Mode Conversion in High-Definition Plasmonic Optical Nanocircuits

Jun 2, 2014 - Symmetric and antisymmetric guided modes on a plasmonic two-wire transmission line have distinct properties and are suitable for differe...
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Mode Conversion in High-Definition Plasmonic Optical Nanocircuits Wen-Hua Dai,† Fan-Cheng Lin,‡ Chen-Bin Huang,† and Jer-Shing Huang*,‡,§,∥ †

Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan § Center for Nanotechnology, Materials Sciences, and Microsystems, National Tsing Hua University, Hsinchu 30013, Taiwan ∥ Frontier Research Center on Fundamental and Applied Sciences of Matters, National Tsing Hua University, Hsinchu 30013, Taiwan ‡

S Supporting Information *

ABSTRACT: Symmetric and antisymmetric guided modes on a plasmonic two-wire transmission line have distinct properties and are suitable for different circuit functions. Being able to locally convert the guided modes is important for realizing multifunctional optical nanocircuits. Here, we experimentally demonstrate successful local conversion between the symmetric and the antisymmetric modes in a single-crystalline gold plasmonic nanocircuit with an optimally designed mode converter for optical signals at 194.2 THz. Mode conversion may find applications in controlling nanoscale light−matter interaction.

KEYWORDS: Surface plasmons, nanoantennas, nanocircuits, plasmonic waveguides

P

low loss. Therefore, the symmetric mode is suitable for power delivery and field amplification with gain materials.24−27 As for the antisymmetric mode, the electric field is tightly confined and highly enhanced in the subwavelength nanogap with welldefined polarization. The extremely small mode volume helps improve the Purcell factor of the typically low-quality-factored plasmonic cavity and thus facilitates nanoscale light−matter interaction.8 For nanoscale wireless communication,28 the antisymmetric mode is also more useful since it drives the radiative modes of a nanoantenna.5,10 In view of realizing multifunctional optical nanocircuits, the ability to convert guided modes at specific positions of interest is particularly important. Here, we present a high-definition single-crystalline gold plasmonic nanocircuit with a mode converter for optical signals at 194.2 THz (vacuum wavelength = 1545 nm). We optimally design and carefully fabricate the nanocircuit with an efficient mode converter, in which phase shift of π between currents on the two wires is introduced by differentiating the wire length. We experimentally demonstrate selective excitation of guided mode and successful local conversion between the symmetric and antisymmetric modes. Explicit mode identification is done by observing the position and the polarization of the scattering signal, since different modes have different impedance and generate scattering signal with mode-dependent polarization at different boundaries.

lasmonic optical nanoantennas can localize light to subwavelength domain and enhance light−matter interaction.1,2 Using plasmonic waveguides, the concentrated optical field can be delivered to positions of interest at the nanoscale.3−6 This offers an opportunity to realize highfrequency optical nanocircuits with subwavelength footprints.7 To give functionalities to the nanocircuits, nanoobjects can be introduced to interact with the near fields and thereby regulate the optical signals.8,9 Since the nanoscale light−matter interaction greatly depends on the degree of impedance matching between the nanoobject and the guided optical field, the ability to control the guided field is of central importance for the realization of functional optical nanocircuits.10 To guide optical signals at nanoscale, metal−insulator−metal (MIM) and insulator−metal−insulator (IMI) plasmonic waveguides are commonly used.11 The simplest IMI waveguide is a single metallic wire.12−15 Two parallel coplanar wires separated by a dielectric nanogap form a plasmonic two-wire transmission line (TWTL).5,16−22 The guided modes on a TWTL can be understood as the hybridization of guided modes on the two individual wires.10,20,22,23 Depending on the phase difference (Δφ) between currents on the two wires, the guided mode on the TWTL can be symmetric (Δφ = 0) or antisymmetric (Δφ = π). The symmetric mode and the antisymmetric mode have distinctively different modal profiles, impedances, and propagation constants and are suitable for different circuit functions. For example, the symmetric mode has a loosen field distribution around the outer surface of the TWTL and exhibits a relatively low effective index, high group velocity, and © XXXX American Chemical Society

Received: March 24, 2014 Revised: May 30, 2014

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symmetry. In this work, we identify the mode by observing both the position and the polarization of the scattering signals. To design a functional plasmonic nanocircuit with an effective mode converter, it is important to know the complex propagation constant of the guided mode. The guided mode on the plasmonic waveguide can be described as ̃

E(r ) = E0eik reiθ

(1)

where k∥̃ is the complex propagation constant and θ is the absolute phase. The real part of the propagation constant describes the phase evolution along the waveguide and determines the path length difference in the design of mode converter.10 The imaginary part concerns the propagation length and limits the total length of the nanocircuit. To convert the modes, an additional phase difference of π between the currents is required.10,20,29 The phase difference in the converter section can be expressed as, Δφ = Re{k ̃ ,1}r1 − Re{k ̃ ,2}r2

(2)

̃ and k∥,2 ̃ are the propagation constants of the where the k∥,1 guided plasmonic modes on the two wires of TWTL. r1and r2 are the corresponding wire lengths in the converter. The propagation constant depends on the wire cross section, wire material, and the environmental index of refraction. In practice, it is challenging to introduce different materials for individual wires or to introduce local index difference for the two wires because they are separated by just a few tens of nanometers. Therefore, in this work, we use two identical wires in a common environment but with different lengths to provide the required phase shift and prove the concept of mode conversion. In this case, the phase shift between the currents is purely determined by the length difference Δr as,

Figure 1. (a) Schematic diagram and modal field distribution of the symmetric (left) and antisymmetric (right) modes on the plasmonic two-wire transmission line. Red hollow double arrows indicate the polarization of the excitation laser. (b) Snapshots of simulated movies taken at 10, 18, and 27 fs, showing that the symmetric (left) mode penetrates the junction and reaches the end of the single metal stripe, whereas the antisymmetric mode (right) is strongly reflected and scattered at the junction interface. The white dashed line marks the position of the junction interface. The straight and bended arrows indicate the propagation and the reflection of the guided modes.

As shown in Figure 1a, the modal field distributions of the symmetric and the antisymmetric mode are quite distinct. Therefore, the excitation polarization and the characteristic impedance of the two modes are completely different. To selectively excite the modes, the polarization of the excitation laser should be carefully controlled such that the symmetry of the excitation and the mode is matched. For the symmetric/ antisymmetric mode, the polarization of the excitation should be parallel/perpendicular to the TWTL.19,22 The distinct impedance leads to totally different power transmission/ reflection efficiency at interfaces where the TWTL connects to other circuit elements. For example, when the TWTL is connected to a single metal stripe (SMS) with same cross section (Figure 1b), the junction interface allows the symmetric mode to pass but reflects the antisymmetric mode. This is due to the fact that symmetric mode has a modal profile well matching that of the fundamental guided mode on a SMS but the antisymmetric mode does not. In Figure 1b, the simulated movie clips clearly show that the symmetric mode does not “see” the TWTL−SMS junction interface and is not scattered until it reaches the very end of the SMS. Differently, the antisymmetric mode is strongly reflected and scattered at the junction interface. Therefore, the TWTL−SMS junction interface serves as a mode filter, which rejects the antisymmetric mode. On the contrary, connecting a TWTL to a dielectric groove in a metal film produces a mode filter at the junction interface, which only allows for the transmission of antisymmetric mode.6 Since different modes encounter a different degree of scattering at the junction interface, one can distinguish the modes by observing the origin position of the scattering signal.19,22 In addition to the scattering position, the polarization of the scattered photons also reveals the mode

Δφ = Re{k ̃ }Δr

(3)

To obtain the phase shift of π, it is required that Δr equals a half of the effective wavelength of the guided mode on a single wire. The complex propagation constant is linked to the complex effective index ñeff of the mode by k ̃ = neff ̃

2π λ0

(4)

The propagation length L of the mode can be calculated from the imaginary part of the effective index using −1 ⎡ 2π ⎤ L = [2k ′]−1 = ⎢2Im{neff ̃ } ⎥ λ0 ⎦ ⎣

(5)

With finite-difference frequency-domain methods (Mode Solver in FDTD Solutions, Lumerical), we numerically solve the complex effective index ñeff for the guided plasmonic modes in our nanocircuits. Limited to the thickness of our selfassembled gold flake (∼100 nm) and the fabrication procedure, we have chosen to use a rectangular cross section (height × width = 100 × 150 nm2) for the wires of the TWTL. The gap between the wires has been set to 100 nm, which is about 1/15 of the vacuum wavelength (1545 nm). Although our fabrication capability allows for fabrication of gap as small as 20 nm, the smallest possible gap size is not always suitable. The design principle is to choose a proper gap size such that reasonable mode confinement and propagation length are obtained. Carefully choosing the length of each circuit section is crucial for plasmonic circuits because plasmonic modes typically B

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For the mode converter section, the relevant quantity is the effective wavelength of the guided mode on a single wire. Using the actual cross section of the fabricated structure, the real part of the effective index is simulated to be 1.3855, corresponding to an effective wavelength of about 1115 nm. Accordingly, the converter is designed to introduce difference in wire length of 558 nm, equivalent to a half of the effective wavelength (Figure 2a). Due to the nanofabrication procedure, all corners in the converter section are designed to be right-angled in this work. Nevertheless, the fabricated structures show rounded corners with a radius of curvature (ROC) of about 50 nm. Our numerical simulations show that, from a straight wire to a bended one with a ROC of 50 nm, the power transmission efficiency drops from 80.9% to 23.1% due to the sharp bends (see Figure S2, Supporting Information). The sharp corners can lead to additional loss and uneven guided power on the two wires, which further results in cross-talk at the output and sets the limit of the mode conversion efficiency. Using adiabatic shape transition for corners should help reduce the loss due to sharp bends. To fabricate high-definition nanocircuits with superior optical property, we employ the hybrid fabrication method, which combines top-down and bottom-up fabrication techniques.30 The structures are fabricated by applying focused-ion beam (FIB) milling into chemically grown single-crystalline gold flakes immobilized on top of a cover glass coated with a thin indium tin oxide layer (40 nm). Using such fabrication technique, we are able to fabricate complex nanocircuits with very high product yield, precision, and reproducibility. Moreover, the fabricated structures are single-crystalline and ultrasmooth. This is important for the success of this work because defects and rough surfaces not only damp the plasmonic mode but also generate background scattering. Figure 2b−d show the scanning electron microscope (SEM) images and zoomed-in images of the gold nanocircuits and mode converter fabricated in this work. For the optical experiment, output from a continuous wave fiber laser (frequency = 194.2 THz, vacuum wavelength = 1545 nm, line width = 1 kHz, NKT Koheras) is collimated, aligned, and focused onto the sample by a microscope objective (100×, N.A. = 0.85, LCPLN100XIR, Olympus). An averaged power of 500 μW at the sample plane is used for the excitation in all experiments. The polarization of the laser is controlled by a λ/2 waveplate (WPH05M, Thorlabs) following a polarizer (LPMIR050, Thorlabs). Since the excitation efficiency for the two modes does not only depend on the polarization but also on the position of the laser focal spot,19 we have carefully adjusted the sample position using a piezo-electric moving stage (P-517.3CD, Physik Instrumente) with a close-loop feedback controller (E-710.C4D, Physik Instrumente) in order to maximize the excitation efficiency for the selected mode. The scattered photons are collected by the same objective and recorded by an InGaAs near-infrared (NIR) camera (acquisition time = 10 ms, Xeva-1.7-320, Xenics). A 50:50 nonpolarizing beam splitter (BS018, Thorlabs) is used to reflect the excitation beam to the sample and to allow the scattering signals to reach the detector. For clear observation of the scattering spots, a beam stop is introduced in front of the NIR camera chip to block the scattering from the laser focal spot. A schematic diagram of the experimental setup can be found in the Supporting Information. To make sure that the two modes can be selectively excited and the scattering signals can be resolved, we first perform the

Figure 2. (a) Design of the gold plasmonic nanocircuit with mode converter. The cross section of the wire is rectangular (height × width = 100 × 150 nm2), and the gap size is 100 nm. The designed path length difference in the converter section is two times the displacement distance marked in red color, i.e., 2 × 279 = 558 nm, equivalent to half of the effective wavelength of the plasmonic mode on a single wire. (b) Scanning electron microscope (SEM) image showing the overview of four gold plasmonic nanocircuits fabricated within one chemically grown self-assembled gold microflake (thickness = 100 nm). The sample is tilted by 52° in this image. (c) Zoomed-in image (top view) of nanocircuit with (right) and without (left) the mode converter in the area marked by yellow dashed rectangle in (b). (d) Zoomed-in image (top view) of the mode converter section in the area marked by blue dashed rectangle in (c).

exhibit higher effective indices and higher losses compared to photonic modes in dielectric waveguides. Taking the dimensions of the rectangular cross section and the gap, losses of the symmetric and antisymmetric mode are simulated to be 2684.8 dB/cm and 7722.3 dB/cm, corresponding to propagation lengths of 16.2 μm and 5.6 μm, respectively. Taking into account the optical resolution of our microscope system, we have carefully designed the length of each section in our nanocircuits such that the scattering signal can be easily observed and resolved. Figure 2a depicts the dimensions of the nanocircuit. The overall length of the circuit is about 8.4 μm, including the first section of TWTL (2.4 μm), the mode converter section (1.0 μm), the second section of TWTL (3.0 μm), and the SMS section (2.0 μm). Such overall length ensures that the scattering signal from the TWTL−SMS junction (signal) is relatively bright compared to the fringes of the excitation focal spot (noise). Under averaged excitation power of 500 μW at the sample plane, the scattering signal typically gives brightness of 3000 counts, and the noise level due to focus fringes is about 200 counts, corresponding to a reasonably high signal-to-noise ratio of about 15. The distance from the TWTL−SMS junction interface to the end of SMS has been designed to be 2.0 μm, which is just long enough for the microscope to spatially resolve the scattering spots. We emphasize the importance of using an optimized circuit length for the observation of bright spots because using a too long waveguide can severely damp the plasmonic mode, while using a too short one may lead to high noise level due to the focus fringes. C

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Figure 3. SEM and optical images of the nanocircuits without (a) and with (b) the mode converter. The laser polarization is parallel (left) and perpendicular (right) to the TWTL in order to selectively excite the symmetric and antisymmetric mode. The polarization of the scattering signals is shown in the normalized polar plots in the corresponding upper panels. Yellow solid lines outline the shape of the nanocircuits, and the gray dashed lines mark the position of the excitation end, junction interface and the end of the nanocircuit. Note that the brightness has been adjusted in order to best visualize the scattering signals. The estimated scattering power in (a) and (b) from left to right are 673 nW, 126 nW, 93 nW, and 20 nW, respectively.

Table 1. Summary of the Simulated Mode Properties and the Experimental Scattering Intensity for Various Conditions input mode (waveguide)

complex effective index, ñ

effective wavelength, λeff (nm)

loss (dB/cm)

propagation length, L (μm)

scattering brightness without MC (counts)

scattering brightness with MC (counts)

symmetric (wire) symmetric (TWTL) antisymmetric (TWTL) symmetric (SMS)

1.3855 + 0.010354i 1.3869 + 0.00760i

1115 1114

3658.2 2684.8

11.9 16.2

673 nW

93 nW

1.4187 + 0.02186i

1089

7722.3

5.6

126 nW

20 nW

1.3913 + 0.00707i

1110

2623.9

17.4

of the excitation since the symmetry of the current is kept inside the nanocircuit. Having confirmed that the two modes can be selectively excited and clearly identified, we further study the mode conversion in a nanocircuit with a well-designed mode converter. As shown in Figure 3b, with a mode converter, the positions of the scattering spots swap. This provides the first direct evidence of mode conversion, which means that the modal field distribution and the impedance of the modes have been changed by the converter. Further analysis on the polarization of the scattering signals reveals a 90° rotation relative to the excitation polarization. This doubly confirms the successful mode conversion in the nanocircuit by the converter. To evaluate the power loss due to the converter, we compare the brightness of the scattering signal in the nanocircuits with and without the mode converter. For the nanocircuit without the mode converter, we have obtained scattering power of 673 nW and 126 nW on the NIR camera for the symmetric and antisymmetric mode, respectively. The difference is a result of the different input and output efficiency as well as the different propagation loss of the two modes. It is worth noting that we did not fabricate the input antenna at the end of TWTL but use the open end as a receiving antenna for simplicity. Such an

optical experiment on the nanocircuit without a converter (Figure 3a). With different excitation polarization, the symmetric and antisymmetric modes in TWTL are selectively excited. These two modes can be clearly distinguished by the position of the scattering spots. While the symmetric mode is scattered at the end of the SMS, the antisymmetric mode is strongly scattered at the TWTL−SMS junction interface. This is in good agreement with the simulated results shown in Figure 1b. In addition to the difference in the spot position, the scattering signals of these two modes also show distinctively different polarization. The top panels in Figure 3a show the polar plots of the scattering signal with the corresponding images and excitation polarization shown in the bottom panels. The scattering of the symmetric mode at the end of SMS shows a polarization axis parallel to the SMS. This is due to the fact that, at the structure boundary, the current represents an effective dipole parallel to the SMS. On the other hand, for the antisymmetric mode, the scattering signal from the end of gap, i.e., the TWTL−SMS junction, is polarized in the direction perpendicular to the long axis of the TWTL, directly revealing that the effective emission dipole at the scattering point is perpendicular to the TWTL. In summary, without the mode converter, the polarization of the scattering is the same as that D

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Figure 4. (a) Frequency dependence of the mode characteristics measured before (red dots) and after (black squares) the mode converter with input of symmetric mode. (b) Frequency dependence of the mode conversion efficiency (blue triangles), power transmission efficiency (red dots), and the overall conversion efficiency (black squares) with the input of symmetric mode. (c) and (d) are plots corresponding to (a) and (b) but with the input of antisymmetric mode.

open end is indeed not optimal for our 194.2 THz optical signal, and the input efficiency should be greatly improved by using a resonant nanoantenna.5,19 With a mode converter section, we have obtained scattering signal of 93 nW and 20 nW for the symmetric-to-antisymmetric and the antisymmetricto-symmetric conversion, respectively. The experimental power transmission efficiency of the nanocircuits without the mode converter is 1.346 × 10−3 and 2.52 × 10−4 for input of symmetric and antisymmetric modes, respectively. With a mode converter, the experimental power transmission efficiency drops to 1.86 × 10−4 and 4 × 10−5 for input of symmetric and antisymmetric modes, respectively. Table 1 summarizes the simulated mode properties and the experimental scattering intensity for all conversion situations under same excitation power. Compared to nanocircuits without converter, the power of the scattering signal is reduced by a factor of about 6. This is due to the reflection at the converter entrance as well as the loss introduced by the addition legs and the bends in the converter section. In particular, the additional loss introduced by the bends in the converter section can lead to uneven power on the two wires in the converter section, which limits the conversion efficiency even though the phase difference is optimal. Consequently, cross-talk and unwanted modes are generated at the output. This effect can be seen in the experimental results shown in Figure 3b. The power of scattering signal shows local maxima (two lobes) with orthogonal polarization, and the polarization contrast is poorer than the case without the mode converter, suggesting incomplete conversion due to the uneven power loss in the conversion section.

Since the mode converter is optimally designed for 194.2 THz, the conversion efficiency is expected to drop as the working frequency is detuned from 194.2 THz. To address this issue of operational bandwidth, we have carried out threedimensional FDTD simulations to obtain the dependence of four quantities on the working frequency. They are the mode characteristic, MC; the mode conversion efficiency, ηm; the power transmission efficiency, ηp; and the overall conversion efficiency, ηoverall. Details about these quantities can be found in our previous publication.10 Briefly, the mode characteristic (MC) reports the spatial distribution of the guided power and is defined as MC = (Ptotal − 2Pgap)/Ptotal with Ptotal being the time-averaged total guided power and the Pgap being the power flux through an optimized cross-sectional area Agap. For a purely antisymmetric mode and a purely symmetric mode, the MC would have an ideal value of −1 and +1, respectively. However, these two modes are not orthogonal and partially overlap in space. Therefore, the MC value never reaches the extreme value of ±1. In this work, we have optimized the Agap to obtain the largest difference in MC (ΔMCmax) for purely symmetric and purely antisymmetric mode, ensuring the best sensitivity to the change of modal distribution of the guided optical mode. The mode conversion efficiency ηm is evaluated using ηm = (|MCout − MCin|)/ΔMCmax, where MCin and MCout are the mode characteristics recorded before and after the mode converter, respectively. Taking into account the power transmission efficiency, ηp = Pout/Pin, we then obtain the overall conversion efficiency ηoverall = ηp·ηm. Figure 4a and c show the MCs as functions of the operational frequency for input of symmetric and antisymmetric mode, respectively. For both input modes, the MC values recorded before the converter section E

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(2) Biagioni, P.; Huang, J.-S.; Hecht, B. Rep. Prog. Phys. 2012, 75, 024402. (3) Bozhevolnyi, S. I.; Volkov, V. S.; Devaux, E.; Ebbesen, T. W. Phys. Rev. Lett. 2005, 95, 046802. (4) Bozhevolnyi, S. I.; Volkov, V. S.; Devaux, E.; Laluet, J.-Y.; Ebbesen, T. W. Nature 2006, 440, 508−511. (5) Huang, J.-S.; Feichtner, T.; Biagioni, P.; Hecht, B. Nano Lett. 2009, 9, 1897−1902. (6) Wen, J.; Romanov, S.; Peschel, U. Opt. Express 2009, 17, 5925− 5932. (7) Schuller, J. A.; Barnard, E. S.; Cai, W.; Jun, Y. C.; White, J. S.; Brongersma, M. L. Nat. Mater. 2010, 9, 193−204. (8) Chang, D. E.; Sørensen, A. S.; Hemmer, P. R.; Lukin, M. D. Phys. Rev. Lett. 2006, 97, 053002. (9) Chang, D. E.; Sorensen, A. S.; Demler, E. A.; Lukin, M. D. Nat. Phys. 2007, 3, 807−812. (10) Hung, Y.-T.; Huang, C.-B.; Huang, J.-S. Opt. Express 2012, 20, 20342−20355. (11) Maier, S. A. Plasmonics: Fundamentals and Applications; Springer: Berlin, 2007; pp 21−37. (12) Takahara, J.; Yamagishi, S.; Taki, H.; Morimoto, A.; Kobayashi, T. Opt. Lett. 1997, 22, 475−477. (13) Verhagen, E.; Spasenović, M.; Polman, A.; Kuipers, L. Phys. Rev. Lett. 2009, 102, 203904. (14) Zhang, S.; Wei, H.; Bao, K.; Håkanson, U.; Halas, N. J.; Nordlander, P.; Xu, H. Phys. Rev. Lett. 2011, 107, 096801. (15) Rewitz, C.; Keitzl, T.; Tuchscherer, P.; Huang, J.-S.; Geisler, P.; Razinskas, G.; Hecht, B.; Brixner, T. Nano Lett. 2012, 12, 45−49. (16) Krenz, P. M.; Olmon, R. L.; Lail, B. A.; Raschke, M. B.; Boreman, G. D. Opt. Express 2010, 18, 21678−21686. (17) Schnell, M.; Alonso Gonzalez, P.; Arzubiaga, L.; Casanova, F.; Hueso, L. E.; Chuvilin, A.; Hillenbrand, R. Nat. Photonics 2011, 5, 283−287. (18) Choo, H.; Kim, M.-K.; Staffaroni, M.; Seok, T. J.; Bokor, J.; Cabrini, S.; Schuck, P. J.; Wu, M. C.; Yablonovitch, E. Nat. Photonics 2012, 6, 838−844. (19) Geisler, P.; Razinskas, G.; Krauss, E.; Wu, X.; Rewitz, C.; Tuchscherer, P.; Goetz, S.; Huang, C.-B.; Brixner, T.; Hecht, B. Phys. Rev. Lett. 2013, 111, 183901. (20) Sun, S.; Chen, H.-T.; Zheng, W.-J.; Guo, G.-Y. Opt. Express 2013, 21, 14591−14605. (21) Blanco-Redondo, A.; Sarriugarte, P.; Garcia-Adeva, A.; Zubia, J.; Hillenbrand, R. Appl. Phys. Lett. 2014, 104, 011105. (22) Ly-Gagnon, D.-S.; Balram, K. C.; White, J. S.; Wahl, P.; Brongersma, M. L.; Miller, D. A. B. Nanophotonics 2012, 1, 9−16. (23) Huang, J.-S.; Kern, J.; Geisler, P.; Weinmann, P.; Kamp, M.; Forchel, A.; Biagioni, P.; Hecht, B. Nano Lett. 2010, 10, 2105−2110. (24) Bergman, D. J.; Stockman, M. I. Phys. Rev. Lett. 2003, 90, 027402. (25) Noginov, M. A.; Podolskiy, V. A.; Zhu, G.; Mayy, M.; Bahoura, M.; Adegoke, J. A.; Ritzo, B. A.; Reynolds, K. Opt. Express 2008, 16, 1385−1392. (26) Gather, M. C.; Meerholz, K.; Danz, N.; Leosson, K. Nat. Photonics 2010, 4, 457−461. (27) Berini, P.; De Leon, I. Nat. Photonics 2012, 6, 16−24. (28) Alu, A.; Engheta, N. Phys. Rev. Lett. 2010, 104, 213902. (29) Castro, J. M.; Geraghty, D. F.; Honkanen, S.; Greiner, C. M.; Iazikov, D.; Mossberg, T. W. Opt. Express 2005, 13, 4180−4184. (30) Huang, J.-S.; Callegari, V.; Geisler, P.; Brüning, C.; Kern, J.; Prangsma, C. J.; Wu, X.; Ziegler, J.; Weinmann, P.; Kamp, M.; Forchel, A.; Biagioni, P.; Sennhauser, U.; Hecht, B. Nat. Commun. 2010, 1, 150. (31) Kats, M. A.; Blanchard, R.; Genevet, P.; Yang, Z.; Qazilbash, M. M.; Basov, D. N.; Ramanathan, S.; Capasso, F. Opt. Lett. 2013, 38, 368−370. (32) Chen, Y. G.; Kao, T. S.; Ng, B.; Li, X.; Luo, X. G.; Luk’yanchuk, B.; Maier, S. A.; Hong, M. H. Opt. Express 2013, 21, 13691−13698. (33) Dickson, W.; Wurtz, G. A.; Evans, P. R.; Pollard, R. J.; Zayats, A. V. Nano Lett. 2008, 8, 281−286.

significantly change after the guided mode passing through the converter section. The difference in MC values show a maximum value at the default working frequency of 194.2 THz and decreases as the frequency is detuned from 194.2 THz. Using the MC values in Figure 4a and c, we have obtained the mode conversion efficiency ηm as a function of frequency (blue triangles in Figure 4b and d). The mode conversion efficiency has a maximum value around default operational frequency. Together with the simulated power transmission efficiency ηp (red dots in Figure 4b and d), we have obtained the overall conversion efficiency ηoverall as a function of frequency (black squares in Figure 4b and d). Within the studied frequency window, the simulated overall conversion efficiencies for input of the symmetric mode and the antisymmetric mode are 11−17% and 21−34%, respectively. Note that such simulated efficiencies do not take into account the in-coupling efficiency at the TWTL input end and the scattering efficiency at the end of gap and the end of SMS. Therefore, they cannot be directly compared to the experimental data. Nevertheless, such analysis helps us understand the working bandwidth of the converter section. In conclusion, we have designed and fabricated highdefinition single-crystalline gold plasmonic nanocircuits and demonstrated successful local mode conversion for optical signals at 194.2 THz. The mode conversion is confirmed by observing the position and the polarization of the scattering signals. To enable active control capability, index tunable materials such as phase transition materials31,32 or liquid crystals33 can be incorporated into mode converter in order to modify the surrounding index of refraction. Since changing the environmental refractive index modifies the propagation constant of the modes on a single wire, the phase shift described in eq 3 can be tuned by the index tunable materials. Under such condition, the nanocircuit with a converter can serve as a plasmonic logic gate that can be controlled by an external input signal, such as light, heat, or electricity. With the ability to locally convert modes, plasmonic optical nanocircuits can be designed to have multiple functions and may find applications in manipulation of light−matter interaction at the nanoscale.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental setup. Effects of sharp bends. 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 Supports from Ministry of Science and Technology of Taiwan under Contract Nos. NSC-99-2113-M-007-020-MY2, NSC101-2113-M-007-002-MY2, and NSC-100-2112-M-007-007MY3 are gratefully acknowledged. J.S.H. thanks C.-S. Huang and the support from Center for Nanotechnology, Materials Sciences, and Microsystems at National Tsing Hua University.

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REFERENCES

(1) Novotny, L.; van Hulst, N. Nat. Photonics 2011, 5, 83−90. F

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