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Measurements of a W-shaped metal-coated surface plasmon polariton waveguides are presented, showing complex confined modes both in the coupled pair of air filled metal V-grooves, as well as within the central metal-coated triangular silicon wedge. Mode calculations support the experimentally measured plasmonic modes. Such W-shaped plasmonic waveguides when integrated with Metal-Oxide-Silicon structures may be utilized for active plasmonic nano-optical devices.
©2008 Optical Society of America
1. Introduction
Recent years advances in miniaturization techniques have allowed the realization of sub-100nm metal-dielectric structures, enabling Surface Plasmon Polariton (SPP) waves in the optical regime with relatively long propagation length [1,2]. SPP-based guiding has been explored intensively in gold stripes tens-of-nanometers thick [3, 4], and more recently also in the complimentary structures of slots and trenches within a gold layer [5,6]. Additional interesting plasmon guiding geometries are ‘triangular’ V-grooves in metal, where Channel-Plasmon-Polariton (CPP) modes can be guided [7,8], or the inverse structure of a triangular metallic wedge [9–11]. The support of guided plasmonic modes in these structured metal-dielectric interfaces can be interpreted in terms of a local enhancement of the effective index (relative to that of an SPP wave guided on a flat surface) due to the irregular interface, resulting in an effective lateral confinement. Some of these guided modes are highly confined near the tip of the V-groove or wedge with high field intensity in the dielectric medium which is appealing for the employment of electro-optical or nonlinear effects.
In this paper we study the characteristics of a W-shaped metal-coated silicon plasmonic waveguide [12]. The W channel is formed by two overlapping metal-coated V-grooves, aimed at future applications where the central metal coated ∧-wedge (a flipped V-groove) filled with silicon, will be used for guiding a tightly confined plasmonic mode. The motivation for studying such a structure engraved in silicon is for the potential applications as Metal-Oxide-Semiconductor (MOS) based photonic device [13], taking advantage of the highly confined optical mode which optimally overlaps the small interaction regions within the silicon which will enhance the carrier-induced index-changes. Fig. 1 offers a cross section of a conceptual design of such a W-shaped plasmonic modulator based on a MOS capacitor for refractive index modulation. A plasmonic mode, tightly confined in the silicon wedge may enhance significantly the overlap with the index change region, which extends only ~10nm beneath the oxide layer to yield a much shorter and highly efficient modulator.
Fig. 1. A conceptual drawing of a W-shaped plasmon MOS based optical modulator. The coupled V-grooves plasmon modes in air and the Λ plasmon mode in silicon are marked.
The W waveguide geometry, combines two coupled air filled metal V-grooves and a metal silicon filled ∧-groove, exhibits interesting plasmonic modes on both sides of the structured metal layer, as illustrated in Fig. 1. We present measurement results of these modes and subsequently analyze the modal structure to interpret the experimental observations.
2. Measurement results of W-shaped plasmon waveguides
The investigated structures are V and W-shaped channels carved in silicon, coated by 400nm thick gold layer. Such structures were manufactured in silicon by employing anisotropic wet etching along <100> crystal planes, offering excellent quality sidewalls important for reduced optical scattering. A silicon-nitride (Si3N4) layer serving as a mask for the etching process was deposited on a <100> silicon wafer. For the V-grooves fabrication, 3µm wide stripes were opened in the nitride layer by photolithography, and KOH was used for anisotropic etching, resulting in V-shaped grooves with side angles of 54.74° with small under-etch. After removing the silicon-nitride, a 400µm gold layer was evaporated
The W structures were fabricated similarly by using two 4um spaced parallel stripe shaped openings in the silicon-nitride mask, each 3um wide, shown in Fig. 2(a) before the removal of the mask layer. The head angle of the triangular wedge was measured to be (55±1)° in coincidence with the expected value. Each of the V grooves comprising the W was 7µm wide and ~5µm deep. After removal of the nitride layer, 400nm thick gold was evaporated. At the working wavelength (1.55µm) this thickness of gold decouples the plasmonic waves on both sides of the metal film: the bottom silicon-gold and the top gold-air interfaces. The reported measurements are for 200µm long waveguides. The plasmonic waveguides were end-fire coupled to a polarization-maintaining lensed fiber, and the input polarization state was controlled by rotating the fiber axis. The output field intensity at the waveguide was imaged via an objective lens onto a sensitive IR CCD camera while the output polarization was analyzed by a polarizing beam-splitter.
Fig. 2. (a) SEM image of the W-shaped silicon wedge in process, showing also the silicon-nitride etch mask. (b) Optical image of the W-shaped plasmon waveguide sample.
The measurements of the basic V-grooves are reported first (Fig. 3). Previous reports on plasmonic modes in V-grooves related to much smaller and sharper geometries e.g. with tip angles in the range of 15–30° [8] where expected cut-off angle was around 70°. The bottom tip angle of our V-groove is much shallower, 70.5°.
Fig. 3. (a) SEM image of V-groove plasmon waveguide. (b),(c) Measured output light vs. polarization.
The V plasmonic waveguide mode intensity, recorded at horizontal polarization (Fig. 3(b)) is exhibiting confined field guided in the V-groove. Vertical polarization output intensity is predominantly governed by the plasmonic mode of the neighboring planar horizontal metal surfaces attributed to the regular “TM” single flat surface SPP mode (Fig. 3(c)). However the presence of the groove resulted in the phase flip of the vertically polarized field as evident from the zero crossing about the center of the groove.
The measurement results of the W-shaped plasmon waveguide are depicted in Fig. 4 showing the output light intensity distribution for a linear input polarization aligned at an angle relative to the sample plane (indicated by an arrow in Fig. 4(a)), as to excite both polarization modes. Polarization analysis of this output intensity distribution shows that the recorded modes exhibit hybrid polarization. The structured gold layer is shown to guide modes on both sides of the film, as evident from Fig. 4(a). Above the film, CPP modes are guided within the coupled metal-air V-grooves, as well as planar SPP mode along the flat surfaces on both sides of the W. Below the metal film, a plasmon mode is guided along the central metal-coated silicon wedge as well as planar SPP modes along the flat surfaces.
Examining the horizontal polarization of the output field (Fig. 4(b)) reveals a plasmonic mode confined within the coupled air filled V-grooves, distributed primarily around the metal surface of the central ∧ part of the W; another mode, having a triangular shape, is confined within the metalized silicon flipped-V-groove - which is the mode of interest for silicon photonics applications. The vertically polarized output field (Fig. 4(c)) is exhibiting phase flipping of the air mode about the structure center as evident from the zero crossing. The W air-modes are hybrid with horizontal and vertical components of similar magnitudes, which is different from those of the isolated V-groove which are predominantly horizontally polarized. The vertically polarized field of the mode within the silicon is visible as well.
Fig. 4. Measured output light distribution from W-shaped plasmon waveguide, input polarization indicated by the arrow in (a). Output polarization is (a) random, (b) Horizontal, (c) Vertical.
This vertical E field in the silicon should be asymmetric and exhibit an intensity notch. However our far-field imaging system, having micrometers resolution and a polarization extinction ratio of ~10, cannot resolve this submicron spatial intensity notch. The Si mode is substantially smaller than the air mode and has a horizontal/vertical polarization ratio > 6 (compared to ~2 for the air groove). Yet it is clear from the measurements that the horizontal field component is peaking at the center of the groove while the vertical component is spread sideways similar to the predicted two lobes (yet not resolving the nano sized notch).
The latter optical mode is tightly confined within the silicon in sub-wavelength dimension and it is a key for enhancing the overlap with carrier modulation regions in the Si.
3. Modal analysis of V- and W-structures
To validate and interpret the experimental results we performed modal calculations, using Finite-Element (FEM) BPM method. The finite element method provides reliable results compared to other modal calculation methods as it better tackles the required high local resolution at the multiple wedge structures. The calculation was performed in H field, to avoid field discontinuities on surfaces which are very prominent for the E field. Since the longitudal field component (Hz) is very small, the E field distributions are almost equal to those of the reciprocal H fields. The refractive index values at λ=1.55um were n(Si)=3.45 and n(Gold)=0.55-j·11.5, and the tips curvature was 70nm. As the actual wedge curvature in the sample was estimated to be ~250nm, the effect of tip curvature radius was examined and was shown to hardly affect field distributions and only slightly change the effective index values.
Fig. 5. Calculated fields of the V-groove for the zero order mode (a) Horizontal, (b) Vertical polarizations.
The modes of a single V-groove 7µm wide and ~5µm deep with 70.5° bottom tip angle were calculated. Two guided plasmonic modes exist and the zero-order symmetrical mode (Hy symmetrical about the groove center), with an effective index value of neff=1.0124–j·0.001 is shown in Fig. 5. Although the tip angle is large, 70.5°, this 5µm deep V-groove supports guided plasmonic modes, which are not very tightly confined. This is evident from the effective index value relatively close to the nspp=1.00377 of a flat air-gold interface, and also from the spatial extent of the mode. Due to the symmetrical excitation, the mode recorded in our experiment is the zero order – with good match to the measured field components. Fig. 6 depicts the 4 calculated guided plasmon modes with neff > nspp for the air filed W wedge.
Fig. 6. Calculated Hy modal fields of the W-shaped plasmon waveguide, exhibiting 4 guided plasmon modes.
Using Fig. 7 we can attribute the resulting air-metal modes to the hybridization of the modes of the W constituents, the central wedge and the V-groove on each side.
Fig. 7. The real part of plasmon modes effective index for the different sub-structures comprising the W structure. Their coupling is evident from the supermodes of the complete structure. (a) nREAL vs. head angle of the for a triangular gold wedge. (b) Isolated triangular gold wedge with a head angle of 70.5° (central part of W). (c) Isolated triangular gold wedge with a head angle of 125.3° (side part of the W). (d) Single V-groove. (e) All the modes of the W-wedge.
The zero order mode (Fig. 6(a), neff=1.02-j·0.0015) is localized at the central wedge of the W and is similar to that of an isolated wedge of the same angle (Fig. 7(b), Re{neff}=1.031) with lowered neff due to coupling. The next 2 modes are the in- and anti- phase combinations of the modes of the two V-grooves that comprises the W, as reflected by their spatial distribution and neff values. The 3rd order mode (Fig. 6(d), neff= 1.0078-j·0.0017) stems from the central wedge (Fig. 7(b), Re(neff)=1.0087) but with significant coupling to the V structures – evident from the larger spatial spread of the modal field and the deviation of the neff value towards that of the V mode.
Comparing the field intensity distributions to the experimental results – we get a very good match with the hybrid field of this 3rd order mode as shown in Fig. 8. We believe that due to process imperfections, the zero order mode localized at the wedge tip is highly scattered. The symmetric excitation (~2µm beam width FHHM) localized at the W center is best overlapping the 3rd order mode.
Fig. 8. Intensity distribution of the 3rd order mode of the coupled air-Au V waveguides - (a) horizontal, (b) vertical polarizations. Insets: respective experimental results (same as figs. 4b,c).
Finally, Fig. 9 shows the fundamental plasmonic mode of the silicon filled V groove, with neff=3.699-j·0.027 which is tightly confined at the tip, and has hybrid polarization. An effective-index analysis of the silicon V-groove (similar to [8]) by splitting the silicon V-groove into an equivalent staircase structure, each step analyzed as a 1D plasmon gap waveguide filled with silicon, resulted with a guided mode with neff=3.685–j·0.0325 – almost identical to that obtained by the FEM simulation.
Due to the significant rounding of the wedge tip in the process, we expect the experimental mode to be less confined – and also less lossy compared to the simulation – as was actually measured. The intensity of the silicon wedge mode was only slightly lower than that of the air filled grooves plasmonic mode and not as large as was calculated.
4. Summary
Measurements of plasmonic modes of a thick-metal W-shaped plasmon waveguide in silicon were presented. Air modes in the V-grooves above the metal layer, and a confined mode in the central flipped silicon V-groove below the metal layer were exhibited – with hybrid characteristics. Mode calculations support the reported measurements and interpret the complex structure by means of coupling (hybridization) created between the W structure ingredients.
Acknowledgments
We acknowledge Andrea Pe’er for the waveguides fabrication and the support of the Ministry of Science and Technology Eshcol scholarship.
References and links
1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, 1988).
2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]
3. 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. 25, 844–846 (2000). [CrossRef]
4. T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82, 668–670 (2003). [CrossRef]
5. Y. Satuby and M. Orenstein, “Surface-plasmon-polariton modes in deep metallic trenches- measurement and analysis,” Opt. Express 15, 4247–4252 (2007). [CrossRef] [PubMed]
6. E. Feigenbaum and M. Orenstein, “Modeling of complementary (void) plasmon waveguiding,” IEEE J. Lightwave Technol. 25, 2547–2562 (2007). [CrossRef]
7. D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29, 1069–1071 (2004). [CrossRef] [PubMed]
8. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95, 046802 (2005). [CrossRef] [PubMed]
9. T. Yatsui, M. Kourogi, and M. Ohtsu, “Plasmon waveguide for optical far/near-field conversion,” Appl. Phys. Lett. 79, 4583–4585 (2001). [CrossRef]
10. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87, 061106 (2005). [CrossRef]
11. E. Feigenbaum and M. Orenstein, “Nano plasmon polariton modes of a wedge cross section metal waveguide,” Opt. Express 14, 8779–8784 (2006). [CrossRef] [PubMed]
12. D. Arbel and M. Orenstein, “W-shaped Plasmon Waveguide for Silicon based Plasmonic Modulator,” in LEOS annual meeting 2006, Montréal, Canada, paper TuL-5. [CrossRef]
13. L. Pavesi and D. J. Lockwood, Silicon Photonics (Springer, Berlin, 2004).
