Abstract

We analyze the resonant electromagnetic response of sub-wavelength plasmonic dimers formed by two silver strips separated by a thin dielectric spacer and embedded in a uniform dielectric media. We demonstrate that the off-resonant electric and resonant, geometric shape-leveraged, magnetic polarizabilities of the dimer element can be designed to have close absolute values in a certain spectral range, resulting in a predominantly unidirectional scattering of the incident field due to pronounced magneto-electric interference. Switching between forward and backward directionality can be achieved with a single element by changing the excitation wavelength, with the scattering direction defined by the relative phases of the polarizabilities. We extend the analysis to some periodic configurations, including the specific case of a perforated metal film, and discuss the differences between the observed unidirectional scattering and the extraordinary transmission effect. The unidirectional response can be preserved and enhanced with periodic arrays of dimers and can find applications in nanoantenna devices, integrated optic circuits, sensors with nanoparticles, photovoltaic systems, or perfect absorbers; while the option of switching between forward and backward unidirectional scattering may create interesting possibilities for manipulating optical pressure forces.

© 2013 Optical Society of America

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  46. K. Guven, M. D. Caliskan, and E. Ozbay, “Experimental observation of left-handed transmission in a bilayer metamaterial under normal-to-plane propagation,” Opt. Express14, 8685–8693 (2006).
    [CrossRef] [PubMed]
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2013

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Lukyanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun.4, 1527 (2013).
[CrossRef] [PubMed]

2012

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano6, 5489–5497 (2012).
[CrossRef] [PubMed]

T. Shegai, S Chen, V. D. Miljković, G. Zengin, P. Johansson, and M. Käll, “A bimetallic nanoantenna for directional colour routing,” Nat. Commun.2, 481 (2012).

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface mie resonators,” Nat. Commun.3, 692 (2012).
[CrossRef] [PubMed]

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater.24, OP281–OP304, (2012).
[PubMed]

A. Rose, S. Larouche, E. Poutrina, and D. R. Smith, “Nonlinear magnetoelectric metamaterials: analysis and homogenization via a microscopic coupled-mode theory,” Phys. Rev. A86, 033816 (2012).
[CrossRef]

M. Albooyeh, D. Morits, and S. A. Tretyakov, “Effective electric and magnetic properties of metasurfaces in transition from crystalline to amorphous state,” Phys. Rev. B85, 205110 (2012).
[CrossRef]

E. Poutrina, C. Ciracì, D. J. Gauthier, and D. R. Smith, “Enhancing four-wave-mixing processes by nanowire arrays coupled to a gold film,” Opt. Express20, 11005–11013 (2012).
[CrossRef] [PubMed]

S. H. A. Lavasani and T. Pakizeh, “Color-switched directional ultracompact optical nanoantennas,” J. Opt. Soc. Am. B29, 1361–1366 (2012).
[CrossRef]

B. Rolly, B. Stout, and N. Bonod, “Boosting the directivity of optical antennas with magnetic and electric dipolar resonant particles,” Opt. Express20, 20376–20386 (2012).
[CrossRef] [PubMed]

T. Pakizeh, “Unidirectional radiation of a magnetic dipole coupled to an ultracompact nanoantenna at visible wavelengths,” J. Opt. Soc. Am. B29, 2446–2452 (2012).
[CrossRef]

A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express20, 20599–20604 (2012).
[CrossRef] [PubMed]

D. P. Brown, M. A. Walker, A. M. Urbas, A. V. Kildishev, S. Xiao, and V. P. Drachev, “Direct measurement of group delay dispersion in metamagnetics for ultrafast pulse shaping,” Opt. Express20, 23082–23087 (2012).
[CrossRef] [PubMed]

2011

A. Ourir and H. H. Ouslimani, “Negative refractive index in symmetric cut-wire pair metamaterial,” Appl. Phys. Lett.98, 113505 (2011).
[CrossRef]

M. Nieto-Vesperinas, R. Gomez-Medina, and J. J. Saenz, “Angle-suppressed scattering and optical forces on submicrometer dielectric particles,” J. Opt. Soc. Am. A28, 54–60 (2011).
[CrossRef]

V. D. Miljkovic, T. Shegai, M. Käll, and P. Johansson, “Mode- specific directional emission from hybridized particle-on-a-film plasmons,” Opt. Express19, 12856–12864 (2011).
[CrossRef]

G. H. Rui, R. L. Nelson, and Q. W. Zhan, “Circularly polarized unidirectional emission via a coupled plasmonic spiral antenna,” Opt. Lett.36, 4533–4535 (2011).
[CrossRef] [PubMed]

N. S. King, Y. Li, C. Ayala-Orozco, T. Brannan, P. Nordlander, and N. J. Halas, “Angle- and spectral-dependent light scattering from plasmonic nanocups,” ACS Nano5, 7254–7262 (2011).
[CrossRef] [PubMed]

T. Shegai, V. D. Miljkovic, K. Bao, H. X. Xu, P. Nordlander, P. Johansson, and M. Käll, “Unidirectional broad-band light emission from supported plasmonic nanowires,” Nano Lett.11, 706–711 (2011).
[CrossRef] [PubMed]

L. Novotny and N. F. van Hulst, “Antennas for light,” Nat. Photonics5, 83–90 (2011).
[CrossRef]

B. García-Cámara, R. A. de la Osa, J. M. Saiz, F. González, and F. Moreno, “Directionality in scattering by nanoparticles: Kerker’s null-scattering conditions revisited,” Opt Lett.36, 728–730 (2011).
[CrossRef]

R. Gomez-Medina, B. Garcia-Camara, I. Suarez-Lacalle, F. Gonzalez, F. Moreno, M. Nieto-Vesperinas, and J. J. Saenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophotonics5, 053512 (2011).
[CrossRef]

2010

A. Alù and N. Engheta, “How does zero forward-scattering in magnetodielectric nanoparticles comply with the optical theorem?,” J. Nanophotonics4, 041590 (2010), and references therein.
[CrossRef]

N. T. Tung, V. T. T. Thuy, J. W. Park, J. Y. Rhee, and Y. P. Lee, “Left-handed transmission in a simple cut-wire pair structure,” J. Appl. Phys.107, 023530 (2010).
[CrossRef]

T. F. Gündoǧdu, K. Güen, M. Gökkavas, C. M. Soukoulis, and E. Özbay, “A Planar metamaterial with dual-band double-negative response at EHF,” J. Sel. Top. Quant. Electron.16, 376–379 (2010).
[CrossRef]

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, 930–932 (2010).
[CrossRef] [PubMed]

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]

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett.104, 026802 (2010).
[CrossRef] [PubMed]

A. Pannipitiya, I. D. Rukhlenko, M. Premaratne, H. T. Hattori, and G. P. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express18, 6191–6204 (2010).
[CrossRef] [PubMed]

B. Garcia-Camara, F. Moreno, F. Gonzalez, and O. J. F. Martin, “Light scattering by an array of electric and magnetic nanoparticles,” Opt. Express18, 10001–10015 (2010).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express18, 11428–11443 (2010).
[CrossRef] [PubMed]

2009

P. C. Chaumet and A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express17, 2224–2234 (2009).
[CrossRef] [PubMed]

J. A. Schuller and M. L. Brongersma, “General properties of dielectric optical antennas,” Opt. Express17, 24084–24095 (2009).
[CrossRef]

T. Pakizeh and M. Käll, “Unidirectional ultracompact optical nanoantennas,” Nano Lett.9, 2343–2349, (2009).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett.102, 233901, (2009).
[CrossRef] [PubMed]

Z. P. Li, F. Hao, Y. Z. Huang, Y. R. Fang, P. Nordlander, and H. X. Xu, “Directional light emission from propagating surface plasmons of silver nanowires,” Nano Lett.9, 4383–4386, (2009).
[CrossRef] [PubMed]

S. N. Burokur, A. Sellier, B. Kanté, and A. de Lustrac, “Symmetry breaking in metallic cut wire pairs metamaterials for negative refractive index,” Appl. Phys. Lett.94, 201111 (2009).
[CrossRef]

2008

A. L. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8, 2171–2175 (2008).
[CrossRef] [PubMed]

C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron.44, 435–447 (2008).
[CrossRef]

N. Noginova, G. Zhu, M. Mavy, and M. A. Noginov, “Magnetic dipole based systems for probing optical magnetism,” J. Appl. Phys.103, 07E901 (2008).
[CrossRef]

2007

O. Merchiers, F. Moreno, F. Gonzalez, and J. M. Saiz, “Light scattering by an ensemble of interacting dipolar particles with both electric and magnetic polarizabilities,” Phys. Rev. A76, 043834 (2007).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon.1, 41–48 (2007).
[CrossRef]

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. Express15, 3333–3341 (2007).
[CrossRef] [PubMed]

2006

K. Guven, M. D. Caliskan, and E. Ozbay, “Experimental observation of left-handed transmission in a bilayer metamaterial under normal-to-plane propagation,” Opt. Express14, 8685–8693 (2006).
[CrossRef] [PubMed]

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett.31, 3620–3622 (2006).
[CrossRef] [PubMed]

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B (R)73, 041101 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

2005

2002

D. R. Smith, S. Schultz, P. Markos, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4186 (2000).
[CrossRef] [PubMed]

1999

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett.83, 2845–2848 (1999).
[CrossRef]

1998

U. Schroter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B58, 15419–15421 (1998).
[CrossRef]

1994

G. W. Mulholland, C. F. Bohren, and K. A. Fuller, “Light-scattering by agglomerates – coupled electric and magnetic dipole method,” Langmuir10, 2533–2546 (1994).
[CrossRef]

1987

1986

S. B. Singham and G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys.84, 2658–2667(1986).
[CrossRef]

1983

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972).
[CrossRef]

1935

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev.48, 928–936 (1935).
[CrossRef]

Agrawal, G. P.

Albooyeh, M.

M. Albooyeh, D. Morits, and S. A. Tretyakov, “Effective electric and magnetic properties of metasurfaces in transition from crystalline to amorphous state,” Phys. Rev. B85, 205110 (2012).
[CrossRef]

Alù, A.

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater.24, OP281–OP304, (2012).
[PubMed]

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N. T. Tung, V. T. T. Thuy, J. W. Park, J. Y. Rhee, and Y. P. Lee, “Left-handed transmission in a simple cut-wire pair structure,” J. Appl. Phys.107, 023530 (2010).
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E. Poutrina, C. Ciracì, D. J. Gauthier, and D. R. Smith, “Enhancing four-wave-mixing processes by nanowire arrays coupled to a gold film,” Opt. Express20, 11005–11013 (2012).
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D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4186 (2000).
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[CrossRef] [PubMed]

Other

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

H. C. Van De Hulst, Light Scatering by Small Nanoparticles (Dover, 1981).

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

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Figures (9)

Fig. 1
Fig. 1

(a) The geometry of a dimer parallel to field propagation direction. The used parameters are L = w = 120 nm, t = 15 nm, d = 7 nm, the spacer refractive index n = 1.58. Silver dielectric function follows the data in [55]. (b) Spectral dependence of field enhancement within the dimer. Color insets: magnetic field distribution within the xz cross-section; Arrows: the direction of the total electric field within the same cross-section. (c) Top: Magnetic field distribution of the eigenmodes within the spacer layer for the first two resonances. Bottom: Ex component of the scattered field for the same resonances, showing the in-phase and out-of-phase field oscillations at the two sides of the dimer; xz cross-section shown; the dimer is located in the center of each color image, indicated by the arrow.

Fig. 2
Fig. 2

Effective susceptibilities retrieved for a dilute layer of dimer elements. (a) The geometry used in the retrieval. (b) Retrieved effective electric (χe) and magnetic (χm) susceptibilities.

Fig. 3
Fig. 3

(a) Orientation of the induced electric and magnetic dipoles assumed in the theory derivation. (b) Top: Near field scattered into the xz plane by a single isolated dimer element with the geometry parameters used in Figs. 1 and 2. The excitations frequencies are taken below (209 THz), at (214 THz), and above (219 THz) the resonance. Bottom: Far field intensity scattered into the xz plane for the same excitation positions. Blue, Red, and Green curves respectively correspond, to the |Ex|2, |Ez|2 scattered far field components, and total scattered far field (Ey-component is negligible in the xz scattering plane). (c) Ratio D of forward to backward scattered field intensity for a dimer with the same geometry.

Fig. 4
Fig. 4

Improving directionality by regulating the strength of a magnetic resonance. (a) Effective parameters of a layer of horizontally oriented dimers, for several thicknesses of the spacer layer. (b) Spectral dependence of the ratio D of forward to backward scattering from a single isolated dimer with the same parameters.

Fig. 5
Fig. 5

(a) Dimer orientation with respect to the incident field. (b) Solid curve: spectral response of a dimer with the same geometry as in Figs. 1 and 3 but oriented orthogonally to propagation direction, as shown in Fig. 5(a). The dashed curve shows the response from Fig. 1(b) (horizontal orientation). (c) Scattering directionality ratio D for this geometry.

Fig. 6
Fig. 6

(a) Effective parameters retrieved for a layer of (sparsely spaced) orthogonally oriented dimer elements with t = 30 nm, L = w = 120 nm, and d = 7 nm, 9 nm, and 11 nm; (b) Ratio D of forward to backward scattered field intensity produced by a single isolated orthogonally oriented dimer with the same geometries as in (a). (c) Top: Scattered far field intensity projected on the surface of a sphere for an isolated dimer with d = 11nm, for the spectral positions below (292 THz) and above (307 THz) the resonance. Bottom: Angular distribution of the scattered into the xz plane electric far field for the same spectral points. Color indicates field components similarly as in Fig. 3(b), bottom.

Fig. 7
Fig. 7

Norm of the far scattered field with the increasing number of elements arranged periodically in the direction transverse to propagation, as shown in the scheme on the left. (a) Normalized by the response of 4 elements. (b) Normalized by the peak value in each case, showing improved directionality with the same periodic arrangements.

Fig. 8
Fig. 8

Analysis of EOT versus the unidirectional scattering produced by horizontally oriented dimer elements. (a) The geometry under consideration. The spacing between the neighboring elements is decreased until the dimers form a single-periodic perforated film. (b) Spectral response while decreasing the separation between the elements. (c) Transmission curve with the largest and the smallest separations.

Fig. 9
Fig. 9

(a) Effective refractive index of a layer formed by dimers spaced periodically in the transverse direction (see Fig. 8(a)), for several spacing values. (b) Evolution of the unidirectionality ratio D while reducing the spacing a between the dimers in a layer.

Equations (6)

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E θ | φ = 0 = 1 4 π ( ω c ) 2 e i k r r [ 1 ε 0 p x cos θ + η m y ] .
E e l = e i k r 4 π ε 0 ( ω c ) 2 1 r 3 r × r × p 0 ,
E m = e i k r 4 π μ 0 ε 0 ( ω c ) 2 1 r 2 r × m 0
E x = 1 4 π ( ω c ) 2 e i k r r [ 1 ε 0 p x ( sin 2 θ sin 2 φ + cos 2 θ ) + η m y cos θ ] ,
E y = 1 4 π ε 0 ( ω c ) 2 e i k r r p x sin 2 θ sin φ cos φ ,
E z = 1 4 π ( ω c ) 2 e i k r r [ 1 ε 0 p z sin θ cos θ cos φ η m y sin θ cos φ ] ,

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