Energy transport in plasmon waveguides on chains of metal nanoplates

Transcription

1 OPTO-ELECTRONICS REVIEW 14(3), DOI: /s y Energy transport in plasmon waveguides on chains of metal nanoplates W.M. SAJ *, T.J. ANTOSIEWICZ, J. PNIEWSKI, and T. SZOPLIK Faculty of Physics, Warsaw University, 7 Pasteura Str., Warsaw, Poland An interest in energy transport in 3D chains of metal nanoparticles is oriented towards future applications in nanoscale optical devices. We consider plasmonic waveguides composed of silver nanoplates arranged in several geometries to find the one with the lowest attenuation. We investigate light propagation of 500-nm wavelength along different chains of silver nanoplates of subwavelength length and width and wavelength-size height. Energy transmission of the waveguides is analysed in the range of nm. We find that chain of short parallel nanoplates guides energy better than two electromagnetically coupled continuous stripes and all other considered nonparallel structures. In a wavelength range of nm, this 2-µm long 3D waveguide transmits 39% of incident energy in a channel of l l/2 cross section area. Keywords: surface plasmons-polaritons, waveguides, nano-optical devices, plasmon resonance, evanescent waves. 1. Introduction Surface plasmon waves are collective oscillations of electrons excited within a thin metal layer of metal-dielectric interface. Plasmons are coupled with polaritons that are electromagnetic waves with high field amplitude propagating in the direction tangential to metal-dielectric interface. In the direction normal to the surface, plasmon-polaritons are evanescent [1 4]. Propagation of long range surface plasmon waves on thin and infinite metal films have been studied since more than two decades [5 7]. It was motivated by a search for methods of signal distribution in very low size channels. Dielectric waveguides with non-plasmonic propagation of optical signals have size limited to half a wavelength due to diffraction phenomenon. Resolution beyond the optical diffraction limit is possible when plasmons are distributed along metal circuits fabricated with e-beam patterning technique. Interest in plasmonic energy transport in channels of limited volume resulted in theoretical description and experiments on 3D chains of metal nanoparticles and 3D metal nanostrips [8 31]. In such structures, it is expected that signals can propagate in transmission lines with a diameter one order of magnitude smaller than a wavelength. In this paper, we analyse several geometries of plasmon waveguides composed of flat silver nanoplates. They are illuminated with the light of 500-nm wavelength polarized perpendicularly to plate walls. A chain of short parallel nanoplates has the lowest attenuation. Then, we investigate propagation and attenuation of light of nm wavelengths in two electromagnetically coupled long stripes and a chain of short parallel nanoplates. A 3D chain of nanoplates guides optical frequencies in a channel of width below the diffraction limit. We investigate influence of scaling down the optimum structure on efficiency of energy transport. * saj@igf.fuw.edu.pl 2. Geometries of plasmon waveguides on silver nanoplates The first geometry considered is a chain of 2D nanorods of 100-nm diameter arranged in the hexagonal lattice, Fig. 1(a) [27]. The chain of nanorods of 3.5-µm length transmits more than 50% of energy of optical wavelengths in the range of nm [27], thus it has lower attenuation than that available in chains of nanoparticles [e.g., 8.23]. However, the hexagonal chain of nanorods bends at p/3 and the bends introduce considerable losses. Therefore we consider several geometries of plasmon waveguides in the form of chains of nanoplates that allow non-discrete bending. Two types of chains with funnel-like nonparallel nanoplates are shown in Fig. 1(b) and 1(c). Nanoplate length and width are 380 and 60 nm, respectively. Chain links are separated by 40 nm. An angle between waveguide axis and each nanoplate is 10. Then, a chain of parallel short nanoplates of similar size, shown in Fig. 1(d), is compared with two continuous nanoplates of 60-nm width of Fig. 1(e). Nanoplate parameters are chosen to meet the possibilities of technological processes that might be involved in a fabrication process. With resolution of standard e-beam lithography, nanoplate thickness of 60 nm is achievable. With nowadays etching and deposition techniques, fabrication of 500-nm, 750-nm, and 1-µm high metal plates is possible. 3. FDTD simulations We use the finite difference time domain (FDTD) method [32] to investigate properties of waveguides illuminated with the light, polarized perpendicularly to plate walls. The permittivity of silver is described using the single pole Drude model 2-1 ew ( ) = e - wp[ ww ( + ig )], (1) Opto-Electron. Rev., 14, no. 3, 2006 W.M. Saj 243

2 Energy transport in plasmon waveguides on chains of metal nanoplates Fig. 1. Isometric views and cross sections of waveguides: (a) nanorods of 100-nm diameter in hexagonal lattice, (b) nanoplates in herring-bone pattern, (c) nanoplates in foot-step pattern, (d) parallel pairs of nanoplates, and (e) continuous parallel stripes. with the parameters e = 3.70, w p = THz, and G = THz calculated from the work of Johnson and Christy [33]. In each case, the simulation volume is nm discretized with Dr = 5 nm step surrounded by 10 layers of UPML absorbing conditions at all boundaries. Simulation time step is Dt = Dr/2c = s. The source has a Gaussian field distribution with a half width of 372 nm. It is placed in the z = 0 nm plane with small misalignment Dr/2 = 2.5 nm along the x axis. The source is introduced with total/scattered field split of a simulation volume. Energy guidance of the considered waveguides is calculated for a wavelength of 500 nm. Field intensities in the wave- 244 Opto-Electron. Rev., 14, no. 3, COSiW SEP, Warsaw

3 guides are calculated as the values of z-axis components of Poynting vector averaged over three periods of the source. Light transmissions of 2-µm long waveguides are calculated using a broadband source. Energy transmission coefficients are calculated as a ratio ( Ex + Ey ) out / ( Ex + Ey ) in of intensities integrated at the output (z = 2225 nm) and the input (z = 0 nm) planes, where E x and E y are the time Fourier transforms of field components. 4. Analysis of energy guidance On a plane metal-dielectric interface, small frequency plasmons-polaritons propagate with group velocities close to the speed of light in the dielectric. When frequency reaches the resonance plasmon frequency, the energy of electromagnetic plasmon-polariton undergoes transition to energy of electrons. Then, plasmon wave vector tends to infinity and the group and phase velocities of the plasmons tend to zero. Whichever mechanism decides upon transmission of light in a fibre, either total internal reflection or photonic band gap guidance, a beam diameter is diffraction limited. Plasmon waveguides may transport light below the diffraction limit in a surrounding dielectric with energy densities a few orders of magnitude higher than those available in optical fibres. High energy concentration results from long wave vectors of plasmons. In Fig. 2, we show the simulation volume containing several nanoplates and vertical (z = 1500 nm) and horizontal (y = 700 nm) cross section planes of energy flow in the z direction. Figure 3 presents distribution of energy in the vertical cross section plane at z = 1500 nm (left column) and flow of energy along a few links of waveguides (right column) shown in the horizontal cross section at y = 700 nm. For geometries with oblique position of nanoplates, losses connected with radiating into the far field are obviously higher than for parallel plates. Surprisingly, a chain of short parallel nanoplates concentrates energy inside the waveguide [Fig. 3(c) left] better than continuous metal stripes [Fig. 3(d) left]. Right column of Fig. 3 visualizes attenuation of energy in the analysed structures. Radiation losses into the far field are the smallest in a chain of short parallel nanoplates. Ohmic losses are supposedly similar in all structures because plate dimensions are the same. We note that subimages within each column of Fig. 3 are normalized independently. Transmission characteristics of the waveguide with plates arranged in herring-bone pattern are calculated for the plates rotated by 10, with respect to the waveguide axis. Figure 3(a) (left) shows the dominance of edge guiding, similarly as in case of continuous plates of Fig. 3(d) (left). Figure 3(a) (right) shows that the output beam has central minimum with side maxima. We observe strong coupling between tops and bottoms of both plates of a single link. It is stronger than coupling between top and bottom edges of the same plate. Intensity distribution on the outer walls of plates is higher than on inner walls and results in high radiation losses into the far field. Fig. 2. Scheme of two cross sections through a simulation volume, where Poynting vectors averaged over a wave period are calculated. Figure 3(b) shows the dominance of edge guiding in the waveguide arranged in foot-step pattern. Spatial shift of subsequent nanoplates results in serpent-like flow of energy. Similarly as in the previous geometry, intensity distribution on the outer walls of plates is higher than on inner walls what results in high radiation losses. Output beam is asymmetric and has central minimum with the side maxima. The waveguiding chain of short parallel nanoplates [Fig. 3(c)] attenuates less than all the other analysed nanoplate structures. Moreover, energy guiding on outside walls is lower than in the case of continuous plates. This can be interpreted as counterintuitive energy flow from the waveguide outside to its centre through openings between plates. The output beam has a distinct central maximum with small side lobs in the x-axis direction. In the waveguide of two parallel continuous plates [Fig. 3(d)], coupling between tops and bottoms of both plates is stronger than that between top and bottom edges of the same plate. Bound modes in continuous plates have energy concentrated between edges of both plates and on the outer walls of plates. In all cases, the Gaussian source is not located exactly on the system axis. The mismatch of the Gaussian source and bound modes results in energy leaks from the centre of the waveguides and in field asymmetry. 5. Influence of scaling the structures on energy guiding It was shown in the previous section that a chain of parallel nanoplates has better guiding properties than all the other structures. For a chain of parallel nanoplates and two paral- Opto-Electron. Rev., 14, no. 3, 2006 W.M. Saj 245

4 Energy transport in plasmon waveguides on chains of metal nanoplates Fig. 3. Z-axis components of Poynting vector averaged over a wave period and calculated at two planes shown in Fig. 2, in waveguides (a) in herring-bone pattern, (b) in foot-step pattern, (c) parallel pairs of nanoplates, and (d) continuous parallel stripes. All plates are separated by 260 nm, embedded in a medium with the refractive index n = 1 and illuminated with Gaussian beam of 500-nm wavelength. 246 Opto-Electron. Rev., 14, no. 3, COSiW SEP, Warsaw

5 Fig. 4. Z-axis components of Poynting vector averaged over a wave period and calculated at the horizontal y = 700 nm cross section plane in the chain of parallel pairs of nanoplates embedded in a medium with the refractive index n = 1 and illuminated with the Gaussian beam of 500-nm wavelength. In rows, the distance between plates increases from 160 nm to 260 nm for every 50 nm. In columns, the height of nanoplates decreases from 1000 nm to 500 nm for every 250 nm. lel unbroken stripes we continue search for optimum relation between guided wavelength and the separation a and the height h of plates for both structures. We scan three separation values 160, 210, and 260 nm and three heights 1000, 750, and 500 nm. Thus, the area ah of transversal channel cross section changes from l l/3 to 2l l/2. Figure 4 shows isolines of guided energy calculated at the horizontal cross section plane at y = 700 nm of the chain of parallel pairs of nanoplates. The narrowest channel is not efficient in energy guiding independently of the plate heights. The best results are observed for l high plates separated by l/2. Distribution of energy at the vertical cross section of this chain of plates shown in Fig. 5 confirms the observation. For 260-nm separation of plates we observe that with decrease in the plate heights, energy concentrates on the waveguide axis. For l/2 high plates guided modes differ distinctly. With increase in plate separation, weak coupling of edge plasmons on outer sides of plates changes to strong plasmon coupling between top and bottom parts of plates. This results in energy concentration within the waveguide. Similar calculations of z-axis components of Poynting vector averaged over a wave period and calculated at the horizontal and vertical cross section of a waveguide on two continuous stripes are shown in Figs. 6 and 7, respectively. It is clear that none of combinations of the separation a and the height h is helpful to decrease attenuation. Figure 6 shows a horizontal cross section on half-height of the waveguide, thus, poor guidance is observed because continuous plates transport energy with edge plasmons mostly. When height of plates decreases, the energy transport moves from inner to outer space. Figure 7 shows that with decrease in height of plates, plasmon coupling between neighbouring plates decreases. For 2l high plates, there is a coupling between top and bottom edges of plates. The plates of l height do not guide plasmons on their inner walls. There is an outer coupling between top and bottom edges of the same plate. 6. Light transmission in plasmon waveguides Figure 8 shows spectral transmission plots calculated using FDTD for all the geometries of waveguides presented in Fig. 1. For the hexagonal chain of nanorods, the transmission is calculated for optical wavelengths of nm and for nanoplate structures for the range from 400 nm to 2 µm. Chain of nanorods has the best efficiency and bandwidth of transported wavelengths, however, it has no bending abilities. Therefore calculations made in 2D are not recalculated for 3D case. The nanoplate structures are calcu- Opto-Electron. Rev., 14, no. 3, 2006 W.M. Saj 247

6 Energy transport in plasmon waveguides on chains of metal nanoplates Fig. 5. Z-axis components of Poynting vector averaged over a wave period and calculated at the vertical cross z = 1500 nm section plane in the chain of parallel pairs of nanoplates embedded in a medium with refractive index n = 1 and illuminated with Gaussian beam of 500-nm wavelength. In rows, the distance between plates increases from 160 nm to 260 nm for every 50 nm. In columns, the height of nanoplates decreases from 1000 nm to 500 nm for every 250 nm. Fig. 6. Z-axis components of Poynting vector averaged over a wave period and calculated at the horizontal cross section plane in parallel continuous nanoplates embedded in a medium with the refractive index n = 1 and illuminated with the Gaussian beam of 500-nm wavelength. In rows, the distance between plates increases from 160 to 260 nm for every 50 nm. In columns, the height of nanoplates decreases from 1000 nm to 500 nm for every 250 nm. 248 Opto-Electron. Rev., 14, no. 3, COSiW SEP, Warsaw

7 Fig. 7. Z-axis components of Poynting vector averaged over a wave period and calculated at the vertical cross section plane in parallel continuous nanoplates embedded in a medium with the refractive index n = 1 and illuminated with the Gaussian beam of 500-nm wavelength. In rows, a distance between the plates increases from 160 nm to 260 nm for every 50 nm. In columns, the height of nanoplates decreases from 1000 to 500 nm for every 250 nm. Fig. 8. Transmission of broadband Gaussian beam through 2-µm long waveguides of (a) nanorods in hexagonal lattice, (b) nanoplates in herring-bone pattern, (c) in foot-step pattern, (d) parallel pairs of nanoplates, and (e) continuous parallel stripes, all embedded in vacuum. Opto-Electron. Rev., 14, no. 3, 2006 W.M. Saj 249

8 Energy transport in plasmon waveguides on chains of metal nanoplates Acknowledgements This research was sponsored by Polish grant 3 T08A We also acknowledge the support from the 6FP Network of Excellence Metamorphose, EC Contract # References Fig. 9. Propagation in a bent herring-bone pattern waveguide with angle of rotation of subsequent segments equal six degrees. An angle between waveguide axis and each nanoplate is 5. lated in 3D. Funnel-like waveguides analysed because of bending possibilities are very lossy in comparison to parallel plate geometries. Transmission plot of a waveguide made of short parallel plates has a few maxima [Fig. 8(d)]. After 2-µm propagation distance, the highest transmission values close to 39% are observed in the wavelength range of nm. Single infinite length plate is considered, e.g., in Refs. 15 and 18. Here, we analyse the propagation properties of two parallel continuous plates. We observe that transmission along the plates of finite length not only increases with decreasing wavelength but also exhibits Fabry-Perot resonances [Fig. 8(e)]. Figure 9 illustrates confined propagation of light along bent plasmon waveguide composed of nanoplates in a herring-bone pattern with subsequent segments rotated by six degrees. In the wavelength range of nm, attenuation in the bent waveguide is close to 2 db/µm. 7. Conclusions Photonic crystal waveguides, operating on photonic bandgap mechanism, require at least three layers of cladding to achieve attenuation at the level of 0.1 db/mm. For a lattice constant equal to light wavelength, the waveguide is 7l wide [34]. Plasmon waveguides on silver nanoparticles demand less space, however, they have higher attenuation of energy. In this paper, we analyse a few geometries of plasmon waveguides made of nanoplates embedded in the vacuum. A chain of parallel short nanoplates is promising for applications in nanophotonic devices. Future research should lead to minimization of energy losses when nanoplates are embedded in a dielectric and investigation of properties of bent, y-junction and coupler structures. 1. H. Raether, Surface Plasmons, Springer, Berlin, C. Sönnichsen, Plasmons in metal nanostructures, PhD Thesis, Ludwig-Maximilians-Universtät München, München, A.V. Zayats and I.I. Smolyaninov, Near-field photonics: surface plasmon polaritons and localized surface plasmons, J. Opt. A: Pure Appl. Opt. 5, S16 S50 (2003). 4. W.L. Barnes, A. Dereux, and T.W. Ebbesen, Surface plasmon subwavelength optics, Nature 424, (2003). 5. D. Sarid, Long-range surface-plasma waves on very thin metal films, Phys. Rev. Lett. 47, (1981). 6. J.J. Burke, G.I. Stegeman, and T. Tamir, Surface-polariton-like waves guided by thin, lossy metal films, Phys. Rev. B33, (1986). 7. W.L. Barnes, S.C. Kitson, T.W. Preist, and J.R. Sambles, Photonic surfaces for surface-plasmon polaritons, J. Opt. Soc. Am. A14, (1997). 8. M. Quinten, A. Leitner, J.R. Krenn, and F.R. Aussenegg, Electromagnetic energy transport via linear chains of silver nanoparticles, Opt. Lett. 23, (1998). 9. 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, Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles, Phys. Rev Lett. 82, (1999). 10. J.C. Weeber, A. Dereux, C. Girard, J.R. Krenn, and J.P. Goudonnet, Plasmon polaritons of metallic nanowires for controlling submicron propagation of light, Phys. Rev. B60, (1999). 11. B. Lamprecht, J.R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner, F.R. Aussenegg, and J.C. Weeber, Surface plasmon propagation in microscale metal stripes, Appl. Phys. Lett. 79, (2001). 12. J.C. Weeber, J.R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J.P. Goudonnet, Near-field observation of surface plasmon polariton propagation on thin metal stripes, Phys. Rev. B, (2001). 13. J.C. Weeber, M.U. González, A.L. Baudrion, and A. Dereux, Surface plasmon routing along right angle bent metal strips, Appl. Phys. Lett. 87, (2005). 14. T. Yatsui, M. Kourogi, and M. Ohtsu, Plasmon waveguide for optical far/near-field conversion, Appl. Phys. Lett. 79, (2001). 15. P. Berini, Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures, Phys. Rev. B61, (2000). 16. R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka- -Skrzek, Experimental observation of plasmon-polariton waves supported by a thin metal film of finite width, Opt. Lett. 52, (2000). 250 Opto-Electron. Rev., 14, no. 3, COSiW SEP, Warsaw

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