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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 8 — Apr. 9, 2012
  • pp: 8929–8938
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Actively tunable bistable optical Yagi-Uda nanoantenna

Ivan S. Maksymov, Andrey E. Miroshnichenko, and Yuri S. Kivshar  »View Author Affiliations


Optics Express, Vol. 20, Issue 8, pp. 8929-8938 (2012)
http://dx.doi.org/10.1364/OE.20.008929


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Abstract

We propose and theoretically demonstrate a novel type of optical Yagi-Uda nanoantennas tunable via variation of the free-carrier density of a semiconductor disk placed in a gap of a metallic dipole feeding element. Unlike its narrowband all-metal counterparts, this nanoantenna exhibits a broadband unidirectional emission and demonstrates a bistable response in a preferential direction of the far-field zone, which opens up unique possibilities for ultrafast control of subwavelength light not attainable with dipole or bowtie architectures.

© 2012 OSA

1. Introduction

Owing to recent advances in nanotechnology, plasmonic nanoantennas have become a subject of considerable theoretical and experimental interest [1

1. V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111, 3888–3912 (2011). [CrossRef] [PubMed]

,2

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

]. Plasmonic resonances in nanoantennas allow breaking through the fundamental diffraction limit [3

3. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010). [CrossRef]

], opening up novel opportunities for controlling light–matter interactions within subwavelength volumes. Several potential applications of nanoantennas have been considered in topics such as spectroscopy and high-resolution near-field microscopy [2

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

], subwavelength light confinement and enhancement [4

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

], photovoltaics [5

5. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010). [CrossRef] [PubMed]

], sensing [6

6. N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10, 631–636 (2011). [CrossRef] [PubMed]

], molecular response enhancement [7

7. F. de Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech. 5, 67–72 (2010). [CrossRef]

], non-classical light emission [8

8. I. S. Maksymov, M. Besbes, J. P. Hugonin, J. Yang, A. Beveratos, I. Sagnes, I. Robert-Philip, and P. Lalanne, “Metal-coated nanocylinder cavity for broadband nonclassical light emission,” Phys. Rev. Lett. 105, 180502 (2010). [CrossRef]

], and communication [9

9. A. Alú and N. Engheta, “Wireless at the nanoscale: optical interconnects using matched nanoantennas,” Phys. Rev. Lett. 104, 213902 (2010). [CrossRef] [PubMed]

].

In many of these applications, controlling and modifying the far-field of a nanoantenna is an important issue that is particularly interesting for obtaining directional beaming effects, which have been demonstrated e.g. with Yagi-Uda architectures [10

10. A. F. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett. 9, 4228–4233 (2009). [CrossRef] [PubMed]

14

14. J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, “Near-field dynamics of optical Yagi–Uda nanoantennas,” Nano Lett. 11, 2819–2824 (2011). [CrossRef] [PubMed]

]. However, an efficient nanoantenna must not only have a large local field enhancement and a high directivity [15

15. I. S. Maksymov, A. R. Davoyan, and Yu. S. Kivshar, “Enhanced emission and light control with tapered plasmonic nanoantennas,” Appl. Phys. Lett. 99, 083304 (2011). [CrossRef]

] but also be wavelength tunable over a wide spectral range [16

16. A. E. Miroshnichenko, I. S. Maksymov, A. R. Davoyan, C. Simovski, P. Belov, and Yu. S. Kivshar, “An arrayed nanoantenna for broadband light emission and detection,” Phys. Status Solidi RRL 5, 347–349 (2011). [CrossRef]

] because it allows a smaller nanoantenna to behave as a larger nanoantenna or as an array of nanoantennas [13

13. D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3D optical Yagi-Uda nanoantenna array,” Nat. Commun. 2, 267 (2011). [CrossRef] [PubMed]

], both saving space and improving performance.

Consequently, a large and growing body of research investigates tunable nanoantennas [17

17. J. N. Farahani, D. W. Pohl, H.–J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005). [CrossRef] [PubMed]

24

24. Y. Alaverdyan, N. Vamivakas, J. Barnes, C. Lebouteiller, J. Hare, and M. Atatüre, “Spectral tunability of a plasmonic antenna with a dielectric nanocrystal,” Opt. Express 19, 18175–18181 (2011). [CrossRef] [PubMed]

]. Many novel control mechanisms try to exploit the concept of metamaterial-based [25

25. R. W. Ziolkowski and A. Erentok, “Metamaterial-based efficient electrically small antennas,” IEEE Trans. Antennas Propag. 54, 2113–2130 (2008). [CrossRef]

] and non-Foster impedance matching circuits [26

26. S. E. Sussman-Fort and R. M. Rudish, “Non-Foster impedance matching of electrically-small antennas,” IEEE Trans. Antennas Propag. 57, 2230–2241 (2009). [CrossRef]

], where one of the possible ways for achieving spectral tuning is based on the use of tunable nanocapacitors and/or nanoinductors [27

27. N. Engheta, A. Salandrino, and A. Alú, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005). [CrossRef] [PubMed]

,28

28. N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007). [CrossRef] [PubMed]

]. Other approaches may rely on vanadium oxide tunable metamaterials [29

29. 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, 2064–2068 (2010). [CrossRef] [PubMed]

], mechanically reconfigurable photonic metamaterials [30

30. J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11, 2142–2144 (2011). [CrossRef] [PubMed]

] or metamaterials hybridized with carbon nanotubes [31

31. A. E. Nikolaenko, F. de Angelis, S. A. Boden, N. Papasimakis, P. Ashburn, E. di Fabrizio, and N. I. Zheludev, “Carbon nanotubes in a photonic metamaterial,” Phys. Rev. Lett. 104, 153902 (2010). [CrossRef] [PubMed]

]. Large spectral tunability can also be obtained using electrically controlled liquid crystals [32

32. P. A. Kossyrev, A. Yin, S. G. Cloutier, D. A. Cardimona, D. Huang, P. M. Asling, and J. M. Xu, “Electric field tuning of plasmonic response of nanodot array in liquid crystal matrix,” Nano Lett. 5, 1978–1981 (2005). [CrossRef] [PubMed]

34

34. C. de Angelis, A. Locatelli, D. Modotto, S. Boscolo, M. Midrio, and A.-D. Capobianco, “Frequency addressing of nano-objects by electrical tuning of optical antennas,” J. Opt. Soc. Am. B 27, 997–1001 (2011). [CrossRef]

], but a very slow response of liquid crystals is not suitable for many application and, in general, a solid-state implementation is more suitable for on-chip integration of nanoantennas.

However, the spectral tuning of optical Yagi-Uda nanoantennas has not been yet demonstrated because their capability to tune to multiple operating frequencies is compromised by their ability to receive and transmit light in a preferential direction (their operating bandwidth is limited to just a few percents around the designed resonance frequency). Tunable Yagi-Uda nanoantennas could have technological applications in building broadband optical wireless communication systems, advanced nano-sensor systems, high performance solar cells as well as wavelength tunable single photon sources and detectors.

Most importantly, the nanoantenna combines the capability of controlling light at the nanoscale with a bistable response in the far-field zone. Optical bistability is a fundamental physical phenomenon that makes it possible to realize all-optical switching, optical limiting, logic gating and amplification of light pulses [35

35. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).

]. The realization of all-optical operations with a nanoantenna can without doubt be regarded as a big step toward creating novel ultra-fast sub-wavelength optical devices capable of manipulating and transmitting light pulses to, from and between nanoemitters.

2. Design and simulation model

The core design and interpretation of the results are performed using CST Microwave Studio software implementing a Finite Integration Technique. Figure 1 shows a plasmonic Yagi-Uda nanoantenna consisting of metal nanorods used for reflector, feeding element and directors. Without loss of generality, in this work we choose silver as the metal because it has the smallest optical losses of any natural metal in the visible and IR spectrum [36

36. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

]. Owing to its relative lower loss, gold can be used instead of silver, which makes our nanoantenna more attractive for biomedical and sensor applications. The elements of the nanoantenna could also be made of nickel. The simultaneous ferromagnetic and plasmonic dual functionality of nickel nanoantennas opens up novel opportunities for magnetic manipulation of light [37

37. J. Chen, P. Albella, Z. Pirzadeh, P. Alonso-González, F. Huth, S. Bonetti, V. Bonanni, J. Åkerman, J. Nogués, P. Vavassori, A. Dmitriev, J. Aizpurua, and R. Hillenbrand, “Plasmonic nickel nanoantennas,” Small 7, 2341–2347 (2011). [CrossRef]

].

Fig. 1 A tunable plasmonic Yagi-Uda nanoantenna consisting of silver nanorods used for reflector, feeding element and directors. The yellow area of the feeding elements corresponds to the semiconductor nano-disk used as loading. The nanoantenna is surrounded by air. The semi-transparent red arrow schematically shows the direction of the incident plane wave.

We optimize the nanoantenna performance for a central wavelength to be ≈ 1μm. We choose the radii of the nanorods and those of their outer rounded edges as r = 25 nm, and the spacing between all elements as w = 30 nm [15

15. I. S. Maksymov, A. R. Davoyan, and Yu. S. Kivshar, “Enhanced emission and light control with tapered plasmonic nanoantennas,” Appl. Phys. Lett. 99, 083304 (2011). [CrossRef]

]. The feeding element consists of two nanorods with non-rounded inner edges, separated by a semiconductor nano-disk. The total length of the feeding elements including the nano-disk is L = 390 nm. The lengths of the reflector and directors are chosen as 1.125L and 0.75L, respectively. We assume that the nano-disk of the feeding element is made of amorphous silicon (a-Si) and that its width constitutes 50 nm. The nanoantenna is surrounded by air because this provides the simplest model to which additional elements of any practical design, such as e.g. a substrate, can be added.

A change in the dielectric permittivity of the nano-disk loading of the feeding element caused by an increase in the free carrier density is modelled using a Drude model based on experimental values εexp(ω) of a-Si [36

36. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

] as
ε(ω)=εexp(ω)(ωpω)211+i1ωτD,
(1)
where ωp=Ne2/ε0mopt*me denotes the plasma frequency, with N the free carrier concentration, mopt*=(me*1+mh*1)1 the optical effective mass of the carriers, and τD = 10−14 s the Drude relaxation time. The optical effective mass for a-Si, mopt*=0.17, is estimated to be close to the value of crystalline silicon [20

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

].

3. Results and discussion

To start with, we investigate near- and far-field zone characteristics of the Yagi-Uda nanoantenna. As we aim at achieving a gradual spectral tuning, we consider the free carrier density in between 0 and 3·1021 cm−3, that is in the range where the feeding elements gradually transfers from a capacitive mode to a partially conductive one in particular frequency range. The nanoantenna is illuminated with a linearly polarized plane wave (the electric field is orientated along the y-coordinate) incident from the rear end of the nanoantenna under the angle of 45 degrees as shown in Fig. 1.

Fig. 2 (Top) Far-field power spectra of the nanoantenna in the maximum emission direction as a function of the wavelength for different free carrier densities from 0 cm−3 to 3 · 1021 cm−3 (from bottom curve and up). Red dashed line indicates the operating wavelength of a Yagi-Uda nanoantenna with the same dimensions but equipped with an all-metal feeding element. (Bottom) Stationary |E| electric field distributions in the near-field zone of the nanoantenna corresponding to the resonance peaks denoted by the capital letters in the top panel.

In order to confirm that in this range the feeding element is in its resonance as should be in the case of a Yagi-Uda antenna [14

14. J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, “Near-field dynamics of optical Yagi–Uda nanoantennas,” Nano Lett. 11, 2819–2824 (2011). [CrossRef] [PubMed]

], in the bottom panel of Fig. 2 we plot stationary distributions of the electric field |E| in the near-field zone of the nanoantenna. As shown in sub-panels A and A’ (here A corresponds to 0 cm−3 and A’ to 3 · 1021 cm−3), the feeding element is at its maximum field strength brighter than all the other elements.

These results demonstrate that the resonance wavelength of the A–A’ resonances is gradually blue-shifted due to decrease of the permittivity in that particular frequency range. It results in possibility to gradually tune the resonant response of the nanoantenna in a 230 nm wavelength range by controlling the loading of the feeding element. Importantly for our further analysis, the electric field between the inner faces of the nanorods of the feeding elements is nearly uniform, as shown by the lines of field in the bottom panel of Fig. 2. This finding will significantly simplify simulations of the nanoantenna.

The analysis of resonances denoted by B–B’ (see the top panel of Fig. 2) does not reveal a significant change in the resonance wavelengths because the electric field is mainly concentrated around the directors of the nanoantenna and does not penetrate into the semiconductor, as shown in the bottom panel of Fig. 2.

The C–C’ resonances are more sensitive to a variation of the conductivity of the nano-disk due to the fact that at 0 cm−3 the electric field mainly concentrates around the reflector but spreads over both the reflector and the feeding element at 3 · 1021 cm−3. The wavelength of C–C’ resonances is blue-shifted towards the operating wavelength of an all-metal Yagi-Uda with the same geometry (red dashed line in the top panel of Fig. 2).

Since both B–B’ and C–C’ resonances the nanoantenna do not exhibit a correct Yagi-Uda behavior manifesting itself by a pronounced resonance of the feeding element [14

14. J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, “Near-field dynamics of optical Yagi–Uda nanoantennas,” Nano Lett. 11, 2819–2824 (2011). [CrossRef] [PubMed]

], in what follows we focus ourselves on A–A’ resonances only.

It is worth noting a highly desirable option of the nanoantenna excitation with a broadband point-like emitter (e.g. a fluorescent molecule) placed near one of the edges of the feeding element [16

16. A. E. Miroshnichenko, I. S. Maksymov, A. R. Davoyan, C. Simovski, P. Belov, and Yu. S. Kivshar, “An arrayed nanoantenna for broadband light emission and detection,” Phys. Status Solidi RRL 5, 347–349 (2011). [CrossRef]

,38

38. J. Li, A. Salandrino, and N. Engheta, “Optical spectrometer at the nanoscale using optical Yagi-Uda nanoantennas,” Phys. Rev. B 79, 195104 (2009). [CrossRef]

]. It allows a realization of a pump-probe operation scheme, where a pump laser is used to control the coupling of the emitter to the nanoantenna at different wavelengths. Moreover, according to the principle of reciprocity the far-field characteristics of the nanoantennas in the emission regime are similar to those in the reception one [2

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

], and, therefore, the nanoantenna can be employed as a tunable nano-receiver.

In active semiconductor nanophotonic devices, such as e.g. all-optical switches based on photonic crystal nano-cavities (see, e.g., [39

39. M. Belotti, J. F. Galisteo–López, S. de Angelis, M. Galli, I. S. Maksymov, L. C. Andreani, D. Peyrade, and Y. Chen, “All-optical switching in 2D silicon photonic crystals with low loss waveguides and optical cavities,” Opt. Express 16, 11624–11636 (2008). [PubMed]

]) and semiconductor antennas for THz radiation [40

40. A. Berrier, R. Ulbricht, M. Bonn, and J. Gómez–Rivas, “Ultrafast active control of localized surface plasmon resonances in silicon bowtie antenna,” Opt. Express 18, 23226–23235 (2010). [CrossRef] [PubMed]

, 41

41. A. Berrier, P. Albella, M. Ameen Poyli, R. Ulbricht, M. Bonn, J. Aizpurua, and J. Gómez–Rivas, “Detection of deep-subwavelength dielectric layers at terahertz frequencies using semiconductor plasmonic resonators,” Opt. Express 20, 5052–5060 (2012). [CrossRef] [PubMed]

], one usually needs free carrier densities of up to 1019 cm−3. As we can see in Fig. 2, in order to tune the response of the Yagi-Uda nanoantenna by ≈ 200 nm one needs to increase the free carrier density by two orders of magnitude as compared with that for the aforementioned nanophotonic devices. Hereafter, we demonstrate that this increase can be achieved at experimentally attainable optical intensities owing to a local field enhancement in the nano-disk loading of the feeding element.

For our further analysis, we consider that the free carrier density N in the semiconductor obeys the rate equation [42

42. S. M. Sze, Physics of Semiconductor Devices (John Wiley and Sons, New York, 1969).

]
N(t)t=N(t)τc+c2ε02n02βTPA8h¯ω0|E(t)|4,
(2)
where τc is the free carrier lifetime, E(t) is the amplitude of the electric field, ω0 is the angular frequency of the excitation plane wave and βTPA is the two-photon absorption coefficient. We take τc = 1 ns and βTPA = 120 cm/GW [20

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

]. Owing to the uniformity of the electric field in the nano-disk loading (see Fig. 2) in the simulations it is safe to assume that the free carrier distribution in the nano-disk is also uniform. It makes it possible to find a self-consistent solution to the nonlinear problem of the free carrier dynamics in the semiconductor using to the following numerical procedure.

First, from the steady-state rate equation we find values of |E| for N = 0...3 · 1021 cm−3. Secondly, we use CST Studio where we fix the wavelength and the amplitude of the incident plane wave, which is a constant in all numerical experiments, and carry out simulations in order to find steady-state values of the electric field Ed in the nano-disk. Then, we calculate the ratio between the electric field amplitude of the incident wave and the electric field induced by this wave in the nano-disk as α=|E||Ed|. Finally, using the relation Einc = αE0 we derive the real amplitudes of the plane wave that should be applied to the feeding element in order to induce the free carrier densities of up to 3 · 1021 cm−3. We have neglected here and in the following the possible nonlinear effects in metal, which are considered negligible compared to the nonlinearities in a-Si. It is also worth noting that this approach automatically takes into consideration an energy shift between near- and far-field zone peak powers [37

37. J. Chen, P. Albella, Z. Pirzadeh, P. Alonso-González, F. Huth, S. Bonetti, V. Bonanni, J. Åkerman, J. Nogués, P. Vavassori, A. Dmitriev, J. Aizpurua, and R. Hillenbrand, “Plasmonic nickel nanoantennas,” Small 7, 2341–2347 (2011). [CrossRef]

, 43

43. A. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A 81, 053818 (2010). [CrossRef]

, 44

44. J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11, 1280–1283 (2010). [CrossRef]

].

Figure 3(a) shows the steady-state dependencies of the free carrier concentration on the optical intensity obtained using the suggested numerical procedure. In our analysis, we limit ourselves to considering the spectral range between 0.95μm and 1.05μm, where we achieve a gradual spectral tuning by illuminating the feeding element with a laser beam (Fig. 2). The resulting dependencies display a clear signature of optical bistability [35

35. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).

]: for the same optical intensity applied to the nanoantenna the free carrier density in the semiconductor nano-disk exhibits two different steady states.

Fig. 3 (a) Free carrier density in the nano-disk loading of the feeding element as a function of the optical intensity at different operating wavelengths. (b) Absolute value of the electric field in the nano-disk loading as a function of the free carrier density at different operating wavelengths.

In order to investigate the origin of the bistable behavior, we study the near-field distribution in the gap of the feeding element. Recent studies have shown that using plasmonic dipole nanoantennas similar to our isolated feeding element, the electric field can be localized in the gap leading to a field enhancement of up to two orders of magnitude at the resonance frequency [45

45. H. X. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000). [CrossRef]

,46

46. P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005). [CrossRef] [PubMed]

]. Figure 3(b) shows absolute values of the electric field in the nano-disk loading as a function of the free carrier density. We observe that the enhancement of the local field in the nano-disk contributes to the generation of additional free carriers and therefore leads to the formation of S-shaped curves typical of bistable systems. The maximum field enhancement takes place at the shortest of the considered operating wavelengths and gradually decreases with an increase in the wavelength. Consequently, a pronounced bistable curve is observed at the shortest wavelength and a weak bistable response corresponds to the longest one. Finally, since the field enhancement magnitude depends on the gap size, we note that the bistable curves can be tuned to a desired shape by varying the nano-disk size, thereby providing additional design flexibility.

It is worth mentioning here that we also investigated the impact of the background material on the relation between the free carrier density and the optical intensity. We found that the presence of a background does not significantly change the performance of the nanoantenna apart from red-shifting its operating wavelengths. Furthermore, the feeding element of the nanoantenna supports multiple resonances that leads to the formation of multiple steady states.

In order to gain more insight into the far-field characteristics of the nanoantenna, in Figs. 4(a)–4(e) we plot its far-field power angular diagrams calculated for different operating wavelengths. It is important for the spectral tuning that in all regimes the nanoantenna performs as an unidirectional emitter with a high front-to-back ratio and nearly constant beam-width of ≈ 80°. Moreover, by plotting the power emitted by the nanoantenna in the maximum emission direction as a function of the optical intensity [see Figs. 4(f)–4(j)], we observe the formation of closed bistability loops at different operating wavelengths.

Fig. 4 (a–e) Far-field power angular diagram of the nanoantenna in the E-plane (solid curves) and H-plane (dashed curves) at operating wavelengths (free carrier densities) of 0.95μm (1.9 · 1021 cm−3), 0.975μm (1.5 · 1021 cm−3), 1μm (1.2 · 1021 cm−3), 1.025μm (0.8 · 1021 cm−3) and 1.05μm (0.55 · 1021 cm−3). A dB scale is used to emphasize the difference in the backward lobes. (f–j) Power emitted by the nanoantenna in the maximum emission direction as a function of the optical intensity.

Closed loops were observed earlier in photonic systems exhibiting nonlinear Fano-Feshbach resonances resulting from the interaction between two Fano resonances located very close to each other [47

47. A. E. Miroshnichenko, “Nonlinear Fano-Feshbach resonances,” Phys. Rev. E 79, 026611 (2009). [CrossRef]

]. They may have appealing applications in realizing ultra-fast all-optical switching devices at the nanoscale since the nanoantenna exhibits two different stable states for the same applied optical intensity. One relevant aspect to underline here consists in the dependence of the total hysteresis area on the operating wavelength. For certain operating wavelength the hysteresis loop may not appear, as shown in Fig. 4(j) for 1.05μm (green curve). Such steep properties of the nonlinear response suggest the use of the Yagi-Uda architecture shown in Fig. 1 as a nonlinear optical device operating as a logical cell, an optical limiter or a signal amplitude modulator [35

35. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).

], also exhibiting emission properties not attainable with dipole plasmonic nanoantennas [29

29. 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, 2064–2068 (2010). [CrossRef] [PubMed]

, 48

48. P.-Y. Chen and A. Alú, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010). [CrossRef]

, 49

49. F. Zhou, Y. Liu, Z.-Y. Li, and Y. Xia, “Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials,” Opt. Express 13, 13337–13344 (2010). [CrossRef]

].

Finally, we calculate the optical intensity that maintains the nanoantenna in the appropriate operating regime. By fixing the operating wavelength at 1.05μm and choosing a bias point in the steep part of the corresponding curve in Fig. 4(j), for the excitation with a 25-ps-long pump laser beam focused to a 1 micron squared spot, we obtain the trigger energy of ≈ 1 pJ. Bistability-based operation of the nanoantenna at shorter wavelengths would require higher pump energies of up to ≈ 5 pJ. These values are achievable in practice and are consistent with the requirements for the ideal bistable optical device [35

35. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).

].

4. Conclusions

We have suggested a simple way to tune dynamically a plasmonic Yagi-Uda nanoantenna and emit light in a wide spectral range. This capability is hardly achievable with conventionally designed Yagi-Uda nanoantennas whose performance is strictly optimized to just a few percent around the design frequency, and it cannot be extended significantly without a penalty. We have shown the capability of the optical Yagi-Uda nanoantennas to perform as a bistable optical device offering new degrees of freedom in controlling the far-field emission. As such, Yagi-Uda nanoantennas can be used for ultra-fast switching, mixing, frequency conversion, modulation and other kinds of all-optical light control and manipulation at the nanoscale. We have shown that the optical energy required to switch the nanoantenna to an unstable state is achievable in experiments.

Acknowledgments

This work was supported by the Australian Research Council. The authors confirm many valuable discussions with their colleagues from the Nonlinear Physics Centre and Metamaterial Meeting Group at the Australian National University.

References and links

1.

V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111, 3888–3912 (2011). [CrossRef] [PubMed]

2.

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

3.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010). [CrossRef]

4.

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

5.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010). [CrossRef] [PubMed]

6.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10, 631–636 (2011). [CrossRef] [PubMed]

7.

F. de Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech. 5, 67–72 (2010). [CrossRef]

8.

I. S. Maksymov, M. Besbes, J. P. Hugonin, J. Yang, A. Beveratos, I. Sagnes, I. Robert-Philip, and P. Lalanne, “Metal-coated nanocylinder cavity for broadband nonclassical light emission,” Phys. Rev. Lett. 105, 180502 (2010). [CrossRef]

9.

A. Alú and N. Engheta, “Wireless at the nanoscale: optical interconnects using matched nanoantennas,” Phys. Rev. Lett. 104, 213902 (2010). [CrossRef] [PubMed]

10.

A. F. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett. 9, 4228–4233 (2009). [CrossRef] [PubMed]

11.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010). [CrossRef] [PubMed]

12.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010). [CrossRef]

13.

D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3D optical Yagi-Uda nanoantenna array,” Nat. Commun. 2, 267 (2011). [CrossRef] [PubMed]

14.

J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, “Near-field dynamics of optical Yagi–Uda nanoantennas,” Nano Lett. 11, 2819–2824 (2011). [CrossRef] [PubMed]

15.

I. S. Maksymov, A. R. Davoyan, and Yu. S. Kivshar, “Enhanced emission and light control with tapered plasmonic nanoantennas,” Appl. Phys. Lett. 99, 083304 (2011). [CrossRef]

16.

A. E. Miroshnichenko, I. S. Maksymov, A. R. Davoyan, C. Simovski, P. Belov, and Yu. S. Kivshar, “An arrayed nanoantenna for broadband light emission and detection,” Phys. Status Solidi RRL 5, 347–349 (2011). [CrossRef]

17.

J. N. Farahani, D. W. Pohl, H.–J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005). [CrossRef] [PubMed]

18.

F. Huang and J. J. Baumberg, “Actively tuned plasmons on elastometrically driven Au nanoparticle dimers,” Nano Lett. 10, 1787–1792 (2010). [CrossRef] [PubMed]

19.

A. Alú and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. 101, 043901 (2008). [CrossRef] [PubMed]

20.

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

21.

M. Abb, P. Albella, J. Aizpurua, and O. L. Muskens, “All-optical control of a single plasmonic nanoantenna –ITO hybrid,” Nano Lett. 11, 2457–2463 (2011). [CrossRef] [PubMed]

22.

T. Shegai, S. Chen, V. Milković, G. Zengin, P. Johansson, and M. Käll, “A bimetallic nanoantenna for directional colour routing,” Nat. Commun. 2, 481 (2011). [CrossRef] [PubMed]

23.

I. S. Maksymov and A. E. Miroshnichenko, “Active control over nanofocusing with nanorod plasmonic antennas,” Opt. Express 19, 5888–5894 (2011). [CrossRef] [PubMed]

24.

Y. Alaverdyan, N. Vamivakas, J. Barnes, C. Lebouteiller, J. Hare, and M. Atatüre, “Spectral tunability of a plasmonic antenna with a dielectric nanocrystal,” Opt. Express 19, 18175–18181 (2011). [CrossRef] [PubMed]

25.

R. W. Ziolkowski and A. Erentok, “Metamaterial-based efficient electrically small antennas,” IEEE Trans. Antennas Propag. 54, 2113–2130 (2008). [CrossRef]

26.

S. E. Sussman-Fort and R. M. Rudish, “Non-Foster impedance matching of electrically-small antennas,” IEEE Trans. Antennas Propag. 57, 2230–2241 (2009). [CrossRef]

27.

N. Engheta, A. Salandrino, and A. Alú, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005). [CrossRef] [PubMed]

28.

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007). [CrossRef] [PubMed]

29.

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, 2064–2068 (2010). [CrossRef] [PubMed]

30.

J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11, 2142–2144 (2011). [CrossRef] [PubMed]

31.

A. E. Nikolaenko, F. de Angelis, S. A. Boden, N. Papasimakis, P. Ashburn, E. di Fabrizio, and N. I. Zheludev, “Carbon nanotubes in a photonic metamaterial,” Phys. Rev. Lett. 104, 153902 (2010). [CrossRef] [PubMed]

32.

P. A. Kossyrev, A. Yin, S. G. Cloutier, D. A. Cardimona, D. Huang, P. M. Asling, and J. M. Xu, “Electric field tuning of plasmonic response of nanodot array in liquid crystal matrix,” Nano Lett. 5, 1978–1981 (2005). [CrossRef] [PubMed]

33.

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J.-C. Weeber, A. Dereux, S. Kostcheev, H. Ibn El 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, 3914–3921 (2009). [CrossRef] [PubMed]

34.

C. de Angelis, A. Locatelli, D. Modotto, S. Boscolo, M. Midrio, and A.-D. Capobianco, “Frequency addressing of nano-objects by electrical tuning of optical antennas,” J. Opt. Soc. Am. B 27, 997–1001 (2011). [CrossRef]

35.

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).

36.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

37.

J. Chen, P. Albella, Z. Pirzadeh, P. Alonso-González, F. Huth, S. Bonetti, V. Bonanni, J. Åkerman, J. Nogués, P. Vavassori, A. Dmitriev, J. Aizpurua, and R. Hillenbrand, “Plasmonic nickel nanoantennas,” Small 7, 2341–2347 (2011). [CrossRef]

38.

J. Li, A. Salandrino, and N. Engheta, “Optical spectrometer at the nanoscale using optical Yagi-Uda nanoantennas,” Phys. Rev. B 79, 195104 (2009). [CrossRef]

39.

M. Belotti, J. F. Galisteo–López, S. de Angelis, M. Galli, I. S. Maksymov, L. C. Andreani, D. Peyrade, and Y. Chen, “All-optical switching in 2D silicon photonic crystals with low loss waveguides and optical cavities,” Opt. Express 16, 11624–11636 (2008). [PubMed]

40.

A. Berrier, R. Ulbricht, M. Bonn, and J. Gómez–Rivas, “Ultrafast active control of localized surface plasmon resonances in silicon bowtie antenna,” Opt. Express 18, 23226–23235 (2010). [CrossRef] [PubMed]

41.

A. Berrier, P. Albella, M. Ameen Poyli, R. Ulbricht, M. Bonn, J. Aizpurua, and J. Gómez–Rivas, “Detection of deep-subwavelength dielectric layers at terahertz frequencies using semiconductor plasmonic resonators,” Opt. Express 20, 5052–5060 (2012). [CrossRef] [PubMed]

42.

S. M. Sze, Physics of Semiconductor Devices (John Wiley and Sons, New York, 1969).

43.

A. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A 81, 053818 (2010). [CrossRef]

44.

J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11, 1280–1283 (2010). [CrossRef]

45.

H. X. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000). [CrossRef]

46.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005). [CrossRef] [PubMed]

47.

A. E. Miroshnichenko, “Nonlinear Fano-Feshbach resonances,” Phys. Rev. E 79, 026611 (2009). [CrossRef]

48.

P.-Y. Chen and A. Alú, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010). [CrossRef]

49.

F. Zhou, Y. Liu, Z.-Y. Li, and Y. Xia, “Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials,” Opt. Express 13, 13337–13344 (2010). [CrossRef]

OCIS Codes
(190.1450) Nonlinear optics : Bistability
(250.5403) Optoelectronics : Plasmonics
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Optics at Surfaces

History
Original Manuscript: February 17, 2012
Revised Manuscript: March 14, 2012
Manuscript Accepted: March 24, 2012
Published: April 2, 2012

Citation
Ivan S. Maksymov, Andrey E. Miroshnichenko, and Yuri S. Kivshar, "Actively tunable bistable optical Yagi-Uda nanoantenna," Opt. Express 20, 8929-8938 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-8929


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References

  1. V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev.111, 3888–3912 (2011). [CrossRef] [PubMed]
  2. L. Novotny and N. F. van Hulst, “Antennas for light,” Nat. Photonics5, 83–90 (2011). [CrossRef]
  3. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4, 83–91 (2010). [CrossRef]
  4. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93, 137404 (2004). [CrossRef] [PubMed]
  5. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9, 205–213 (2010). [CrossRef] [PubMed]
  6. N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater.10, 631–636 (2011). [CrossRef] [PubMed]
  7. F. de Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotech.5, 67–72 (2010). [CrossRef]
  8. I. S. Maksymov, M. Besbes, J. P. Hugonin, J. Yang, A. Beveratos, I. Sagnes, I. Robert-Philip, and P. Lalanne, “Metal-coated nanocylinder cavity for broadband nonclassical light emission,” Phys. Rev. Lett.105, 180502 (2010). [CrossRef]
  9. A. Alú and N. Engheta, “Wireless at the nanoscale: optical interconnects using matched nanoantennas,” Phys. Rev. Lett.104, 213902 (2010). [CrossRef] [PubMed]
  10. A. F. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett.9, 4228–4233 (2009). [CrossRef] [PubMed]
  11. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science329, 930–933 (2010). [CrossRef] [PubMed]
  12. T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics4, 312–315 (2010). [CrossRef]
  13. D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3D optical Yagi-Uda nanoantenna array,” Nat. Commun.2, 267 (2011). [CrossRef] [PubMed]
  14. J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, “Near-field dynamics of optical Yagi–Uda nanoantennas,” Nano Lett.11, 2819–2824 (2011). [CrossRef] [PubMed]
  15. I. S. Maksymov, A. R. Davoyan, and Yu. S. Kivshar, “Enhanced emission and light control with tapered plasmonic nanoantennas,” Appl. Phys. Lett.99, 083304 (2011). [CrossRef]
  16. A. E. Miroshnichenko, I. S. Maksymov, A. R. Davoyan, C. Simovski, P. Belov, and Yu. S. Kivshar, “An arrayed nanoantenna for broadband light emission and detection,” Phys. Status Solidi RRL5, 347–349 (2011). [CrossRef]
  17. J. N. Farahani, D. W. Pohl, H.–J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: a tunable superemitter,” Phys. Rev. Lett.95, 017402 (2005). [CrossRef] [PubMed]
  18. F. Huang and J. J. Baumberg, “Actively tuned plasmons on elastometrically driven Au nanoparticle dimers,” Nano Lett.10, 1787–1792 (2010). [CrossRef] [PubMed]
  19. A. Alú and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett.101, 043901 (2008). [CrossRef] [PubMed]
  20. N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett.10, 1741–1746 (2010). [CrossRef] [PubMed]
  21. M. Abb, P. Albella, J. Aizpurua, and O. L. Muskens, “All-optical control of a single plasmonic nanoantenna –ITO hybrid,” Nano Lett.11, 2457–2463 (2011). [CrossRef] [PubMed]
  22. T. Shegai, S. Chen, V. Milković, G. Zengin, P. Johansson, and M. Käll, “A bimetallic nanoantenna for directional colour routing,” Nat. Commun.2, 481 (2011). [CrossRef] [PubMed]
  23. I. S. Maksymov and A. E. Miroshnichenko, “Active control over nanofocusing with nanorod plasmonic antennas,” Opt. Express19, 5888–5894 (2011). [CrossRef] [PubMed]
  24. Y. Alaverdyan, N. Vamivakas, J. Barnes, C. Lebouteiller, J. Hare, and M. Atatüre, “Spectral tunability of a plasmonic antenna with a dielectric nanocrystal,” Opt. Express19, 18175–18181 (2011). [CrossRef] [PubMed]
  25. R. W. Ziolkowski and A. Erentok, “Metamaterial-based efficient electrically small antennas,” IEEE Trans. Antennas Propag.54, 2113–2130 (2008). [CrossRef]
  26. S. E. Sussman-Fort and R. M. Rudish, “Non-Foster impedance matching of electrically-small antennas,” IEEE Trans. Antennas Propag.57, 2230–2241 (2009). [CrossRef]
  27. N. Engheta, A. Salandrino, and A. Alú, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett.95, 095504 (2005). [CrossRef] [PubMed]
  28. N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science317, 1698–1702 (2007). [CrossRef] [PubMed]
  29. 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, 2064–2068 (2010). [CrossRef] [PubMed]
  30. J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett.11, 2142–2144 (2011). [CrossRef] [PubMed]
  31. A. E. Nikolaenko, F. de Angelis, S. A. Boden, N. Papasimakis, P. Ashburn, E. di Fabrizio, and N. I. Zheludev, “Carbon nanotubes in a photonic metamaterial,” Phys. Rev. Lett.104, 153902 (2010). [CrossRef] [PubMed]
  32. P. A. Kossyrev, A. Yin, S. G. Cloutier, D. A. Cardimona, D. Huang, P. M. Asling, and J. M. Xu, “Electric field tuning of plasmonic response of nanodot array in liquid crystal matrix,” Nano Lett.5, 1978–1981 (2005). [CrossRef] [PubMed]
  33. J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J.-C. Weeber, A. Dereux, S. Kostcheev, H. Ibn El 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, 3914–3921 (2009). [CrossRef] [PubMed]
  34. C. de Angelis, A. Locatelli, D. Modotto, S. Boscolo, M. Midrio, and A.-D. Capobianco, “Frequency addressing of nano-objects by electrical tuning of optical antennas,” J. Opt. Soc. Am. B27, 997–1001 (2011). [CrossRef]
  35. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).
  36. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).
  37. J. Chen, P. Albella, Z. Pirzadeh, P. Alonso-González, F. Huth, S. Bonetti, V. Bonanni, J. Åkerman, J. Nogués, P. Vavassori, A. Dmitriev, J. Aizpurua, and R. Hillenbrand, “Plasmonic nickel nanoantennas,” Small7, 2341–2347 (2011). [CrossRef]
  38. J. Li, A. Salandrino, and N. Engheta, “Optical spectrometer at the nanoscale using optical Yagi-Uda nanoantennas,” Phys. Rev. B79, 195104 (2009). [CrossRef]
  39. M. Belotti, J. F. Galisteo–López, S. de Angelis, M. Galli, I. S. Maksymov, L. C. Andreani, D. Peyrade, and Y. Chen, “All-optical switching in 2D silicon photonic crystals with low loss waveguides and optical cavities,” Opt. Express16, 11624–11636 (2008). [PubMed]
  40. A. Berrier, R. Ulbricht, M. Bonn, and J. Gómez–Rivas, “Ultrafast active control of localized surface plasmon resonances in silicon bowtie antenna,” Opt. Express18, 23226–23235 (2010). [CrossRef] [PubMed]
  41. A. Berrier, P. Albella, M. Ameen Poyli, R. Ulbricht, M. Bonn, J. Aizpurua, and J. Gómez–Rivas, “Detection of deep-subwavelength dielectric layers at terahertz frequencies using semiconductor plasmonic resonators,” Opt. Express20, 5052–5060 (2012). [CrossRef] [PubMed]
  42. S. M. Sze, Physics of Semiconductor Devices (John Wiley and Sons, New York, 1969).
  43. A. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A81, 053818 (2010). [CrossRef]
  44. J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett.11, 1280–1283 (2010). [CrossRef]
  45. H. X. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E62, 4318–4324 (2000). [CrossRef]
  46. P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308, 1607–1609 (2005). [CrossRef] [PubMed]
  47. A. E. Miroshnichenko, “Nonlinear Fano-Feshbach resonances,” Phys. Rev. E79, 026611 (2009). [CrossRef]
  48. P.-Y. Chen and A. Alú, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B82, 235405 (2010). [CrossRef]
  49. F. Zhou, Y. Liu, Z.-Y. Li, and Y. Xia, “Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials,” Opt. Express13, 13337–13344 (2010). [CrossRef]

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