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  • Editor: Alan E. Willner
  • Vol. 38, Iss. 14 — Jul. 15, 2013
  • pp: 2621–2624
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Scattering of core-shell nanowires with the interference of electric and magnetic resonances

Wei Liu, Andrey E. Miroshnichenko, Rupert F. Oulton, Dragomir N. Neshev, Ortwin Hess, and Yuri S. Kivshar  »View Author Affiliations


Optics Letters, Vol. 38, Issue 14, pp. 2621-2624 (2013)
http://dx.doi.org/10.1364/OL.38.002621


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Abstract

We study the scattering of normally incident waves by core-shell nanowires, which support both electric and magnetic resonances. Within such nanowires, for p-polarized incident waves, each electric resonance corresponds to two degenerate scattering channels while the magnetic resonance corresponds to only one channel. Consequently, when the electric dipole (ED) and magnetic dipole (MD) are tuned to overlap spectrally, the magnitude of the ED is twice that of the magnetic one, leading to a pair of angles of vanishing scattering. We further demonstrate that the scattering features of nanowires are polarization dependent, and vanishing scattering angles also can be induced by Fano resonances due to the interference of higher-order electric modes with the broad MD mode.

© 2013 Optical Society of America

Investigations on scattering of light by subwavelength particles play a fundamental role in many fields, with applications in optical communications, meteorology, sensing, and other interdisciplinary fields, including medical and biological research [1

1. M. Kerker, The Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).

3

3. R. Huschka, J. Zuloaga, M. W. Knight, L. V. Brown, P. Nordlander, and N. J. Halas, J. Am. Chem. Soc. 133, 12247 (2011). [CrossRef]

]. For most scattering problems, efficient shaping of the scattering pattern is one of the most crucial issues and is vitally important for applications, such as nanoantennas [4

4. L. Novotny and N. van Hulst, Nat. Photonics 5, 83 (2011).

,5

5. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010). [CrossRef]

] and photovoltaic devices [6

6. H. A. Atwater and A. Polman, Nat. Mater. 9, 865 (2010). [CrossRef]

]. However, most approaches on the scattering shaping currently rely on the engineering of electric responses of nanostructures, because most materials have only dominant electric responses [1

1. M. Kerker, The Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).

,2

2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

,7

7. B. S. Luk’yanchuk and V. Ternovsky, Phys. Rev. B 73, 235432 (2006).

,8

8. B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, J. Opt. 15, 073001 (2013). [CrossRef]

].

The presence of magnetic resonances in scattering systems brings extra freedom for scattering engineering due to the interplay of both electric and magnetic responses [9

9. M. Kerker, D. S. Wang, and C. L. Giles, J. Opt. Soc. Am. 73, 765 (1983). [CrossRef]

]. However, in nature only a limited number of materials exhibit magnetic properties at optical frequencies. These are mainly due to magnetic dipole (MD) transitions in, for example, rare-earth atoms and are known to only operate in a narrow spectral range accompanied by high intrinsic losses.

Recently, inspired by the emerging field of metamaterials, many nonmagnetic structures have been proven to support artificial magnetic resonances. The high permittivity nanowires and spheres are outstanding examples [10

10. L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. Lett. 98, 157403 (2007). [CrossRef]

20

20. R. Paniagua-Dominguez, D. R. Abujetas, and J. A. Sanchez-Gil, Sci. Rep. 3, 1057 (2013).

]. The existence of both electric and magnetic resonances in such high permittivity nanoparticles has led to the demonstration of novel scattering phenomena [18

18. J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, Phys. Rev. Lett. 99, 107401 (2007). [CrossRef]

24

24. S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett. 13, 1806 (2013).

], including the vanishing backward scattering proposed by Kerker, et al. [9

9. M. Kerker, D. S. Wang, and C. L. Giles, J. Opt. Soc. Am. 73, 765 (1983). [CrossRef]

]. For those demonstrations, however, the electric and MDs were mostly spectrally separated and, consequently, the total scattering was in the nonresonant regime with reduced total magnitude. It is not until recently that the vanishing backward scattering in the resonant superscattering regime was achieved through overlapping an electric dipole (ED) and a MD of the same magnitude in core-shell nanospheres [25

25. W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, ACS Nano 6, 5489 (2012). [CrossRef]

,26

26. W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. B 86, 081407(R) (2012).

]. Following these first ideas, it is now becoming increasingly important to apply the superscattering regime to scatterers with other geometries and explore the polarization effects of the scattering as well as the influence of higher-order modes on the scattering pattern.

In this Letter, we study the scattering of (metal) core-shell (high-permittivity dielectric) nanowires, which support both electric and magnetic resonances. We find that for p-polarized incident waves, the ED and MD can be tuned to overlap spectrally. Because the ED corresponds to two degenerate scattering channels while the MD corresponds to only one channel, its magnitude is twice the magnitude of the MD. Consequently, in sharp contrast to spherical structures investigated before, where the scattering is suppressed only at the backward direction, here we demonstrate a pair of angles along which the scattering is vanishing. It is also demonstrated that the scattering features are highly polarization dependent, and the vanishing scattering angles can also be obtained through the Fano resonance, which is induced by the interference of the broad MD and the narrow, higher-order electric modes.

Figure 1 shows a schematic of the structure being studied. The infinitely long nanowire is arranged along the z direction with a silver core (the permittivity is from [27

27. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).

]) and a dielectric shell (n=3.5). Here, the incident plane wave propagates along x direction and the scattered light is confined at the xy plane. The electric field of the incident wave is either polarized along y (p wave) or along z (s wave). The scattering of a nanowire (single-layered or multilayered) can be solved analytically and the scattering efficiency is [1

1. M. Kerker, The Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).

,2

2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

]:
Qscas,p=2kr[(a0s,p)2+2m=1(ams,p)2],
(1)
where k is the angular wave number in the background material (vacuum in this study); r is the radius of the outmost layer; a0 and am are the scattering coefficients, and the superscripts s and p corresponds to s wave and p wave, respectively. More specifically a0 and a1 correspond to the magnetic (electric) and electric (magnetic) dipoles for p (s) waves, respectively, [11

11. K. Vynck, D. Felbacq, E. Centeno, A. I. Cabuz, D. Cassagne, and B. Guizal, Phys. Rev. Lett. 102, 133901 (2009). [CrossRef]

]. The scattering coefficient am relates to an angular field distribution of eimθ [11

11. K. Vynck, D. Felbacq, E. Centeno, A. I. Cabuz, D. Cassagne, and B. Guizal, Phys. Rev. Lett. 102, 133901 (2009). [CrossRef]

], which corresponds to two angular momentum channels with angular momentums ±m, where the scattering angle θ is defined in Fig. 1. In contrast, a0 corresponds to a uniform angular field distribution with no angular momentum along z direction [1

1. M. Kerker, The Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).

,2

2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

]. As a result, the contribution from am to the scattering efficiency is twice that from a0. At the same time, the angular scattering amplitude can be expressed as [1

1. M. Kerker, The Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).

,2

2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

]:
SAs,p(θ)=2/πk|a0s,p+2m=1ams,pcos(mθ)|.
(2)

Fig. 1. Schematic of scattering of normally incident p-polarized plane waves by a core-shell nanowire. The core nanowire is silver of radius r1 and the shell is n=3.5 dielectric of radius r2. The scattering angle is defined as θ.

Figure 2 shows the scattering efficiency spectra (SES) for incident p-wave, including the total scattering efficiency and the contributions from a0p (MD) and a1p (single channel, ED). First, we studied a single-layered nanowire (r1=0, r2=145nm) and the SES is shown in Fig. 2(a). It is clear that although both dominant ED and MD are supported with resonances centered at point E and M, respectively, they are spectrally separated. In Fig. 2(a) we also show the near-field distributions of longitudinal magnetic field intensity (|Hz|2, color map) and transverse electric field (Et, arrows) of points E and M. Dashed green lines indicate the nanowire background boundaries. It is clear that ED and MD are supported at points E and M, respectively: at point E, the Hz field shows a typical dipolar distribution with transverse electric filed almost linearly polarized; at point M, Hz field is almost azimuthally symmetric inside the nanowire, accompanied by circulating displacement currents, indicating the existence of an artificial MD [12

12. A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, Phys. Rev. B 82, 045404 (2010).

16

16. A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).

]. Fig. 2(c) shows the scattering patterns at both points. Typical dipole-like scattering patterns are observed: at point E, the ED is dominant and oriented along y direction with a two-lobe scattering pattern in the xy plane; at point M, the MD is dominant and oriented along z direction with an almost circular scattering pattern in the xy plane. Then we studied a two-layered core-shell nanowire, shown in Fig. 1. As Fig. 2(b) shows, it is clear that when the inner radius r1=70nm and the outer radius r2=145nm, the ED and MD can overlap, thus creating a superscattering spectral regime (the corresponding single channel limit in terms of scattering efficiency is approximately 2.4) [28

28. Z. C. Ruan and S. H. Fan, Phys. Rev. Lett. 105, 013901 (2010). [CrossRef]

]. We note here that the overlapping wavelength of ED and MD for such structures is highly tunable, and can be shifted to shorter or longer wavelengths for smaller or larger scales of the nanowires with specific aspect ratios. Also in the spectral regime in Fig. 2(b), the ED and MD are dominant and Eq. (2) can be simplified as:
SAp(θ)=2/πk|a0p+2a1pcos(θ)|.
(3)

Fig. 2. Scattering efficiency spectra of p wave (total and the contribution from a0p and a1p) for (a) uniform dielectric nanowire with r1=0, r2=145nm and (b) (silver) core—(n=3.5 dielectric) shell nanowire with r1=70nm and r2=145nm. Above (a) the near-field distributions of |Hz|2 (color map) and transverse electric field Et (arrows) at points E and M are shown. Dashed green lines indicate the nanowire background boundaries. (c) and (d) show the scattering patterns for the points indicated in (a) and (b): λS=1.106μm, λA=1.242μm, λE=0.895μm, and λM=1.363μm.

At the overlapping resonant point S, as indicated in Fig. 2(b), both a0p and a1p are real [1

1. M. Kerker, The Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).

] and a0p=a1p=b. Thus, at this point we have SAp(θ)=b2/πk|1+2cos(θ)|, which indicates that when θ=120°, 240° [cos(θ)=1/2] the scattering is vanishing. Figure 2(d) shows the normalized scattering amplitude at point S. We note that at point A, indicated in Fig. 2(b), the scattering pattern is identical as that of point S. The difference is that point A is in the nonresonant regime and the overall scattering is less than half of that at point S.

Fig. 3. (a) Same as in Fig. 2(b) but for incident s wave. (b) The ratio of SAs/SAp with equal p wave and s wave incidence along θ=120° and 240°. The inset shows an enlarged area of λ=1.1901.210μm. (c) and (d) show the scattering patterns for the points indicated in (a) and (b) with λB=1.202μm and λS=1.106μm.

Finally, we study the interference of MD and the electric quadruple mode (QM, characterized by a2) for p-wave. In Fig. 4(a) we show the SES for the same core-shell structure at the spectral range of 800–1000 nm. The contribution from QM and MD are dominant and then Eq. (2) can be expressed as:
SAp(θ)=2/πk|a0p+2a2pcos(2θ)|.
(4)
Compared to the QM, the MD response is rather broad, and its interference with the narrow QM will produce sharp Fano resonances [8

8. B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, J. Opt. 15, 073001 (2013). [CrossRef]

,29

29. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010). [CrossRef]

,30

30. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010). [CrossRef]

]. Figure 4(b) shows the normalized scattering amplitude when 1+cos(2θ)=0, and the two modes can almost cancel each other, resulting in vanishing scattering along two pairs of angles: θ=60°, 120°, 240°, and 300°. A typical Fano asymmetric line shape is observed. The specific scattering patters for the Fano dip (point D) and Fano peak (point P) are shown in Figs. 4(c) and 4(d), respectively, clearly indicating the destructive and constructive interferences along those angles.

Fig. 4. (a) Same as in Fig. 2(b) but in the spectral regime of λ=0.81μm. (b) normalized scattering amplitude along θ=60°, 120°, 240°, and 300°. (c) and (d) show the scattering patterns for the points indicated in (b) with λD=0.883μm and λP=0.895μm.

In summary, we have studied scattering of core-shell nanowires, which support both electric and magnetic resonances. We have demonstrated how to achieve a pair of vanishing scattering angles in the superscattering regime of overlapped ED and MD for p waves. We also have demonstrated the polarization dependence of these scattering features and Fano resonance induced vanishing scattering angles. Our study generalizes the Kerker proposal for backward scattering suppression, and our approaches can be extended to higher-order modes or to other noncylindrical structures where different vanishing scattering angles can be obtained in the resonant strong scattering regimes. We believe our results shed new light on the direction of scattering shaping based on interferences of both electric and magnetic resonances, which can play a major role in applications such as nanoantennas, nanolasers, sensors, and solar cells

We thank S. Deng for useful discussions and acknowledge support from the Australian Research Council and the Leverhulme Trust.

References

1.

M. Kerker, The Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).

2.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

3.

R. Huschka, J. Zuloaga, M. W. Knight, L. V. Brown, P. Nordlander, and N. J. Halas, J. Am. Chem. Soc. 133, 12247 (2011). [CrossRef]

4.

L. Novotny and N. van Hulst, Nat. Photonics 5, 83 (2011).

5.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010). [CrossRef]

6.

H. A. Atwater and A. Polman, Nat. Mater. 9, 865 (2010). [CrossRef]

7.

B. S. Luk’yanchuk and V. Ternovsky, Phys. Rev. B 73, 235432 (2006).

8.

B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, J. Opt. 15, 073001 (2013). [CrossRef]

9.

M. Kerker, D. S. Wang, and C. L. Giles, J. Opt. Soc. Am. 73, 765 (1983). [CrossRef]

10.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. Lett. 98, 157403 (2007). [CrossRef]

11.

K. Vynck, D. Felbacq, E. Centeno, A. I. Cabuz, D. Cassagne, and B. Guizal, Phys. Rev. Lett. 102, 133901 (2009). [CrossRef]

12.

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, Phys. Rev. B 82, 045404 (2010).

13.

A. Garcia-Etxarri, R. Gomez-Medina, L. S. Froufe-Perez, C. Lopez, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, Opt. Express 19, 4815 (2011). [CrossRef]

14.

R. Gomez-Medina, B. Garcia-Camara, I. Suarez-Lacalle, F. Gonzalez, F. Moreno, M. Nieto-Vesperinas, and J. J. Sáenz, J. Nanophoton. 5, 053512 (2011).

15.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. S. Luk’yanchuk, Science Reporter 2, 492 (2012).

16.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).

17.

R. Paniagua-Dominguez, F. Lopez-Tejeira, R. Marques, and J. A. Sanchez-Gil, New J. Phys. 13, 123017 (2011).

18.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, Phys. Rev. Lett. 99, 107401 (2007). [CrossRef]

19.

P. Y. Fan, U. K. Chettiar, L. Y. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, Nat. Photonics 6, 380 (2012).

20.

R. Paniagua-Dominguez, D. R. Abujetas, and J. A. Sanchez-Gil, Sci. Rep. 3, 1057 (2013).

21.

D. S. Filonov, A. E. Krasnok, A. P. Slobozhanyuk, P. V. Kapitanova, E. A. Nenasheva, Y. S. Kivshar, and P. A. Belov, Appl. Phys. Lett. 100, 201113 (2012). [CrossRef]

22.

J. M. Geffrin, B. Garcia-Camara, R. Gomez-Medina, P. Albella, L. S. Froufe-Perez, C. Eyraud, A. Litman, R. Vaillon, F. Gonzalez, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012). [CrossRef]

23.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. S. Luk’yanchuk, Nat. Commun. 4, 1527 (2013). [CrossRef]

24.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett. 13, 1806 (2013).

25.

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, ACS Nano 6, 5489 (2012). [CrossRef]

26.

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. B 86, 081407(R) (2012).

27.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).

28.

Z. C. Ruan and S. H. Fan, Phys. Rev. Lett. 105, 013901 (2010). [CrossRef]

29.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010). [CrossRef]

30.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.5740) Physical optics : Resonance
(290.0290) Scattering : Scattering

ToC Category:
Scattering

History
Original Manuscript: May 22, 2013
Revised Manuscript: June 16, 2013
Manuscript Accepted: June 18, 2013
Published: July 15, 2013

Citation
Wei Liu, Andrey E. Miroshnichenko, Rupert F. Oulton, Dragomir N. Neshev, Ortwin Hess, and Yuri S. Kivshar, "Scattering of core-shell nanowires with the interference of electric and magnetic resonances," Opt. Lett. 38, 2621-2624 (2013)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-38-14-2621


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References

  1. M. Kerker, The Scattering of Light, and Other Electromagnetic Radiation (Academic, 1969).
  2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  3. R. Huschka, J. Zuloaga, M. W. Knight, L. V. Brown, P. Nordlander, and N. J. Halas, J. Am. Chem. Soc. 133, 12247 (2011). [CrossRef]
  4. L. Novotny and N. van Hulst, Nat. Photonics 5, 83 (2011).
  5. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010). [CrossRef]
  6. H. A. Atwater and A. Polman, Nat. Mater. 9, 865 (2010). [CrossRef]
  7. B. S. Luk’yanchuk and V. Ternovsky, Phys. Rev. B 73, 235432 (2006).
  8. B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, J. Opt. 15, 073001 (2013). [CrossRef]
  9. M. Kerker, D. S. Wang, and C. L. Giles, J. Opt. Soc. Am. 73, 765 (1983). [CrossRef]
  10. L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. Lett. 98, 157403 (2007). [CrossRef]
  11. K. Vynck, D. Felbacq, E. Centeno, A. I. Cabuz, D. Cassagne, and B. Guizal, Phys. Rev. Lett. 102, 133901 (2009). [CrossRef]
  12. A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, Phys. Rev. B 82, 045404 (2010).
  13. A. Garcia-Etxarri, R. Gomez-Medina, L. S. Froufe-Perez, C. Lopez, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, Opt. Express 19, 4815 (2011). [CrossRef]
  14. R. Gomez-Medina, B. Garcia-Camara, I. Suarez-Lacalle, F. Gonzalez, F. Moreno, M. Nieto-Vesperinas, and J. J. Sáenz, J. Nanophoton. 5, 053512 (2011).
  15. A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. S. Luk’yanchuk, Science Reporter 2, 492 (2012).
  16. A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).
  17. R. Paniagua-Dominguez, F. Lopez-Tejeira, R. Marques, and J. A. Sanchez-Gil, New J. Phys. 13, 123017 (2011).
  18. J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, Phys. Rev. Lett. 99, 107401 (2007). [CrossRef]
  19. P. Y. Fan, U. K. Chettiar, L. Y. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, Nat. Photonics 6, 380 (2012).
  20. R. Paniagua-Dominguez, D. R. Abujetas, and J. A. Sanchez-Gil, Sci. Rep. 3, 1057 (2013).
  21. D. S. Filonov, A. E. Krasnok, A. P. Slobozhanyuk, P. V. Kapitanova, E. A. Nenasheva, Y. S. Kivshar, and P. A. Belov, Appl. Phys. Lett. 100, 201113 (2012). [CrossRef]
  22. J. M. Geffrin, B. Garcia-Camara, R. Gomez-Medina, P. Albella, L. S. Froufe-Perez, C. Eyraud, A. Litman, R. Vaillon, F. Gonzalez, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012). [CrossRef]
  23. Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. S. Luk’yanchuk, Nat. Commun. 4, 1527 (2013). [CrossRef]
  24. S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett. 13, 1806 (2013).
  25. W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, ACS Nano 6, 5489 (2012). [CrossRef]
  26. W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. B 86, 081407(R) (2012).
  27. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
  28. Z. C. Ruan and S. H. Fan, Phys. Rev. Lett. 105, 013901 (2010). [CrossRef]
  29. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010). [CrossRef]
  30. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010). [CrossRef]

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