Abstract

We study the light scattering profile of a subwavelength layered gold–dielectric–gold nanosphere, which unveils exciting ultrasharp scattering–switching signatures based on high spectral proximity of the scattering resonance and cloaking states. Analytical expressions are derived for polarizability, resonance/cloaking conditions, and for scattering cross section of this layered metal–dielectric–metal (MDM) nanosphere, under the quasi-static limit. Our analysis allows one to thoroughly investigate its spectral response, over the entire parametric space of its dimensions and the incident light wavelength. Especially, the scattering spectra reveal multiple Fano-type, ultrasharp spectral profiles with high tunability, in terms of abrupt scattering–switching wavelengths and cloaking bandwidth, when absorption losses in the metallic layers are neglected in the analysis. Upon inclusion of bulk metallic losses along with enhanced electron surface scattering effects, these sharp spectral signatures are found to get severely faded in a realistic layered MDM nanosphere. The results obtained analytically, in each case, are found to be in excellent agreement with the numerical ones calculated based on Mie theory. We demonstrate that the ultrasharp scattering signatures of a pragmatic MDM nanosphere can be revived by introducing semiconductor gain inclusions in the middle dielectric layer, mitigating losses in the metallic layers.

© 2013 Optical Society of America

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2013 (5)

F. Monticone, C. Argyropoulos, and A. Alu, “Multilayered plasmonic covers for comb-like scattering response and optical tagging,” Phys. Rev. Lett. 110, 113901 (2013).
[CrossRef]

D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8, 142–146 (2013).
[CrossRef]

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal–dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[CrossRef]

D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Effect of number density on optimal design of gold nanoshells for plasmonic photothermal therapy,” Biomed. Opt. Express 4, 15–31 (2013).
[CrossRef]

A. Mirzaei, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Cloaking and enhanced scattering of core–shell plasmonic nanowires,” Opt. Express 21, 10454–10459 (2013).
[CrossRef]

2012 (9)

D. Handapangoda, I. D. Rukhlenko, and M. Premaratne, “Optimizing the design of planar heterostructures for plasmonic waveguiding,” J. Opt. Soc. Am. B 29, 553–558 (2012).
[CrossRef]

A. Moradi, “Plasmon hybridization in coated metallic nanowires,” J. Opt. Soc. Am. B 29, 625–629 (2012).
[CrossRef]

W. Zhu, I. D. Rukhlenko, and M. Premaratne, “Linear transformation optics for plasmonics,” J. Opt. Soc. Am. B 29, 2659–2664 (2012).
[CrossRef]

F. Monticone, C. Argyropoulos, and A. Alu, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci. Rep. 2, 912–918 (2012).
[CrossRef]

J. F. Ho, B. Lukyanchuk, and J. B. Zhang, “Tunable Fano resonances in silver–silica–silver multilayer nanoshells,” Appl. Phys. A 107, 133–137 (2012).
[CrossRef]

J. Zhu, Y. Ren, S. Zhao, and J. Zhao, “The effect of inserted gold nanosphere on the local field enhancement of gold nanoshell,” Mater. Chem. Phys. 133, 1060–1065 (2012).
[CrossRef]

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

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

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi (RRL) 6, 46–48 (2012).
[CrossRef]

2011 (6)

D. Wu, S. Jiang, and X. Liu, “Tunable Fano resonances in three-layered bimetallic Au and Ag nanoshell,” J. Phys. Chem. C 115, 23797–23801 (2011).
[CrossRef]

M. Wang, M. Cao, X. Chen, and N. Gu, “Subradiant plasmon modes in multilayer metal–dielectric nanoshells,” J. Phys. Chem. C 115, 20920–20925 (2011).
[CrossRef]

I. D. Rukhlenko, A. Pannipitiya, and M. Premaratne, “Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides,” Opt. Lett. 36, 3374–3376 (2011).
[CrossRef]

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Surface plasmon-polariton propagation in piecewise linear chains of composite nanospheres: the role of optical gain and chain layout,” Opt. Express 19, 19973–19986 (2011).
[CrossRef]

A. Pannipitiya, I. D. Rukhlenko, and M. Premaratne, “Analytical theory of optical bistability in plasmonic nanoresonators,” J. Opt. Soc. Am. B 28, 2820–2826 (2011).
[CrossRef]

Z. Jian, L. Jian-jun, and Z. Jun-wu, “Tuning the dipolar plasmon hybridization of multishell metal–dielectric nanostructure: gold nanosphere in a gold nanoshell,” Plasmonics 6, 527–534 (2011).
[CrossRef]

2010 (8)

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

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, 2694–2701 (2010).
[CrossRef]

T. Som and B. Karmakar, “Surface plasmon resonance and enhanced fluorescence application of single-step synthesized elliptical nano gold-embedded antimony glass dichroic nanocomposites,” Plasmonics 5, 149–159 (2010).
[CrossRef]

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[CrossRef]

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

B. Lukyanchuk, 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]

K. Bao, N. A. Mirin, and P. Nordlander, “Fano resonances in planar silver nanosphere clusters,” Appl. Phys. A 100, 333–339 (2010).
[CrossRef]

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, 131113 (2010).
[CrossRef]

2009 (4)

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef]

A. Alu, “Mantle cloak: invisibility induced by a surface,” Phys. Rev. B 80, 245115 (2009).
[CrossRef]

R. Acevedo, R. Lombardini, N. J. Halas, and B. R. Johnson, “Plasmonic enhancement of Raman optical activity in molecules near metal nanoshells,” J. Phys. Chem. A 113, 13173–13183 (2009).
[CrossRef]

E. Cojocaru, “Exact analytical approaches for elliptic cylindrical invisibility cloaks,” J. Opt. Soc. Am. B 26, 1119–1128 (2009).
[CrossRef]

2008 (3)

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

D. Wu, X. Xu, and X. Liu, “Tunable near-infrared optical properties of three-layered metal nanoshells,” J. Chem. Phys. 129, 074711 (2008).
[CrossRef]

M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16, 1385–1392 (2008).
[CrossRef]

2006 (1)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

2005 (1)

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

2004 (1)

N. K. Grady, N. J. Halas, and P. Nordlander, “Influence of dielectric function properties on the optical response of plasmon resonant metallic nanoparticles,” Chem. Phys. Lett. 399, 167–171 (2004).
[CrossRef]

2003 (1)

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

1999 (1)

1993 (1)

J. W. Haus, H. S. Zhou, S. Takami, M. Hirasawa, I. Honma, and H. Komiyama, “Enhanced optical properties of metal-coated nanoparticles,” J. Appl. Phys. 73, 1043–1048 (1993).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Acevedo, R.

R. Acevedo, R. Lombardini, N. J. Halas, and B. R. Johnson, “Plasmonic enhancement of Raman optical activity in molecules near metal nanoshells,” J. Phys. Chem. A 113, 13173–13183 (2009).
[CrossRef]

Adegoke, J. A.

Alu, A.

F. Monticone, C. Argyropoulos, and A. Alu, “Multilayered plasmonic covers for comb-like scattering response and optical tagging,” Phys. Rev. Lett. 110, 113901 (2013).
[CrossRef]

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

F. Monticone, C. Argyropoulos, and A. Alu, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci. Rep. 2, 912–918 (2012).
[CrossRef]

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

A. Alu, “Mantle cloak: invisibility induced by a surface,” Phys. Rev. B 80, 245115 (2009).
[CrossRef]

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Argyropoulos, C.

F. Monticone, C. Argyropoulos, and A. Alu, “Multilayered plasmonic covers for comb-like scattering response and optical tagging,” Phys. Rev. Lett. 110, 113901 (2013).
[CrossRef]

F. Monticone, C. Argyropoulos, and A. Alu, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci. Rep. 2, 912–918 (2012).
[CrossRef]

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

Averitt, R. D.

Bahoura, M.

Bao, K.

K. Bao, N. A. Mirin, and P. Nordlander, “Fano resonances in planar silver nanosphere clusters,” Appl. Phys. A 100, 333–339 (2010).
[CrossRef]

Bardhan, R.

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, 2694–2701 (2010).
[CrossRef]

Belov, P. A.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal–dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[CrossRef]

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi (RRL) 6, 46–48 (2012).
[CrossRef]

Boltasseva, A.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

Cao, M.

M. Wang, M. Cao, X. Chen, and N. Gu, “Subradiant plasmon modes in multilayer metal–dielectric nanoshells,” J. Phys. Chem. C 115, 20920–20925 (2011).
[CrossRef]

Chen, P. Y.

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

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

Chen, X.

M. Wang, M. Cao, X. Chen, and N. Gu, “Subradiant plasmon modes in multilayer metal–dielectric nanoshells,” J. Phys. Chem. C 115, 20920–20925 (2011).
[CrossRef]

Cheng, W.

D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8, 142–146 (2013).
[CrossRef]

D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Effect of number density on optimal design of gold nanoshells for plasmonic photothermal therapy,” Biomed. Opt. Express 4, 15–31 (2013).
[CrossRef]

Chong, C. T.

B. Lukyanchuk, 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]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Cojocaru, E.

DAguanno, G.

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

Emani, N. K.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

Engheta, N.

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Erickson, T. A.

T. A. Erickson and J. W. Tunnell, “Gold nanoshells in biomedical applications,” in Mixed Metal Nanomaterials, C. S. S. R. Kumar, ed. Vol. 3 of Nanomaterials for the Life Sciences (Wiley-VCH Verlag GmbH & Co. KGaA, 2009), pp. 1–44.

Fan, S.

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[CrossRef]

Fedorov, S. V.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal–dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[CrossRef]

Filonov, D. S.

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi (RRL) 6, 46–48 (2012).
[CrossRef]

Flach, S.

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P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
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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, 2694–2701 (2010).
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R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal–dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
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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, 131113 (2010).
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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, 131113 (2010).
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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, 131113 (2010).
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B. Lukyanchuk, 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).
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Adv. Mater. (1)

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

Appl. Phys. A (2)

K. Bao, N. A. Mirin, and P. Nordlander, “Fano resonances in planar silver nanosphere clusters,” Appl. Phys. A 100, 333–339 (2010).
[CrossRef]

J. F. Ho, B. Lukyanchuk, and J. B. Zhang, “Tunable Fano resonances in silver–silica–silver multilayer nanoshells,” Appl. Phys. A 107, 133–137 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

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, 131113 (2010).
[CrossRef]

Biomed. Opt. Express (1)

Chem. Phys. Lett. (1)

N. K. Grady, N. J. Halas, and P. Nordlander, “Influence of dielectric function properties on the optical response of plasmon resonant metallic nanoparticles,” Chem. Phys. Lett. 399, 167–171 (2004).
[CrossRef]

J. Appl. Phys. (1)

J. W. Haus, H. S. Zhou, S. Takami, M. Hirasawa, I. Honma, and H. Komiyama, “Enhanced optical properties of metal-coated nanoparticles,” J. Appl. Phys. 73, 1043–1048 (1993).
[CrossRef]

J. Chem. Phys. (1)

D. Wu, X. Xu, and X. Liu, “Tunable near-infrared optical properties of three-layered metal nanoshells,” J. Chem. Phys. 129, 074711 (2008).
[CrossRef]

J. Opt. Soc. Am. B (6)

J. Phys. Chem. A (1)

R. Acevedo, R. Lombardini, N. J. Halas, and B. R. Johnson, “Plasmonic enhancement of Raman optical activity in molecules near metal nanoshells,” J. Phys. Chem. A 113, 13173–13183 (2009).
[CrossRef]

J. Phys. Chem. C (3)

D. Wu, S. Jiang, and X. Liu, “Tunable Fano resonances in three-layered bimetallic Au and Ag nanoshell,” J. Phys. Chem. C 115, 23797–23801 (2011).
[CrossRef]

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[CrossRef]

M. Wang, M. Cao, X. Chen, and N. Gu, “Subradiant plasmon modes in multilayer metal–dielectric nanoshells,” J. Phys. Chem. C 115, 20920–20925 (2011).
[CrossRef]

Laser Photon. Rev. (1)

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010).
[CrossRef]

Mater. Chem. Phys. (1)

J. Zhu, Y. Ren, S. Zhao, and J. Zhao, “The effect of inserted gold nanosphere on the local field enhancement of gold nanoshell,” Mater. Chem. Phys. 133, 1060–1065 (2012).
[CrossRef]

Nano Lett. (1)

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, 2694–2701 (2010).
[CrossRef]

Nanoscale Res. Lett. (1)

D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8, 142–146 (2013).
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Nat. Mater. (2)

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Figures (6)

Fig. 1.
Fig. 1.

Cross section of three-layer nanosphere illuminated by incident field E0; k is the wave vector and ϑ is the acute angle between the polarization direction of E0 and the position vector r. ϑ^ and r^ are the unit vectors along tangential and radial directions, respectively.

Fig. 2.
Fig. 2.

Normalized scattering cross section (σsca) as a function of geometrical parameters and incident wavelength (in the lossless regime). The variation of σsca with (q=r2/r3) and λ for three different fixed (p=r1/r3) values are shown in (a)–(c), while (d)–(f) depict σsca contours as functions of p and λ for q=0.6, 0.8, and 0.9. Red represents resonant scattering states, whereas blue denotes cloaking states. Black dotted regions in (a)–(f) show abrupt switching profiles. In all cases, ε2=2.04 and ε4=1.

Fig. 3.
Fig. 3.

Normalized scattering cross section (σsca) of a gold–silica–gold nanosphere (40 nm in diameter), calculated using Mie theory. In the lossless Drude permittivity regime, multiple resonant scattering (H) and cloaking states (L) are observed in case of (a) p=0.35, q=0.6, (b) p=0.1, q=0.8, and (c) p=0.2, q=0.9. For (a)–(c), ε2=2.04 and ε4=1. (d) Plasmon resonance modes of an MDM nanosphere.

Fig. 4.
Fig. 4.

Contour plots of the normalized scattering cross section (σsca) of a gold–silica–gold nanosphere, 40 nm in diameter, calculated using analytical method: (a)–(c) with bulk metallic losses and (d)–(f) with size-dependent metallic losses. (g)–(i) Show the numerically calculated scattering spectra, obtained along the dashed lines indicated in (d)–(f), respectively. In all cases, ε2=2.04 and ε4=1.

Fig. 5.
Fig. 5.

Analytically calculated scattering cross section (σsca) for an MDM nanosphere with q=0.6, where (a) ε2=2.040.04i and (e) ε2=2.040.3i. [(b) and (f)], [(c) and (g)], and [(d) and (h)] depict numerically calculated σsca (normalized), along the dashed (p=0.3), dotted (p=0.35), and dashed–dotted (p=0.4) lines in (a) and (e), respectively. For (b)–(d) ε2=2.040.04i and for (f)–(h) ε2=2.040.3i. In all cases, ε4=1.

Fig. 6.
Fig. 6.

Electric field distribution, as a factor (expressed in dB) of the incident field, for (a) resonant scattering state [H2 in Fig. 5(g)] at λ=595nm and (b) cloaking state [L2 in Fig. 5(g)] at λ=577nm of a 7/12/20 (r1/r2/r3)nm loss-compensated gold–dielectric–gold nanosphere (ε2=2.040.3i). Polarization and propagation direction of the electric field is the same as shown in Fig. 1.

Tables (2)

Tables Icon

Table 1. Scattering–Switching Possibilities in the Scattering Spectrum of a 7/12/20 Gold–Silica–Gold Nanosphere Shown in Fig. 3(a)a

Tables Icon

Table 2. Scattering–Switching Possibilities in the Scattering Spectrum of a Loss-Compensated 7/12/20 Gold–Dielectric–Gold Nanosphere Shown in Fig. 5(g)a

Equations (26)

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Φi(r,ϑ)=(Air+Bi/r2)cosϑ,
Φiϑ|r=ri=Φi+1ϑ|r=ri,
εiΦir|r=ri=εi+1Φi+1r|r=ri.
E1=A1cosϑr^+A1sinϑϑ^,
E2=(A2+2B2r3)cosϑr^+(A2+B2r3)sinϑϑ^,
E3=(A3+2B3r3)cosϑr^+(A3+B3r3)sinϑϑ^,
E4=(E0+2B4r3)cosϑr^+(E0+B4r3)sinϑϑ^,
A1=ε2ε3ε4(3r2r3)3ξE0,A2=ε1+2ε23ε2A1,
A3=(ε1+2ε2)(ε2+2ε3)r23+2(ε1ε2)(ε2ε3)r139ε2ε3r23A1,
B2=(ε2ε1)r133ε2A1,
B3=(ε3+2ε4)r33A3+3ε4r33E02(ε3ε4),
B4=(A3+E0)r33+B3
ξ=2r23[r23(ε1+2ε2)(ε2ε3)+r13(ε1ε2)(2ε2+ε3)](ε4ε3)+r33[2r13(ε2ε1)(ε2ε3)r23(ε1+2ε2)(ε2+2ε3)](ε3+2ε4).
α=4πε0r332(ε3ε4)ξ[18r13r33(ε1ε2)(ε2ε3)ε3ε4+9r23r33(ε1+2ε2)(ε2+2ε3)ε3ε4+(2ε3+ε4)ξ],
α=4πε0r33NumαDenα,
Numα=Q(ε1+2ε2){ε2[ε3+2Qε3+(Q1)ε4]+ε3[2(Q1)ε3+(2+Q)ε4]}P(ε1ε2){2ε2[ε3+2Qε3+(Q1)ε4]+ε3[2(Q1)ε3+(2+Q)ε4]}
Denα=2Q[Q(ε1+2ε2)(ε2ε3)+P(ε1ε2)(2ε2+ε3)](ε3+ε4)+[2P(ε1+ε2)(ε2ε3)Q(ε1+2ε2)(ε2+2ε3)](ε3+2ε4).
σsca=16πε02k4|α|2,σabs=kε0Imα,
NumP=ε1ε3[ε2+2Qε24(Q1)ε3+2(2+Q)ε4]+(ε1+2ε2){ε2ε3+2[(Q1)(ε3)2+(ε3)2+Q(ε2ε3)(ε3ε4)+ε2ε4+2ε3ε4]}
DenP=ε1ε3[ε2+2Qε2+2(Q1)ε3(2+Q)ε4]+(ε1ε2){(Q1)(ε3)2ε3[ε2+2Qε2+(Q1)ε3]+[2(Q1)ε2+(2+Q)ε3]ε4}.
Denα=2Q˜ε1[2Q˜(ε1ε2)(ε2+ε3)(ε1+2ε2)(ε2+2ε3)],
(r1r2)3=2(ε2)2(ε1+2ε2)(ε2+2ε3)2[(ε2)2+(ε1ε2)(ε2ε3)],
P=Q(ε1+2ε2){ε2[ε3+2Qε3+(Q1)ε4]ε3[2(Q1)ε3+(2+Q)ε4]}/((ε1+ε2){2ε2[ε3+2Qε3+(Q1)ε4]+ε3[2(Q1)ε3+(2+Q)ε4]}).
P=Q(ε1+2ε2){ε2[ε3+2Qε32(Q1)ε4]+2ε3[ε3Qε3+(2+Q)ε4]}/(2(ε1+ε2){ε2[ε3+2Qε32(Q1)ε4]+ε3[(Q1)ε3(2+Q)ε4]}).
σsca=λ22πn=1(2n+1)(|an|2+|bn|2),
ε1=ε3=1+χωp2ω2+iω(γ+vF/δ),

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