Letter pubs.acs.org/NanoLett
Deep-Subwavelength Semiconductor Nanowire Surface Plasmon Polariton Couplers Patrick E. Landreman and Mark L. Brongersma* Geballe Laboratory for Advanced Materials, Stanford University, 476 Lomita Mall, Stanford, California 94305, United States S Supporting Information *
ABSTRACT: The increased importance of plasmonic devices has prompted a sizable research activity directed toward the development of ultracompact and high-performance couplers. Here, we present a novel scheme for efficient, highly localized, and directional sourcing of surface plasmon polaritons (SPPs) that relies on the excitation of leaky mode optical resonances supported by high-refractive index, semiconductor nanowires. High coupling efficiencies are demonstrated via finite difference frequency domain simulations and experimentally by leakage radiation microscopy. This efficiency is quantified by means of a coupling cross section, the magnitude of which can exceed twice the geometric cross section of the nanowire by exploiting its leaky resonant modes. We provide intuition into why the SPP coupling via certain wire modes is more effective than others based on their symmetry properties. Furthermore, we provide an example showing that dielectric scatterers may perform as well as metallic scatterers in coupling to SPPs. KEYWORDS: Nanowires, leakage radiation microscopy, surface plasmon, mode coupling, mie theory lasmonics is an active field of science and technology that aims to manipulate light below the diffraction limit with nanoscale metallic structures.1 A diverse set of plasmonics applications continues to emerge in areas including information technology,2 interface science,3 and biological sensing.4 Many of these rely on an ability to controllably excite and manipulate the propagation of surface plasmon polaritons (SPPs) on extended metal structures. For this reason, it is important to develop increasingly effective methods to locally excite and direct SPPs on metal surfaces. The intrinsic momentum mismatch between free-space photons and SPPs dictates that a coupling structure is needed to excite SPPs. Numerous techniques for sourcing these waves exist. The most well-established are those proposed by Kretschmann5 and Otto,6 which employ a high refractive index glass prism or microscope objective.7,8 Periodic grating structures can also provide the required momentum to incident photons to allow for efficient coupling to SPPs.9 In both cases, the coupling structures are much larger than the wavelength of light. To accomplish a highly localized excitation of propagating SPPs, one can use subwavelength light scatterers,10−14 illumination of truncations of films and wires,15 optical excitation via near-field optical microscopy tips,16 inelastic electron tunneling from STM tips,17 high energy electron beams in electron microscopes,18,19 or optically excited quantum emitters near metal surfaces, including dyes,20 semiconductor nanocrystals,21 and nanotubes.22 The highly localized nature of these structures is accompanied by access to a broad range of momentum values, and this allows for direct excitation of a SPP mode. Using more complex structures SPPs
P
© XXXX American Chemical Society
can also be launched into a specific, desired direction23−26 and in a spectrally selective fashion.27 Recently electrically pumped SPP LEDs28−31 and lasers32,33 have also been demonstrated which allow for integration of plasmonic devices with electronic and dielectric optical components. Separate from the development of SPP launchers, there has been a growing interest in the strong light scattering properties of high refractive index semiconductor nanostructures. Such structures support resonant optical modes whose resonant frequency can be tuned across the visible and infrared spectral range.34−40 As the strength of dielectric scattering resonances rivals that of plasmonic resonances, it is an interesting question whether deep-subwavelength dielectric structures can be used to also effectively launch SPPs.41 As of yet, it is unknown whether one can make use of the optical resonances in these structures to effectively launch SPPs without the undesired intrinsic optical losses associated with using nanometallic launchers. In this study we quantify the ability of high-index, semiconductor nanowires (NWs) to launch SPPs. Such wires can be grown with extreme control over size and from many different semiconductor materials. We use Si NWs of various diameters and investigate the spectral efficiency of the coupling. Our research demonstrates that the resonant optical modes supported by these structures can be used to realize efficient coupling at a desired target frequency, which is controlled by Received: August 8, 2013 Revised: December 10, 2013
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scattering problem, we start with a discussion of the scattering properties of cylinders in a uniform medium and then proceed by adding the metal. In analyzing the scattering properties of NWs, it is helpful to view them as miniaturized versions of the well-established microcylinder resonators that can trap light in circulating orbits by multiple total internal reflections from the periphery. Based on this viewpoint, it can be understood that scattering resonances occur whenever an integer number of wavelengths fits around the circumference of the wire. These resonances enable the NWs to serve as optical antennas capable of collecting and concentrating light from areas much greater than their geometrical cross-section. In Mie theory, this is quantified in terms of a scattering cross section σsca which is given by the ratio of scattered power to the power incident on the scatterer. By normalizing σsca to the geometric area of the NW, one obtains a relative scattering cross section, denoted as the scattering efficiency Qsca. Figure 2a shows calculations of Qsca for top-illuminated, infinitely long Si NWs versus the NW diameter and incident wavelength. The polarization direction of the electric field was chosen normal to the NW axis (TE illumination). This allows excitation of TE modes of the NW and subsequent coupling to longitudinal SPP waves that propagate away from the NW. The most striking features of this plot are the scattering resonances that redshift linearly with increasing NW diameter. This observation is consistent with our intuitive expectation to observe resonances whenever an integer number of wavelengths fit around the NW circumference. It is noteworthy that under optimal conditions a NW may exhibit a scattering cross section over four times larger than its physical size. This is indicative of an optical antenna effect in which free-space light waves first couple to a localized, leaky resonant mode of a nanostructure and subsequently are reradiated (i.e., scattered) according to the optical properties of the excited mode. In order to understand the scattering properties of the NW, it is thus important to analyze the nature of its leaky optical modes. Following the Mie solution to Maxwell’s equations for light scattering from a sphere, the resonant scattering properties of a cylindrical NW can be determined by decomposing the incident, scattered, and internal electromagnetic fields into a basis set of vector cylindrical harmonics. The enforcement of boundary conditions on the NW surface then allows for computation of the expansion coefficients of the scattered field. For a top-illuminated cylindrical NW in vacuum, the leaky mode resonances (LMRs) occur when
the NW size and refractive index. Figure 1a shows a schematic of an experiment in which SPPs are launched by a Si NW. The
Figure 1. (a) Illustration of the coupling geometry, where a silicon nanowire placed on a semi-infinite gold film is illuminated by a plane wave at normal incidence. The field components of a surface plasmon propagating away from the wire require magnetic fields parallel to the wire axis. (b) The nanowire can be described as having a SPP coupling cross section σSPP that quantifies the effectiveness of the coupling of free-space photons to SPPs. (c) Electromagnetic simulation of the SPP launching. The region bounded within the dashed line displays the total field (TF) resulting from a plane wave incident on a Si NW with a 10 nm oxide shell. Outside of the bounded region, only the scattered light due to the presence of the wire is visible. The color scale has been saturated to highlight the presence of SPP-like and free-space modes in the scattered field (SF).
Jm′ (nkoa) Jm (nkoa)
NW (purple) is top-illuminated with a collimated beam of light (green). The polarization of the incident light is chosen to allow coupling to transverse magnetic SPP waves on an Au film. In Figure 1b we define a SPP coupling cross section σSPP as the ratio of the total power of the SPPs launched to the left and right (PT = PL + PR) to the power flow per unit length for an incident plane wave flux, |S⃗inc|. By normalizing σSPP to the NW’s geometrical area one obtains a SPP coupling efficiency QSPP. Figure 1c shows an example of a finite difference frequency domain (FDFD) simulation by which the coupling efficiency can be estimated. The light scattering properties of subwavelength cylinders are well understood and described by the analytical Lorentz−Mie formalism.42 In anticipation that the launching of SPPs by a NW will bear a strong resemblance to this famous light
=n
Hm′ (koa) Hm(koa)
(1)
for TE illumination. Here, n is the index of refraction of the NW, ko the free-space wavevector of light, a the radius of the cylinder, Jm the mth order Bessel function of the first kind, and Hm the mth order Hankel function of the first kind. The magnitude of m corresponds to a term in the expansion of the scattered fields into cylindrical vector harmonic components (m = 0, 1, 2, etc.). This number also conveniently denotes the number of effective wavelengths that fit around the circumference of the wire (as determined by the number of nodes in the field). The inset field plots in Figure 2a display several of the lowest-order resonant field patterns. Next, we analyze how the light scattering properties of a NW are modified when placed near a metal surface. Metals support SPP modes and thus provide a new scattering channel for the B
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Figure 2. (a) Free-space scattering efficiency of a top-illuminated Si NW surrounded by vacuum. Bands of high scattering efficiency arise from the excitation of leaky mode resonances supported by such NWs. Insets depict the real magnetic field within NWs of different diameter as excited by a plane wave (images have been scaled to allow easy comparison of the field profiles). (b) Numerical solution for the SPP coupling efficiency of a wire placed on a semi-infinite gold film. Scattering resonances are lightly perturbed but retain their characteristic redshift with increasing size as well as their field patterns. Horizontal lines indicate the NW diameters that were analyzed experimentally.
mode must match that of a SPP mode, which possesses a dominant electric field normal to the metallic interface. Thus, we can understand the high SPP coupling efficiency seen in Figure 2b via the excitation of a TE01 mode of the NW, the angular symmetry of which results in a strong electric field normal to the metal surface on both sides of the wire (see Figure 3a). The TE11 mode, characterized by a strong, in-plane
NW. To quantitatively explore the scattering into this channel, we map the SPP coupling efficiency QSPP for a normally incident TE plane wave versus the NW diameter and illumination wavelength (see Figure 2b). This quantity is calculated by taking the ratio of the SPP coupling cross section and the geometric cross section of the NW. To obtain values for QSPP, we simulated a Si cylinder with a 10-nm-thick oxide shell placed in contact with a semi-infinite gold slab using a home-built FDFD solver. After computing the scattered fields near the NW, the power carried by the launched SPPs was obtained by an overlap integral technique that projects out the SPP part of the field.43 Full details of this calculation are available in the Supporting Information of this paper. The maps of Qsca and QSPP look qualitatively similar, and both feature a multitude of bands that are linked to the excitation of various LMRs. We find a maximum value for QSPP of ∼2.1 in the considered parameter space. This indicates that we can design a NW coupler capable of capturing incident light from an effective area over twice its geometrical size and coupling that power into SPPs, equally directed to the left and right. It is of value to note that the free-space scattering efficiencies are similar in magnitude to the SPP coupling efficiencies. Whereas the scattered light from a NW in free space is distributed over a large number of different free-space channels (i.e., different directions), the metal surface offers an opportunity to scatter light very effectively into one well-defined SPP mode. The difference between the maps of Qsca and QSPP may be attributed to two factors. First, the excitation fields producing the scattering in each case are quite different. The NW in free space only sees an incident plane wave, while a NW near a substrate is subject to both the incident plane wave as well as the wave reflected from the metal surface. When the wire is close to the surface, near-field interactions between the highindex NW and metal further complicate the scattering problem. Second, to attain efficient coupling to SPPs, coupled mode theory44 dictates that the angular symmetry of a given NW
Figure 3. Cross-sectional electric and magnetic field patterns associated with the two lowest-order TE leaky modes supported by a semiconductor NW. The TE01 mode (a) represents a magnetic dipole excited along the NW axis with strong E field components in the vertical direction on the left and right of the wire. The TE11 mode (b) serves as an electric dipole directed in the horizontal plane. On the left and right of the wire, regions with opposing electric fields in the vertical direction are found. The fields of a propagating SPP are shown in c for comparison.
electric field, is less effective at coupling to SPPs (see Figure 3b) despite that, in free space, this mode features a higher scattering efficiency than the TE01 mode. For higher order modes, featuring more complex field profiles, it becomes increasingly difficult to predict the field coupling without fullfield simulations. Having demonstrated that NWs should effectively couple light to SPPs via simulations, we set out to experimentally verify this using leakage radiation microscopy (LRM). LRM is a wellestablished37,45,46 technique that provides both real-space and C
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length was selected with an acousto-optical tunable filter (AOTF). After passing through a single-mode fiber (used as a spatial filter), a Gaussian beam was generated and directed onto a NW. The alignment of the Gaussian illumination and the NW was established using the real image output of the LRM as shown in Figure 4b. A typical k-space image taken at the back-focal plane of our LRM is shown in Figure 4d. The dark region in the center is created by a beam block, used to prevent the directly transmitted laser beam from saturating the CCD. Two bright ⃗ and −kSPP ⃗ for features occur at the expected location of kSPP plasmons propagating away from the NW in a direction normal to the NW axis. Single NWs thus serve as bidirectional SPP launchers. For each illumination wavelength, the power coupled to SPPs was quantified by integrating the pixel counts in the red ⃗ at that particular wavelength. This power was spot around kSPP then normalized by the total power in the illumination spot, producing a value proportional to QSPP. Figure 5 shows the results of repeating the above process for four different NWs and for a range of visible wavelengths to
reciprocal-space images of SPPs propagating on metal films. SPPs propagating on the top surface of a thin Au film can couple (i.e., “leak”) into propagating modes in a high-index, glass substrate. This leakage radiation is directed into a welldefined angle θLR that is determined by the magnitude of the SPP propagation constant kSPP and the magnitude of the freespace k-vector in the substrate ksub. The reason for this is that momentum matching requires that the parallel component of the k-vector in the glass must equal the magnitude of kSPP (see Figure 4a).
Figure 4. Overview of leakage radiation microscopy on Si nanowires. (a) Schematic showing the leaky SPP mode supported by a thin Au film on a silica substrate. The wavevectors of the SPP and leakage radiation that is coupled at an angle θLR are shown. The inset shows a scanning electron microscopy (SEM) image of a typical CVD-grown Si NW that is 430 nm in diameter. (b) Optical microscope image of a 250 nm diameter Si NW on a 40 nm Au film, illuminated by white light. The image is collected through the Au-covered glass substrate. (c) The same NW illuminated with the supercontinuum source at a wavelength of 555 nm. A beam block in the back focal image plane removes the direct transmission from the laser source, resulting in a dark field image. The high- and low-periodicity fringes result from interference between free-space scattered light and SPP leakage radiation. (d) The k-space image taken by LRM. Each pixel in this image corresponds to a unique scattering angle of light, or, alternatively, a unique k-vector in the plane of the metal film. The gray circle (solid line) outlines a region in k-space (ie. a solid scattering angle) from which no light is collected due to the presence of the beam block in the LRM. The magnitude of the SPP wavevector for our sample geometry is indicated by the dashed circle. The red spots on this circle indicate the generation of SPPs in two well-defined directions normal to the NW length. The pixel intensity of these fringes can be integrated as a measure of the power launched in SPPs.
Figure 5. Comparison of experimental and simulated results. The blue dots indicate values measured by LRM (right axis), while the red solid line corresponds to values calculated from FDFD simulations (left axis). The simulated results shown here are indicated by horizontal, dashed lines in Figure 2b. Error bars represent one standard deviation from repeated application of our image processing algorithm.
Silicon NWs were grown from Au nanoparticle catalysts by chemical vapor deposition (CVD).47 These wires were spuncast onto a glass slide covered with a 40-nm-thick Au film. The diameters of several NWs were measured in a scanning electron microscope (see inset to Figure 4a). The diameters of the selected NWs are indicated with horizontal white lines on Figure 2b. The NWs were top-illuminated with visible light from a supercontinuum laser source. The illumination wave-
realize coupling efficiency spectra. These experimental spectra are plotted alongside our numerically predicted spectra, which are the cross sections to Figure 2b as indicated by the dashed white lines. There is reasonable quantitative agreement between the experiments and the calculations in terms of the spectral position, width, and magnitude of the coupling features. D
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Additional simulations confirmed that subtle modifications of the NW shape near the metal surface can modify the spectral shape and relative magnitude of coupling features, although the position and width of these features are similar (see Supporting Information). We believe that this explains the discrepancies between our experimental and simulated results. Having demonstrated that a dielectric scatterer is capable of effectively coupling to SPPs, it remains to consider the strength of this coupling vis-à-vis metallic nanoparticles. Metals are often considered more lossy than semiconductors in the visible regime; thus one might expect semiconductor resonators to possess a higher quality factor and thus possibly a higher SPP coupling efficiency. Based on this premise, we repeated our FDFD calculations for a Au cylinder and one of indium tin oxide (ITO) above its plasma frequency, where it serves as a semiconductor. The permittivities for Au were derived from the same Drude model as was used for the Au substrate; those of ITO were obtained from ellipsometry measurements of sputtered films. At a wavelength of 550 nm, the permittivity measured for ITO was 3.69 − 0.19j. Figure 6 compares the
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ASSOCIATED CONTENT
S Supporting Information *
Calculation of QSPP from finite-difference simulations, dependence of coupling features on NW shape, and impact of absorption in semiconductor materials on SPP coupling efficiency. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Special thanks go to Dr. Anu Chandran, Prof. Erik Garnett, Dr. Pengyu Fan, Dr. Edward Barnard, and Dr. Alok Vasudev for myriad helpful discussions and technical support on this project. Tom Carver of the Stanford Microfabrication Facility deposited the metals for our substrates. We would like to thank the Air Force Office of Scientific Research (AFOSR) and the United States Department of Energy for their generous financial support.
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REFERENCES
(1) Schuller, J. A.; Barnard, E. S.; Cai, W.; Jun, Y. C.; White, J. S.; Brongersma, M. L. Nat. Mater. 2010, 9, 193−204. (2) Cai, W.; White, J.; Brongersma, M. Nano Lett. 2009, 9, 4403− 4411. (3) Sigal, G. B.; Mrksich, M.; Whitesides, G. M. Langmuir 1997, 13, 2749−2755. (4) Anker, J. N.; Hall, W. P.; Nilam, C.; Zhao, J.; Van Duyne, R. Nat. Mater. 2008, 7, 442−453. (5) Kretschmann, E. Z. Phys. 1971, 241, 313−324. (6) Otto, A. Z. Phys. 1968, 216, 398−410. (7) Kano, H.; Mizuguchi, S.; Kawata, S. J. Opt. Soc. Am. B 1998, 15, 1381−1386. (8) Zia, R.; Schuller, J.; Brongersma, M. Phys. Rev. B 2006, 74, 1−12. (9) Kitson, S.; Barnes, W.; Sambles, J. Phys. Rev. Lett. 1996, 77, 2670−2673. (10) Smolyaninov, I.; Mazzoni, D.; Davis, C. Phys. Rev. Lett. 1996, 77, 3877−3880. (11) Ditlbacher, H.; Krenn, J. R.; Felidj, N.; Lamprecht, B.; Schider, G.; Salerno, M.; Leitner, A.; Aussenegg, F. R. Appl. Phys. Lett. 2002, 80, 404. (12) Mock, J. J.; Hill, R. T.; Degiron, A.; Zauscher, S.; Chilkoti, A.; Smith, D. R. Nano Lett. 2008, 8, 2245−52. (13) Knight, M. W.; Grady, N. K.; Bardhan, R.; Hao, F.; Nordlander, P.; Halas, N. J. Nano Lett. 2007, 7, 2346−50. (14) Hu, M.; Ghoshal, A.; Marquez, M.; Kik, P. G. J. Phys. Chem. C 2010, 114, 7509−7514. (15) Ditlbacher, H.; Hohenau, A.; Wagner, D.; Kreibig, U.; Rogers, M.; Hofer, F.; Aussenegg, F.; Krenn, J. Phys. Rev. Lett. 2005, 95, 257403. (16) Hecht, B.; Bielefeldt, H.; Novotny, L.; Inouye, Y.; Pohl, D. Phys. Rev. Lett. 1996, 77, 1889−1892. (17) Berndt, R.; Gimzewski, J.; Johansson, P. Phys. Rev. Lett. 1991, 67, 3796−3799. (18) Bashevoy, M. V; Jonsson, F.; Krasavin, a V; Zheludev, N. I.; Chen, Y.; Stockman, M. I. Nano Lett. 2006, 6, 1113−5. (19) Cai, W.; Sainidou, R.; Xu, J.; Polman, A.; García de Abajo, F. J. Nano Lett. 2009, 9, 1176−81. (20) Lakowicz, J. R.; Ray, K.; Chowdhury, M.; Szmacinski, H.; Fu, Y.; Zhang, J.; Nowaczyk, K. Analyst 2008, 133, 1308−46.
Figure 6. Simulated coupling efficiencies of metallic vs dielectric subwavelength scatterers. The geometry is identical to that of the Si NW case. The wavelength of the incident light (550 nm) was chosen to be below the bandgap of ITO (
