Abstract

A number of recent studies have shown that hybridized antiphase dipolar plasmons, qualitatively similar to magnetic dipole resonances, can be excited in metal–dielectric–metal structures over a wide frequency range. Here, we study how structural asymmetry in plasmonic nanosandwiches, composed of two Au disks separated by a thin SiO2 layer, affects their near- and far-field optical properties using point-dipole analysis, electrodynamics simulations, and optical spectroscopy. We find that the strength of the antiphase resonant mode can be increased significantly compared to a symmetrical sandwich if the diameters or thicknesses of the nanodisks in the sandwich are made to differ. Such asymmetrical nanosandwiches also exhibit a generally stronger magnetic response, as characterized by the magnetic near-field enhancement in the region between the disks. However, symmetry breaking also leads to pronounced directionality effects in the magnetic near-field, i.e., the enhancement depends on which side of the sandwich that is first illuminated.

© 2008 Optical Society of America

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References

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    [CrossRef]
  2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  3. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686-1686 (2007).
    [CrossRef] [PubMed]
  4. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699-1701 (2007).
    [CrossRef] [PubMed]
  5. 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,” Science 314, 977-980 (2006).
    [CrossRef] [PubMed]
  6. W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterial,” Nat. Photonics 1, 224-227 (2007).
    [CrossRef]
  7. J. B. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  8. R. A. Shalby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
    [CrossRef]
  9. C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index material: new frontiers in optics,” Adv. Mater. (Weinheim, Ger.) 18, 1941-1952 (2006).
    [CrossRef]
  10. C. Enkrich, F. P. Willard, D. Gerthsen, J. Zhou, T. Koschny, C. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near infrared magnetic metamaterials,” Adv. Mater. (Weinheim, Ger.) 17, 2547-2549 (2005).
    [CrossRef]
  11. C. M. Soukoulis, S. Linden, and M. Wegner, “Negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
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  12. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41-48 (2007).
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  13. G. Dolling, M. Wegner, C. M. Soukoulis, and S. Linden, “Negative-index metamaterials at 780 nm wavelength,” Opt. Lett. 32, 53-55 (2007).
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  14. T. Li, H. Liu, F. M. Wang, J. Q. Li, Y. Y. Zhu, and S. N. Zhu, “Surface plasmon-induced optical magnetic response in perforated trilayer metamaterial,” Phys. Rev. E 76, 016606 (2007).
    [CrossRef]
  15. A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
    [CrossRef] [PubMed]
  16. A. Ishikawa, T. Tanaka, and S. Kawata, “Frequency dependence of the magnetic response of split-ring resonators,” J. Opt. Soc. Am. B 24, 510-515 (2007).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. Z. Huang, J. Xue, Y. Hou, J. Chu, and D. H. Zhang, “Optical magnetic response from parallel plate metamaterials,” Phys. Rev. B 74, 193105 (2006).
    [CrossRef]
  25. 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. Express 15, 3333-3341 (2007).
    [CrossRef] [PubMed]
  26. H. K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076-1083 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  29. G. Shvets and Y. A. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A, Pure Appl. Opt. 8, S122-S130 (2006).
    [CrossRef]
  30. G. Dolling, M. Wegner, and S. Linden, “Realization of a three-functional layer negative-index photonic material,” Opt. Lett. 32, 551-553 (2007).
    [CrossRef] [PubMed]
  31. A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3, 294-299 (2007).
    [CrossRef] [PubMed]
  32. H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole-mask colloidal lithography,” Adv. Mater. (Weinheim, Ger.) 19, 4297-4302 (2007).
    [CrossRef]
  33. C. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  34. D. M. Sullivan, Electromagnetic Simulation Using FDTD Method (IEEE, 2000).
    [CrossRef]
  35. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  36. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

2007

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686-1686 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterial,” Nat. Photonics 1, 224-227 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegner, “Negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

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

T. Li, H. Liu, F. M. Wang, J. Q. Li, Y. Y. Zhu, and S. N. Zhu, “Surface plasmon-induced optical magnetic response in perforated trilayer metamaterial,” Phys. Rev. E 76, 016606 (2007).
[CrossRef]

A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3, 294-299 (2007).
[CrossRef] [PubMed]

H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole-mask colloidal lithography,” Adv. Mater. (Weinheim, Ger.) 19, 4297-4302 (2007).
[CrossRef]

G. Dolling, M. Wegner, and S. Linden, “Realization of a three-functional layer negative-index photonic material,” Opt. Lett. 32, 551-553 (2007).
[CrossRef] [PubMed]

H. K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076-1083 (2007).
[CrossRef] [PubMed]

A. Ishikawa, T. Tanaka, and S. Kawata, “Frequency dependence of the magnetic response of split-ring resonators,” J. Opt. Soc. Am. B 24, 510-515 (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. Express 15, 3333-3341 (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegner, C. M. Soukoulis, and S. Linden, “Negative-index metamaterials at 780 nm wavelength,” Opt. Lett. 32, 53-55 (2007).
[CrossRef]

2006

N. Fetch, C. Enkrich, and M. Wegner, “Large-area magnetic metamaterials via compact interference lithography,” Opt. Express 15, 501-507 (2006).
[CrossRef]

A. V. Kildishev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and V. M. Shalaev, “Negative refractive index in optics of metal-dielectric composites,” J. Opt. Soc. Am. B 23, 423-433 (2006).
[CrossRef]

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies,” J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, “Negative index metamaterials combining magnetic resonance with metal films,” Opt. Express 14, 7872-7877 (2006).
[CrossRef] [PubMed]

T. Pakizeh, M. S. Abrishamian, N. Granpayeh, A. Dmitriev, and M. Käll, “Magnetic field enhancement in gold nanosandwiches,” Opt. Express 14, 8240-8246 (2006).
[CrossRef] [PubMed]

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106-1115 (2006).
[CrossRef]

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, “Evaluation of gold nanowire pairs as a potential negative index material,” Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

Z. Huang, J. Xue, Y. Hou, J. Chu, and D. H. Zhang, “Optical magnetic response from parallel plate metamaterials,” Phys. Rev. B 74, 193105 (2006).
[CrossRef]

G. Shvets and Y. A. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A, Pure Appl. Opt. 8, S122-S130 (2006).
[CrossRef]

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index material: new frontiers in optics,” Adv. Mater. (Weinheim, Ger.) 18, 1941-1952 (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,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

2005

C. Enkrich, F. P. Willard, D. Gerthsen, J. Zhou, T. Koschny, C. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near infrared magnetic metamaterials,” Adv. Mater. (Weinheim, Ger.) 17, 2547-2549 (2005).
[CrossRef]

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

2001

R. A. Shalby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999

J. B. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1996

A. N. Lagarkov and A. K. Sarychev, “Electromagnetic properties of composites containing elongated conducting inclusions,” Phys. Rev. B 53, 6318-6336 (1996).
[CrossRef]

1972

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

1968

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ϵ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Adv. Mater. (Weinheim, Ger.)

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index material: new frontiers in optics,” Adv. Mater. (Weinheim, Ger.) 18, 1941-1952 (2006).
[CrossRef]

C. Enkrich, F. P. Willard, D. Gerthsen, J. Zhou, T. Koschny, C. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near infrared magnetic metamaterials,” Adv. Mater. (Weinheim, Ger.) 17, 2547-2549 (2005).
[CrossRef]

H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole-mask colloidal lithography,” Adv. Mater. (Weinheim, Ger.) 19, 4297-4302 (2007).
[CrossRef]

Appl. Phys. B

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, “Evaluation of gold nanowire pairs as a potential negative index material,” Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106-1115 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

J. B. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

G. Shvets and Y. A. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A, Pure Appl. Opt. 8, S122-S130 (2006).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterial,” Nat. Photonics 1, 224-227 (2007).
[CrossRef]

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

Opt. Express

Opt. Lett.

Phys. Rev. B

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

A. N. Lagarkov and A. K. Sarychev, “Electromagnetic properties of composites containing elongated conducting inclusions,” Phys. Rev. B 53, 6318-6336 (1996).
[CrossRef]

Z. Huang, J. Xue, Y. Hou, J. Chu, and D. H. Zhang, “Optical magnetic response from parallel plate metamaterials,” Phys. Rev. B 74, 193105 (2006).
[CrossRef]

Phys. Rev. E

T. Li, H. Liu, F. M. Wang, J. Q. Li, Y. Y. Zhu, and S. N. Zhu, “Surface plasmon-induced optical magnetic response in perforated trilayer metamaterial,” Phys. Rev. E 76, 016606 (2007).
[CrossRef]

Phys. Rev. Lett.

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Science

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686-1686 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

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,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

R. A. Shalby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegner, “Negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Small

A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold nanosandwiches: tunable bimodal plasmonic resonators,” Small 3, 294-299 (2007).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ϵ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other

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

C. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

D. M. Sullivan, Electromagnetic Simulation Using FDTD Method (IEEE, 2000).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Au plasmonic nanosandwiches. (a) Schematic of the nanosandwich geometry with variable parameters (nanodisk diameters D 1 and D 2 , nanodisk thicknesses T 1 and T 2 , and surface-to-surface separation d). (b) and (c) Change in nanodisk thickness or diameter results in asymmetrical configurations, respectively. (d) Point-dipole representation of a nanosandwich characterized by electric dipole polarizabilities α 1 and α 2 and center-to-center separation s. (e)–(h) Hole-mask lithography is employed to fabricate arrays of nanosandwiches. SEM top view of an array of Au - SiO 2 - Au nanosandwiches with (e) D 1 = 120 nm , D 2 = 96 nm , T 1 = T 2 = 24 nm , and d = 12 nm . (f) Same structures imaged at an 80 ° angle; (g) for comparison, nanosandwiches with same D 1 , D 2 , and T 2 but with T 1 = 16 nm corresponding to the model in (b) and with (h) D 1 = 96 nm , D 2 = 68 nm , T 1 = T 2 = 24 nm , and d = 12 nm , corresponding to the model in (c). Scale bar for (f)–(h) shown in (h) is 100 nm .

Fig. 2
Fig. 2

Optical properties of a pair of interacting oblate spheroids illuminated in the end-fire configuration calculated by the coupled dipole approximation method. Column 1(a1)–(d1) refers to a symmetrical pair of spheroids, column 2(a2)–(d2) to an asymmetrical pair illuminated from above (see Fig. 1), and column 3(a3)–(d3) to the same asymmetrical pair illuminated from below. The first row (a1)–(a3) and the second row (b1)–(b3) show the amplitudes and phases, respectively, of the renormalized particle polarizabilities for the upper (solid curve) and lower (dashed curve) particles in the pair. The third row (c1)–(c3) shows the projection of the particle polarizabilities on the in-phase (solid curve) and antiphase (dashed curve) normal modes of the symmetrical pair. The last row (d1)–(d3) shows far-field extinction spectra (solid curves) and magnetic near-field intensity enhancement spectra at the midpoint between the particles (dashed curves).

Fig. 3
Fig. 3

Magnetic field intensity enhancement spectra for nanosandwiches with varying diameters of the nanodisks, D 1 = 88 + 8 X nm and D 2 = 88 8 X nm for X = 0 (symmetrical case, dashed curve) and X = 2 illuminated from above (solid curve) and below (dashed-dotted curve). The thicknesses of the disks and their surface-to-surface separation are kept constant T 1 = T 2 = 24 nm , d = 12 nm . The inset shows the variation in maximum enhancement (peak height) as a function of asymmetry X in the case of illumination from above (solid curve, closed squares), and below (dashed curve, closed circles).

Fig. 4
Fig. 4

Magnetic field ( H y ) and electric field ( E x ) distribution plots for nanosandwiches with fixed T 1 = T 2 = 24 nm , d = 12 nm , variable D 1 and D 2 , and illumination from above. (a) D 1 = D 2 = 88 nm , (b) D 1 = 104 nm , D 2 = 72 nm , and (c) D 1 = 128 nm , D 2 = 48 nm . The plots have been made for wavelengths corresponding to a maximum magnetic field enhancement for the respective structures.

Fig. 5
Fig. 5

Calculated extinction spectra for the optimal magnetic field enhancement case, T 1 = T 2 = 24 nm , d = 12 nm , and D 1 = 104 , D 2 = 72 nm (dashed curve) compared to an experimental extinction spectrum (solid curve) for a similar structure with T 1 = T 2 = 24 nm , d = 12 nm , D 1 100 nm , and D 2 70 nm .

Fig. 6
Fig. 6

Spectral changes induced by a variation of the thickness of the lower disk in a sandwich. (a) Calculated magnetic field enhancement spectra for sandwiches with D 1 = D 2 = 88 nm , d = 12 nm , T 2 = 24 nm , and T 1 = 24 nm (symmetrical structure, dashed-dotted curve), T 1 = 12 nm (solid/dashed curve, illumination from above/below), and T 1 = 32 nm (solid curve with circles, illumination from above). (b) Calculated extinction spectra for the configurations with T 1 = 12 nm (solid curve) and T 1 = 24 nm (dashed-dotted curve). (c) Experimental extinction spectra for nanosandwiches with D 1 100 nm , D 2 80 nm , d = 12 nm , T 2 = 24 nm , T 1 = 12 nm (solid curve) and T 1 = 24 nm (dashed-dotted curve).

Fig. 7
Fig. 7

Magnetic field ( H y ) and electric field ( E x ) enhancement in Au nanosandwiches with D 1 = D 2 = 88 nm , T 2 = 24 nm , interdisk spacing d = 12 nm , and (a) T 1 = 12 nm , illumination from above; (b) T 1 = 12 nm , illumination from below; (c) T 1 = 32 nm , illumination from above. The plots have been made for wavelengths corresponding to maximum magnetic field enhancement for the respective structures.

Fig. 8
Fig. 8

Variation in extinction spectra as the thicknesses of both disks in a sandwich are increased. (a) Calculated extinction spectra from D-FDTD simulations for the configuration with D 1 = 192 nm , D 2 = 152 nm , d = 16 , and variable T 1 = T 2 . (b) Corresponding experimental extinction spectra for a configuration with D 1 = 190 nm , D 2 = 154 nm , d = 16 , and variable T 1 = T 2 .

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

E = k 2 P 4 π ϵ 0 [ exp ( i k ( r + s 2 ) ) ( r + s 2 ) exp ( i k ( r s 2 ) ) ( r s 2 ) ] i k 3 P s 4 π ϵ 0 exp ( i k r ) r = η I l s 4 π k 2 exp ( i k r ) r ,
ϵ r ( ω ) = ϵ ω p 2 ω ( ω + i v c ) + n = 1 4 G n ω n 2 ( ω n 2 ω 2 ) i ω Γ n .
P i ( ω ) = α i ( ω ) [ E 0 ( r , ω ) + A i j ( r , ω ) P j ( ω ) ] ,
α i ( ω ) = a i 2 c i 3 L i ω 0 i 2 ω 0 i 2 ω 2 i ω v c ,
α ̃ 1 ( ω ) = α 1 ( ω ) [ s 3 ( s 3 α 2 ( ω ) ) s 6 α 1 ( ω ) α 2 ( ω ) e 2 i k s ] ,
α ̃ 2 ( ω ) = α 2 ( ω ) [ s 3 ( s 3 α 1 ( ω ) e 2 i k s ) s 6 α 1 ( ω ) α 2 ( ω ) e 2 i k s ] .
ω ± 2 = 1 2 ( ω 01 2 + ω 02 2 ) [ 1 ± 1 2 ( 1 K s 6 ) ω 01 2 ω 02 2 ( ω 01 2 + ω 02 2 ) 2 ] ,
H y H 0 2 = H 1 + H 2 + H 0 H 0 2 = i ω η 4 π s 2 ( α ̃ 1 e i k s α ̃ 2 ) + 1 2 .
C ext = 4 π k E 0 2 j = 1 2 Im ( E 0 , r j * P j ) .

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