Surface-Plasmon-Polariton modes in deep metallic trenches-measurement and analysis

SPP photonic waveguiding inside trenches engraved in 400nm thick gold layer and symmetrically embedded in a dielectric host was experimentally studied using excitation at λ=1.55μm. This waveguide has a similarity to a coplanar transmission line configuration, although plasmonic hybrid modes are supported (rather than TEM waves). Excitation by TE and TM polarizations was studied and the emergence of long propagating plasmonic modes was observed. Mode solving using Full Vectorial Magnetic-Field Beam Propagation Method, validated the observed results, and disclosed the nature of the fundamental long range mode, coexisting with higher order guided modes in such SPP waveguide. ©2007 Optical Society of America OCIS codes: (240.6680) Surface Plasmons; (230.7380) Waveguides, channeled. References and links 1. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986). http://link.aps.org/abstract/PRB/v33/p5186 2. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61, 10484 (2000). http://prola.aps.org/abstract/PRB/v61/i15/p10484_1 3. R. Zia, A. Chandran, and M. L. Brongersma, "Dielectric waveguide model for guided surface polaritons," Opt. Lett. 30, 1473-1475 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-12-1473 4. R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, "Experimental observation of plasmon polariton waves supported by a thin metal film of finite width," Opt. Lett. 25, 844-846 (2000). http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-11-844 5. P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmonpolariton waveguides,” J. Appl. Phys. 98, 043109 (2005) http://dx.doi.org/10.1063/1.2008385. 6. T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmonpolariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82, 668-670 (2003). http://scitation.aip.org/journals/doc/APPLAB-ft/vol_82/iss_5/668_1.html. 7. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63, 125417 (2001). http://link.aps.org/abstract/PRB/v63/e125417 8. 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, 51-53 (2001). http://dx.doi.org/10.1063/1.1380236 9. 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 64, 045411 (2001). http://link.aps.org/abstract/PRB/v64/e045411 10. J. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distributions of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003). http://link.aps.org/abstract/PRB/v68/e115401 11. R. Zia, J. A. Schuller, and M. L. Brongersma, “Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides,” Phys. Rev. B 74, 165415 (2006). http://link.aps.org/abstract/PRB/v74/e165415 12. Y. Satuby and M. Orenstein, "Experimental observation of Surface Plasmon-Polariton Waves in deep trench metal waveguides," in Integrated Photonics Research and Applications/Nanophotonics, Technical Digest (CD) (Optical Society of America, 2006), paper IWC4. http://www.opticsinfobase.org/abstract.cfm?URI=IPRA-2006-IWC4 13. L. Liu, Z. Han, and S. He, "Novel surface plasmon waveguide for high integration," Opt. Express 13, 66456650 (2005). #79644 $15.00 USD Received 1 February 2007; revised 21 March 2007; accepted 21 March 2007 (C) 2007 OSA 2 April 2007 / Vol. 15, No. 7 / OPTICS EXPRESS 4247 14. S. I. Bozhevolnyi, "Effective-index modeling of channel plasmon polaritons," Opt. Express 14, 9467-9476 (2006). 15. Sergey I. Bozhevolnyi, Valentyn S. Volkov, Eloïse Devaux, Jean-Yves Laluet and Thomas W. Ebbesen “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508-511 (2006). http://www.nature.com/nature/journal/v440/n7083/full/nature04594.html 16. K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003). http://scitation.aip.org/journals/doc/APPLABft/vol_82/iss_8/1158_1.html 17. R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71, 165431 (2005). http://link.aps.org/abstract/PRB/v71/e165431 18. S. J. Al-Bader, "Optical transmission on metallic wires-fundamental modes," IEEE Journal of Quantum Electronics 40, 325329 (2004). http://dx.doi.org/10.1109/JQE.2003.823016 19. J. Shibayama, T. Yamazaki, J. Yamauchi, H. Nakano, “Eigenmode analysis of a light-guiding metal line loaded on a dielectric substrate using the imaginary-distance beam-propagation method,” IEEE Journal of Lightwave Technology 23, 15331539 (2005) http://dx.doi.org/10.1109/JLT.2005.843449 20. G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE Journal of Quantum Electronics 28, 363-370 (1992). http://dx.doi.org/10.1109/3.119536 21. E. D. Palik ed, Handbook of Optical Constants of Solids, (Academic Press, 1998)


Introduction
Optical waveguiding using Surface-Plasmon-Polariton (SPP) is gaining interest, as a means for optical confinement at the nano scale, using dielectric-metal nano sized structures.A structure comprised of negative permittivity metal core layer and a positive permittivity surrounding dielectric host, is known to support guided optical Transverse Magnetic (TM) surface waves.Exact analysis of SPP waveguiding for an infinitely wide metal layer is well known [ 1], however finite width metal stripe can be only either numerically analyzed [ 22] or approximately solved [ 3], resulting in some long range propagating modes (several millimeters) for a metal thickness of few 10's of nanometer.These modes were also measured at λ=1.55μm using 10-31nm thick gold layer and exhibited low losses [4][5][6].Plasmonic modes of asymmetrical stripes were also numerically solved [7] and experimental observed [8][9][10][11].
Our experimental path led us from the exploration of 20nm thick gold stripes, embedded in a symmetrical dielectric host.These stripes were examined with TM excitation at λ=1.55μm and exhibited a transition from "Gaussian like" single mode pattern to a pattern having enhanced field intensity at the stripe edges, when the stripe width was increased above ~8μm.The edge field was exploited by closely coupling two such edges to form a plasmonic coplanar structure -the slot configuration (reported in a conference [12]).The slot [Fig.1(a)] which is exactly complementary to the stripe was carved in an infinitely wide but thin (20nm) gold layer.The modes propagating in the slots were supported by the near-by metal edges and were excited only by TM input.These modes are predominantly the coupled modes of the two supporting metallic edges which is not the ideal case for coplanar configuration -where the fields of interest should be determined mainly by the parallel sidewalls of the void.Thus, we present the structures of this paper -the plasmonic trench [Fig.1(b)].Trenches within asymmetrical environment were discussed theoretically [13,14], but they exhibit substantially different mode characteristics from the modes of the highly symmetrical embedded trenches of the current paper and are more similar to modes of channel Plasmon waveguides [15].Equipped with the familiarity of modes supported by a gap in infinitely thick metal [16], we explored the light propagation in trenches carved in relatively thick (400nm) gold layer.At this thickness -the surface plasmons at the upper and lower sides of the metal layer are detached -such that we may expect that the vertical metal walls will play a major role in the determination of the modal field.
The guided modes were studied experimentally at λ=1.55μm to determine the modal field distributions as well their vector (polarization) characteristics.The modal fields were also numerically resolved using Full Vectorial Magnetic-Field Finite Difference Beam Propagation Analysis Method (FVH-FDM) with transparent boundary conditions [20].Similar numerical technique was successfully employed for SPP waveguiding [17][18][19] and also validated by us for known stripes configurations.The theoretical results not only validated the experimental observations, but also enabled distinguishing fundamental long range mode from the higher order ones.

Results
We prepared gold trench waveguides, embedded in a polymer based dielectric surrounding, to support SPP waveguiding at λ=1.55μm.A standard Silicon (Si) wafer, with a 10μm thick thermal oxide, was coated by a 13μm thick benzocyclobutene (BCB) layer as the lower cladding.Employing standard photolithography and lift off techniques, a 400nm Au layer deposited on top was used to create the vertical walls metal trenches [Fig.1(c)].Subsequently, a second 13μm thick BCB layer was used as the upper cladding and the samples were diced to lengths of 1mm up to 5mm length.
A laser source at λ=1.55μm excited SPP waves in the waveguides, by an end-fire coupling using a lensed polarization maintaining (PM) fiber, enabling precise control of the excitation's polarization.We denote by TM (TE) excitation an electric field which is aligned in the Y-axis direction (X-axis direction), i.e. vertical (tangential) to the layer planes.The modal profile at the output facet was imaged and recorded, using high resolution objective lens, onto an InGaAs detector matrix based camera.
As shown schematically in Fig. 1(b), the thick metal layers support two single surface TM polarized (E y / H x ) SPP modes propagating each on either the upper or lower surfaces.Due to the metal thickness, single surface SPP can be supported also by the stripe's sidewall, having a perpendicular (E x / H y ) polarization.Thus, engraving a trench in a thick metal layer which generates two adjacent sidewalls, enables the propagation of two coupled SPPs, each is supported by one of the sidewalls.This is the source for the main field lobe of the trench mode, while additional constituents are related to coupling of the fields on the large metal surfaces near the edges.The overall resulting mode is expected to be hybrid mode with spatially separated field components (in the trench and near the edges) which can be resolved experimentally by applying a polarizer in front of the camera.
Exciting a 2mm long trench by TE polarized light yields the modal pattern depicted in Figs.2(a Comparing the measured results to calculated modes was performed by FVH-FDM mode solving technique, by solving the wave equation for the transverse magnetic field components.The theoretical structure was comprised of 400nm thick metal layer having the permittivity of Au at λ=1.55μm to be ε r = -96.9-j •10.967 [ 21], embedded in a dielectric host with a dielectric constant: n = 1.5 (ε r = 2.25).The resulting modes exhibited field pattern matching the measured trench mode, yet enlightening some more information: the effective indices were n eff = 1.496 -j• 0.000164 and n eff = 1.49768 -j• 0.0000513 for the 6μm and 10μm width trenches respectively, manifesting that these modes propagation length, in terms of power attenuation by 1 / e , are approximately 0.75mm and 2.4mm for 6μm and 10μm width trenches, offering a low losses SPP guiding, similar to Long-Range-SPP modes, supported by thin metal stripes.The H y field (and the related E x ) is mainly located in the mid trench central lobe.The H x field (and the related E y ) comprises the side lobes along the two surfaces of the gold layer, in the vicinity of the trench, with maximum amplitude half of the peak value of the central lobed H y field.These modal features are similar at the two different trench's widths, as can be seen at Figs. 2. and 3.
The study was repeated for TE excitation (E y field) by rotating the PM fiber by 90 0 .The measured result for a 6μm width trench and its FVH-FDM simulation, are depicted in Fig. 4.Both reveal the excitation of a higher lateral mode in the mid trench, having a single radial zero crossing.The (H x /E y ) field of the mode supported on the metal edges is relatively enhanced (3 times larger than H y ), namely the edge portions carry more power than the central lobe.The calculated modal effective index is n eff = 1.5079 -j • 0.001468, which signifies a slow-wave with a shorter propagation distance, similar to a single surface SPP.To discriminate between the polarization components of the hybrid modes, we employed polarization resolved imaging.For TE input (E x / H y ) of a 8μm wide trench, the excited mode was the higher order one and the polarization resolved imaging is depicted in Fig. 5.The component on the gold layer surfaces is mainly E y /H x , while the main lobe is predominantly comprised of the E x /H y field component.Similar mode characteristics were obtained for trenches in the whole range of 6μm to 12μm width.However, narrower trenches (4μm and below) supported predominantly TM modes, where the in-trench lobe is completely eliminated as can be seen in Fig. 6.Modal pattern of a SPP wave, supported by 4μm wide trench engraved in a 400nm thick gold layer, embedded in a dielectric host (n = 1.5), excited at λ=1.55μm..

Conclusion
We have demonstrated unique SPP assisted waveguiding based on trench geometry.By fabricating trenches significantly deeper than the optical penetration depth of the metal at the applied wavelength, it was shown both experimentally and numerically (and for various trench sizes) that the fundamental mode confined in the trench is mainly E x / H y polarized, and exhibits long range (millimeters) propagation.We have measured also higher order modes of such a structure, which exhibit enhanced field on the metal surfaces outside the trench as well as shorter propagation length.All results were compared successfully to calculated trench modes.
)-2(b) for 6μm wide trench, and in Figs.3(a)-3(b), for 10μm wide trench.In both, the TE excitation (E x field -tangential to the layers) resulted in a well defined intensity lobe inside the trench and a residual optical power surrounding the edges of the metal layer.The captured image of the output facet is shown both in gray as well as pseudo-colors scales.Comparing modal output power of 1mm and 2mm long samples, suggested a typical propagation length of approximately 1mm.

Fig. 2 .
Fig. 2. Modal pattern of a 6μm wide trench engraved in a 400nm thick gold layer, embedded in a dielectric host (n = 1.5),TE (Ex field) excited at λ=1.55μm.The gold layer borders are graphically illustrated.Experimental imaging of optical power at the output facet (a-b) in comparison to FVH-FDM calculated guided mode having a propagation constant: n eff = 1.496 + j • 0.000164 .The Ex / Hy electromagnetic field components (c) peak value is twice the one of the Ey / Hx electromagnetic field components (d).

Fig. 3 .
Fig. 3. Modal pattern of a 10μm wide trench engraved in a 400nm thick gold layer, embedded in a dielectric host (n = 1.5),TE (Ex field) excited at λ=1.55μm.The gold layer borders are graphically illustrated.Experimental imaging of optical power at the output facet (a-b) in comparison to FVH-FDM calculated guided mode having a propagation constant: n eff = 1.49768 + j • 0.0000513.The Ex / Hy electromagnetic field component (c) peak value is 3½ times higher than the Ey / Hx electromagnetic field components (d).

Fig. 4 .
Fig. 4. Pattern of a higher mode, supported by 6μm wide trench engraved in a 400nm thick gold layer, embedded in a dielectric host (n = 1.5), excited at λ=1.55μm.Experimental imaging of optical power at the output facet (a-b) in comparison to FVH-FDM calculated guided mode having a propagation constant: n eff = 1.5079 + j • 0.001468.The Ex / Hy electromagnetic field component (c) peak value is 1/3 of the Ey / Hx electromagnetic field components (d)

Fig. 5 .
Fig. 5. Polarization resolved modal pattern of a higher mode, supported by 8μm wide trench engraved in a 400nm thick gold layer, embedded in a dielectric host (n = 1.5), excited at λ=1.55μm.Ex / Hy field components are mid trench located (a), and Ey / Hx components are mainly along gold layer surfaces (b).