Gap Surface Plasmon Waveguides with Enhanced Integration and

Letter pubs.acs.org/NanoLett

Gap Surface Plasmon Waveguides with Enhanced Integration and Functionality Dmitri K. Gramotnev,*,†,‡ Michael G. Nielsen,‡ Shiaw Juen Tan,§ Martin L. Kurth,§ and Sergey I. Bozhevolnyi‡ †

Nanophotonics, GPO Box 786, Albany Creek, Queensland 4035, Australia Institute of Technology and Innovation (ITI), University of Southern Denmark, Niels Bohrs Allé 1, DK-5230 Odense M, Denmark § Applied Optics and Nanotechnology Program, Faculty of Science and Technology, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia ‡

ABSTRACT: We propose and investigate theoretically and experimentally L-shaped gap surface plasmon waveguides (L-GSPWs) formed by a dielectric film (strip) partially enclosed between two metal films. The proposed L-GSPWs combine the benefits of strong plasmon localization in a nanogap, significant propagation distance, low cross-talk between two neighboring waveguides, high transmission through a sharp 90° bend, and simplicity of fabrication by means of the standard lithography combined with the thin film deposition. KEYWORDS: Gap surface plasmons, plasmonic waveguides, bend losses, cross-talk, thin films

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guides,28 and are formed by a thin dielectric strip partially enclosed between two metal films (Figure 1). In this structure, the width of the gap is determined by the thickness of the deposited dielectric film, rather than by the resolution of a lithographic technique. This opens a possibility for a much more precise, repeatable, and broad variation of the geometrical parameters of the gap/slot, including fabrication of gaps/ trenches with very high aspect ratio filled with dielectric. Such structures can easily be fabricated using a standard two-step lithography combined with film deposition (Figure 1d−f). L-GSPWs were fabricated on a Si substrate covered in thick gold underlay. The thickness of the gold underlay (H2 ≈ 100 nm) was significantly larger than the skin depth. Therefore, for all purposes, including the numerical simulation of these waveguides, the effect of the Si substrate on the L-GSPW modes can be neglected, and the gold underlay can be assumed infinitely thick as H2 → +∞. The SiO2 strips on the thick gold underlay (Figure 1d−f) were fabricated using the standard lithographic procedure with the subsequent lift off applied to the 170 nm thick SiO2 film with a 3 nm thick titanium adhesion layer deposited by means of RF-sputtering. The second lithography with the lift off applied to the gold overlay (with H1 ≈ 100 nm and ∼3 nm titanium adhesion layer) was then used to form the guiding structure with the overlap of width W ≈ 600 nm of the SiO2 strip and the gold overlay (Figure 1a). LGSPWs were fabricated with four different lengths (L ≈ 7, 10, 15, and 20 μm), so that to enable the determination of the propagation distance of the L-GSPW mode(s). Each of the fabricated waveguides had input and output diffraction gratings with the period Λ ≈ 0.512 μm at the ends of the guiding

etallic nanostructures have been intensely investigated both theoretically and experimentally for their unique properties offering a possibility for the development of a new generation of efficient waveguides and interconnects with strong subwavelength localization of optical signals in highly integrated nano-optical devices, circuits, and sensors.1−5 These structures are also expected, through plasmon nanofocusing, to provide efficient coupling of electromagnetic radiation and optical communication systems to nanoscale objects, single molecules, and nanoelectronic devices and components.5 A variety of different types of metallic nanostructures guiding optical signals have been proposed and described. These include metal nanorods6 and nanostrips,7 V-shaped metallic grooves,8−16 triangular metal wedges,15−18 and slot plasmonic waveguides.19−25 Plasmonic slot and groove waveguides seem to be one of the best options for the design of efficient subwavelength interconnects and optical components with high degree of integration.5,12 However, fabrication of slot and groove plasmonic waveguides typically presents a challenge, as it requires precise nanoscale lithography24 or focused ion-beam milling to fabricate a nanoslot or a groove with precise nanometer dimensions and high aspect ratio in a metal film or membrane. Even more technical problems arise if a rectangular profile of the slot is required or desirable. In addition, such waveguides may display significant cross-talk when placed close together,26,27 which may reduce the degree of integration of such plasmonic slot and groove waveguides. Additional screening structures proposed in ref 27 to reduce the crosstalk between two closely spaced slot waveguides require further precise fabrication with nanoscale resolution. In this Letter, we analyze theoretically and experimentally an L-shaped gap surface plasmon waveguide (L-GSPW) configuration that is free from the indicated deficiencies of the previously considered slot waveguides. The proposed L-GSPWs resemble, in their geometry, the trench plasmonic wave© 2011 American Chemical Society

Received: October 14, 2011 Revised: December 19, 2011 Published: December 27, 2011 359

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Figure 2. (a−d) The experimentally observed output radiation from the output gratings (shown by the arrows) for the four L-GSPWs with the indicated different lengths L and the following input powers Pin: (a) 0.68, (b) 1, (c) 1.75, and (d) 4.89 mW. (e) The fabricated LGSPW with approximately the same parameters as those in Figure 1d−f but with a sharp 90° bend and the lengths of the bend arms La = 7 μm. (f) The image of the obtained output from the grating at the end of the second arm of the bend shown by the arrow. Figure 1. (a) The considered L-GSPWs of width W formed by partial enclosure of a thin SiO2 film of thickness D between two gold films of thicknesses H1 (overlay) and H2 (underlay). (b,c) Two closely spaced L-GSPWs in the back-to-back (b) and back-to-front (c) configurations in an integrated circuit with the width of the metal screening partition S separating them. (d−f) Experimental realization of L-GSPWs with the parameters W = 600 nm, H1 = H2 = 100 nm, D = 170 nm, and different waveguide lengths L = 7, 10, 15, 20 μm (only L-GSPWs with the three larger lengths are shown in the presented microscopic image).

structure (Figure 1d−f) to ensure efficient coupling of the waveguide mode and bulk radiation. The grating fringes were formed during the second lithography with the lift off applied to the 100 nm thick gold overlay. The thickness D ≈ 170 nm of the SiO2 layer was measured using ellipsometry (TFProbe ellipsometer, Angstrom Sun Technologies), which also gave the refractive index of the SiO2 layer εd ≈ 2.11 at the wavelength λvac = 775 nm. The metal permittivity at the same wavelength was εm ≈ −23.6 + 1.7i (ref 29). The input grating was illuminated by a tightly focused laser beam with the wavelength λvac = 775 nm, power Pin, and polarization of the electric field along the z-axis (Figure 2a−d). The output signals (with the power Pout) were measured by means of a CCD camera from the output gratings (Figure 2a− d). The power of the incident generating beam Pin at the input grating was increased with increasing length of the waveguide L to compensate for dissipative loss of the guided mode. Figure 3a shows the experimentally measured normalized signal η = Pout/Pin from the output grating as a function of distance Lp = L − Lgr that the excited L-GSPW mode travels along the waveguide (here, Lgr = 3Λ ≈ 1.536 μm is the length of the input grating). The solid curve represents the statistical exponential fit

⎧ −z ⎫ ⎬ η = η0 exp⎨ ⎩ LGSP ⎭

Figure 3. (a) The experimental (solid curve) and theoretical (dashed curve for the fundamental L-GSPW mode) dependences of the normalized power output from the output grating on distance Lp that the generated guided plasmon travels along L-GSPW at the vacuum wavelength λvac = 775 nm; the structural parameters are the same as for Figure 1d−f, and the coupling efficiency for the output grating is assumed to be 100%, while the theoretical and experimental coupling efficiencies for the input grating are ∼4.5 and ∼3.3%, respectively. The gray band shows the 90% confidence interval for the obtained experimental dependence. (b) The theoretical dependences of the real (solid curves) and imaginary (dashed curves) parts of the effective index for the fundamental (curves 1 and 2) and second (curves 3 and 4) L-GSPW modes on waveguide width W; the other parameters being the same as for Figure 1d−f. The horizontal solid and dashed lines correspond to the real and imaginary parts, respectively, of the effective refractive index of the gap plasmon in a uniform gap (in the absence of the overlay termination).

(1)

to the experimental points (Figure 3a), where the efficiency of conversion of the guided L-GSPW mode into the bulk radiation in the output grating is assumed to be 100%, η0 = η(z = 0) ≈ 360

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0.033 ± 0.007 (with its standard error), and LGSP ≈ (6.7 ± 0.7) μm is the power propagation length of the L-GSPW mode (with its standard error) in the considered waveguide. The obtained value of η0 means that the efficiency of conversion of the incident bulk radiation into the L-GSPW mode was ∼3.3 ± 0.7%. The gray band in Figure 3a shows the 90% confidence interval for this fit. This means that the actual dependence of the output power on distance Lp must lie within the gray band with the probability of 90%. The error ranges for η0 and LGSP, corresponding to the 90% error band for the obtained experimental dependence, are ±0.015 and ±1.7 μm, respectively. To confirm the experimental conclusions about the generation of the guided mode(s) in the fabricated L-GSPWs, the numerical analysis of these waveguides was conducted by means of the finite element analysis using the COMSOL Multiphysics software package. In particular, it was shown that considered L-GSPWs (Figure 1d−f) support two modes with distinct field distributions (Figure 4). In particular, it can be

the obtained experimental value LGSP ≈ 6.72 μm, it appears to be within the experimental error for the 90% confidence interval. Similarly, the theoretical distance dependence (the dashed curve) in Figure 3a also lies within the error band for the 90% confidence interval for the experimental curve. Both real and imaginary parts of the effective refractive index for the fundamental and second L-GSPW modes show nontrivial dependences on the waveguide width W (Figure 3b). In particular, for both the modes, there exist cutoff waveguide widths Wc1 ≈ 100 nm and Wc2 ≈ 515 nm. If W < Wc1 (or W < Wc2), then the real part of the effective refractive index of the fundamental (or second) mode becomes smaller than the real part of the refractive index (∼1.405) of the surface plasmon in the gold-SiO2(170 nm)-air structure. Thus, the fundamental and second modes exist as localized guided LGSPW modes only if W > Wc1 and W > Wc2, respectively. Otherwise, they leak into the surface plasmon in the goldSiO2(170 nm)-air structure. Though increasing L-GSPW width W causes the real parts of the effective refractive indices of both the modes Re(neff) to monotonically increase (curves 1 and 3 in Figure 3b), they do not tend to or reach the real part of the effective refractive index for the gap surface plasmon in the uniform gap with no termination of the overlay (the horizontal solid line in Figure 3b). Therefore, the L-GSPW modes can always be represented by a propagating gap plasmon experiencing successive reflections from the termination of the gold overlay and the termination of the SiO2 layer. This conclusion is confirmed by the distributions of the electric field in the L-GSPW modes (Figure 4), showing that the dominant portion of the field (mode energy) is concentrated in the gap under the gold overlay. The imaginary part of the effective refractive index of both the L-GSPW modes Im{neff} (curves 2 and 4 in Figure 3b) display significant maxima (corresponding to minima of the propagation length) at around W ∼ 170 nm (for the fundamental mode) and W ∼ 600 nm (for the second mode). Further increase of W results in a monotonic decrease of dissipation of both the L-GSPW modes. However, similar to the real parts of the effective refractive indices, their imaginary parts neither tend to nor reach the imaginary part of the refractive index for the gap surface plasmon in the uniform infinite gap with no termination of the overlay (the horizontal dashed line in Figure 3b). Therefore, plasmon dissipation in LGSPW is always larger than in the uniform gap filled with the same dielectric and having the same width D. The differences between the theoretical and experimental Lpdependences of the output signal (Figure 3a) could be due to fabrication imperfections, especially near the edge of the SiO2 film (Figure 1d−f and 2e). The larger experimental value LGSP ≈ 6.72 μm of the propagation length compared to its theoretical value LGSP ≈ 5.4 μm for the fundamental mode could also be due to excitation of the second L-GSPW mode, whose propagation length can be larger near the cutoff width Wc2 (Figure 3b), and whose excitation efficiency could be increased by the fabrication imperfections (such as, for example, changing thickness of the SiO2 layer near its edge formed by the lift off). L-GSPWs are subject to the conventional for plasmonic waveguides trade-off between plasmon localization (ensuring larger degree of integration) and propagation distance of the guided modes. The experimentally observed and theoretically predicted propagation distances LGSP for the fundamental L-

Figure 4. Typical calculated distributions of the magnitude of the electric field (a,c) and the y-component of the electric field (b,d) for the fundamental (a,b) and second (c,d) L-GSPW modes. The structural parameters are the same as for Figures 1d−f.

seen that for both the L-GSPW modes, the dominant portion of the field is concentrated in the gap under the gold overlay. Note that, for the second mode, Ey changes its sign between the terminations of the SiO2 layer and the gold overlay (Figure 4d). This means that the charge at the interface between the gold overlay and the SiO2 layer also changes its sign when x is varied from 0 to 0.6 μm (Figure 4d). Generation of a mode with such symmetry of the charge and field distributions in L-GSPW is inefficient when using the incident laser beam with the polarization along the z-axis. Therefore, though the structure supports two different modes at the considered L-GSPW parameters, only fundamental mode can be efficiently generated in the experiment. Therefore, the explanation of the obtained experimental results should mainly involve the fundamental L-GSPW mode (Figure 4a,b). The numerically calculated propagation length for the fundamental mode with the considered L-GSPW parameters [W = 600 nm, H1 = H2 = 100 nm, D = 170 nm, λvac = 775 nm, εd ≈ 2.11, and εm = −23.6 + 1.7i (ref 29)] gave LGSP ≈ 5.4 μm. Assuming also that the efficiencies of coupling between the fundamental L-GSPW mode and bulk radiation in the input and output gratings were 4.5 and 100%, respectively, we obtain a theoretical dependence of the normalized power output on the waveguide width W (the dashed curve in Figure 3a). Though the theoretical value of LGSP ≈ 5.4 μm is smaller than 361

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significantly exceeds the mode propagation length, eliminating thereby the issue of cross-talk in practical design considerations. Effective reduction of the cross-talk by metal screening occurs not only in the back-to-back configuration of two L-GSPWs (Figure 1b) but also in the back-to-front arrangements (Figure 1c). In this case, it is sufficient to have a nanoscale separating metal partition of a thickness larger than the skin depth (∼30 nm) to ensure effective cross-talk suppression between the neighboring L-GSPWs. In conclusion, we have observed experimentally and investigated theoretically a new type of gap surface plasmon waveguide that combines simple and reliable fabrication, possibility of high mode localization and integration, significant propagation distances for the guided modes, and high transmission through sharp 90° bends with low radiation bend losses. Further analysis of the waveguides with sharp bends, directional couplers, and other integrated optics components using L-GSPWs will be necessary to optimize their performance and better understand the underlining physical principles. Nevertheless, the obtained results have already demonstrated significantly improved functionality and fabrication of the proposed L-GSPWs, as well as their significant potential for the design of integrated optics components.

GSPW mode appear large enough to ensure propagation of the guided signal over more than a dozen of plasmonic wavelengths (or even longer when operating at telecom wavelengths), which is typical for other types of gap surface plasmon waveguides19−24 and is deemed sufficient for the design of nanoscale plasmonic interconnects and devices. In some cases, L-GSPWs offer further advantages in this regard, for example, compared to slot waveguides with silicon core.24 Because of small dielectric permittivity of the SiO2 (compared to silicon), the considered L-GSPWs can be used in a wide range of frequencies (including optical and near-infrared frequencies, as opposed to just telecom wavelengths24) and typically have larger propagation distances. We have also fabricated a sharply bent L-GSPW (Figure 2e) and observed significant transmission of the generated signal through the bend (Figure 2f). Notably, no scattering was observed coming from the waveguide bend with the overall image quality being very similar to that of images obtained with straight waveguides (compare Figure 2a−d and Figure 2f). It was however found problematic to make quantitative estimation of the bend transmission. The main problem was that, in our current experimental setup, we used a polarizationdependent beam splitter resulting in different energy distributions (and thus coupling efficiencies) in the focused laser beam for straight and bent waveguides (compare Figure 2a−d and Figure 2f). In addition, the straight and bent waveguides and the corresponding coupling gratings appeared to come out different (compare Figures 1d−f and Figure 2e), making it questionable to directly use the values of coupling efficiency and mode propagation loss determined with the straight waveguides for the analysis of the bend waveguide configuration. However, the important aspect is that significant and detectable energy transmission through the sharp 90° bend in L-GSPW has been confirmed experimentally. Highly efficient energy transmission through a sharp 90° bend with minimal radiation losses should be expected because in the considered geometry of the bend (Figure 2e) the overlay metal film effectively screens the mode thus preventing it from leaking it into bulk radiation at the bend. Further optimization of the bend to suppress the plasmon reflected back into the first arm of the bend and thus achieve the maximal possible power transmission can be done by introducing a corner defect into the bend, similar to how it was done for the V-groove30 and slot31 waveguides. The same screening effect of the metal overlay is also a reason for the reduced cross-talk between two closely spaced and positioned back-to-back L-GSPWs (Figure 1b). In addition, for not very large thicknesses D of the SiO2 layer, the mode field near the termination of this layer is close to zero (Figures 4a,b), and this is another reason for low cross-talk in the two-waveguide geometry shown in Figure 1b. For example, for the considered structural parameters of the two L-GSPWs separated by the partition of the width S = 20 nm (Figure 1b), the coupling length Lc (i.e., the length within which the energy from one L-GSPW is coupled into the neighboring L-GSPW across the partition) is ∼103 and ∼16 μm for the fundamental and second mode, respectively. Reducing the width of the partition to S = 10 nm results in Lc ∼ 51 and ∼8.5 μm for the considered modes, respectively. The significantly smaller coupling lengths for the second mode are explained by larger field in this mode near the partition (Figure 4), which results in more efficient coupling. Considering the fundamental L-GSPW mode, even for a 10 nm wide partition, the coupling length

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

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ACKNOWLEDGMENTS We acknowledge financial support for this work from the VELUX Foundation and from the Danish Council for Independent Research (the FTP project ANAP, Contract No. 09-072949).

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REFERENCES

(1) Maier, S. A.; Atwater, H. A. J. Appl. Phys. 2005, 98, 011101. (2) Barnes, W. L. J. Opt. A: Pure Appl. Opt. 2006, 8, S87−S93. (3) Lal, S.; Link, S.; Halas, N. J. Nat. Photonics 2007, 1, 641−648. (4) Ebbesen, T. W.; Genet, C.; Bozhevolnyi, S. I. Phys. Today 2008, 61, 44−50. (5) Gramotnev, D. K.; Bozhevolnyi, S. I. Nat. Photonics 2010, 4, 83− 91. (6) Takahara, J.; Yamagishi, S.; Taki, H.; Morimoto, A.; Kobayashi, T. Opt. Lett. 1997, 22, 475−477. (7) Krenn, J. R.; Lamprecht, B.; Ditlbacher, H.; Schider, G.; Salerno, M.; Leitner, A.; Aussenegg, F. R. Europhys. Lett. 2002, 60, 663−669. (8) Pile, D. F. P.; Gramotnev, D. K. Opt. Lett. 2004, 29, 1069−1071. (9) Gramotnev, D. K.; Pile, D. F. P. Appl. Phys. Lett. 2004, 85, 6323− 6325. (10) Bozhevolnyi, S. I.; Volkov, V. S.; Devaux, E.; Ebbesen, T. W. Phys. Rev. Lett. 2005, 95, 046802. (11) Volkov, V. S.; Bozhevolnyi, S. I.; Devaux, E.; Ebbesen, T. W. Appl. Phys. Lett. 2006, 89, 143108. (12) Bozhevolnyi, S. I.; Volkov, V. S.; Devaux, E.; Laluet, J.-Y.; Ebbesen, T. W. Nature 2006, 440, 508−511. (13) Bozhevolyni, S. I.; Volkov, V. S.; Devaux, E.; Laluet, J.-Y.; Ebbesen, T. W. Appl. Phys. A 2007, 89, 225−231. (14) Vernon, K. C.; Gramotnev, D. K.; Pile, D. F. P. J. Appl. Phys. 2008, 103, 034304. (15) Moreno, E.; Garcia-Vidal, F. J.; Rodrigo, S. G.; Martin-Moreno, L.; Bozhevolnyi, S. I. Opt. Lett. 2006, 31, 3447−3449. (16) Yan, M.; Qiu, M. J. Opt. Soc. Am. B 2007, 24, 2333−2342. 362

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(17) Pile, D. F. P.; Ogawa, T.; Gramotnev, D. K.; Okamoto, T.; Haraguchi, M.; Fukui, M.; Matsuzaki, Y.; Matsuo, S. Appl. Phys. Lett. 2005, 87, 061106. (18) Boltasseva, A.; Volkov, V. S.; Nielsen, R. B.; Moreno, E.; Rodrigo, S. G.; Bozhevolnyi, S. I. Opt. Express 2008, 16, 5252−5260. (19) Liu, L.; Han, Z.; He, S. Optics Express 2005, 13, 6645−6650. (20) Veronis, G.; Fan, S. Opt. Lett. 2005, 30, 3359−3361. (21) Veronis, G.; Fan, S. Appl. Phys. Lett. 2005, 87, 131102. (22) Pile, D. F. P.; Ogawa, T.; Gramotnev, D. K.; Matsuzaki, Y.; Vernon, K. C.; Yamaguchi, K.; Okamoto, T.; Haraguchi, M.; Fukui, M. Appl. Phys. Lett. 2005, 87, 261114. (23) Pile, D. F. P.; Gramotnev, D. K.; Oulton, R. F.; Zhang, X. Opt. Express 2007, 15, 13669−13674. (24) Chen, L.; Shakya, J.; Lipson, M. Opt. Lett. 2006, 31, 2133−2135. (25) Zia, R.; Selker, M. D.; Catrysse, P. B.; Brongersma, M. L. J. Opt. Soc. Am. A 2004, 21, 2442. (26) Gramotnev, D. K.; Vernon, K. C.; Pile, D. F. P. Appl. Phys. B 2008, 93, 99−106. (27) Veronis, G.; Fan, S. Opt. Express 2008, 16, 2129−2140. (28) Bozhevolnyi, S. I. Opt. Express 2006, 14, 9467−9476. (29) Palik, E. D. Handbook of Optical Constants of Solids; Academic: New York, 1985. (30) Pile, D. F. P.; Gramotnev, D. K. Opt. Lett. 2005, 30, 1186−1188. (31) Mason, D. R.; Gramotnev, D. K.; Kim, K. S. Opt. Express 2010, 18, 16140−16145.

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