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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 8218–8232
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Coupled 2D Ag nano-resonator chains for enhanced and spatially tailored second harmonic generation

Marco Centini, Alessio Benedetti, Concita Sibilia, and Mario Bertolotti  »View Author Affiliations


Optics Express, Vol. 19, Issue 9, pp. 8218-8232 (2011)
http://dx.doi.org/10.1364/OE.19.008218


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Abstract

We report results of second harmonic generation calculations performed on Silver coupled 2D-nanoresonators. Coupling is responsible for the creation of resonant modes that can be localized on small portions of the structure or distributed over the whole structure. Different field profiles can be obtained by varying the parameters of the input field (i.e. the wavelength). The second harmonic generation nonlinear process is enhanced by the excitation of coupled surface plasmon polaritons. The emitted field is strongly affected by the linear properties of the structure behaving as a nano antenna. We note that different configurations of the pump field lead to different second harmonic far-field emission patterns. Also, we show that the angular emission of the second harmonic field contains information about the spatial location of the pump field hot spots at different frequencies. Applications to a new class of nano sources for single molecule fluorescence and sensors are proposed.

© 2011 OSA

1. Introduction

Recently the development of nanotechnologies has made possible the creation of techniques for manipulation of matter at the nanoscale; consequently artificial materials exhibiting new properties compared with natural materials have been created. In particular, concerning the optical properties, it has been proved that some devices allow the confinement of light (more generally of the electromagnetic field), on sub wavelength spatial scales, beyond the limit imposed by the theory of diffraction. Nanofabrication processes are at the basis of the development of artificial materials, called meta materials (MM), operating in the range of wavelengths of visible or near infrared. They can be characterized macroscopically as homogeneous media with unique properties compared to natural materials [1

1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

8

8. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]

]. The understanding of the macroscopic properties at a deeper level requires a knowledge of the properties of the single element that makes up the material, the “meta atom”. For this reason a part of research activities in the field of nano photonics is dedicated to the study of the optical response of nano particles or small clusters of particles with particular interest to the study of nano metallic structures also called plasmonic nanostructures (NS) [9

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

]. In the case of three-dimensional NS, if the appropriate resonance conditions are fulfilled, we observe the excitation of modes on the surface of the structure called localized surface plasmon polaritons (LSPP) [9

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

]. The confinement of the electromagnetic field on such a small size is very sensitive to small changes in morphology or surface imperfections which alter the conditions of resonance. These features are on the basis of the applications that have been proposed for the realization of highly sensitive sensors and biosensors [10

10. S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009). [CrossRef] [PubMed]

] and for the improvement of the performances of solar cells by optimizing the amount of light energy converted into electrical energy [11

11. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

]. Reference [12

12. A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009). [CrossRef]

] highlights the potential applications of plasmonic NS to enhance the fluorescence of single molecules and to produce integrated circuits able to perform logical operations on very small spaces [13

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

]. MM have recently been proposed to enhance the luminescence of a quantum dot by controlling the radiation spectrum [14

14. K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010). [CrossRef]

]. Similar mechanisms are used to monitor the far-field emission of nano sources by maximizing efficiency in terms of power transfer and directionality. For example, in [15

15. 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(5994), 930–933 (2010). [CrossRef] [PubMed]

] it was proved experimentally the control and the optimization of the emission of radiation by a quantum dot coupled to a nano-antenna designed according to the criteria of Yagi-Uda, widely used for radio frequency antennas.

2. Linear properties

3. Second harmonic generation

We also show in Fig. 5
Fig. 5 (a) Log10 of the modulus of the y component of the generated SH electric field normalized with respect to the amplitude of the x polarized, upward propagating, incident field with a wavelength of 950 nm; (b) differential nonlinear scattering cross section for a SH field wavelength of 475 nm. White lines have been used to identify the boundaries of the rods.
the Log10 of the modulus of the y component of the electric field at the SH frequency divided by the amplitude of the input field (a) and the differential nonlinear scattering cross section corresponding to the case of maximum efficiency (b) - pump field wavelength is 950 nm. In order to improve the appearance and readability of the depicted near field SH patterns we chose to plot the SH field in log scale. Indeed the near field exhibits highly evanescent components and sharp variations on a very short scale (few nanometers). In particular we note SH peaks at the corners of the rods. These peaks, due to the pump hot spots, depends on the sharpness of the corners. In our calculations this feature is limited by the size of the unit cell used for the discretization of the rods (1.5x1.5 nm2). However, being our numerical integration method valid for arbitrary geometries, for practical applications and/or for comparisons with real structures we can easily consider round corners according to the fabrication tolerances. We also note that the SH field is localized inside the nanocavity. This is possible because at the SH field frequency the relative permittivity of Ag is still negative. The doubly resonant behavior both at the FF and at the SH frequency is responsible for a higher enhancement of the efficiency of the generation process with respect to the case of gold nanorods (see for example results of ref. [33

33. A. Benedetti, M. Centini, C. Sibilia, and M. Bertolotti, “Engineering the second harmonic generation pattern from coupled gold nanowires,” J. Opt. Soc. Am. B 27(3), 408–416 (2010). [CrossRef]

]).

Finally we depict the generated SH field near the 8-rod nanostructure at the considered wavelengths (Figs. 11
Fig. 11 Log10 of the modulus of the y component of the SH frequency field normalized with respect to the amplitude of the x-polarized incident field of wavelength of: (a) 920 nm (SH @ 460 nm); (b) 960 nm (SH @ 480 nm); (c) 980 nm (SH @ 490 nm) and (d) 1030 nm (SH at 515 nm). White lines have been used to identify the boundaries of the rods.
). We note that different SH near field patterns are obtained by tuning the FF wavelengths in a range from 920nm to −1030 nm. Thus, as expected, different FF localization patterns (Fig. 9(a), 9(c) and Fig. 10(a), 10(c)) produce different SH far field (Fig. 9(b), 9(d) and Fig. 10(b), 10(d)) and near field patterns (Fig. 11(a), 11(b), 11(c), 11(d)).

4. Conclusion

Our numerical results have shown that plasmonic NS can be realized to optimize and tailor second harmonic generation by taking advantage of multiple coupled nanoresonators. Enhancements of 2-3 orders of magnitude with respect to the case of single metal nanoparticles have been predicted. Moreover we have shown that both FF field localization and spatial distribution on the nanoscale can drastically affect the nonlinear response of the system. Maximum efficiency of the generation process is expected in the range where the absorption cross section is maximum but a more detailed investigation requires the calculation of the near field and far field SH generation. Indeed, by tuning the pump wavelength it is possible to modify the arrangement of the feeder (being the nonlinear polarization the source of the SH field) and then the generated field pattern. This property might be used to address a subwavelength size portion of the structure where the field is highly localized. Also the FF field pattern could be tailored by coherent control using two counterpropagating pump beams or with spatial phase-shaped beams as discussed in [50

50. G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, “Controlling the optical near field of nanoantennas with spatial phase-shaped beams,” Nano Lett. 9(10), 3608–3611 (2009). [CrossRef] [PubMed]

]. In this way a nano source of SH field could be addressed and it could be possible to use it to study the fluorescence of a single molecule located in the hot spot by far field detection at the proper angle of emission, for example. Optimization of the structures in order to obtain high directionality or high selectivity can be performed by changing size and shapes of the nanoresonators. Also, an array of these kind of “meta atoms” displaying high selectivity in SH directionality could be used to improve the superprism effect discussed in [51

51. E. Centeno, “Second-harmonic superprism effect in photonic crystals,” Opt. Lett. 30(9), 1054–1056 (2005). [CrossRef] [PubMed]

] for photonic crystals or to bring it on a more compact scale.

References and links

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2.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

3.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402 (2005). [CrossRef] [PubMed]

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W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007). [CrossRef] [PubMed]

5.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

6.

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]

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V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). [CrossRef]

8.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]

9.

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

10.

S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009). [CrossRef] [PubMed]

11.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

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A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009). [CrossRef]

13.

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

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K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010). [CrossRef]

15.

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(5994), 930–933 (2010). [CrossRef] [PubMed]

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Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010). [CrossRef] [PubMed]

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W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76(11), 115411 (2007). [CrossRef]

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A. Nevet, N. Berkovitch, A. Hayat, P. Ginzburg, S. Ginzach, O. Sorias, and M. Orenstein, “Plasmonic nanoantennas for broad-band enhancement of two-photon emission from semiconductors,” Nano Lett. 10(5), 1848–1852 (2010). [CrossRef] [PubMed]

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W. Fan, S. Zhang, N.-C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood Jr, K. J. Malloy, and S. R. J. Brueck, “Second harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006). [CrossRef]

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B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers,” Nano Lett. 7(5), 1251–1255 (2007). [CrossRef] [PubMed]

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51.

E. Centeno, “Second-harmonic superprism effect in photonic crystals,” Opt. Lett. 30(9), 1054–1056 (2005). [CrossRef] [PubMed]

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(190.3970) Nonlinear optics : Microparticle nonlinear optics
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Nonlinear Optics

History
Original Manuscript: February 7, 2011
Revised Manuscript: March 13, 2011
Manuscript Accepted: March 14, 2011
Published: April 14, 2011

Virtual Issues
Vol. 6, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Marco Centini, Alessio Benedetti, Concita Sibilia, and Mario Bertolotti, "Coupled 2D Ag nano-resonator chains for enhanced and spatially tailored second harmonic generation," Opt. Express 19, 8218-8232 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8218


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References

  1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]
  2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
  3. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402 (2005). [CrossRef] [PubMed]
  4. W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333–3341 (2007). [CrossRef] [PubMed]
  5. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]
  6. S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]
  7. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). [CrossRef]
  8. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]
  9. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  10. S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009). [CrossRef] [PubMed]
  11. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]
  12. A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009). [CrossRef]
  13. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  14. K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010). [CrossRef]
  15. 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(5994), 930–933 (2010). [CrossRef] [PubMed]
  16. Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010). [CrossRef] [PubMed]
  17. W. Dickson, G. A. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. V. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76(11), 115411 (2007). [CrossRef]
  18. A. Nevet, N. Berkovitch, A. Hayat, P. Ginzburg, S. Ginzach, O. Sorias, and M. Orenstein, “Plasmonic nanoantennas for broad-band enhancement of two-photon emission from semiconductors,” Nano Lett. 10(5), 1848–1852 (2010). [CrossRef] [PubMed]
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