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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 18 — Aug. 27, 2012
  • pp: 20342–20355
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Plasmonic mode converter for controlling optical impedance and nanoscale light-matter interaction

Yun-Ting Hung, Chen-Bin Huang, and Jer-Shing Huang  »View Author Affiliations


Optics Express, Vol. 20, Issue 18, pp. 20342-20355 (2012)
http://dx.doi.org/10.1364/OE.20.020342


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Abstract

To enable multiple functions of plasmonic nanocircuits, it is of key importance to control the propagation properties and the modal distribution of the guided optical modes such that their impedance matches to that of nearby quantum systems and desired light-matter interaction can be achieved. Here, we present efficient mode converters for manipulating guided modes on a plasmonic two-wire transmission line. The mode conversion is achieved through varying the path length, wire cross section and the surrounding index of refraction. Instead of pure optical interference, strong near-field coupling of surface plasmons results in great momentum splitting and modal profile variation. We theoretically demonstrate control over nanoantenna radiation and discuss the possibility to enhance nanoscale light-matter interaction. The proposed converter may find applications in surface plasmon amplification, index sensing and enhanced nanoscale spectroscopy.

© 2012 OSA

1. Introduction

Surface plasmon polaritons (SPPs) are promising for the realization of optical nanocircuits [1

1. E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

] and provide possible solutions to control light-matter interaction on the nanometer scale [2

2. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]

], paving the way to quantum optics with surface plasmons [3

3. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006). [CrossRef] [PubMed]

, 4

4. D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3(11), 807–812 (2007). [CrossRef]

]. Recently, prototype nanocircuits using gap nanoantennas [5

5. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011). [CrossRef]

, 6

6. P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75(2), 024402 (2012). [CrossRef] [PubMed]

] in connection with plasmonic two-wire transmission lines (TWTLs) have been theoretically proposed [7

7. J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009). [CrossRef] [PubMed]

9

9. J.-S. Huang, D. V. Voronine, P. Tuchscherer, T. Brixner, and B. Hecht, “Deterministic spatiotemporal control of optical fields in nanoantennas and plasmonic circuits,” Phys. Rev. B 79(19), 195441 (2009). [CrossRef]

] and experimentally studied [10

10. P. M. Krenz, R. L. Olmon, B. A. Lail, M. B. Raschke, and G. D. Boreman, “Near-field measurement of infrared coplanar strip transmission line attenuation and propagation constants,” Opt. Express 18(21), 21678–21686 (2010). [CrossRef] [PubMed]

12

12. J. Wen, P. Banzer, A. Kriesch, D. Ploss, B. Schmauss, and U. Peschel, “Experimental cross-polarization detection of coupling far-field light to highly confined plasmonic gap modes via nanoantennas,” Appl. Phys. Lett. 98(10), 101109 (2011). [CrossRef]

], showing a realizable approach to the manipulation of electromagnetic field for enhanced spectroscopy [13

13. N. Yang, Y. Tang, and A. E. Cohen, “Spectroscopy in sculpted fields,” Nano Today 4(3), 269–279 (2009). [CrossRef]

, 14

14. S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: Plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012). [CrossRef]

]

In order to guide the localized optical fields, various plasmonic nanowaveguides have been proposed and studied [15

15. J. C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, “Near-field observation of surface plasmon polariton propagation on thin metal stripes,” Phys. Rev. B 64(4), 045411 (2001). [CrossRef]

20

20. C. Rewitz, T. Keitzl, P. Tuchscherer, J.-S. Huang, P. Geisler, G. Razinskas, B. Hecht, and T. Brixner, “Ultrafast plasmon propagation in nanowires characterized by far-field spectral interferometry,” Nano Lett. 12(1), 45–49 (2012). [CrossRef] [PubMed]

]. Two commonly used waveguides are metal nanowires [15

15. J. C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, “Near-field observation of surface plasmon polariton propagation on thin metal stripes,” Phys. Rev. B 64(4), 045411 (2001). [CrossRef]

, 18

18. E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102(20), 203904 (2009). [CrossRef] [PubMed]

20

20. C. Rewitz, T. Keitzl, P. Tuchscherer, J.-S. Huang, P. Geisler, G. Razinskas, B. Hecht, and T. Brixner, “Ultrafast plasmon propagation in nanowires characterized by far-field spectral interferometry,” Nano Lett. 12(1), 45–49 (2012). [CrossRef] [PubMed]

] and nanogrooves in metallic films [16

16. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005). [CrossRef] [PubMed]

, 17

17. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]

] representing the insulator-metal-insulator (IMI) and metal-insulator-metal (MIM) waveguides [21

21. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

], respectively. Plasmonic TWTLs consisting of two parallel metallic nanowires with a nanosized dielectric gap may function both as IMI and MIM waveguides depending on the phase difference ΔΦ between the displacement currents on the wires. With in-phase displacement currents (ΔΦ = 0), the charge distribution is symmetric across the gap, hence the electric field hardly enters the gap and the power is mostly guided through the outer surface of the two wires. Such a spatially less confined mode has a transverse magnetic (TM) character and is analogous to the guided fundamental mode on an IMI waveguide. With out-of-phase currents (ΔΦ = ± π), the opposite charges result in a highly confined field in the dielectric nanogap [7

7. J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009). [CrossRef] [PubMed]

, 22

22. J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006). [CrossRef] [PubMed]

, 23

23. J. Kern, S. Grossmann, N. V. Tarakina, T. Häckel, M. Emmerling, M. Kamp, J.-S. Huang, P. Biagioni, J. C. Prangsma, and B. Hecht, “Atomic-scale confinement of optical fields,” arXiv, http://arxiv.org/abs/1112.5008v2, (2011).

] and the polarization of the electric field is well transverse to the propagation direction, i.e. transverse electric (TE).

Here, we present efficient mode converters for controlling the optical impedance and light-matter interaction in an integrated plasmonic nanocircuit. To achieve deterministic mode conversion, additional phase difference between the guided SPPs on individual wires is introduced by three means, namely by differentiating the path length, the waveguide cross section and the surrounding refractive index. Compared to conventional Mach-Zehnder interferometers, the proposed mode converters rely on strong near-field coupling of guided SPPs instead of interference of guided photonic modes. With the proposed mode converter, we demonstrate improved impedance matching and controlled emission from a nanoantenna in a complex nanocircuit. We also discuss possible applications in index sensing and enhancing nanoscale light-matter interaction, and provide realizable fabrication strategies. Our plasmonic mode converter is of great interest for the realization of practical multi-functional nanocircuits and enhanced spectroscopy using nanoscopic enhanced optical field.

2. Analysis on plasmonic waveguiding

Theoretical and numerical analyses on plasmonic single-wire waveguide and TWTL are provided in this section. Our numerical studies are performed using three-dimensional finite-difference time-domain (FDTD) method and eigen-mode solver based on finite-difference frequency-domain (FDFD) method [31

31. FDTD solutions, Lumerical Solutions Inc., Vancouver, Canada. http://www.lumerical.com/.

] at a fixed frequency of 361.196 THz, corresponding to a wavelength of 830 nm in vacuum. We have chosen the operational wavelength in order to conform to our current equipped laser system for further experiments. However, we emphasize here that the design principle demonstrated in the work is general and not limited to 830 nm. The dielectric function of gold is fitted to experimental values [32

32. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

] and the minimum mesh size is set to 1 nm3. Nanowires with rectangular cross section are surrounded either by vacuum or by a homogeneous dielectric material. In three dimensional FDTD simulations, all boundaries are set to contain 12 perfectly matched layers and are positioned at least half wavelength away from the structure to avoid absorption of the near field.

2.1. Waveguiding on a single nanowire

Changing the cross sectional geometry [33

33. L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(5), 4094–4106 (1994). [CrossRef] [PubMed]

35

35. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004). [CrossRef] [PubMed]

], permittivity of metal εm [36

36. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009). [CrossRef]

] or dielectric function of the surrounding medium εd [37

37. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010). [CrossRef] [PubMed]

39

39. Y. Gao, Q. Gan, Z. Xin, X. Cheng, and F. J. Bartoli, “Plasmonic Mach-Zehnder interferometer for ultrasensitive on-chip biosensing,” ACS Nano 5(12), 9836–9844 (2011). [CrossRef] [PubMed]

] can lead to a strong modification of the wavevector of the guided SPPs. Such unique properties of plasmonic waveguides find no counter parts in low-frequency electronic circuitry where metals behave as perfect conductors.

Figure 2(a)
Fig. 2 Propagation constant (k, blue squares) and the propagation length ([k']1, green circles) of the guided SPPs, i.e. the lowest order TM mode, on a solitary single metallic nanowire as functions of (a) the width of the nanowire and (b) the refractive index n of the surrounding medium. The height of the wire is fixed at 30 nm and the surrounding refractive index is set to 1.0 for (a). The wire cross section is fixed at 30 × 30 nm2 for (b). The red circles in both plots mark the propagation constant (k=14.8rad/μm) of a nanowire with cross section of 30 × 30 nm2 embedded in a medium with n = 1.0. The inset shows a representative field intensity profile of the guided 0th-order TM mode on a single nanowire.
shows the propagation constant k and the propagation length [k']1 as a function of the width of wire cross section. The propagation constant decreases and the propagation length increases as the width increases. For thicker wires (width > 60 nm), the propagation constant gradually saturates due to the finite penetration depth, which is about 30 nm for gold at 361.196 THz. A consequence is that the contribution from higher order modes becomes significant for thicker wires [19

19. S. Zhang, H. Wei, K. Bao, U. Håkanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral surface plasmon polaritons on metallic nanowires,” Phys. Rev. Lett. 107(9), 096801 (2011). [CrossRef] [PubMed]

, 20

20. C. Rewitz, T. Keitzl, P. Tuchscherer, J.-S. Huang, P. Geisler, G. Razinskas, B. Hecht, and T. Brixner, “Ultrafast plasmon propagation in nanowires characterized by far-field spectral interferometry,” Nano Lett. 12(1), 45–49 (2012). [CrossRef] [PubMed]

]. To avoid the complexity, we use only very thin nanowires with rectangular cross section of 30 × 30 nm2 and consider only the contribution from the 0th-order TM mode on a single gold nanowire [34

34. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997). [CrossRef] [PubMed]

]. With such a small cross section, the contribution from higher order modes is negligible due to either very short propagation length or very low initial amplitude [7

7. J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009). [CrossRef] [PubMed]

, 19

19. S. Zhang, H. Wei, K. Bao, U. Håkanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral surface plasmon polaritons on metallic nanowires,” Phys. Rev. Lett. 107(9), 096801 (2011). [CrossRef] [PubMed]

].

Figure 2(b) shows the dependence of the propagation constant and propagation length on the refractive index n of the surrounding medium. As can be seen, both quantities are sensitive to the variation of the surrounding refractive index. The propagation constant exhibits roughly a linear dependence on the refractive index with a slope s=23.76radμm1RIU1 around 830 nm (RIU, refractive index unit). The slope increases with decreasing the wire cross section and represents the sensitivity to the index change which may find applications in plasmonic sensing [39

39. Y. Gao, Q. Gan, Z. Xin, X. Cheng, and F. J. Bartoli, “Plasmonic Mach-Zehnder interferometer for ultrasensitive on-chip biosensing,” ACS Nano 5(12), 9836–9844 (2011). [CrossRef] [PubMed]

]. We will later exploit such dependence of wavevector on the refractive index to control the emission of a nanoantenna.

2.2. Waveguiding on a plasmonic TWTL

While the coupling between nanoparticle dimmers are usually observed by the shift in the resonant frequency, the coupling between guided SPPs at a fixed operation frequency is revealed in the wavevector splitting. Such strong coupling is missing for guided photonic modes on dielectric or photonic crystal waveguides and cannot be exploited in conventional optical interferometry, where the signal modulation is a result of pure interference effect. From an experimental point of view, operating the circuit at a constant frequency can be beneficial since variation due to the dispersion of material dielectric function or frequency-dependent polarizability of the quantum systems can be avoided. Figure 3(b) plots the propagation constant and propagation length as a function of the gap size. The splitting of the propagation constant decreases with increasing gap size, indicating a weaker coupling strength for larger gap size. For gap size larger than 300 nm, the propagation constants for the two modes reach a common value of k=14.8rad/μm, which coincides the value for a solitary single wire with the same cross section (red circled data points in Fig. 2). The gap size of 300 nm thus marks the distance at which the SPPs on two wires no longer couple.

For deeper investigations over the coupling between guided SPPs on individual wires, we have recorded the near-field intensity for a TWTL with a Y-split, as shown in Fig. 4
Fig. 4 Near-field intensity enhancement of the standing waves on a TWTL with a Y-split. The TWTL (cross section: 30 × 30 nm2, gap: 10 nm) splits into two single wires separated by a distance of 610 nm. Either TE or TM mode is injected from the left side of the TWTL. Field intensity of the injected TM mode (blue solid line) and TE mode (red solid line) before the Y-split is recorded 5 nm away from the outer surface of the TWTL and at the center of the gap, respectively, as depicted with blue and red solid lines in the upper panel. After the Y-split, field intensity distributions is recorded 5 nm away from the surface of the wires, as depicted with dotted line in the upper panel. Propagation constant (k) and the corresponding wavelength (λ) of each guided mode are marked. Regardless of the injected mode, after the Y-split, the wavevector and effective wavelength of the guided mode restore to the values of a single wire due to the vanishing near-field coupling.
. Either TE or TM mode is injected from the left side. The near-field intensity is recorded inside the gap for TE injection and 5 nm away from the outer surface of the wire for TM mode. With a + 45 and −45 degree bend of each of the two wires, the TWTL splits into two parallel single nanowires separated with a distance of 610 nm, which ensures a negligible coupling between the wires. The two open ends of the nanowires then reflect the guided SPPs and result in standing wave patterns that allow for analyzing the effective wavelength and wavevector of the guided modes. It can be clearly seen that, regardless of the injected modes, after the Y-split the wavevector restores to the value of guided SPPs on single nanowires, i.e. k,SPP=14.8rad/μm. Such simple structure may serve as a model system for the study of the coupling between guided SPPs. It is worth noting that our Y-split is not adiabatic and significant power loss is expected. To estimate the total loss caused by the Y-split, one needs to know the power reflection at the Y-split due to impedance mismatch and the power loss after the Y-split owing to the wire bending. Since different injected modes exhibit distinct characteristic impedance, they experience different degree of impedance mismatch at the Y-split. Analyzing the standing wave pattern on the TWTL for each mode should provide the information of power reflection [7

7. J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009). [CrossRef] [PubMed]

]. Such analysis requires, however, the TWTL to be very long due to the long propagation length of the TM mode and is out of the scope of this work. Since the injected mode on the TWTL, i.e. TE or TM mode, is fully converted back to the guided mode on a single wire, the loss can be readily obtained by analyzing the bending loss of a single wire waveguide. In our design, the loss introduced by the 45 degree bending is optimized to about 0.2 dB.

3. Plasmonic mode converters

3.1. Conversion mechanisms

Figure 5(b) plots the maps of the enhancement of electric field intensity on a plane cutting through the structure at the middle height. After passing through the mode converter, the loose field distribution of the injected TM mode is clearly switched to a concentrated TE mode in the nanogap. Here, we terminated the TWTL with an open end in order to build up a clear standing wave pattern for the analysis of the wavevector and impedance matching [7

7. J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009). [CrossRef] [PubMed]

]. By analyzing the near-field intensity undulation, where the distance between two maxima corresponds to half of the wavelength of the guided mode, the propagation constant of guided mode can be obtained. As shown in the top panel of Fig. 5(b), the field inside the gap clearly reveals a distance of 127 nm between two maxima, corresponding to a propagation constant of 24.7rad/μm, which is very close to the value for purely TE mode (k,TE=25.3rad/μm). Although we have chosen to inject TM guided mode, all converters work well with TE injection. It is worth mentioning that the three tuning principles illustrated here work well independently but may also be combined to obtain higher flexibility. In view of practical use, mode converters using the difference in path length or cross sectional geometry require careful design and the conversion efficiency is fixed once the fabrication process is completed. In contrast, converter using the difference in the refractive index is more powerful since the index can be tuned actively by using active materials such as photoconductive semiconductors [43

43. S. Chandrasekhar, A. S. Vengurlekar, V. T. Karulkar, and S. K. Roy, “Temperature, light intensity and microstructure dependence of the refractive index of polycrystalline silicon films,” Thin Solid Films 169(2), 205–212 (1989). [CrossRef]

45

45. N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett. 10(5), 1741–1746 (2010). [CrossRef] [PubMed]

], phase transition materials [46

46. A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001). [CrossRef] [PubMed]

, 47

47. M. Seo, J. Kyoung, H. Park, S. Koo, H.-S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010). [CrossRef] [PubMed]

] and liquid crystals [48

48. S. Y. Park and D. Stroud, “Splitting of surface plasmon frequencies of metal particles in a nematic liquid crystal,” Appl. Phys. Lett. 85(14), 2920–2922 (2004). [CrossRef]

50

50. J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J.-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A.-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9(11), 3914–3921 (2009). [CrossRef] [PubMed]

].

3.2. Conversion efficiency

4. Applications in a complex integrated nanocircuit

Since the radiative mode of the nanoantenna can only be driven by the TE mode, the emitted power by the antenna can be expressed as
Pout=ηantenna×(1Γp2)×e2k,TE'r3×ηoverall×e2k,TM'r2×(1Γp1)×PS,
(12)
where PS is the injected power, Γp1 is the power reflectivity at the junction between single stripe and TWTL, Γp2 is the power reflectivity at the TWTL-to-antenna junction and ηantenna is the radiation efficiency of the nanoantenna [7

7. J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009). [CrossRef] [PubMed]

]. It is clear that the emission power of the nanoantenna is a linear function of the overall conversion efficiency. Since ηoverall=ηpηm, the emission power is controlled by ηm. Figure 6(e) plots the mode conversion efficiency ηm, power conversion efficiency ηp and the overall conversion efficiency ηoverall, along with the emission power Pout from the optimized nanoantenna as a function of the refractive index of the material inside the green box. It can be seen that the power conversion efficiency is relatively constant with respect to the change of surrounding refractive index and the radiated power follows the trend of ηm. Taking the slope s of the linear relationship between the wavevector and the index of refraction, as shown in Fig. 2(b), the mode conversion efficiency can be expressed as a function of the difference in refractive index of media surrounding the two wires in the converter area
ηm=12[cos(ΔkLc+π)+1]=12[cos(sΔnLc+π)+1].
(13)
Therefore, the emission power of the antenna can be expressed as a cosine function of the index difference and the sensitivity for index sensing is proportional to sLc. In principle, the sensitivity can be improved by using smaller wire cross section or longer converter. However, the effect of increasing loss for longer waveguide needs to be taken into account in order to obtain optimized geometry. It is worth mentioning that the control over the antenna radiation can be made active by, for example, covering one of the wires with a photoconductive material or with well-designed microfluidic channels such that deterministic difference in the refractive index can be actively introduced.

5. Perspective on nanoscale light-matter interaction

Plasmonic nanostructures show general similarities to natural chemical molecules [52

52. A. Guerrero-Martínez, M. Grzelczak, and L. M. Liz-Marzán, “Molecular thinking for nanoplasmonic design,” ACS Nano 6(5), 3655–3662 (2012). [CrossRef] [PubMed]

] and the optical impedance of nanoantennas and quantum emitters can be described under an unified framework [53

53. J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105(11), 117701 (2010). [CrossRef] [PubMed]

]. As we have demonstrated, using TWTL and our mode converter, we may control the emission of a nanoantenna by controlling the optical impedance of the guided power. Replacing the nanoantenna with a quantum emitter that has its own optical impedance, such as a single molecule, we may, in principle, manipulate the light-matter interaction in a similar way. In view of nanoscale light-matter interaction, the much reduced mode volume Vmode substantially enhances the coupling strength g[Vmode]12 between the nanocavity and single quantum systems [3

3. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006). [CrossRef] [PubMed]

]. In addition, the well-defined polarization of the electric field may further improve the interaction between the guided field and the quantum systems residing in the nanogap. From classical point of view, the energy of a molecule with dipole moment μ in a polarized electric field E is just their dot product,
Eμ=|E||μ|cosϕ,
(14)
where ϕ denotes the angle between the two vectors. If the electric field and the dipole moments can be aligned such that ϕ=0, the light-matter interaction can be further enhanced. From experimental point of view, the alignment of quantum systems may be accomplished through the use of thin crystalline host films [54

54. A. M. Boiron, B. Lounis, and M. Orrit, “Single molecules of dibenzanthanthrene in n-hexadecane,” J. Chem. Phys. 105(10), 3969–3974 (1996). [CrossRef]

, 55

55. W. E. M. T. Basché, M. Orrit, and U. P. Wild, Single-Molecule Optical Detection, Imaging and Spectroscopy (Wiley-VCH, 1997).

]. Using recently proposed hybrid fabrication approach for atomically smooth plasmonic nanostructure [56

56. J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nat. Commun. 1(9), 150 (2010). [CrossRef] [PubMed]

] and the “stacked” geometry for extremely small gap [57

57. D. W. Pohl, S. G. Rodrigo, and L. Novotny, “Stacked optical antennas,” Appl. Phys. Lett. 98(2), 023111–023113 (2011). [CrossRef]

], it is possible to integrate thin layer of various materials, including gain, liquid crystal, photoconductive semiconductor or graphene to enable multiple functions of nanocircuits.

6. Conclusion

We have presented realizable plasmonic mode converters to manipulate the guided modes on a plasmonic TWTL. The mode conversion is accomplished through the introduction of additional phase difference between guided SPPs on individual wires by differing the path length, the cross section, and by changing the surrounding index of refraction. We analyzed the conversion efficiency of the mode converter and demonstrated its capability in manipulating the optical impedance of guided mode and therefore the emission power of a nanoantenna in a complex nanocircuit. Being able to manipulate the guided mode is important for the control over guiding properties and optical impedance of the mode and provides possibility to achieve active manipulation of the interaction between optical field and nanoobjects. One may think about building up a nanocavity consisting of a piece of TWTL terminated by two gap nanoantennas, the capability to control the mode and near-to-far field conversion efficiency then means the ability to tune the reflectivity and thus the quality factor of the cavity. Our converter may find interesting applications in optical impedance control, nanosensors and nanoresonators. We anticipate a number of applications in optical nanocircuits and active control of the light-matter interaction at the nanoscale.

Acknowledgments

The work was supported by the National Science Council of Taiwan under grants NSC 99-2113-M-007-020-MY2 and NSC 100-2112-M-007-007-MY3. J.-S. H. thanks C.-S. Huang and Dr. T. Lankau for valuable discussions.

References and links

1.

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

2.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]

3.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006). [CrossRef] [PubMed]

4.

D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3(11), 807–812 (2007). [CrossRef]

5.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011). [CrossRef]

6.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75(2), 024402 (2012). [CrossRef] [PubMed]

7.

J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009). [CrossRef] [PubMed]

8.

J. Wen, S. Romanov, and U. Peschel, “Excitation of plasmonic gap waveguides by nanoantennas,” Opt. Express 17(8), 5925–5932 (2009). [CrossRef] [PubMed]

9.

J.-S. Huang, D. V. Voronine, P. Tuchscherer, T. Brixner, and B. Hecht, “Deterministic spatiotemporal control of optical fields in nanoantennas and plasmonic circuits,” Phys. Rev. B 79(19), 195441 (2009). [CrossRef]

10.

P. M. Krenz, R. L. Olmon, B. A. Lail, M. B. Raschke, and G. D. Boreman, “Near-field measurement of infrared coplanar strip transmission line attenuation and propagation constants,” Opt. Express 18(21), 21678–21686 (2010). [CrossRef] [PubMed]

11.

M. Schnell, P. Alonso Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011). [CrossRef]

12.

J. Wen, P. Banzer, A. Kriesch, D. Ploss, B. Schmauss, and U. Peschel, “Experimental cross-polarization detection of coupling far-field light to highly confined plasmonic gap modes via nanoantennas,” Appl. Phys. Lett. 98(10), 101109 (2011). [CrossRef]

13.

N. Yang, Y. Tang, and A. E. Cohen, “Spectroscopy in sculpted fields,” Nano Today 4(3), 269–279 (2009). [CrossRef]

14.

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: Plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012). [CrossRef]

15.

J. C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, “Near-field observation of surface plasmon polariton propagation on thin metal stripes,” Phys. Rev. B 64(4), 045411 (2001). [CrossRef]

16.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005). [CrossRef] [PubMed]

17.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]

18.

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102(20), 203904 (2009). [CrossRef] [PubMed]

19.

S. Zhang, H. Wei, K. Bao, U. Håkanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral surface plasmon polaritons on metallic nanowires,” Phys. Rev. Lett. 107(9), 096801 (2011). [CrossRef] [PubMed]

20.

C. Rewitz, T. Keitzl, P. Tuchscherer, J.-S. Huang, P. Geisler, G. Razinskas, B. Hecht, and T. Brixner, “Ultrafast plasmon propagation in nanowires characterized by far-field spectral interferometry,” Nano Lett. 12(1), 45–49 (2012). [CrossRef] [PubMed]

21.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

22.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006). [CrossRef] [PubMed]

23.

J. Kern, S. Grossmann, N. V. Tarakina, T. Häckel, M. Emmerling, M. Kamp, J.-S. Huang, P. Biagioni, J. C. Prangsma, and B. Hecht, “Atomic-scale confinement of optical fields,” arXiv, http://arxiv.org/abs/1112.5008v2, (2011).

24.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003). [CrossRef] [PubMed]

25.

M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16(2), 1385–1392 (2008). [CrossRef] [PubMed]

26.

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010). [CrossRef]

27.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010). [CrossRef]

28.

A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett. 11(6), 2231–2235 (2011). [CrossRef] [PubMed]

29.

P. Berini and I. De Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics 6(1), 16–24 (2011). [CrossRef]

30.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]

31.

FDTD solutions, Lumerical Solutions Inc., Vancouver, Canada. http://www.lumerical.com/.

32.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

33.

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(5), 4094–4106 (1994). [CrossRef] [PubMed]

34.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997). [CrossRef] [PubMed]

35.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004). [CrossRef] [PubMed]

36.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009). [CrossRef]

37.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010). [CrossRef] [PubMed]

38.

E. Verhagen, L. K. Kuipers, and A. Polman, “Plasmonic nanofocusing in a dielectric wedge,” Nano Lett. 10(9), 3665–3669 (2010). [CrossRef] [PubMed]

39.

Y. Gao, Q. Gan, Z. Xin, X. Cheng, and F. J. Bartoli, “Plasmonic Mach-Zehnder interferometer for ultrasensitive on-chip biosensing,” ACS Nano 5(12), 9836–9844 (2011). [CrossRef] [PubMed]

40.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004). [CrossRef]

41.

J.-S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10(6), 2105–2110 (2010). [CrossRef] [PubMed]

42.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005). [CrossRef] [PubMed]

43.

S. Chandrasekhar, A. S. Vengurlekar, V. T. Karulkar, and S. K. Roy, “Temperature, light intensity and microstructure dependence of the refractive index of polycrystalline silicon films,” Thin Solid Films 169(2), 205–212 (1989). [CrossRef]

44.

E. M. True and L. McCaughan, “Large nonresonant light-induced refractive-index changes in thin films of amorphous arsenic sulfide,” Opt. Lett. 16(7), 458–460 (1991). [CrossRef] [PubMed]

45.

N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett. 10(5), 1741–1746 (2010). [CrossRef] [PubMed]

46.

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001). [CrossRef] [PubMed]

47.

M. Seo, J. Kyoung, H. Park, S. Koo, H.-S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010). [CrossRef] [PubMed]

48.

S. Y. Park and D. Stroud, “Splitting of surface plasmon frequencies of metal particles in a nematic liquid crystal,” Appl. Phys. Lett. 85(14), 2920–2922 (2004). [CrossRef]

49.

W. Dickson, G. A. Wurtz, P. R. Evans, R. J. Pollard, and A. V. Zayats, “Electronically controlled surface plasmon dispersion and optical transmission through metallic hole arrays using liquid crystal,” Nano Lett. 8(1), 281–286 (2008). [CrossRef] [PubMed]

50.

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J.-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A.-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9(11), 3914–3921 (2009). [CrossRef] [PubMed]

51.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

52.

A. Guerrero-Martínez, M. Grzelczak, and L. M. Liz-Marzán, “Molecular thinking for nanoplasmonic design,” ACS Nano 6(5), 3655–3662 (2012). [CrossRef] [PubMed]

53.

J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105(11), 117701 (2010). [CrossRef] [PubMed]

54.

A. M. Boiron, B. Lounis, and M. Orrit, “Single molecules of dibenzanthanthrene in n-hexadecane,” J. Chem. Phys. 105(10), 3969–3974 (1996). [CrossRef]

55.

W. E. M. T. Basché, M. Orrit, and U. P. Wild, Single-Molecule Optical Detection, Imaging and Spectroscopy (Wiley-VCH, 1997).

56.

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nat. Commun. 1(9), 150 (2010). [CrossRef] [PubMed]

57.

D. W. Pohl, S. G. Rodrigo, and L. Novotny, “Stacked optical antennas,” Appl. Phys. Lett. 98(2), 023111–023113 (2011). [CrossRef]

OCIS Codes
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(240.6680) Optics at surfaces : Surface plasmons
(250.7360) Optoelectronics : Waveguide modulators
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: June 20, 2012
Revised Manuscript: August 13, 2012
Manuscript Accepted: August 16, 2012
Published: August 21, 2012

Virtual Issues
Vol. 7, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Yun-Ting Hung, Chen-Bin Huang, and Jer-Shing Huang, "Plasmonic mode converter for controlling optical impedance and nanoscale light-matter interaction," Opt. Express 20, 20342-20355 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-18-20342


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References

  1. E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006). [CrossRef] [PubMed]
  2. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010). [CrossRef] [PubMed]
  3. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97(5), 053002 (2006). [CrossRef] [PubMed]
  4. D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys.3(11), 807–812 (2007). [CrossRef]
  5. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics5(2), 83–90 (2011). [CrossRef]
  6. P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012). [CrossRef] [PubMed]
  7. J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett.9(5), 1897–1902 (2009). [CrossRef] [PubMed]
  8. J. Wen, S. Romanov, and U. Peschel, “Excitation of plasmonic gap waveguides by nanoantennas,” Opt. Express17(8), 5925–5932 (2009). [CrossRef] [PubMed]
  9. J.-S. Huang, D. V. Voronine, P. Tuchscherer, T. Brixner, and B. Hecht, “Deterministic spatiotemporal control of optical fields in nanoantennas and plasmonic circuits,” Phys. Rev. B79(19), 195441 (2009). [CrossRef]
  10. P. M. Krenz, R. L. Olmon, B. A. Lail, M. B. Raschke, and G. D. Boreman, “Near-field measurement of infrared coplanar strip transmission line attenuation and propagation constants,” Opt. Express18(21), 21678–21686 (2010). [CrossRef] [PubMed]
  11. M. Schnell, P. Alonso Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics5(5), 283–287 (2011). [CrossRef]
  12. J. Wen, P. Banzer, A. Kriesch, D. Ploss, B. Schmauss, and U. Peschel, “Experimental cross-polarization detection of coupling far-field light to highly confined plasmonic gap modes via nanoantennas,” Appl. Phys. Lett.98(10), 101109 (2011). [CrossRef]
  13. N. Yang, Y. Tang, and A. E. Cohen, “Spectroscopy in sculpted fields,” Nano Today4(3), 269–279 (2009). [CrossRef]
  14. S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: Plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett.3(7), 945–952 (2012). [CrossRef]
  15. J. C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, “Near-field observation of surface plasmon polariton propagation on thin metal stripes,” Phys. Rev. B64(4), 045411 (2001). [CrossRef]
  16. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett.95(4), 046802 (2005). [CrossRef] [PubMed]
  17. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006). [CrossRef] [PubMed]
  18. E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett.102(20), 203904 (2009). [CrossRef] [PubMed]
  19. S. Zhang, H. Wei, K. Bao, U. Håkanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral surface plasmon polaritons on metallic nanowires,” Phys. Rev. Lett.107(9), 096801 (2011). [CrossRef] [PubMed]
  20. C. Rewitz, T. Keitzl, P. Tuchscherer, J.-S. Huang, P. Geisler, G. Razinskas, B. Hecht, and T. Brixner, “Ultrafast plasmon propagation in nanowires characterized by far-field spectral interferometry,” Nano Lett.12(1), 45–49 (2012). [CrossRef] [PubMed]
  21. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  22. J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett.6(9), 1928–1932 (2006). [CrossRef] [PubMed]
  23. J. Kern, S. Grossmann, N. V. Tarakina, T. Häckel, M. Emmerling, M. Kamp, J.-S. Huang, P. Biagioni, J. C. Prangsma, and B. Hecht, “Atomic-scale confinement of optical fields,” arXiv, http://arxiv.org/abs/1112.5008v2 , (2011).
  24. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett.90(2), 027402 (2003). [CrossRef] [PubMed]
  25. M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express16(2), 1385–1392 (2008). [CrossRef] [PubMed]
  26. I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics4(6), 382–387 (2010). [CrossRef]
  27. M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics4(7), 457–461 (2010). [CrossRef]
  28. A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett.11(6), 2231–2235 (2011). [CrossRef] [PubMed]
  29. P. Berini and I. De Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics6(1), 16–24 (2011). [CrossRef]
  30. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett.97(1), 017402 (2006). [CrossRef] [PubMed]
  31. FDTD solutions, Lumerical Solutions Inc., Vancouver, Canada. http://www.lumerical.com/ .
  32. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  33. L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics50(5), 4094–4106 (1994). [CrossRef] [PubMed]
  34. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.22(7), 475–477 (1997). [CrossRef] [PubMed]
  35. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004). [CrossRef] [PubMed]
  36. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics3(1), 55–58 (2009). [CrossRef]
  37. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett.10(6), 1991–1997 (2010). [CrossRef] [PubMed]
  38. E. Verhagen, L. K. Kuipers, and A. Polman, “Plasmonic nanofocusing in a dielectric wedge,” Nano Lett.10(9), 3665–3669 (2010). [CrossRef] [PubMed]
  39. Y. Gao, Q. Gan, Z. Xin, X. Cheng, and F. J. Bartoli, “Plasmonic Mach-Zehnder interferometer for ultrasensitive on-chip biosensing,” ACS Nano5(12), 9836–9844 (2011). [CrossRef] [PubMed]
  40. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett.4(5), 899–903 (2004). [CrossRef]
  41. J.-S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett.10(6), 2105–2110 (2010). [CrossRef] [PubMed]
  42. P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett.94(1), 017402 (2005). [CrossRef] [PubMed]
  43. S. Chandrasekhar, A. S. Vengurlekar, V. T. Karulkar, and S. K. Roy, “Temperature, light intensity and microstructure dependence of the refractive index of polycrystalline silicon films,” Thin Solid Films169(2), 205–212 (1989). [CrossRef]
  44. E. M. True and L. McCaughan, “Large nonresonant light-induced refractive-index changes in thin films of amorphous arsenic sulfide,” Opt. Lett.16(7), 458–460 (1991). [CrossRef] [PubMed]
  45. N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett.10(5), 1741–1746 (2010). [CrossRef] [PubMed]
  46. A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett.87(23), 237401 (2001). [CrossRef] [PubMed]
  47. M. Seo, J. Kyoung, H. Park, S. Koo, H.-S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett.10(6), 2064–2068 (2010). [CrossRef] [PubMed]
  48. S. Y. Park and D. Stroud, “Splitting of surface plasmon frequencies of metal particles in a nematic liquid crystal,” Appl. Phys. Lett.85(14), 2920–2922 (2004). [CrossRef]
  49. W. Dickson, G. A. Wurtz, P. R. Evans, R. J. Pollard, and A. V. Zayats, “Electronically controlled surface plasmon dispersion and optical transmission through metallic hole arrays using liquid crystal,” Nano Lett.8(1), 281–286 (2008). [CrossRef] [PubMed]
  50. J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J.-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A.-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett.9(11), 3914–3921 (2009). [CrossRef] [PubMed]
  51. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
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