Taiwan University, Taipei,Taiwan 10617, R.O.C. Department of Physics, National Taiwan University, Taipei, Taiwan 10617, R.O.C. Wei-Chih Liu Department of Physics, National Taiwan Normal University, Taipei, Taiwan 11676, R.O.C. (Received 6 September 2004) Localized surface plasmon resonances of noble-metal nanoparticles lead to high enhancements of local electromagnetic fields near the nanoparticle surface and play a key role in surface-enhanced Raman scattering, surface-enhanced fluorescence, near-field microscopy, and plasmonic devices. Recently, research results have shown that electromagnetic energy can transfer along a metallic nanoparticle chain because of coupled plasmon modes. In this paper, finite-difference time-domain method was used to study the surface plasmon resonances in coupled silver nanocylinder (nanoparticle) arrays and slab-like periodic modulation structures. From the far-field transmittance and reflectance, three different resonance modes were excited for the periodic nanocylinder arrays and only one resonance was excited for the periodic modulation structure. The near-field intensity distributions exhibited highly enhanced fields at the center of the gaps for nanoparticle arrays and at the caves of the periodic modulation structure. PACS numbers: 73.20.Mf, 73.22.-f, 73.22.Lp, 78.66.Bz, 78.67.Bf Keywords: Metallic nanocylinder array, Metallic nanoparticle, Surface plasmon, Finite-difference timedomain method I. INTRODUCTION Surface plasmon polariton (SPP) is an electromagnetic surface wave which propagates along an interface between a metal and a dielectric. It is a coherent surface charge fluctuation coupled to electromagnetic fields, which decay exponentially in the direction perpendicular to the surface. On a flat metal surface, the surface plasmon is difficult to excite directly, because the momentum (wave vector) of the surface plasmon polariton for a given frequency is always greater than that of a propagating wave. However, on a metallic grating, the dispersion of SPP splits into bands, just like the energy states of electrons in a periodic potential, which make direct coupling between SPP and propagation waves possible. The excited SPP resonance results in strong optical absorption, and this effect has been extensively studied in the last century [1,2]. In addition, Ebbesen et al. reported extraordinarily high optical transmission through a metallic film perforated with a periodic array of subwavelength holes [3 6]. The interaction of the incident light with the surface plasmons leads to an enhancement of the transmission which is several orders of magnitude above the prediction of standard aperture theory [7]. E-mail: wcliu@phy.ntnu.edu.tw -S194- In the range of visible light, an individual noble-metal nanoparticle exhibits a wealth of optical properties directly related to the geometry-dependent surface plasmon resonances. The surface plasmon resonances lead to enhancements of localized electromagnetic fields near the nanoparticle surface. When two nanoparticles are brought together, interaction between plasmon modes of the individual particles generates additional resonances for the coupled system when the distance between two particles is small enough in comparison with the size of the nanoparticles [8,9]. Those additional plasmon resonances were associated to polarization charges induced by illuminated electromagnetic waves. The plasmon resonances are very sensitive to the geometry of nanoparticles, which results from the complex electromagnetic interaction between the nanoparticles. The underlying physics and complex optical properties of nanoparticles continue to be an attractive area because of many potential applications such as surface-enhanced Raman scattering (SERS) [10 12], surface-enhanced fluorescence [13,14], optical spectroscopy [15], chemical and biological sensors [16 18], and near-field microscopy [19, 20]. Our previous research has found that the complicated behavior of plasmon resonance in a coupled system is related to the enhanced local optical intensity occurred in the AgO x -type super-resolution near-field structure (super- RENS) [21 28]. Super-RENS is a multilayer structure

Surface Plasmon Resonance in Metallic Nanocylinder Array Tai Chi Chu et al. -S195- which is applied to the high-density optical disk and can overcome the problems of traditional near-field optical data storage techniques, such as low recording rate and damage to fiber probes. The highly enhanced localized surface plasmons improve the reading efficiency of the super-rens disks. Metallic nanoparticles support localized surface plasmon modes, while surface plasmon polariton modes are found on noble-metal films. However, the surface plasmon resonances of nanoparticles that form a periodic array with narrow separation may be affected by the interaction between particles. Advances in fabrication techniques enable a study of the electromagnetic interactions between metal nanoparticle periodical arrays with various spacing between particles. Recently, it has been shown that energy can be transmitted along a onedimensional metallic nanoparticle chain, which is due to the excitation of propagating surface-plasmon modes [29 35]. This phenomenon could have important consequences for integrated optical circuits, which have important applications in guiding, modulating, and amplifying light in nano-size regime. To understand the complex behavior of surface plasmon resonances, we used a two-dimensional finite-difference time-domain (FDTD) simulation method to numerically study the surface plasmon resonance of coupled silver nanocylinder (nanoparticle) arrays and a slab-like periodic modulation structure. Since the excitation of surface plasmon resonances results in transmission enhancement [3 9], near-to-far field transformation [36] was used to realize the connection between the near-field enhancements and far-field transmittance on surface plasmon resonances. II. SIMULATION MODEL The numerical method is a two-dimensional method FDTD with periodic boundary condition and perfect matched layers, which has the advantages of a reduced memory requirement in computation and a simple process in handling the complex structure. The incident light is a p polarized plane wave of 650 nm wavelength. The refractive index of the silver was 0.055 + 4.44i and the dispersive behavior of silver was simulated by the Lorentz model [37]. In this paper, two structures as shown in Figure 1 were used for comparison. Figure 1(a) shows silver nanocylinders of the same radius set periodically in vacuum with 6 nm and 10 nm separation, respectively. For another structure shown in Figure 1(b), there were 1 nm overlaps between elliptical silver nanocylinders in the normal direction of incident light, and the diameter of each elliptical nanocylinder in the direction of illuminated light was 100 nm. The elliptical silver nanocylinder arrays formed a metallic nano thin film with periodic modulation. A surface plasmon on a single flat interface between a metal and a dielectric can not be excited by radiating light onto that surface, because the wave vector of the plasmon parallel to the surface is larger than that of light with the same frequency. Periodic structures provide the incident light with additional momentum, and the surface plasmon polariton may be excited when the match condition of the wave vector is satisfied. The resonance modes of a periodic nanoparticle array are basically linear combinations of single-particle surface plasmon modes, which are coherent oscillations of electronic charges within a single grain [38]. Hence, the structure of a periodic metal nanoparticle array may support more complex resonance modes than the slab-like periodic modulation structure, which on the other hand is similar to a shallow grating. In previous research on surface plasmon resonances, reflection spectra or transmission spectra were used to illustrate the frequency dependences of plasmon resonances. In this paper, the frequency of incident light was fixed, to avoid the complicated effects from the dispersive behavior of silver. Instead, the periods of the metallic structures were changed to seek the plasmon resonance conditions. To study the far-field optical properties induced by the excitation of surface plasmon resonances, a near-to-far transformation was used to obtain the farfield response from near-field results [36]. We studied the spatial dependences of plasmon resonances, so that the far-field transmittance and reflectance from near-field results of nanocylinders with various sizes clearly demonstrated the relation between metallic nanostructure and plasmon resonances. III. RESULTS AND DISCUSSION The calculated far-field transmittance and reflectance for silver nanocylinders of the same radius which were set Fig. 1. Two simulation structures: (a) periodic silver nanocylinders of the same radius with constant separations, (b) elliptical silver nanocylinders with 1 nm overlap; the diameter of the elliptical nanocylinder along the propagation direction of incident light was 100 nm.

-S196- Journal of the Korean Physical Society, Vol. 47, August 2005 Fig. 2. Far-field transmittance and reflectance of periodic modulation for periodic nanocylinders with (a) 6 nm and (b) 10 nm separation. periodically in vacuum with 6 nm and 10 nm separation are shown in Figure 2. For both cases, transmittance was lower for the nanocylinders whose radii were smaller than 100 nm, and three resonant peaks were presented in the transmittance curve when the radii of the nanocylinders were larger than 100 nm. Each resonance peak of transmittance indicated a plasmon resonance mode, and the transmittance of the third resonance peak was the lowest of all. For the case of nanocylinders with 6 nm separation, the three resonance peaks were at 150 nm, 200 nm, and 280 nm radius, respectively. With the separation between nanocylinders increasing to 10 nm, the resonance peaks shift 10 nm, and the resonance peaks were at 160 nm, 210 nm, and 290 nm, respectively. For the third resonance mode, the transmittance of nanocylinders with 6 nm separation was larger than the case with 10 nm separation. However, the transmittances with 6 nm separation were smaller than the cases with 10 nm separation for the first two resonance modes. Figure 3 shows the near-field intensity distribution of the three resonance modes for the case of nanocylinders with 6 nm separation. The three resonance modes are visible in Figure 2(a). The local enhancement was concentrated in the gap between the nanoparticles, but Fig. 3. Near-field intensity distribution of the periodic nanocylinders with 6 nm separation; (a) radius = 150 nm, (b) radius = 200 nm, and (c) radius = 280 nm. the near-field intensity distributions presented different behavior among the three resonance modes. In Figure 5(a), we provide the near-field distribution between the nanoparticles along the dotted line. For the first resonance in Figure 5(a), the intensity distribution was asymmetric, with a maximum in the center of the gap and two enhanced peaks on each side of the gap. The enhanced peak of the illumination side was higher than the other side. The intensity distribution of the second resonance was a symmetric mode with a high enhancement in the center of the gap, as shown in Figure 3(b). The behavior of the third resonance, for the nanocylinders with 280 nm radius, was similar to the first resonance mode, but the intensity was lower than the first one. On increasing the separation between the nanoparticles from 6 nm to 10 nm, the resonance modes exhibited different characteristics, as shown in Figure 4. Figure 5(b) shows the near-field distribution between the particles along the dotted line. For the first resonance, the intensity distribution was symmetric, with the enhanced peaks on each side of the gap higher than the fields in the center of the gap. However, the second and third resonances for the cases of nanocylinders with 210 nm and 290 nm radius, were asymmetric modes. For the second resonance, the fields on the side of illuminated light were higher than the other side, with a maximum in the center of the gap. The third resonance was also an

Surface Plasmon Resonance in Metallic Nanocylinder Array Tai Chi Chu et al. -S197- Fig. 4. Near-field intensity distribution of the periodic nanocylinders with 10 nm separation; (a) radius = 150 nm, (b) radius = 200 nm, and (c) radius = 280 nm. asymmetric mode, with two maximum peaks at each side of the gap and a peak in the center of the gap. Field intensities on the side of illuminated light were lower than the other side. In both the cases of 6 nm and 10 nm separation, the peak at the center of the gap between particles of the second resonance mode was higher than the others. The first resonance looked similar to the third resonance, and the enhanced fields of the third resonance were much larger than those of the first resonance. The resonances of nanocylinder arrays with 6 nm spacing were very different from those of nanocylinder arrays with 10 nm spacing. In the cases with 6 nm spacing, the enhanced fields were much sharper and larger than the cases with 10 nm spacing; a probable reason is that the interactions between nanoparticles increased with decreasing separation. Figure 6 shows the far-field transmittance and reflectance of the slab-like periodic modulation case for comparison. The elliptical silver nanocylinders were periodically aligned with 1 nm overlap, which means that the silver nanocylinder arrays formed a metallic nano thin film with periodic modulation. This structure was also similar to a shallow grating, and the nanoparticle array was similar to a deep grating. The radius of the elliptical nanocylinder in the direction of illuminated light (x axis) was 50 nm, and the radius of the other axis (y axis) was varied for comparison. The surface Fig. 5. Intensity distribution between periodic nanocylinders (along the dotted line). (a) 6 nm separation and (b) 10 nm separation. Fig. 6. Far-field transmittance and reflectance of the elliptical nanocylinder arrays with 1 nm overlap. plasmon was excited in the case with 305 nm radius of y axis, so the period of the resonance peak is 609 nm. The period match to the surface plasmon of flat metal interface is 617 nm, which is close to the period of the resonance peak for the case of elliptical nanocylinder arrays. The near-field intensity distribution of the surface plasmon resonance is shown in Figure 7. The intensity dis-

-S198- Fig. 7. Near-field intensity distribution of the elliptical nanocylinders with 305 nm radius in y axis. Journal of the Korean Physical Society, Vol. 47, August 2005 fields, so the deep grating or extremely varied structure could help the oscillation of polarization charges [39,40]. Figure 8 shows the Poynting vectors for the nanocylinder array of 150 nm radius with 6 nm separation and the elliptical silver nanocylinders of 305 nm radius in y-axis with 1 nm overlap. The energy flow of the first resonance for the nanocylinder array with 6 nm separation, shown in Figure 8(a), was confined in the center of the gap between nanoparticles, and the maxima of energy flow were induced at the convergence point. For the slab-like modulation case, the energy flow was focused at two caves on each side of the overlapping particles, as shown in Figure 8(b). The energy flow indicated the interaction between incident light and nanoparticles and clearly distinguished the plasmon modes of the above two cases. The concentration of the energy was much higher for the separated nanoparticles than that of the overlapping nanoparticles, which exemplified the structure dependence of surface plasmon resonances. IV. CONCLUSIONS Fig. 8. Poynting vectors of (a) the nanocylinder array of 150 nm radius with 6 nm separation and (b) the elliptical nanocylinders of 305 nm radius in y-axis with 1 nm overlap. tribution was very different from the field distributions of nanocylinder arrays, and the near fields were highly focused and enhanced at the caves of the grating. The resonant behavior of the nanocylinder arrays was much more complicated than the situation with shallow gratings, because the surface plasmon resonance was strongly geometry-dependent. The surface plasmon was a coherent surface charge fluctuation coupled to electromagnetic In this paper, we used 2D FDTD numerical simulation to study coupled silver nanocylinder (nanoparticle) arrays and slab-like periodic modulated nanostructures. The near-field and far-field results for nanocylinder arrays and shallow modulated nano-size thin film showed different resonance behaviors. From the far-field transmittance, the plasmon resonances of nanocylinder arrays were excited more easily, because the sharply varied nanostructures supported the coherent oscillation of polarization charges. The complicated interaction between nanocylinders resulted in three different resonances at radii less than 300 nm, and these resonance modes show very different behaviors in near-field distributions. The spatial dependences of plasmon resonances indicated that complex nanostructures can support more coherent oscillation modes of polarization charges. On the other hand, the slab-like modulated nanostructures supported only one resonance mode which is close to the surface plasmon mode of a plane silver surface. The Poynting vectors of the above two cases presented distinguished features and illustrated the sensitive structure dependence of the surface plasmon modes. Our research provided a better understanding of the plasmon resonance of the periodic nanoparticles and nanocylinders, which laid the foundation for practical plasmonic devices. ACKNOWLEDGMENTS We express our thanks for the financial support from the National Science Council, Taiwan, R.O.C. and the Ministry of Economic Affairs of Taiwan, R.O.C., (Grant Number 93-EC-17-A-08-S1-0006).

Surface Plasmon Resonance in Metallic Nanocylinder Array Tai Chi Chu et al. -S199- REFERENCES [1] V. M. Agranovich and D. L. Mills, Surface Polaritons: Electromagnetic Waves at Surfaces and Interfaces (North-Holland, Amsterdam, 1982). [2] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988). [3] T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio and P. A. Wolff, Nature 391, 667 (1998). [4] L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001). [5] A. Degiron, H. Z. Lezec and T. W. Ebbesen, Appl. Phys. Lett. 81, 4327 (2002). [6] W. L. Barnes, A. Dereux and T. W. Ebbesen, Nature 424, 824 (2003). [7] H. A. Bethe, Phys. Rev. 66, 163 (1944). [8] J. P. Kottmann and O. J. F. Martin, Opt. Lett. 26, 1096 (2001). [9] J. P. Kottmann and O. J. F. Martin, Opt. Express 6, 213 (2001). [10] G. C. Schatz and R. P. Van Duyne, in Handbook of Vibrational Spectroscopy, edited by J. M. Chalmers and P. R. Griffiths (Wiley, Chichester, 2002). [11] S. M. Nie and S. R. Emery, Science 275, 1102 (1997). [12] A. Wokaun, J. P. Gordon and P. F. Liao, Phys. Rev. Lett. 48, 957 (1982). [13] H. Ditlbacher, N. Felidj, J. R. Krenn, B. Lamprecht, A. Leitner and F. R. Aussenegg, Appl. Phys. B 73, 373 (2001). [14] O. Kulakovich, N. Strekal, A. Yaroshevich, S. Maskevich, S. Gaponenko, I. Nabiev, U. Woggon and M. Artemyev, Nano Lett. 2, 1449 (2002). [15] R. M. Stockle, Y. D. Suh, V. Deckert and R. Zenobi, Chem. Phys. Lett. 318, 131 (2000). [16] R. L. Rich and D. G. Myszka, Curr. Opin. Biotech. 11, 54 (2000). [17] D. A. Schultz, Curr. Opin. Biotech. 14, 13 (2003). [18] I. R. Hooper and J. R. Sambles, J. Appl. Phys. 96, 3004 (2004). [19] D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, J. S. Suh, R. Botet and V. M. Shalaev, Phys. Rev. Lett. 72, 4149 (1994). [20] D. W. Pohl, in Near-Field Optics and Surface Plasmon Polaritons, edited by S. Kawata (Springer-Verlag, Heidelberg, 2001) and references therein. [21] D. P. Tsai, C. W. Yang, W. C. Lin, F. H. Ho, H. J. Huang, M. Y. Chen, T. F. Tseng, C. H. Lee and C. J. Yeh, Jpn. J. Appl. Phys. 39, 982 (2000). [22] D. P. Tsai and W. C. Lin, Appl. Phys. Lett. 77, 1413 (2000). [23] W.-C. Liu, C.-Y. Wen, K.-H. Chen, W. C. Lin and D. P. Tsai, Appl. Phys. Lett. 78, 685 (2001). [24] W. C. Lin, T. S. Kao, H. H. Chang, Y. H. Lin, Y. H. Fu, D. P. Tsai, C. Y. Wen and K. H. Chen, Jpn. J. Appl. Phys. 42, 1029 (2003). [25] F. H. Ho, H. H. Chang, Y. H. Lin, B.-M. Chen, S.-Y. Wang and D. P. Tsai, Jpn. J. Appl. Phys. 42, 1000 (2003). [26] W.-C. Liu and D. P. Tsai, Jpn. J. Appl. Phys. 42, 1031 (2003). [27] W.-C. Liu, M.-Y. Ng and D. P. Tsai, Jpn. J. Appl. Phys. 43, 4713 (2004). [28] J. Tominaga and D. P. Tsai (Ed.), Optical Nanotechnologies (Springer-Verlag, Berlin, 2003). [29] M. Quinten, A. Letiner, J. R. Krenn and F. R. Aussenegg, Opt. Lett. 23, 1331 (1998). [30] J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg and C. Girard, Phys. Rev. Lett. 82, 2590 (1999). [31] M. L. Brongersma, J. W. Hartman and H. A. Atwater, Phys. Rev. B 62, R16356 (2000). [32] S. A. Maier, P. G. Kik and H. A. Atwater, Appl. Phys. Lett. 81, 1714 (2002). [33] S. A. Maier, M. L. Brongersma, P. G. Kik and H. A. Atwater, Phys. Rev. B 65, 193408 (2002). [34] S. A. Maier, P. G. Kik and H. A. Atwater, Phys. Rev. B 67, 205402 (2003). [35] S. Y. Park and D. Stroud, Phys. Rev. B 69, 125418 (2004). [36] A. Taflove, Computational Electrodynamics (Artech House, Boston-London, 1995), p. 203. [37] J. B. Judkins and R. W. Ziolkowski, J. Opt. Soc. Am. A 12, 1974 (1995). [38] U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, Berlin, 1995). [39] W.-C. Tan, T. W. Preist, J. R. Sambles and N. P. Wanstall, Phys. Rev. B 59, 12661 (1999). [40] W.-C. Liu and D. P. Tsai, Phys. Rev. B 65, 155423 (2002).