OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 23619–23630
« Show journal navigation

Tunablity of the unconventional Fano resonances in coated nanowires with radial anisotropy

H. L. Chen and L. Gao  »View Author Affiliations


Optics Express, Vol. 21, Issue 20, pp. 23619-23630 (2013)
http://dx.doi.org/10.1364/OE.21.023619


View Full Text Article

Acrobat PDF (1167 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We establish full-wave electromagnetic scattering theory to study the near-field and far-field spectra of radially anisotropic coated nanowires. For coated nanowires containing radially anisotropic core and plasmonic shell, unconventional Fano resonances are predicted due to the interference between dipole cloaking mode and dipole resonant mode. In contrast to Z-shaped Fano profile with small modulation depth for coated nanospheres in Argyropoulos et al, Phys. Rev. Lett. 108, 263905 (2012), we predict S-shaped Fano profile with high depth for coated nanowires. An off-resonance field enhancement in the radially anisotropic core is found at the Fano dip, and its’ magnitude is approximately the same as that the one at the low-energy resonant wavelength. Furthermore, with our adjustment of the inner size and the permittivity elements of the anisotropic core, tunable Fano-like profiles can be realized. These results may be useful for potential applications in different fields of nanotechnology.

© 2013 OSA

1. Introduction

Fano profiles are typical spectral features arising from the coupling of a discrete state with a continuum, which were discovered in the realm of atomic physics by Fano in 1961 [1

1. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878(1961). [CrossRef]

]. With the advent of plasmonics and metamaterials, plasmonic Fano resonances have received much attention because of their broad ranges of applications, including the design of novel metamaterials, filters, sensors, and nonlinear devices. Generally, plasmonic Fano resonances have narrow linewidths due to the coupling between the broad bright resonance mode and the narrow dark one. For the reviews, we refer the readers to [2

2. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298(2010). [CrossRef]

, 3

3. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715(2010). [CrossRef]

].

Fano resonances were also found to play an important role in the light scattering by nanostructures. For instance, ring/disk nanocavities and nanodisks were designed to realize the tunable Fano resonances [4

4. F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett. 8(11), 3983–3988(2008). [CrossRef] [PubMed]

6

6. Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett. 11(10), 4475–4479(2011). [CrossRef] [PubMed]

]. Due to the coupling between the spectrally localized surface plasmon resonance of the silver nanoparticle and the continuum of interband transitions of the gold one, Fano profiles were observed from Au nanorod dimers [7

7. K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano 5(7), 5976–5986(2011). [CrossRef] [PubMed]

] and from bimetallic nanostructures including heterogeneous dimers [8

8. G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett. 101(19), 197401(2008). [CrossRef] [PubMed]

, 9

9. Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett. 96(13), 131113(2010). [CrossRef]

]. Later, enhanced Fano resonances in compositionally asymmetric plasmonic nanoparticle heterodimers was predicted theoretically and experimentally [10

10. S. Sheikholeslami, Y. W. Jun, P. K. Jain, and A. P. Alivisatos, “Coupling of optical resonances in a compositionally asymmetric plasmonic nanoparticle dimer,” Nano Lett. 10(7), 2655–2660(2010). [CrossRef] [PubMed]

, 11

11. O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C 115(14), 6410–6414(2011). [CrossRef]

]. In addition, core-shell nanoparticles were designed to study Fano resonances in optical response too [12

12. S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett. 10(7), 2694–2701(2010). [CrossRef] [PubMed]

16

16. D. J. Wu, S. M. Liang, and X. J. Liu, “A tunable Fano resonance in silver nanoshell with a spherically anisotropic core,” J. Chem. Phys. 136(3), 034502(2012). [CrossRef] [PubMed]

].

On the other hand, Tribelsky et al established the conditions for observing Fano resonances at elastic light scattering by small spherical particles, and the interactions between the narrow surface quadrupolar resonances and the broad volume dipolar modes lead to the Fano-like profiles [17

17. M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett. 100(4), 043903(2008). [CrossRef] [PubMed]

, 18

18. B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt. 15(7), 073001 (2013). [CrossRef]

]. They further found that unconventional Fano resonances could occur beyond the applicability of the Rayleigh approximation, when the interference of different electromagnetic modes excited in the particles with the same multipole moment was crucial. For this purpose, two kinds of such resonances in light scattering by particles with large permittivity and the ones with spatial dispersion were given [19

19. M. I. Tribelksy, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett. 97(4), 44005(2012). [CrossRef]

]. More recently, Arruda et al investigated light scattering by coated spheres composed of a dispersive plasmonic core and a dielectric shell, and they predicted unconventional Fano effect and off-resonance field enhancement because of the interference between the various plasmonic modes with the same multipole moment inside the shell [20

20. T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A 87(4), 043841(2013). [CrossRef]

].

In this paper, in order to study the interesting phenomenon of Fano resonance, we would like to consider plasmonic coated nanowire with radial anisotropy. Actually, the radial anisotropy in two-dimensional case was indeed found in cylindrical anisotropic material such as WS2 nanotubes [21

21. M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett. 87(7), 075501(2001). [CrossRef] [PubMed]

, 22

22. D. Taverna, M. Kociak, V. Charbois, and L. Henrard, “Electron energy-loss spectrum of an electron passing near a locally anisotropic nanotube,” Phys. Rev. B 66(23), 235419(2002). [CrossRef]

]. In addition, with such a two-dimensional radial anisotropy, spatial power combination for omnidirectional radiation [23

23. Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett. 108(21), 213903(2012). [CrossRef] [PubMed]

, 24

24. Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” EPL 100(3), 34005(2012). [CrossRef]

] and cylindrical cloak without superluminal propagation were experimentally demonstrated [25

25. S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109(22), 223903(2012). [CrossRef]

]. Theoretically, the analytical models for the cylindrical cloak with radial anisotropy were established [26

26. X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A 79(15), 155122(2009).

, 27

27. Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics 5(3), 251–258(2010). [CrossRef]

], and plasmonic and non-Rayleigh electromagnetic scattering from radially anisotropic nanowires were reported [28

28. Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res. 106, 335–347(2010). [CrossRef]

, 29

29. H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A 86(3), 033825(2012). [CrossRef]

]. Here we investigate the Fano resonance coupling by combining the cloaking state and the plasmonic resonant state in coated nanowires with radial anisotropy. In comparison with the system of isotropic core-shell plasmonic particles with Z-shape Fano profile in the plot of extinction cross section as a function of the incident wavelength [30

30. C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905(2012). [CrossRef] [PubMed]

], we observe S-shaped curve due to the coupling between the dipole cloaking and plasmonic resonance in radially anisotropic coated nanowires. Besides that, the coated nanowire provides higher modulation depth in the Fano profile than the coated sphere does. Moreover, the introduction of the radial anisotropy and the core-shell nanostructures are helpful for us to realize the tunable Fano resonances.

This paper is organized as follows. In Section 2, we establish full-wave electromagnetic theory of light scattering by coated nanowires in which both the core and the shell are radially anisotropic in the permittivity and permeability tensors. In Section 3, we study the near-field and far-field behavior analytically in the quasistatic limit. In Section 4, numerical results are shown for the tunable Fano resonances. Conclusions and discussion are made in Section 5.

2. Full-wave electromagnetic theory

We consider electromagnetic wave scattering from the coated nanowire consisting of the core of radius a and the shell of radius b, as shown in Fig. 1. For radial anisotropy, the relative permittivity and permeability tensors of the core and the shell are expressed as in cylindrical coordinates (r, θ, z) [28

28. Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res. 106, 335–347(2010). [CrossRef]

, 29

29. H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A 86(3), 033825(2012). [CrossRef]

, 31

31. X. P. Yu and L. Gao, “Nonlinear dielectric response in partially resonant composites with radial dielectric anisotropy,” Phys. Lett. A 359(5), 516–522(2006). [CrossRef]

],
εi=(εir000εiθ000εiz),μi=(μir000μiθ000μiz),i=c,s
(1)
where εr (μr), and εθ(μθ) stand for the relative radial and tangential permittivity (permeability) elements, while εz (μz) corresponds to the element in the z-axis direction.

Fig. 1 Geometry of the infinitely-long coated nanowire. The incident wave propagates in the direction of x.

If we assume the time dependence of the electromagnetic wave to be eiωt, the local electric and magnetic fields in the core and shell are written as,
×H=iωε0εiEand×E=iωμ0μiH.
(2)

For the transverse-magnetic (TM) incident wave with the magnitude polarized along the z direction, we have Hr = Hθ = 0. Then, after some analytical derivations, we obtain the governing equation for the magnetic field Hz,
1r[r(rεiθHzr)]+1r2θ(1εirHzθ)+ω2ε0μ0μizHz=0.
(3)
Assuming Hz = Φ(r)eimθ with m being arbitrary integers, the radial function Φ(r) is found to satisfy
r2d2Φ(r)dr2+rdΦ(r)dr+(ω2ε0μ0εiθμizr2m2εiθεir)Φ(r)=0.
(4)
As a consequence, the incident, transmitted and scattered magnetic fields can be, respectively, expanded as [28

28. Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res. 106, 335–347(2010). [CrossRef]

, 29

29. H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A 86(3), 033825(2012). [CrossRef]

],
Hz=m=imAmJcm(kcr)eimθ,r<a,
(5)
Hz=m=im[BmJsm(ksr)+CmNsm(ksr)]eimθ,a<r<b,
(6)
Hz=m=im[Jm(k0r)+DmHm(k0r)]eimθ,r>b,
(7)
where Jn (x), Nn (x), and Hn (x) are n th-order Bessel, Neumann and Hankel functions. In addition, we denote cm=|m|εcθ/εcr and sm=|m|εsθ/εsr[24

24. Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” EPL 100(3), 34005(2012). [CrossRef]

], and kc=k0εcθμcz, ks=k0εsθμsz with k0 = ω/c.

The coefficients can be solved by applying the boundary conditions on r = a and r = b, and are given by,
Am=|0Jsm(ksa)Nsm(ksa)00ksJsm(ksa)ksNsm(ksa)0Jm(k0b)Jsm(ksb)Nsm(ksb)Hm(k0b)k0Jm(k0b)1εsθksJsm(ksb)1εsθksNsm(ksb)k0Hm(k0b)||Jcm(kca)Jsm(ksa)Nsm(ksa)0εsθεcθkcJcm(kca)ksJsm(ksa)ksNsm(ksa)00Jsm(ksb)Nsm(ksb)Hm(k0b)01εsθksJsm(ksb)1εsθksNsm(ksb)k0Hm(k0b)|,
(8)
Bm=|Jcm(kca)0Nsm(ksa)0εsθεcθkcJcm(kca)0ksNsm(ksa)00Jm(k0b)Nsm(ksb)Hm(k0b)0k0Jm(k0b)1εsθksNsm(ksb)k0Hm(k0b)||Jcm(kca)Jsm(ksa)Nsm(ksa)0εsθεcθkcJcm(kca)ksJsm(ksa)ksNsm(ksa)00Jsm(ksb)Nsm(ksb)Hm(k0b)01εsθksJsm(ksb)1εsθksNsm(ksb)k0Hm(k0b)|,
(9)
Cm=|Jcm(kca)Jsm(ksa)00εsθεcθkcJcm(kca)ksJsm(ksa)000Jsm(ksb)Jm(k0b)Hm(k0b)01εsθksJsm(ksb)k0Jm(k0b)k0Hm(k0b)||Jcm(kca)Jsm(ksa)Nsm(ksa)0εsθεcθkcJcm(kca)ksJsm(ksa)ksNsm(ksa)00Jsm(ksb)Nsm(ksb)Hm(k0b)01εsθksJsm(ksb)1εsθksNsm(ksb)k0Hm(k0b)|,
(10)
and
Dm=|Jcm(kca)Jsm(ksa)Nsm(ksa)0εsθεcθkcJcm(kca)ksJsm(ksa)ksNsm(ksa)00Jsm(ksb)Nsm(ksb)Jm(k0b)01εsθksJsm(ksb)1εsθksNsm(ksb)k0Jm(k0b)||Jcm(kca)Jsm(ksa)Nsm(ksa)0εsθεcθkcJcm(kca)ksJsm(ksa)ksNsm(ksa)00Jsm(ksb)Nsm(ksb)Hm(k0b)01εsθksJsm(ksb)1εsθksNsm(ksb)k0Hm(k0b)|.
(11)

With these coefficients at hand, one can derive the analytical expressions for local fields easily in the quasistatic limit.

3. near-field and far-field behavior in the quasistatic limit

In this section, we would like to consider the near-field and far-field situations in the quasistatic limit [31

31. X. P. Yu and L. Gao, “Nonlinear dielectric response in partially resonant composites with radial dielectric anisotropy,” Phys. Lett. A 359(5), 516–522(2006). [CrossRef]

]. For simplicity, we consider that the coated nanowire is nonmagnetic, and the shell is isotropic with εsr = εst = εs. In the quasistatic limit, we have kca → 0, ksb → 0, and k0b → 0.

The local magnetic fields can be approximately written as,
Hz=NM+PcQ(ra)εcθ/εcr,r<a,Hz=NM+PsQ,a<r<b,Hz=PoQ,r>b,
(12)
with
N=iπ2[2b+bk02ln(k0b2)][2a+aks2ln(ksa2)],
M=(1+2iln(k0b/2)π)[bks2π(1aεs+ak02ln(ksa/2)2)]+(2ibπbk022)[2πa+ks2πln(ksb/2)+ak02εsπln(a/b)],
Pc=8ab2k0εsεcrεcθ,
Ps=4b2k0εsr[a2(εcrεcθεs)+r2(εcrεcθ+εs)],
Po=ib2k02r(k02r2π4i)[a2(εcrεcθεs)(1+εs)+b2(εcrεcθ+εs)(1εs)],
Q=b2(εcrεcθ+εs)[4ib2k02π+εs(4i+b2k02π)]+a2(εcrεcθεs)[b2k02π4i+εs(4i+b2k02π)].

From Eq. (12), it is evident that when the equivalent permittivity for the anisotropic core εceεcrεcθ is kept unchanged, the magnetic fields in the shell and outside the cylinder are independent of εcr (or εcθ). On the contrary, the magnetic fields in the core may be enhanced for εcr > εcθ or be weakened for εcr < εcθ [31

31. X. P. Yu and L. Gao, “Nonlinear dielectric response in partially resonant composites with radial dielectric anisotropy,” Phys. Lett. A 359(5), 516–522(2006). [CrossRef]

].

On the other hand, in the quasistatic limit, when the denominator of scattering coefficient D1 is zero, the system is in the resonant state. As a consequence, one yields,
η(εcrεcθεs)(εs1)+(εcrεcθ+εs)(εs+1)=0,
(13)
with the aspect ratio η = (a/b)2.

Conversely, for the cloaking state, the numerator of scattering coefficient D1 equals zero, i.e.,
η(εcrεcθεs)(εs+1)+(εcrεcθ+εs)(εs1)=0
(14)
It is of interest to find that, for small values of η, both Eqs. (13) and (14) converge to the same condition,
εcrεcθ=εs.
(15)
Equation (15) is just the quasistatic Fano-like resonance or anti-resonance condition for the coated nanocylinder. Here we would like to mention that in deriving above equations, we have adopted such approximations as J0 (x) ≈ 1, N0 (x) ≈ 2/π ln (x/2), J′0 (x) ≈ −x/2, N′0 (x) ≈ 2/πx, J1 (x) ≈ x/2, J′1 (x) ≈ 1/2, and J′ν (x) ≈ νJν(x)/x, N′ν (x) ≈ −νNν(x)/x for a noninteger ν.

4. Numerical results

We are now in a position to present numerical results. To observe the Fano resonance, we assume the shell to be plasmonic with the lossless Drude-type permittivity εs=εωp2/ω2. For silver, we have ωp = 1.367 × 1016rad/s and ε = 5 [30

30. C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905(2012). [CrossRef] [PubMed]

].

In Fig. 2, we plot the extinction efficiency Qext=2/(k0b)m=+Re(Dm) as a function of the incident wavelength λ and the aspect ratio η. For the outer radius b much smaller than the incident wavelength λ, as far as the dependence of the extinction spectra on the core permittivity in concerned, we find that it is dependent mainly on the equivalent core permittivity εcrεcθ not on the single element εcr (or εcθ). As a consequence, we choose the isotropic core such as εcr = εcθ = 2. From Fig. 2(a), it is evident that there are two resonant regions, at which the extinction efficiency can achieve the maximal values. The corresponding two plasmonic antisymmetric and symmetric modes result from the coupling between the dipole plasmon of solid Ag cylinder (cylindrical modes) and that of Ag cavity cylinder (cavity modes) [32

32. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422(2003). [CrossRef] [PubMed]

]. In our case, the cylindrical (or cavity) modes can be excited in the systems in which Au nanocylinders with the radius b are embedded in the air medium at the cylindrical-like resonant wavelength λcylinder=2πcε+ε0/ωp (or in which the anisotropic core with the radius a are embedded in the bulk Ag materials at the void-like resonant wavelength λcavity=2πcε+εcrεct/ωp. In view of the fact that λcylinder < λcavity, the antisymmetric (or high-energy) coupling mode at λ1− is dependent on the cylindrical modes much and takes place in the outer interface of the coated cylinder, while the symmetric mode at λ1+ arises in the interface between the anisotropic core and the plasmonic shell. In the quasistatic limit, both the resonant wavelengths λ1− and λ1+ can be described by Eq. (13) analytically, as shown in Fig. 2(b). The full-wave electromagnetic results are in reasonable agreement with the analytical formula Eq. (13) (see solid red lines). On the contrary, the coated cylinders may be in the cloaking state, where the extinction efficiency takes the minimum and the coated cylinder is transparent [see Fig. 2(c)]. Again, the condition for the dipole cloaking state Eq. (14) in the quasistatic limit describes the numerical results qualitatively. From Fig. 2(c), we can see that the plasmonic cloaking is an inherently nonresonant phenomenon, and thus has a much broader bandwidth than the resonant bandwidths in Fig. 2(b).

Fig. 2 (a) Extinction efficiency Qext as a function of the incident wavelength λ and the aspect ratio η for εcr = εcθ = 2 and b = 30nm. (b) The resonant efficiency and (c) the cloaking efficiency where the small efficiency and the large efficiency are, respectively, marked in gray. Resonant scattering (red solid line) and cloaking (blue solid line) conditions are also shown.

As the cloaking and the resonant scattering based on the plasmonic coated cylinders can be served as the dark and bright modes, it is possible to observe the Fano-resonant coupling in plasmonic coated cylinders. In Fig. 3, we plot the extinction efficiency of the coated nanocylinders as a function of the incident wavelength. The Fano resonant mode is excited at 365nm, near which a dip and a peak appear in the extinction efficiency, as shown in Fig. 3(a). To verify the asymmetric profile, the Fano formula for such kind of resonance was adopted to fit with the form [2

2. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298(2010). [CrossRef]

, 3

3. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715(2010). [CrossRef]

]
F(ε)=σ0(ε+q)21+ε2
(16)
where ε = 2(EER)/τ (ER and τ are the position and width of the resonance), σ0 is a amplitude constant, and q is the asymmetry parameter [13

13. A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A 81(5), 053818 (2010). [CrossRef]

]. The resulting extinction in the vicinity of the resonance and its Fano fit are presented in the insert of Fig. 3(b). It is evident that the Fano formula describes positions of the minimum and maximum with the asymmetry parameter q = −1.98 accurately. Physically, the symmetrical (low-energy) dipolar resonant mode interferes with the dipole (nonresonant) cloaking state, resulting in the Fano-like asymmetrical profile, as shown in Fig. 3(b). To one’s interest, the asymmetric Fano profile for the coated nanocylinders [see Fig. 3(a)] is quite different from that [see Fig. 3(c)] for the coated nanospheres. At first, the Fano profile for the coated cylinders looks like the letter “S” [see the insert of Fig. 3(b)], in which the dip occurs followed by the resonant peak due to the coupling between the dipolar cloaking mode and the dipolar symmetrical low-energy (long-wavelength) resonant mode. On the contrary, the Fano curve for the coated sphere looks like the letter “Z” if one observes it from the right to the left. And Fano resonances for the coated sphere result from the coupling between the dipolar asymmetrical high-energy (short wavelength) resonant mode with the dipolar cloaking mode, which can be easily understood from Fig. 3(d). Secondly, in comparison with the plasmonic coated nanospheres, the coated nanocylinders provide high modulation depth. In case of realistic losses in the metallic shell, the resonant peak is less pronounced, and the Fano-resonance becomes broader, as expected. Incidentally, no matter what for the coated nanospheres or nanocylinders, the Fano mechanism here has distinct difference with the conventional Fano one, in which the bright dipolar mode interferes with the dark quadrupolar or magnetic mode [17

17. M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett. 100(4), 043903(2008). [CrossRef] [PubMed]

].

Fig. 3 Extinction efficiency (Qext) versus the incident wavelength from the coated nanocylinders [Fig. 3(a)] and coated nanospheres [Fig. 3(c)] for a = 1nm and b = 30nm. To understand the Fano-like profiles, the cloaking (blue solid line) and resonant scattering (red dash line) are shown for the cylindrical (spherical) case in Fig. 3(b) [Fig. 3(d)].

Fig. 4 Distributions of the magnetic fields for (a) high-energy asymmetrical dipolar resonant scattering wavelength [point I with λ = 345.671nm in Fig. 3(a)], (b) dipolar cloaking wavelength [point II with λ = 364.961nm in Fig. 3(a)], and (c) low-energy symmetric dipolar resonant scattering wavelength [point III with λ = 365.379nm in Fig. 3(a)].

Figure 5 shows the extinction efficiency of dipole modes for large size of the coated nanocylinders b = 100nm. It is evident that with increasing the inner radius a, both the Fano cloaking wavelength and the Fano resonant wavelength λ1+ exhibit appreciable red-shift, which can be qualitatively understood from Fig. 3(b). In addition, the magnitude of the Fano resonant peak becomes strong. This is due to the fact that, the increased core radius or the thin shell can provide the strong coupling between the cylindrical and the cavity modes, resulting in strong Fano peak and even wide Fano profile. Therefore, one yields a tunable Fano-like profile with our adjustment of the inner size a. Actually, since we vary the inner radius a only, the high-energy antisymmetric mode, which takes place around the outer surface, must exhibit weak dependence on the size a. As a consequence, the high-energy resonant wavelength λ1− and its corresponding magnitude keep almost invariant with increasing a.

Fig. 5 Extinction efficiency of dipole modes versus the incident wavelength for various core radii. Other parameters are εcr = εcθ = 2 and b = 100nm.

In the end, we aim at the effect of radial anisotropy on the Fano-like profile, as shown in Fig. 6. For comparison, we only include the results for the anisotropic core with the same equivalent permittivity εce=εcrεcθ=2, while εcr (or εcθ) is varied. It is evident that with increasing εcr, the whole Fano-like profile keeps almost invariant except that its location exhibits red-shift slightly. According to above hybridization theory for the coated cylinders, the change of the anisotropic permittivity of the core will have some influence on the long-wavelength dipolar resonant modes and the dipole cloaking modes, and hence the location of the Fano-like profile due to the coupling between the dipolar long-wavelength symmetric modes with the dipolar cloaking modes shifts. Here we would like to mention that such a shift is quite small, and no shift will appear for our further increasing or decreasing εcr.

Fig. 6 Extinction efficiency versus wavelength for a = 10nm and b = 100nm. In comparison, we keep εce = 2, with various εcr (or εcθ) such as εcr = 1/32 (navy dash dot line), εcr = 1/8 (magenta dash line), εcr = 1/2 (blue dot line), εcr = 2 (black solid line), εcr = 8 (red dot line), εcr = 32 (olive dash line), and εcr = 128 (violet dash dot line).

5. Conclusion

In this paper, we have established full-wave electromagnetic theory for the radially anisotropic coated cylinders. Fano profiles in the extinction spectra from the coated nanowires containing the anisotropic core and the isotropic plasmonic shell have been evidenced due to the interference between the dipole symmetrical (low-energy) resonant state and the dipole cloaking state. They are found to possess the shape of letter “S”, which is quite different from Z-shaped profiles for the coated nanospheres, in which there is the coupling between the dipole asymmetrical (high-energy) resonant state and the dipole cloaking state. Due to the prominent modulations lengths, Fano resonances in the coated nanocylinders can be more easily observable than those in the nanospheres. In addition, both the radial anisotropy and the core-shell microstructure provide us alternative freedoms to realize tunable Fano resonances.

Here some comments are in order. With nonconcentric coated nanocylinders, multiple Fano-like resonances can be realized because of the geometrical symmetry breaking induced by axial offset of the core [33

33. J. J. Zhang and A. Zayats, “Multiple Fano resonances in single-layere nonconcentric core-shell nanostructures,” Opt. Express 21(7), 8426–8436(2013). [CrossRef] [PubMed]

]. It would be of great interest to take into account both the symmetry breaking and the radial anisotropy simultaneously in such nanostructures. As for the nonlinear plasmonics [34

34. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748(2012). [CrossRef]

], the resulting strong electromagnetic fields allow the weak nonlinear processes such as optical bistablity [30

30. C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905(2012). [CrossRef] [PubMed]

] and second harmonic generations [35

35. J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B 86(7), 075430(2012). [CrossRef]

] to be significantly enhanced near Fano resonances. In this connection, nonlinear Fano profiles in the present nanostructures may be observed too. Furthermore, one can infer some properties of the stored energy in radially anisotropic nanocylinders from analysis of the extinction properties and the near-field spectra. However, to get a deep understanding on the stored energy in the coated nanocylinders with radial anisotropy, one should compute the stored electromagnetic fields and energy directly [36

36. T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt. 14(6), 065101(2012). [CrossRef]

, 37

37. T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence,” J. Opt. Soc. Am. A 27(7), 1679–1686(2012). [CrossRef]

]. Work along this line is in progress and will be reported elsewhere.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 11074183 and No. 11374223), the National Basic Research Program (No. 2012CB921501), the Key Project in Natural Science Foundation of Jiangsu Education Committee (No. 10KJA140044), the Ph. D. Programs Foundation of Ministry of Education of China (No. 20123201110010), and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

References and links

1.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878(1961). [CrossRef]

2.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298(2010). [CrossRef]

3.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715(2010). [CrossRef]

4.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett. 8(11), 3983–3988(2008). [CrossRef] [PubMed]

5.

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano 3(3), 643–652(2009). [CrossRef] [PubMed]

6.

Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett. 11(10), 4475–4479(2011). [CrossRef] [PubMed]

7.

K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano 5(7), 5976–5986(2011). [CrossRef] [PubMed]

8.

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett. 101(19), 197401(2008). [CrossRef] [PubMed]

9.

Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett. 96(13), 131113(2010). [CrossRef]

10.

S. Sheikholeslami, Y. W. Jun, P. K. Jain, and A. P. Alivisatos, “Coupling of optical resonances in a compositionally asymmetric plasmonic nanoparticle dimer,” Nano Lett. 10(7), 2655–2660(2010). [CrossRef] [PubMed]

11.

O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C 115(14), 6410–6414(2011). [CrossRef]

12.

S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett. 10(7), 2694–2701(2010). [CrossRef] [PubMed]

13.

A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A 81(5), 053818 (2010). [CrossRef]

14.

O. Pena-Rodriguez and U. Pal, “Au/Ag core-shell nanoparticles: efficient all-plasmonic Fano-resonance generators,” Nanoscale 3(9), 3609–3612(2011). [CrossRef] [PubMed]

15.

H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small 8(10), 1503–1509(2012). [CrossRef] [PubMed]

16.

D. J. Wu, S. M. Liang, and X. J. Liu, “A tunable Fano resonance in silver nanoshell with a spherically anisotropic core,” J. Chem. Phys. 136(3), 034502(2012). [CrossRef] [PubMed]

17.

M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett. 100(4), 043903(2008). [CrossRef] [PubMed]

18.

B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt. 15(7), 073001 (2013). [CrossRef]

19.

M. I. Tribelksy, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett. 97(4), 44005(2012). [CrossRef]

20.

T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A 87(4), 043841(2013). [CrossRef]

21.

M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett. 87(7), 075501(2001). [CrossRef] [PubMed]

22.

D. Taverna, M. Kociak, V. Charbois, and L. Henrard, “Electron energy-loss spectrum of an electron passing near a locally anisotropic nanotube,” Phys. Rev. B 66(23), 235419(2002). [CrossRef]

23.

Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett. 108(21), 213903(2012). [CrossRef] [PubMed]

24.

Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” EPL 100(3), 34005(2012). [CrossRef]

25.

S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109(22), 223903(2012). [CrossRef]

26.

X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A 79(15), 155122(2009).

27.

Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics 5(3), 251–258(2010). [CrossRef]

28.

Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res. 106, 335–347(2010). [CrossRef]

29.

H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A 86(3), 033825(2012). [CrossRef]

30.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905(2012). [CrossRef] [PubMed]

31.

X. P. Yu and L. Gao, “Nonlinear dielectric response in partially resonant composites with radial dielectric anisotropy,” Phys. Lett. A 359(5), 516–522(2006). [CrossRef]

32.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422(2003). [CrossRef] [PubMed]

33.

J. J. Zhang and A. Zayats, “Multiple Fano resonances in single-layere nonconcentric core-shell nanostructures,” Opt. Express 21(7), 8426–8436(2013). [CrossRef] [PubMed]

34.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748(2012). [CrossRef]

35.

J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B 86(7), 075430(2012). [CrossRef]

36.

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt. 14(6), 065101(2012). [CrossRef]

37.

T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence,” J. Opt. Soc. Am. A 27(7), 1679–1686(2012). [CrossRef]

OCIS Codes
(160.4760) Materials : Optical properties
(260.0260) Physical optics : Physical optics
(260.2110) Physical optics : Electromagnetic optics
(260.5740) Physical optics : Resonance
(160.3918) Materials : Metamaterials

ToC Category:
Physical Optics

History
Original Manuscript: August 14, 2013
Revised Manuscript: September 13, 2013
Manuscript Accepted: September 16, 2013
Published: September 26, 2013

Citation
H. L. Chen and L. Gao, "Tunablity of the unconventional Fano resonances in coated nanowires with radial anisotropy," Opt. Express 21, 23619-23630 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23619


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878(1961). [CrossRef]
  2. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298(2010). [CrossRef]
  3. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715(2010). [CrossRef]
  4. F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988(2008). [CrossRef] [PubMed]
  5. F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and Fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652(2009). [CrossRef] [PubMed]
  6. Z. Y. Fang, J. Y. Cai, Z. B. Yan, P. Nordlander, N. J. Halas, and X. Zhu, “Removing a wedge from a metallic nanodisk reveals a Fano resonance,” Nano Lett.11(10), 4475–4479(2011). [CrossRef] [PubMed]
  7. K. C. Woo, L. Shao, H. J. Chen, Y. Liang, J. F. Wang, and H. Q. Lin, “Universal scaling and Fano resonance in the plasmon coupling between gold nanorods,” ACS Nano5(7), 5976–5986(2011). [CrossRef] [PubMed]
  8. G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallee, and P. F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett.101(19), 197401(2008). [CrossRef] [PubMed]
  9. Z. J. Yang, Z. S. Zhang, W. Zhang, Z. H. Hao, and Q. Q. Wang, “Twinned Fano interferences induced by hybridized plasmons in Au-Ag nanorod heterodimers,” Appl. Phys. Lett.96(13), 131113(2010). [CrossRef]
  10. S. Sheikholeslami, Y. W. Jun, P. K. Jain, and A. P. Alivisatos, “Coupling of optical resonances in a compositionally asymmetric plasmonic nanoparticle dimer,” Nano Lett.10(7), 2655–2660(2010). [CrossRef] [PubMed]
  11. O. Pena-Rodriguez, U. Pal, M. Campoy-Quiles, L. Rodriguez-Fernandez, M. Garriga, and M. I. Alonso, “Enhanced Fano resonance in asymmetrical Au:Ag heterodimers,” J. Phys. Chem. C115(14), 6410–6414(2011). [CrossRef]
  12. S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: nanoparticles with built-in Fano resonances,” Nano Lett.10(7), 2694–2701(2010). [CrossRef] [PubMed]
  13. A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A81(5), 053818 (2010). [CrossRef]
  14. O. Pena-Rodriguez and U. Pal, “Au/Ag core-shell nanoparticles: efficient all-plasmonic Fano-resonance generators,” Nanoscale3(9), 3609–3612(2011). [CrossRef] [PubMed]
  15. H. J. Chen, L. Shao, Y. C. Man, C. M. Zhao, J. F. Wang, and B. C. Yang, “Fano resonance in (gold core)-(dielectric shell) nanostructures without symmetry breaking,” Small8(10), 1503–1509(2012). [CrossRef] [PubMed]
  16. D. J. Wu, S. M. Liang, and X. J. Liu, “A tunable Fano resonance in silver nanoshell with a spherically anisotropic core,” J. Chem. Phys.136(3), 034502(2012). [CrossRef] [PubMed]
  17. M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonances,” Phys. Rev. Lett.100(4), 043903(2008). [CrossRef] [PubMed]
  18. B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt.15(7), 073001 (2013). [CrossRef]
  19. M. I. Tribelksy, A. E. Miroshnichenko, and Y. S. Kivshar, “Unconventional Fano resonances in light scattering by small particles,” Europhys. Lett.97(4), 44005(2012). [CrossRef]
  20. T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A87(4), 043841(2013). [CrossRef]
  21. M. Kociak, O. Stephan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, “Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles,” Phys. Rev. Lett.87(7), 075501(2001). [CrossRef] [PubMed]
  22. D. Taverna, M. Kociak, V. Charbois, and L. Henrard, “Electron energy-loss spectrum of an electron passing near a locally anisotropic nanotube,” Phys. Rev. B66(23), 235419(2002). [CrossRef]
  23. Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett.108(21), 213903(2012). [CrossRef] [PubMed]
  24. Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” EPL100(3), 34005(2012). [CrossRef]
  25. S. Xu, X. X. Cheng, R. R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. L. Huang, X. M. Zhang, F. X. Yu, B. L. Zhang, and H. S. Chen, “Experimental Demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett.109(22), 223903(2012). [CrossRef]
  26. X. Sheng, H.S. Chen, B. L. Zhang, B. I. Wu, and J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. A79(15), 155122(2009).
  27. Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics5(3), 251–258(2010). [CrossRef]
  28. Y. W. Jin, D. L. Gao, and L. Gao, “Plasmonic resonant light scattering by a cylinder with radial anisotropy,” Prog. Electromag. Res.106, 335–347(2010). [CrossRef]
  29. H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A86(3), 033825(2012). [CrossRef]
  30. C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett.108(26), 263905(2012). [CrossRef] [PubMed]
  31. X. P. Yu and L. Gao, “Nonlinear dielectric response in partially resonant composites with radial dielectric anisotropy,” Phys. Lett. A359(5), 516–522(2006). [CrossRef]
  32. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422(2003). [CrossRef] [PubMed]
  33. J. J. Zhang and A. Zayats, “Multiple Fano resonances in single-layere nonconcentric core-shell nanostructures,” Opt. Express21(7), 8426–8436(2013). [CrossRef] [PubMed]
  34. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6, 737–748(2012). [CrossRef]
  35. J. Butet, G. Bachelier, I. Russier-Antoine, F. Bertorelle, A. Mosset, N. Lascoux, C. Jonin, E. Benichou, and P. F. Brevet, “Nonlinear Fano profiles in the optical second-harmonic generation from silver nanoparticles,” Phys. Rev. B86(7), 075430(2012). [CrossRef]
  36. T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt.14(6), 065101(2012). [CrossRef]
  37. T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence,” J. Opt. Soc. Am. A27(7), 1679–1686(2012). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited