LETTER pubs.acs.org/NanoLett
Plasmonic Focusing in Symmetry Broken Nanocorrals )
Zheyu Fang,† Qian Peng,† Wentao Song,† Fenghuan Hao,§ Jia Wang,§ Peter Nordlander, and Xing Zhu*,†,‡ †
School of Physics, State Key Laboratory for Mesoscopic Physics, Peking University, Beijing 100871, China National Center for Nanoscience and Technology, Beijing 100190, China § Department of Precision Instruments, Tsinghua University, Beijing 100084, China Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, United States
)
‡
bS Supporting Information ABSTRACT: Plasmonic focusing was investigated in symmetry broken nanocorrals under linearly polarized illumination. Near-field optical measurements of the perpendicular electric field show that a single subwavelength spot size of 320 nm can be generated. The interference pattern within the corral can be controlled by changing the polarization of optical excitation and the degree of symmetry breaking. The intensity enhancement factor was investigated using finite-difference time-domain simulations and confirmed by analytical calculations taking into account the plasmon damping and multiple reflections against the corral wall. KEYWORDS: Plasmon, symmetry breaking, plasmonic corral, scanning near-field optical microscopy, finite-difference time domain
S
urface plasmon polaritons (SPPs) are collective electromagnetic excitations that propagate at an interface between dielectric and metallic layers, evanescently confined in the direction perpendicular to the interface.1 SPP waves have a shorter wavelength and stronger field enhancement than light, making them favorable for many applications. For example, with a shorter wavelength, SPP waves can be focused into smaller subwavelength spot sizes which enable applications in areas such as nano-optics,1,2 super-resolution imaging,3-5 nanolithography,6 high harmonic generation,7 plasmonic waveguiding,8,9 near-field imaging and sensing,10-12 etc. Efforts have been devoted to find a way to focus SPP waves by using constructive interference with appropriate optical excitation, such as incident beams of different polarization.13,14 However, an efficient manipulation of the plasmon focus size, shape, and strength cannot be achieved by only controlling the optical excitation condition, and it is important to pursue also variations in geometries and configurations to optimize the plasmonic focusing effect. For a plasmonic lens (circular groove in the metal film), plasmonic focusing of the SPP-induced perpendicular electric field |Ez| into a single spot at the center cannot be achieved using linearly polarized illumination due to the destructive interference between counter-propagating SPP waves.15-17 However, for the same circular structure, illumination using a radially polarized incident beam results in an intense single focal spot at the geometric center due to the constructive interference of the SPP generated around the corral.18 Thus, compared to linearly polarized excitation, radially polarized illumination achieves a subwavelength focal r 2010 American Chemical Society
spot that can be used for further super-resolution imaging. In practical applications, the use of radially polarized incident light represents a significant challenge since efficient focusing is only achieved when the center of the incident beam is perfectly aligned with the center of the lens. This alignment can be difficult to achieve experimentally and limits the application to an individual circularly symmetric corral. There is therefore a clear need for development of nanostructures that can enable focusing using linearly polarized incident light. Focusing user linear polarization would also enable simultaneous focusing in substrates consisting of multiple lenses and may be of importance in technological applications. In this letter, we designed and fabricated symmetry broken (or phase shifted) plasmonic corrals (protrusions of the film) to generate a single SPP |Ez| focal spot using linearly polarized illumination. The focusing properties of this structure are verified experimentally using scanning near-field optical microscopy (SNOM) for different structural parameters. Finite-difference time-domain (FDTD) simulations were performed to replicate the SPP interference pattern, and the SPP focusing result was also analyzed using an analytical approach considering the energy dissipation during the plasmon propagation. As substrates, both axially symmetric and symmetry broken plasmonic corrals consisting of two semicorrals of different radii Rleft and Rright were fabricated by using the template stripping Received: December 13, 2010 Revised: December 22, 2010 Published: December 27, 2010 893
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Figure 3. Measured near-field optical intensity distribution of axially symmetric plasmonic corrals illuminated by a (a) radially polarized incident laser and (b) linearly polarized incident laser, respectively. The structural parameters of the corral are as in Figure 2.
evaporated onto the negative pattern surface; (iv) a SiO2 substrate glued with an epoxy resin adhesive was used to stick with the Au film; (v) the Au corral then was obtained by stripping off the SiO2 substrate from the PMMA surface. Figure 2a,b shows schematics of the electric fields in an axially symmetric and a symmetry broken plasmonic corral under different optical excitations. The red arrows represent the wave vector of the incident light, and the green and blue arrows indicate different electric field components. The purpose of the symmetry breaking is to generate a phase shift of the propagating SPPs, which can be used to regulate the total phase of the electric field at the corral center. For the symmetry broken structure, this phase shift is determined by the radius mismatch between the left and right side semicorral (Rleft - Rright). Figure 2c,d shows SEM images of an axially symmetric (c) and a symmetry broken (d) plasmonic corrals. The thickness of the Au film is 150 nm, and the height of the corrals is 75 nm. Both corral widths are D = 200 nm, and the inner radius for the symmetric corral is R = 1.5 μm. The left radius of the symmetry broken corral is Rleft = 1.5 μm, and the right radius Rright = is 1.18 μm. The |Ez|2 distribution of the SPP wave was measured using a tapping mode SNOM with a homemade metallic apertureless probe. The tip-sample distance was controlled by a SNOM controller (RHK Co.). The optical signal was collected by using an avalanche photodiode (APD) through an optical lens. In Figure 3, the |Ez|2 distribution is shown for an axially symmetric Au plasmonic corral illuminated by a radially polarized beam. Due to the rotational symmetry of both the corral structure and the optical source, the |Ez| component of the SPPs launched from all azimuthal directions interferes constructively resulting in an intense focal spot at the center of the corral (Figure 3a). From the near-field optical distribution, the field enhancement factor at the corral center can be estimated to be around 8.5 under the radially polarized beam. When the incident laser is switched to linear polarization, as shown in Figure 3b, two distinct SPP focus spots are generated and separate by a dark spot in the center. For the axially symmetric corral, the electric field from the SPPs interferes destructively as discussed elsewhere.14 Figure 4a,b shows the measured near-field distribution for a symmetry broken corral with radius mismatch of 0.5λSPP for radially and linearly polarized illumination taken for the SNOM tip at h = 50 nm above the sample surface. Figure 4a shows the near-field distribution for radial polarization. It can be seen from Figure 4a that there is no constructive SPP interference along the y direction but two distinct focal spots on opposite sides of the center. These two plasmon lobes, with field enhancement around 6.5, are generated by the different phase shift for plasmons
Figure 1. Procedure of the template stripping (TS) method with an EBLpatterned PMMA layer as a template to fabricate high-quality metallic nanostructures.
Figure 2. Schematic of an axially symmetric and a symmetry broken plasmonic corrals under radially (a) and linearly polarized (b) illuminations, respectively. SEM images of Au axially symmetric (c) and symmetry broken plasmonic corral (c) fabricated on the Au film.
(TS) method19,20 as illustrated in Figure 1: (i) A ploymethyl methacrylate (PMMA) film with desired thickness was spun on a Si wafer; (ii) using electron beam lithography (EBL), a circular groove pattern was exposed; (iii) a Au film with the thickness larger than the PMMA layer to ensure complete coverage was 894
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Figure 5. FDTD simulation of |Ez| distribution with the symmetry broken (0.5λSPP) plasmonic corral under linearly polarized illumination. The structural parameters of the corral are D = 200 nm, Rleft = 3.0 μm, and Rright = 2.68 μm.
the FDTD simulations shown in Figure 4d. This kind of SPP interference can be effectively controlled by simply changing the amount of the symmetry breaking (phase shift), e.g., radius mismatch. For a radius mismatch of 1.0λSPP, resulting in a phase shift of 2π, the interference pattern can be turned to destructive resulting in a dark spot in the center; however, when the mismatch increases to 1.5λSPP, the interference again becomes constructive resulting in an even stronger focal spot in the center. The measured focal spot size has a full width at half-maximum (fwhm) diameter around 320 nm (λ/2), which is in the subwavelength scale of the incident light. (See Supporting Information for details.) The SPP radial component |Er| of the symmetry broken corral was also investigated by a collection mode aperture SNOM (Nanonics) using a metal-coated cantilever fiber probe with an aperture size of 50 nm. Figure 4f shows the |Er|2 intensity (around 0.4) for a symmetry broken corral with radius mismatch of 4.5λSPP under a linearly polarized beam. It can be seen that the intensity of the SPP |Ez| component is about 12.5 times higher than the |Er| component. It should be noticed that the period of the fringes outside the left side of the corral is λSPP instead of 0.5λSPP, which is the fringe period outside the right side of the corral. This difference can be understood simply from the interference of the electric fields from the incident light and the field from the SPPs (see Supporting Information for details). Briefly, the directly transmitted light and the field from the SPP are temporally coherent because the SPP is excited by the illuminating light. For the region to the left, the local electric field is the sum of the incident field and the field from the SPP launched at the left semicorral. Any SPP launched at the right semicorral will be reflected back to the right by the much larger left semicorral. The interference of the incident field and the SPP field in the left region thus give an interference pattern of a period of λSPP. However, for the region to the right, the local electric field is the sum of the incident field and the field from SPPs launched at both the left and right semicorrals. The interference between these two SPP waves thus results in an interference pattern of a period 0.5λSPP. To get a better understanding of the focusing property of the symmetry broken plasmonic corral and the spatial dependence of the induced fields, Figure 5 shows the calculated |Ez| distribution in a perpendicular plane through the center. This simulation confirms that most SPP waves are reflected at the corral boundaries and interfere at the geometric center of the structure. The figure
Figure 4. (a,b) SPP |Ez|2 distributions of the symmetry broken corral (0.5λSPP) under radially and linearly polarized lasers taken for the SNOM tip at 50 nm above the sample surface. (c,d) Phase images simulated by the FDTD method with parameters of (a) and (b), respectively. (e) SPP |Ez|2 distribution of the same corral taken for the SNOM tip at 300 nm above the sample surface. (f) SPP |Er|2 distribution of the symmetry broken corral (4.5λSPP) under a linearly polarized laser. The structural parameter of the corrals in panels (a-e) are as in Figure 2, and in panel (f), Rleft = 3.0 μm and Rright = 0.12 μm.
originating from the two semicorrals. This is clearly visible in the phase image simulated with the FDTD method (Figure 4c). The inhomogeneity of the lobe intensity is caused by the radius mismatch of the structure. SPPs are excited at the position of the plasmonic corral and then propagate inward toward the center, thus more SPP propagation modes are excited from the side with a larger radius and thus form a brighter lobe spot. The scattered light can be neglected compared with the field from the SPP modes when the tip-sample distance is smaller than the SPP decay length δSPP in the z direction (δSPP = 181 nm). (See Supporting Information for more details.) We also find that with an increase of the tip-sample distance, the detected intensity of these two lobes decreases (with field enhancements around 3), and finally, the lobe at the right side can be brighter than the left side one, as shown in Figure 4e. The reason for this intensity reversal is that far away from the substrate surface (h = 300 nm, h > δSPP) the scattered light contributes more of the electric field intensity than the SPP modes. (See Supporting Information for details.) These two SPP lobes can be focused to one spot at the center when the incident polarization changed from radial to linear (see Figure 4b). This sharp focal spot with a field enhancement around 5 is induced by the constructive interference at the center, when the relative phase for SPPs launched from the right and left semicorrals differs by π as expected for a radius mismatch of 0.5λSPP. This constructive interference is clearly apparent in 895
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In Figure 6a, the red dashed line shows the results from the analytical prediction of eq 1 with the parameter β determined from FDTD calculations of the field enhancements on the inner surface of the corral wall for each radius and Im(KSPP) approximated by the wave vector of the SPP propagating on an infinite metal surface. The reason why the field enhancements are larger for D = 200 nm than for 150 nm is that the thicker corral has a higher cross section for plasmon excitation resulting in a larger β. It is clear that this simple analytical model well reproduces the results from the full FDTD simulations but that the submicrometer oscillations with corral radius are not accounted for. We now show that these oscillations can be accounted for by considering SPP subsequent multiple reflections against the corral walls. For this case, eq 1 needs to be extended as ¥ X Rn ð2Þ Ez ¥β 3 2πR 3 e - ImðKSPP ÞR n¼0
where n stands for the number of reflections against the corral wall and R is the Ez component after SPP propagation from the center to the wall and then back to the center (a distance 2R). The quantity R can be expressed as R ¼ ηe - 2ImðKSPP ÞR eiφðRÞ
Figure 6. (a) FDTD simulated field enhancement at the center of a symmetric corral for different corral radii R and widths D = 150 nm (black solid) and D = 200 nm (blue solid) for radial polarization. The analytical prediction obtained using eq 1 is shown with the red dashed line. (b) Field enhancement calculated using FDTD (blue) and the analytical prediction taking multiple reflections into account including plasmon damping, eq 2 (green dashed), for D = 200 nm.
shows that the induced electric field is significantly extended in the z-direction. This optical “needle” field is similar to that reported by other groups.14,16,21 In comparison with the plasmonic lens (grooves in metal film), the plasmonic corral can produce stronger focus intensity at the geometric center and also more extended “needle” fields owing to the high SPP reflectivity at the corral boundary. Figure 6a shows the field enhancement in the center of axially symmetric corrals as a function of corral radius R calculated using full FDTD simulations. The figures show results for two different thicknesses, D = 150 and 200 nm. For both wall thicknesses, the field enhancements increase monotonically for small corral radii R and with peaks at an optimal corral radius around 7 μm. For larger corral radii, the field enhancement factors decrease monotonically. The simulation results show that the field enhancements are improved for a larger wall thickness D. Although the results reveal weak submicrometer oscillations with corral radius, the envelopes of the two FDTD simulations are very similar (black and blue solid curves). To develop a more fundamental understanding of the focusing mechanism of the plasmonic corral, a simple analytical model is now developed. Because each small segment DRΔθ of the corral wall can be considered as a SPP launcher, the SPP amplitude in the center of the corral is thus the sum of SPPs launched by each wall segment. When considering the plasmon damping e-Im(KSPP)S, where S is the propagation distance of the SPP waves, the resulting Ez component at the center (from the corral wall to the corral center) can thus be written as E z ¥β 3 2πR 3 e - ImðKSPP ÞR
ð3Þ
where η is the reflection coefficient and φ(R) is the phase shift during the plasmon propagation. Since the SPP in the corral is a cylindrical wave rather than the plane wave, the phase shift φ cannot be expressed as for a plane wave 2Re(KSPP)R þ π. However, for a stationary wave in a onedimensional structure, the φ for the wave propagating from one end to the other end can be directly related to the number of nodes, φ = lπ, in between the boundaries (the phase shift for the neighboring nodes is π). In the Supporting Information, we show how the phase shift φ(R) and reflection coefficient η can be calculated analytically. By substituting these quantities into the expression for R in eq 3, the electric field at the center as eq 2 can be evaluated. Figure 6b shows a comparison between the FDTD simulation and the result from eq 2 for a symmetric corral under radially polarized light illumination as a function of corral radius (R). The analytical calculation now clearly reproduces also the submicrometer oscillations of the electric field in the center of the corral. This analysis can be extended also to the symmetry broken corral and to the case of linear polarization of the incident light (see Supporting Information for details). In conclusion, we have shown that plasmonic focusing into a single focal spot can be accomplished using linearly polarized incident light in a symmetry broken plasmonic corral. For the perpendicular SPP induced electric field, a single focus with a spot size smaller than the diffraction limit (320 nm) was obtained. The experimental results were confirmed by FDTD simulations and analytical calculations including plasmon damping. The symmetry broken plasmonic corrals which can provide focusing using linearly polarized light provide a much simpler plasmonic structure than symmetric corrals or lenses that require radially polarized light and a careful center alignment of the incident light for efficient focusing.
’ ASSOCIATED CONTENT
bS
Supporting Information. Symmetry broken corral under radially polarized illumination; symmetry broken corral under linearly polarized illumination; and analytical calculation model.
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This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We thank Naomi J. Halas for useful discussions and comments. This work was supported by National Basic Research Program of China (973 Program), Grant No. 2007CB936800, and National Natural Science Foundation of China (Grant No. 10574002). PN was supported by the Robert A. Welch Foundation under grant C-1222. ’ REFERENCES (1) Barnes, W. L.; Dereux, A.; Ebbersen, T. W. Nature 2003, 424, 824–830. (2) Ozbay, E. Science 2006, 311, 189–193. (3) Lassiter, J. B.; Sobhani, H.; Fan, J. A.; Kundu, J.; Capasso, F.; Nordlander, P.; Halas, N. J. Nano Lett. 2010, 10, 3184–3189. (4) Liu, Z.; Lee, H.; Xiong, Y.; Sun, C.; Zhang, X. Science 2007, 315, 1686. (5) Smolyaninov, I. I.; Hung, Y.; Davis, C. C. Science 2007, 315, 1699–1701. (6) Vedantam, S.; Lee, H.; Tang, J.; Conway, J.; Staffaroni, M.; Yablonovitch, E. Nano Lett. 2009, 9, 3447–3452. (7) Kim, S.; Jin, J.; Kim, Y.-J.; Park, I.-Y.; Kim, Y.; Kim, S.-W. Nature 2008, 453, 757–760. (8) Bozhevolnyi, S. I.; Volkov, V. S.; Devaux, E.; Laluet, J.; Ebbesen, T. W. Nature 2006, 440, 508–511. (9) Fang, Z. Y.; Lin, C. F.; Ma, R. M.; Huang, S.; Zhu, X. ACS Nano 2010, 4, 75–82. (10) Rothenhaeusler, B.; Knoll, W. Nature 1988, 332, 615–617. (11) Hoeppener, C.; Beams, R.; Novotny, L. Nano Lett. 2009, 9, 903–908. (12) Fang, N.; Lee, H.; Sun, C.; Zhang, X. Science 2005, 308, 534– 537. (13) Babayan, Y.; McMahon, J. M.; Li, S. Z.; Gray, S. K.; Schatz, G. C.; Odom, T. W. ACS Nano 2009, 3, 615–620. (14) Lerman, G. M.; Yanai, A.; Levy, U. Nano Lett. 2009, 9, 2139– 2143. (15) Nordlander, P. ACS Nano 2009, 3, 488–492. (16) Chen, W. B.; Abeysinghe, D. C.; Nelson, R. L.; Zhan, Q. W. Nano Lett. 2009, 9, 4320–4325. (17) Srituravanich, W.; Pan, L.; Wang, Y.; Sun, C.; Bogy, D. B.; Zhang, X. Nat. Nanotechnol. 2008, 3, 733–737. (18) Chen, W. B.; Abeysinghe, D. C.; Nelson, R. L.; Zhan, Q. W. Nano Lett. 2010, 10, 2075–2079. (19) Zhu, X. L.; Zhang, Y.; Zhang, J. S.; Xu, J.; Ma, Y.; Li, Z. Y.; Yu, D. P. Adv. Mater. 201010.1002/adma.20100131. (20) Lindquist, N. C.; Nagpal, P.; Lesuffleur, A.; Norris, D. J.; Oh, S.-H. Nano Lett. 2010, 10, 1369–1373. (21) Wang, H. F.; Shi, L. P.; Lukyanchuk, B.; Sheppard, C.; Chong, C. T. Nat. Photonics 2008, 2, 501–505.
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