Abstract

Metallic nanowires (NW) coated with a high permittivity dielectric are proposed as means to strongly reduce the light scattering of the conducting NW, rendering them transparent at infrared wavelengths of interest in telecommunications. Based on a simple, universal law derived from electrostatics arguments, we find appropriate parameters to reduce the scattering efficiency of hybrid metal-dielectric NW by up to three orders of magnitude as compared with the scattering efficiency of the homogeneous metallic NW. We show that metal@dielectric structures are much more robust against fabrication imperfections than analogous dielectric@metal ones. The bandwidth of the transparent region entirely covers the near IR telecommunications range. Although this effect is optimum at normal incidence and for a given polarization, rigorous theoretical and numerical calculations reveal that transparency is robust against changes in polarization and angle of incidence, and also holds for relatively dense periodic or random arrangements. A wealth of applications based on metal-NWs may benefit from such invisibility.

© 2013 OSA

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2013

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett.13, 1806–1809 (2013).
[PubMed]

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

A. Mirzaei, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Cloaking and enhanced scattering of core-shell plasmonic nanowires,” Opt. Express21, 10454–10459 (2013).
[CrossRef] [PubMed]

Y. Urzhumov, N. Landy, T. Driscoll, D. Basov, and D. R. Smith, “Thin low-loss dielectric coatings for free-space cloaking,” Opt. Lett.38, 1606–1608 (2013).
[CrossRef]

R. Paniagua-Domínguez, D. R. Abujetas, and J. A. Sánchez-Gil, “Ultra low-loss, isotropic optical negative-index metamaterial based on hybrid metal-semiconductor nanowires,” Sci. Rep.3, 1507 (2013).
[CrossRef]

A. Kim, Y. Won, K. Woo, C.-H. Kim, and J. Moon, “Highly transparent low resistance ZnO/Ag nanowire/ZnO composite electrode for thin film solar cells,” ACS Nano7, 1081–1091 (2013).
[CrossRef] [PubMed]

2012

K. Ellmer, “Past achievements and future challenges in the development of optically transparent electrodes,” Nat. Photonics6, 809–817 (2012).
[CrossRef]

S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design,” Nano Lett.12, 4971–4976 (2012).
[CrossRef] [PubMed]

S. Lal, J. H. Hafner, N. J. Halas, S. Link, and P. Nordlander, “Noble metal nanowires: from plasmon waveguides to passive and active devices,” Acc. Chem. Res45, 1887–1895 (2012).
[CrossRef] [PubMed]

P. Mundru, V. Pappakrishnan, and D. Genov, “Material- and geometry-independent multishell cloaking device,” Phys. Rev. B85, 045402 (2012).
[CrossRef]

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

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

F. Gömöry, M. Solovyov, J. Ŝouc, C. Navau, J. Prat-Camps, and A. Sánchez, “Experimental realization of a magnetic cloak,” Science335, 1466–1468 (2012).
[CrossRef] [PubMed]

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photonics6, 380–385 (2012).
[CrossRef]

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]

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. G. Rivas, “Nanowire antenna emission,” Nano Lett.12, 5481–5486 (2012).
[CrossRef] [PubMed]

2011

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, “Metallo-dielectric core-shell nanospheres as building blocks for optical three-dimensional isotropic negative-index metamaterials,” New J. Phys.13, 123017 (2011).
[CrossRef]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express19, 4815–4826 (2011).
[CrossRef] [PubMed]

2010

2009

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

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12, 60–69 (2009).
[CrossRef]

C. S. Levin, C. Hofmann, T. A. Ali, A. T. Kelly, E. Morosan, P. Nordlander, K. H. Whitmire, and N. J. Halas, “Magnetic-plasmonic core-shell nanoparticles,” ACS Nano3, 1379–1388 (2009).
[CrossRef] [PubMed]

2007

2006

A. Alù and N. Engheta, “Erratum: Achieving transparency with plasmonic and metamaterial coatings [Phys. Rev. E, 72, 016623 (2005)],” Phys. Rev. E73, 019906(E) (2006).
[CrossRef]

Y. Li, F. Qian, J. Xiang, and C. M. Lieber, “Nanowire electronic and optoelectronic devices,” Mater. Today9, 18–27 (2006).
[CrossRef]

2005

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E72, 016623 (2005).
[CrossRef]

2003

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Chem. Phys. Lett.302, 419–422 (2003).

1998

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett.288, 243–247 (1998).
[CrossRef]

1976

H. Chew and M. Kerker, “Abnormally low electromagnetic scattering cross sections,” J. Opt. Soc. Am.5, 445–449 (1976).
[CrossRef]

1975

1972

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

1970

G. A. Shah, “Scattering of plane electromagnetic waves by infinite concentric circular cylinders at oblique incidence,” Mon. Not. R. Astron. Soc148, 93–102 (1970).

1961

Abujetas, D. R.

R. Paniagua-Domínguez, D. R. Abujetas, and J. A. Sánchez-Gil, “Ultra low-loss, isotropic optical negative-index metamaterial based on hybrid metal-semiconductor nanowires,” Sci. Rep.3, 1507 (2013).
[CrossRef]

Afshinmanesh, F.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photonics6, 380–385 (2012).
[CrossRef]

Aizpurua, J.

Albaladejo, S.

Albella, P.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

Ali, T. A.

C. S. Levin, C. Hofmann, T. A. Ali, A. T. Kelly, E. Morosan, P. Nordlander, K. H. Whitmire, and N. J. Halas, “Magnetic-plasmonic core-shell nanoparticles,” ACS Nano3, 1379–1388 (2009).
[CrossRef] [PubMed]

Alù, A.

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

A. Alù, D. Rainwater, and A. Kerkhoff, “Plasmonic cloaking of cylinders: finite length, oblique illumination and cross-polarization coupling,” New J. Phys.12, 103028 (2010).
[CrossRef]

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

A. Alù and N. Engheta, “Erratum: Achieving transparency with plasmonic and metamaterial coatings [Phys. Rev. E, 72, 016623 (2005)],” Phys. Rev. E73, 019906(E) (2006).
[CrossRef]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E72, 016623 (2005).
[CrossRef]

Armelles, G.

Averitt, R.

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett.288, 243–247 (1998).
[CrossRef]

Barten, T.

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. G. Rivas, “Nanowire antenna emission,” Nano Lett.12, 5481–5486 (2012).
[CrossRef] [PubMed]

Basov, D.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 1998).
[CrossRef]

Brongersma, M. L.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photonics6, 380–385 (2012).
[CrossRef]

Cahoon, J. F.

S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design,” Nano Lett.12, 4971–4976 (2012).
[CrossRef] [PubMed]

Cao, L.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photonics6, 380–385 (2012).
[CrossRef]

Carminati, R.

Chantada, L.

Chen, P. Y.

Chen, P.-Y.

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

Chettiar, U. K.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photonics6, 380–385 (2012).
[CrossRef]

Chew, H.

H. Chew and M. Kerker, “Abnormally low electromagnetic scattering cross sections,” J. Opt. Soc. Am.5, 445–449 (1976).
[CrossRef]

Christy, R. W.

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

Day, R. W.

S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design,” Nano Lett.12, 4971–4976 (2012).
[CrossRef] [PubMed]

Driscoll, T.

Ellmer, K.

K. Ellmer, “Past achievements and future challenges in the development of optically transparent electrodes,” Nat. Photonics6, 809–817 (2012).
[CrossRef]

Engheta, N.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photonics6, 380–385 (2012).
[CrossRef]

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

A. Alù and N. Engheta, “Erratum: Achieving transparency with plasmonic and metamaterial coatings [Phys. Rev. E, 72, 016623 (2005)],” Phys. Rev. E73, 019906(E) (2006).
[CrossRef]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E72, 016623 (2005).
[CrossRef]

Eyraud, C.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

Fan, P.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photonics6, 380–385 (2012).
[CrossRef]

Feng, Y.

Fleming, S. C.

Fontana, Y.

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. G. Rivas, “Nanowire antenna emission,” Nano Lett.12, 5481–5486 (2012).
[CrossRef] [PubMed]

Froufe-Pérez, L.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

Froufe-Pérez, L. S.

Fu, Y. H.

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

García-Cámara, B.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

García-Etxarri, A.

García-Martín, A.

Geffrin, J.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

Genov, D.

P. Mundru, V. Pappakrishnan, and D. Genov, “Material- and geometry-independent multishell cloaking device,” Phys. Rev. B85, 045402 (2012).
[CrossRef]

Gómez-Medina, R.

Gömöry, F.

F. Gömöry, M. Solovyov, J. Ŝouc, C. Navau, J. Prat-Camps, and A. Sánchez, “Experimental realization of a magnetic cloak,” Science335, 1466–1468 (2012).
[CrossRef] [PubMed]

González, F.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

Grzela, G.

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. G. Rivas, “Nanowire antenna emission,” Nano Lett.12, 5481–5486 (2012).
[CrossRef] [PubMed]

Hafner, J. H.

S. Lal, J. H. Hafner, N. J. Halas, S. Link, and P. Nordlander, “Noble metal nanowires: from plasmon waveguides to passive and active devices,” Acc. Chem. Res45, 1887–1895 (2012).
[CrossRef] [PubMed]

Halas, N.

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett.288, 243–247 (1998).
[CrossRef]

Halas, N. J.

S. Lal, J. H. Hafner, N. J. Halas, S. Link, and P. Nordlander, “Noble metal nanowires: from plasmon waveguides to passive and active devices,” Acc. Chem. Res45, 1887–1895 (2012).
[CrossRef] [PubMed]

C. S. Levin, C. Hofmann, T. A. Ali, A. T. Kelly, E. Morosan, P. Nordlander, K. H. Whitmire, and N. J. Halas, “Magnetic-plasmonic core-shell nanoparticles,” ACS Nano3, 1379–1388 (2009).
[CrossRef] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Chem. Phys. Lett.302, 419–422 (2003).

Hofmann, C.

C. S. Levin, C. Hofmann, T. A. Ali, A. T. Kelly, E. Morosan, P. Nordlander, K. H. Whitmire, and N. J. Halas, “Magnetic-plasmonic core-shell nanoparticles,” ACS Nano3, 1379–1388 (2009).
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S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett.13, 1806–1809 (2013).
[PubMed]

Jiang, T.

Johnson, P. B.

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

Kelly, A. T.

C. S. Levin, C. Hofmann, T. A. Ali, A. T. Kelly, E. Morosan, P. Nordlander, K. H. Whitmire, and N. J. Halas, “Magnetic-plasmonic core-shell nanoparticles,” ACS Nano3, 1379–1388 (2009).
[CrossRef] [PubMed]

Kempa, T. J.

S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design,” Nano Lett.12, 4971–4976 (2012).
[CrossRef] [PubMed]

Kerker, M.

Kerkhoff, A.

A. Alù, D. Rainwater, and A. Kerkhoff, “Plasmonic cloaking of cylinders: finite length, oblique illumination and cross-polarization coupling,” New J. Phys.12, 103028 (2010).
[CrossRef]

Kim, A.

A. Kim, Y. Won, K. Woo, C.-H. Kim, and J. Moon, “Highly transparent low resistance ZnO/Ag nanowire/ZnO composite electrode for thin film solar cells,” ACS Nano7, 1081–1091 (2013).
[CrossRef] [PubMed]

Kim, C.-H.

A. Kim, Y. Won, K. Woo, C.-H. Kim, and J. Moon, “Highly transparent low resistance ZnO/Ag nanowire/ZnO composite electrode for thin film solar cells,” ACS Nano7, 1081–1091 (2013).
[CrossRef] [PubMed]

Kim, S.-K.

S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design,” Nano Lett.12, 4971–4976 (2012).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. Mirzaei, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Cloaking and enhanced scattering of core-shell plasmonic nanowires,” Opt. Express21, 10454–10459 (2013).
[CrossRef] [PubMed]

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]

Kuhlmey, B. T.

Kuznetsov, A. I.

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

Lal, S.

S. Lal, J. H. Hafner, N. J. Halas, S. Link, and P. Nordlander, “Noble metal nanowires: from plasmon waveguides to passive and active devices,” Acc. Chem. Res45, 1887–1895 (2012).
[CrossRef] [PubMed]

Landy, N.

Lapin, Z.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett.13, 1806–1809 (2013).
[PubMed]

Levin, C. S.

C. S. Levin, C. Hofmann, T. A. Ali, A. T. Kelly, E. Morosan, P. Nordlander, K. H. Whitmire, and N. J. Halas, “Magnetic-plasmonic core-shell nanoparticles,” ACS Nano3, 1379–1388 (2009).
[CrossRef] [PubMed]

Li, Y.

Y. Li, F. Qian, J. Xiang, and C. M. Lieber, “Nanowire electronic and optoelectronic devices,” Mater. Today9, 18–27 (2006).
[CrossRef]

Lieber, C. M.

S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design,” Nano Lett.12, 4971–4976 (2012).
[CrossRef] [PubMed]

Y. Li, F. Qian, J. Xiang, and C. M. Lieber, “Nanowire electronic and optoelectronic devices,” Mater. Today9, 18–27 (2006).
[CrossRef]

Link, S.

S. Lal, J. H. Hafner, N. J. Halas, S. Link, and P. Nordlander, “Noble metal nanowires: from plasmon waveguides to passive and active devices,” Acc. Chem. Res45, 1887–1895 (2012).
[CrossRef] [PubMed]

Lippens, D.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12, 60–69 (2009).
[CrossRef]

Litman, A.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

Liu, W.

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]

López, C.

López-Tejeira, F.

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, “Metallo-dielectric core-shell nanospheres as building blocks for optical three-dimensional isotropic negative-index metamaterials,” New J. Phys.13, 123017 (2011).
[CrossRef]

Lukýanchuk, B.

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

Marinchio, H.

Marqués, R.

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, “Metallo-dielectric core-shell nanospheres as building blocks for optical three-dimensional isotropic negative-index metamaterials,” New J. Phys.13, 123017 (2011).
[CrossRef]

Matijevic, E.

Miroshnichenko, A. E.

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

A. Mirzaei, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Cloaking and enhanced scattering of core-shell plasmonic nanowires,” Opt. Express21, 10454–10459 (2013).
[CrossRef] [PubMed]

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]

Mirzaei, A.

Moon, J.

A. Kim, Y. Won, K. Woo, C.-H. Kim, and J. Moon, “Highly transparent low resistance ZnO/Ag nanowire/ZnO composite electrode for thin film solar cells,” ACS Nano7, 1081–1091 (2013).
[CrossRef] [PubMed]

Moreno, F.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

Morosan, E.

C. S. Levin, C. Hofmann, T. A. Ali, A. T. Kelly, E. Morosan, P. Nordlander, K. H. Whitmire, and N. J. Halas, “Magnetic-plasmonic core-shell nanoparticles,” ACS Nano3, 1379–1388 (2009).
[CrossRef] [PubMed]

Mundru, P.

P. Mundru, V. Pappakrishnan, and D. Genov, “Material- and geometry-independent multishell cloaking device,” Phys. Rev. B85, 045402 (2012).
[CrossRef]

Navau, C.

F. Gömöry, M. Solovyov, J. Ŝouc, C. Navau, J. Prat-Camps, and A. Sánchez, “Experimental realization of a magnetic cloak,” Science335, 1466–1468 (2012).
[CrossRef] [PubMed]

Neshev, D. N.

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]

Nieto-Vesperinas, M.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express19, 4815–4826 (2011).
[CrossRef] [PubMed]

Nordlander, P.

S. Lal, J. H. Hafner, N. J. Halas, S. Link, and P. Nordlander, “Noble metal nanowires: from plasmon waveguides to passive and active devices,” Acc. Chem. Res45, 1887–1895 (2012).
[CrossRef] [PubMed]

C. S. Levin, C. Hofmann, T. A. Ali, A. T. Kelly, E. Morosan, P. Nordlander, K. H. Whitmire, and N. J. Halas, “Magnetic-plasmonic core-shell nanoparticles,” ACS Nano3, 1379–1388 (2009).
[CrossRef] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Chem. Phys. Lett.302, 419–422 (2003).

Novotny, L.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett.13, 1806–1809 (2013).
[PubMed]

Oldenburg, S.

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett.288, 243–247 (1998).
[CrossRef]

Paniagua-Domínguez, R.

R. Paniagua-Domínguez, D. R. Abujetas, and J. A. Sánchez-Gil, “Ultra low-loss, isotropic optical negative-index metamaterial based on hybrid metal-semiconductor nanowires,” Sci. Rep.3, 1507 (2013).
[CrossRef]

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. G. Rivas, “Nanowire antenna emission,” Nano Lett.12, 5481–5486 (2012).
[CrossRef] [PubMed]

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, “Metallo-dielectric core-shell nanospheres as building blocks for optical three-dimensional isotropic negative-index metamaterials,” New J. Phys.13, 123017 (2011).
[CrossRef]

Pappakrishnan, V.

P. Mundru, V. Pappakrishnan, and D. Genov, “Material- and geometry-independent multishell cloaking device,” Phys. Rev. B85, 045402 (2012).
[CrossRef]

Park, H.-G.

S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design,” Nano Lett.12, 4971–4976 (2012).
[CrossRef] [PubMed]

Paschotta, R.

R. Paschotta, Encyclopedia of laser physics and technology (Wiley, 2008).

Person, S.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett.13, 1806–1809 (2013).
[PubMed]

Prat-Camps, J.

F. Gömöry, M. Solovyov, J. Ŝouc, C. Navau, J. Prat-Camps, and A. Sánchez, “Experimental realization of a magnetic cloak,” Science335, 1466–1468 (2012).
[CrossRef] [PubMed]

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Chem. Phys. Lett.302, 419–422 (2003).

Qian, F.

Y. Li, F. Qian, J. Xiang, and C. M. Lieber, “Nanowire electronic and optoelectronic devices,” Mater. Today9, 18–27 (2006).
[CrossRef]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Chem. Phys. Lett.302, 419–422 (2003).

Rainwater, D.

A. Alù, D. Rainwater, and A. Kerkhoff, “Plasmonic cloaking of cylinders: finite length, oblique illumination and cross-polarization coupling,” New J. Phys.12, 103028 (2010).
[CrossRef]

Rivas, J. G.

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. G. Rivas, “Nanowire antenna emission,” Nano Lett.12, 5481–5486 (2012).
[CrossRef] [PubMed]

Sáenz, J.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

Sáenz, J. J.

Sánchez, A.

F. Gömöry, M. Solovyov, J. Ŝouc, C. Navau, J. Prat-Camps, and A. Sánchez, “Experimental realization of a magnetic cloak,” Science335, 1466–1468 (2012).
[CrossRef] [PubMed]

Sánchez-Gil, J. A.

R. Paniagua-Domínguez, D. R. Abujetas, and J. A. Sánchez-Gil, “Ultra low-loss, isotropic optical negative-index metamaterial based on hybrid metal-semiconductor nanowires,” Sci. Rep.3, 1507 (2013).
[CrossRef]

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. G. Rivas, “Nanowire antenna emission,” Nano Lett.12, 5481–5486 (2012).
[CrossRef] [PubMed]

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, “Metallo-dielectric core-shell nanospheres as building blocks for optical three-dimensional isotropic negative-index metamaterials,” New J. Phys.13, 123017 (2011).
[CrossRef]

Scheffold, F.

Shadrivov, I. V.

Shah, G. A.

G. A. Shah, “Scattering of plane electromagnetic waves by infinite concentric circular cylinders at oblique incidence,” Mon. Not. R. Astron. Soc148, 93–102 (1970).

Smith, D. R.

Solovyov, M.

F. Gömöry, M. Solovyov, J. Ŝouc, C. Navau, J. Prat-Camps, and A. Sánchez, “Experimental realization of a magnetic cloak,” Science335, 1466–1468 (2012).
[CrossRef] [PubMed]

Song, K.-D.

S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design,” Nano Lett.12, 4971–4976 (2012).
[CrossRef] [PubMed]

Soric, J.

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

Souc, J.

F. Gömöry, M. Solovyov, J. Ŝouc, C. Navau, J. Prat-Camps, and A. Sánchez, “Experimental realization of a magnetic cloak,” Science335, 1466–1468 (2012).
[CrossRef] [PubMed]

Torrado, J. F.

Tuniz, A.

Urzhumov, Y.

Vaillon, R.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

Westcott, S.

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett.288, 243–247 (1998).
[CrossRef]

Whitmire, K. H.

C. S. Levin, C. Hofmann, T. A. Ali, A. T. Kelly, E. Morosan, P. Nordlander, K. H. Whitmire, and N. J. Halas, “Magnetic-plasmonic core-shell nanoparticles,” ACS Nano3, 1379–1388 (2009).
[CrossRef] [PubMed]

Wicks, G.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett.13, 1806–1809 (2013).
[PubMed]

Won, Y.

A. Kim, Y. Won, K. Woo, C.-H. Kim, and J. Moon, “Highly transparent low resistance ZnO/Ag nanowire/ZnO composite electrode for thin film solar cells,” ACS Nano7, 1081–1091 (2013).
[CrossRef] [PubMed]

Woo, K.

A. Kim, Y. Won, K. Woo, C.-H. Kim, and J. Moon, “Highly transparent low resistance ZnO/Ag nanowire/ZnO composite electrode for thin film solar cells,” ACS Nano7, 1081–1091 (2013).
[CrossRef] [PubMed]

Xiang, J.

Y. Li, F. Qian, J. Xiang, and C. M. Lieber, “Nanowire electronic and optoelectronic devices,” Mater. Today9, 18–27 (2006).
[CrossRef]

Yu, Y. F.

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

Zhang, F.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12, 60–69 (2009).
[CrossRef]

Zhao, Q.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12, 60–69 (2009).
[CrossRef]

Zhou, J.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12, 60–69 (2009).
[CrossRef]

Acc. Chem. Res

S. Lal, J. H. Hafner, N. J. Halas, S. Link, and P. Nordlander, “Noble metal nanowires: from plasmon waveguides to passive and active devices,” Acc. Chem. Res45, 1887–1895 (2012).
[CrossRef] [PubMed]

ACS Nano

A. Kim, Y. Won, K. Woo, C.-H. Kim, and J. Moon, “Highly transparent low resistance ZnO/Ag nanowire/ZnO composite electrode for thin film solar cells,” ACS Nano7, 1081–1091 (2013).
[CrossRef] [PubMed]

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]

C. S. Levin, C. Hofmann, T. A. Ali, A. T. Kelly, E. Morosan, P. Nordlander, K. H. Whitmire, and N. J. Halas, “Magnetic-plasmonic core-shell nanoparticles,” ACS Nano3, 1379–1388 (2009).
[CrossRef] [PubMed]

Adv. Mater.

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

Chem. Phys. Lett.

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett.288, 243–247 (1998).
[CrossRef]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Chem. Phys. Lett.302, 419–422 (2003).

J. Opt. Soc. Am.

Mater. Today

Y. Li, F. Qian, J. Xiang, and C. M. Lieber, “Nanowire electronic and optoelectronic devices,” Mater. Today9, 18–27 (2006).
[CrossRef]

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12, 60–69 (2009).
[CrossRef]

Mon. Not. R. Astron. Soc

G. A. Shah, “Scattering of plane electromagnetic waves by infinite concentric circular cylinders at oblique incidence,” Mon. Not. R. Astron. Soc148, 93–102 (1970).

Nano Lett.

S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design,” Nano Lett.12, 4971–4976 (2012).
[CrossRef] [PubMed]

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett.13, 1806–1809 (2013).
[PubMed]

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. G. Rivas, “Nanowire antenna emission,” Nano Lett.12, 5481–5486 (2012).
[CrossRef] [PubMed]

Nat. Commun.

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

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward-and backscattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun.3, 1171 (2012).
[CrossRef]

Nat. Photonics

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photonics6, 380–385 (2012).
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K. Ellmer, “Past achievements and future challenges in the development of optically transparent electrodes,” Nat. Photonics6, 809–817 (2012).
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New J. Phys.

A. Alù, D. Rainwater, and A. Kerkhoff, “Plasmonic cloaking of cylinders: finite length, oblique illumination and cross-polarization coupling,” New J. Phys.12, 103028 (2010).
[CrossRef]

R. Paniagua-Domínguez, F. López-Tejeira, R. Marqués, and J. A. Sánchez-Gil, “Metallo-dielectric core-shell nanospheres as building blocks for optical three-dimensional isotropic negative-index metamaterials,” New J. Phys.13, 123017 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

P. Mundru, V. Pappakrishnan, and D. Genov, “Material- and geometry-independent multishell cloaking device,” Phys. Rev. B85, 045402 (2012).
[CrossRef]

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

Phys. Rev. E

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E72, 016623 (2005).
[CrossRef]

A. Alù and N. Engheta, “Erratum: Achieving transparency with plasmonic and metamaterial coatings [Phys. Rev. E, 72, 016623 (2005)],” Phys. Rev. E73, 019906(E) (2006).
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Phys. Rev. Lett.

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett.102, 233901 (2009).
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Sci. Rep.

R. Paniagua-Domínguez, D. R. Abujetas, and J. A. Sánchez-Gil, “Ultra low-loss, isotropic optical negative-index metamaterial based on hybrid metal-semiconductor nanowires,” Sci. Rep.3, 1507 (2013).
[CrossRef]

Science

F. Gömöry, M. Solovyov, J. Ŝouc, C. Navau, J. Prat-Camps, and A. Sánchez, “Experimental realization of a magnetic cloak,” Science335, 1466–1468 (2012).
[CrossRef] [PubMed]

Other

R. Paschotta, Encyclopedia of laser physics and technology (Wiley, 2008).

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 1998).
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Supplementary Material (6)

» Media 1: MPG (214 KB)     
» Media 2: MPG (238 KB)     
» Media 3: MPG (206 KB)     
» Media 4: MPG (268 KB)     
» Media 5: MPG (266 KB)     
» Media 6: MPG (252 KB)     

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Figures (5)

Fig. 1
Fig. 1

(a) Sketch of the system under consideration together with the relevant parameters. (b–d), scattering efficiency Qscat as obtained from the quasi-static approximation. TM polarization (dashed line), TE polarization (dotted line) and unpolarized (solid line) radiation is considered for both Ag@Si (black curves) and Si@Ag (red curves) structures. (b) Qscat at a constant wavelength λ = 1550 nm is plotted as a function of the core to shell radii ratio. (c), the spectra for the different polarizations are presented. The size ratio Rc/Rs is fixed in such a way that Qscat is minimized in TM polarization for each structure. (d) Qscat spectra are presented when the core radius is reduced by 5%.

Fig. 2
Fig. 2

(a) Scattering efficiency spectra as a function of the core (silver) radius for a fixed shell (silicon) outer radius Rs = 45 nm. (b) Scattering efficiency spectra for a Ag@Si core-shell NW (Rs = 13.6 nm, Rs = 13.6 nm) and different polarizations: TM (black dashed), TE (black dotted) and unpolarized (black solid line). For the sake of comparison we also represent Qscat for a homogeneous Ag NW (red curve, R = 13.6 nm), a homogeneous Si NW (blue curve, R = 45 nm), and for a homogeneous 90 nm thick glass slab (refractive index n=1.45). (c–e) Maps of the electric field along the cylinder axis direction in TM polarization at a working wavelength of λ = 1550 nm (corresponding to the minimum of the black curve in b). (c) Bare silver NW. (d) Homogeneous silicon NW. (e) Ag@Si NW.

Fig. 3
Fig. 3

(a) Scattering efficiency spectra for a Ag@Si core-shell NW (Rc = 13.6 nm and Rs = 45 nm) as a function of (a) the angle of incidence (ϕ) for TE polarized light and (b) the polarization angle (χ) at normal incidence for the same structure.

Fig. 4
Fig. 4

(a) Scattering efficiency of Ag@Si core-shell NW dimers (Rs = 13.6 nm, Rc = 45 nm) for TM polarized plane waves with a wave vector perpendicular to the plane defined by the dimer for different distances d between the nanowires (see legends). (b) Scattering efficiency for the same dimers as in (a), with a wave vector perpendicular to the cylinder axis and in the same plane as the one defined by the dimer. (c) Map of the electric field ( Media 1) along the cylinder axis direction at a wavelength of λ = 1550 nm for TM polarized waves for an ensemble of bare Ag NWs (R = 13.6 nm) distributed randomly within a slab. (d) Electric field map ( Media 2) corresponding to the the same arrangement of (c). The scattering units in this case are Ag@Si core-shell NWs (Rc = 13.6 nm, Rs = 45nm).

Fig. 5
Fig. 5

(a) Map of the electric field ( Media 3) along the cylinder axis direction at a wavelength of λ = 1550 nm for TM polarized waves for an ensemble of bare Ag NWs (R = 13.6 nm) distributed randomly within a slab of 4μm by 1.5μm. (b) Electric field ( Media 4) map corresponding to the the same arrangement of (a). The scattering units in this case are Ag@Si core-shell NWs (Rc = 13.6 nm, Rs = 45 nm), the filling fraction of the arrangement is 16%. (c) Electric field ( Media 5) map corresponding to the same structure as in (b), with the addition of random disorder in both core and shell radii with a standard deviation of 3% arround the optimal values. (d) ( Media 6) the same as in (c) with a 5% standard deviation.

Equations (10)

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α 0 ( T M ) = A [ ( ε c ε h ) R 2 + ( ε s ε h ) ( 1 R 2 ) ]
Q scat ( T M ) = | α ( T M ) | 2 k h 3 / ( 8 ε h 2 R s ) .
( R t r ( T M ) ) 2 = ε h ε s ε c ε s
α 0 ( T E ) = 2 A ( ε s ε h ) ( ε s + ε c ) + ( ε c ε s ) ( ε h + ε s ) R 2 ( ε s + ε h ) ( ε s + ε c ) ( ε c ε s ) ( ε h ε s ) R 2 .
Q scat ( T E ) = | α ( T E ) | 2 k h 3 / ( 16 ε h 2 R s ) .
( R t r ( T E ) ) 2 = ( ε h ε s ) ( ε c + ε s ) ( ε h + ε s ) ( ε c ε s ) = ( R t r ( T M ) ) 2 ( ε s + ε c ) ( ε s + ε h ) .
Δ R R t r ( T E ) R l s p ( T E ) R t r ( T E ) + R l s p ( T E ) = | ε h ε s |
σ s ( T M , A g @ S i ) σ s ( T M , A g ) | 1 + ε s ε h ε c ε h ε c ( t r ) ε h ( t r ) ε h ( t r ) ε s ( t r ) | 2
σ s ( T M , A g @ S i ) σ s ( T M , A g ) | 1 ε c ( t r ) ε c | 2
Q scat ( T M ) ( λ = λ t r ) π 5 ε h ( R s λ t r ) 3 ( ε c ε h ε s ε s ε c ) 2 ,

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