Abstract

A new surface plasmon resonator, in the form of a metal cylinder shaped like a teardrop, is proposed and modeled using hypersingular integral equations. Illuminating the apex of the teardrop along its axis of symmetry with TM-polarised light excites equal-magnitude surface plasmons counter-propagating around its periphery. Interference of these counter-propagating surface plasmons leads to resonant modes having very sharp line-widths (~0.6 nm) and large quality factors (~3400). In water, a Au teardrop supports resonant modes having large bulk sensitivities (~1900 nm/RIU) and remarkably large figures-of-merit (~1700), about 1000 × larger than the figure-of-merit of, e.g., isolated Au nano-spheres. The scattering cross-section of the structure near resonant modes exhibits a Fano-like line-shape. The teardrop should find applications as a high-quality surface plasmon resonator or as a biosensing element.

© 2012 OSA

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2011

2010

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett.10(8), 3184–3189 (2010).
[CrossRef] [PubMed]

J. X. Cao, H. Liu, T. Li, S. M. Wang, Z. G. Dong, L. Li, C. Zhu, Y. Wang, and S. N. Zhu, “High-sensing properties of magnetic plasmon resonances in double- and triple-rod structures,” Appl. Phys. Lett.97(7), 071905 (2010).
[CrossRef]

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105(15), 153902 (2010).
[CrossRef] [PubMed]

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

E. Verhagen, L. K. Kuipers, and A. Polman, “Plasmonic nanofocusing in a dielectric wedge,” Nano Lett.10(9), 3665–3669 (2010).
[CrossRef] [PubMed]

2009

F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652 (2009).
[CrossRef] [PubMed]

N. A. Mirin, K. Bao, and P. Nordlander, “Fano resonances in plasmonic nanoparticle aggregates,” J. Phys. Chem. A113(16), 4028–4034 (2009).
[CrossRef] [PubMed]

2008

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys.10(10), 105010 (2008).
[CrossRef]

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photon. Rev.2(3), 136–159 (2008).
[CrossRef]

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008).
[CrossRef] [PubMed]

H. Y. She, L. W. Li, O. J. Martin, and J. R. Mosig, “Surface polaritons of small coated cylinders illuminated by normal incident TM and TE plane waves,” Opt. Express16(2), 1007–1019 (2008).
[CrossRef] [PubMed]

2007

2006

2005

L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

2004

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B70(12), 125113 (2004).
[CrossRef]

2001

J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon resonances spectrum of silver nanowires,” Appl. Phys. B73(4), 299–304 (2001).
[CrossRef]

1993

E. Marx, “Electromagnetic scattering from a dielectric wedge and the single hypersingular integral equation,” IEEE Trans. Antenn. Propag.41(8), 1001–1008 (1993).
[CrossRef]

Aizpurua, J.

Ayache, M.

Baets, R.

Bao, K.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: A route to increased-sensitivity localized Surface Plasmon resonance sensors revealed,” Nano Lett.11, 1657–1663 (2011).
[CrossRef] [PubMed]

N. A. Mirin, K. Bao, and P. Nordlander, “Fano resonances in plasmonic nanoparticle aggregates,” J. Phys. Chem. A113(16), 4028–4034 (2009).
[CrossRef] [PubMed]

Bartolozzi, I.

Berini, P.

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys.10(10), 105010 (2008).
[CrossRef]

P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express14(26), 13030–13042 (2006).
[CrossRef] [PubMed]

Bienstman, P.

K. Q. Le and P. Bienstman, “Enhanced sensitivity of silicon-on-insulator surface plasmon interferometer with additional silicon layer,” IEEE Photon. J.3(3), 538–545 (2011).
[CrossRef]

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express15(12), 7610–7615 (2007).
[CrossRef] [PubMed]

Bryant, G.

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photon. Rev.2(3), 136–159 (2008).
[CrossRef]

Cao, J. X.

J. X. Cao, H. Liu, T. Li, S. M. Wang, Z. G. Dong, L. Li, C. Zhu, Y. Wang, and S. N. Zhu, “High-sensing properties of magnetic plasmon resonances in double- and triple-rod structures,” Appl. Phys. Lett.97(7), 071905 (2010).
[CrossRef]

Capasso, F.

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett.10(8), 3184–3189 (2010).
[CrossRef] [PubMed]

Chang, S. H.

L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

Chen, H.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008).
[CrossRef] [PubMed]

Chong, C. T.

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

Christ, A.

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B70(12), 125113 (2004).
[CrossRef]

De Vos, K.

Dong, C. H.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105(15), 153902 (2010).
[CrossRef] [PubMed]

Dong, Z. G.

J. X. Cao, H. Liu, T. Li, S. M. Wang, Z. G. Dong, L. Li, C. Zhu, Y. Wang, and S. N. Zhu, “High-sensing properties of magnetic plasmon resonances in double- and triple-rod structures,” Appl. Phys. Lett.97(7), 071905 (2010).
[CrossRef]

Fainman, Y.

Fan, J. A.

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett.10(8), 3184–3189 (2010).
[CrossRef] [PubMed]

Feng, L.

Galler, N.

Giessen, H.

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

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B70(12), 125113 (2004).
[CrossRef]

Gippius, N. A.

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B70(12), 125113 (2004).
[CrossRef]

Gong, Q.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105(15), 153902 (2010).
[CrossRef] [PubMed]

Halas, N. J.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: A route to increased-sensitivity localized Surface Plasmon resonance sensors revealed,” Nano Lett.11, 1657–1663 (2011).
[CrossRef] [PubMed]

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett.10(8), 3184–3189 (2010).
[CrossRef] [PubMed]

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

Han, Z. F.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105(15), 153902 (2010).
[CrossRef] [PubMed]

Hao, F.

F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652 (2009).
[CrossRef] [PubMed]

Homola, J.

Khajavikhan, M.

Kottmann, J. P.

J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon resonances spectrum of silver nanowires,” Appl. Phys. B73(4), 299–304 (2001).
[CrossRef]

Kou, X.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008).
[CrossRef] [PubMed]

Krenn, J. R.

Kuhl, J.

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B70(12), 125113 (2004).
[CrossRef]

Kuipers, L. K.

E. Verhagen, L. K. Kuipers, and A. Polman, “Plasmonic nanofocusing in a dielectric wedge,” Nano Lett.10(9), 3665–3669 (2010).
[CrossRef] [PubMed]

Kundu, J.

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett.10(8), 3184–3189 (2010).
[CrossRef] [PubMed]

Kvasnicka, P.

Large, N.

Lassiter, J. B.

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett.10(8), 3184–3189 (2010).
[CrossRef] [PubMed]

Le, K. Q.

K. Q. Le and P. Bienstman, “Enhanced sensitivity of silicon-on-insulator surface plasmon interferometer with additional silicon layer,” IEEE Photon. J.3(3), 538–545 (2011).
[CrossRef]

Li, B. B.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105(15), 153902 (2010).
[CrossRef] [PubMed]

Li, L.

J. X. Cao, H. Liu, T. Li, S. M. Wang, Z. G. Dong, L. Li, C. Zhu, Y. Wang, and S. N. Zhu, “High-sensing properties of magnetic plasmon resonances in double- and triple-rod structures,” Appl. Phys. Lett.97(7), 071905 (2010).
[CrossRef]

Li, L. W.

Li, T.

J. X. Cao, H. Liu, T. Li, S. M. Wang, Z. G. Dong, L. Li, C. Zhu, Y. Wang, and S. N. Zhu, “High-sensing properties of magnetic plasmon resonances in double- and triple-rod structures,” Appl. Phys. Lett.97(7), 071905 (2010).
[CrossRef]

Li, Y.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105(15), 153902 (2010).
[CrossRef] [PubMed]

Lin, V. K.

Liu, H.

J. X. Cao, H. Liu, T. Li, S. M. Wang, Z. G. Dong, L. Li, C. Zhu, Y. Wang, and S. N. Zhu, “High-sensing properties of magnetic plasmon resonances in double- and triple-rod structures,” Appl. Phys. Lett.97(7), 071905 (2010).
[CrossRef]

Luk’yanchuk, B.

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

Maier, S. A.

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

F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652 (2009).
[CrossRef] [PubMed]

Martin, O. J.

Martin, O. J. F.

J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon resonances spectrum of silver nanowires,” Appl. Phys. B73(4), 299–304 (2001).
[CrossRef]

Marty, R.

Marx, E.

E. Marx, “Electromagnetic scattering from a dielectric wedge and the single hypersingular integral equation,” IEEE Trans. Antenn. Propag.41(8), 1001–1008 (1993).
[CrossRef]

Mirin, N. A.

N. A. Mirin, K. Bao, and P. Nordlander, “Fano resonances in plasmonic nanoparticle aggregates,” J. Phys. Chem. A113(16), 4028–4034 (2009).
[CrossRef] [PubMed]

Mlayah, A.

Mosig, J. R.

Ni, W.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008).
[CrossRef] [PubMed]

Nordlander, P.

S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: A route to increased-sensitivity localized Surface Plasmon resonance sensors revealed,” Nano Lett.11, 1657–1663 (2011).
[CrossRef] [PubMed]

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett.10(8), 3184–3189 (2010).
[CrossRef] [PubMed]

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

N. A. Mirin, K. Bao, and P. Nordlander, “Fano resonances in plasmonic nanoparticle aggregates,” J. Phys. Chem. A113(16), 4028–4034 (2009).
[CrossRef] [PubMed]

F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652 (2009).
[CrossRef] [PubMed]

Pelton, M.

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photon. Rev.2(3), 136–159 (2008).
[CrossRef]

Piliarik, M.

Polman, A.

E. Verhagen, L. K. Kuipers, and A. Polman, “Plasmonic nanofocusing in a dielectric wedge,” Nano Lett.10(9), 3665–3669 (2010).
[CrossRef] [PubMed]

Schacht, E.

Schatz, G. C.

L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

She, H. Y.

Sherry, L. J.

L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

Sobhani, H.

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett.10(8), 3184–3189 (2010).
[CrossRef] [PubMed]

Sonnefraud, Y.

F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652 (2009).
[CrossRef] [PubMed]

Tan, D. T.

Teo, S. L.

Tikhodeev, S. G.

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B70(12), 125113 (2004).
[CrossRef]

Tripathy, S.

Van Dorpe, P.

F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano3(3), 643–652 (2009).
[CrossRef] [PubMed]

Van Duyne, R. P.

L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

Verhagen, E.

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S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: A route to increased-sensitivity localized Surface Plasmon resonance sensors revealed,” Nano Lett.11, 1657–1663 (2011).
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[CrossRef]

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S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: A route to increased-sensitivity localized Surface Plasmon resonance sensors revealed,” Nano Lett.11, 1657–1663 (2011).
[CrossRef] [PubMed]

L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005).
[CrossRef] [PubMed]

E. Verhagen, L. K. Kuipers, and A. Polman, “Plasmonic nanofocusing in a dielectric wedge,” Nano Lett.10(9), 3665–3669 (2010).
[CrossRef] [PubMed]

Nat. Mater.

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

Phys. Rev. Lett.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105(15), 153902 (2010).
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Figures (4)

Fig. 1
Fig. 1

Cross-section of a metal teardrop-shaped cylindrical resonator (εm) surrounded by dielectric (εd), illuminated by a TM-polarised plane wave at ϕinc.

Fig. 2
Fig. 2

Scattering cross-section of a Au teardrop in vacuum (thick red curve) and water (thin blue curve); the latter was multiplied by 0.5 before plotting.

Fig. 3
Fig. 3

Distribution of |Escat| and of its y-component |Eyscat| normalised to E0, plotted on log and linear scales, for modes 1 (a-d) and 2 (e-h) of Table 1.

Fig. 4
Fig. 4

Mono-static radar cross-section (in µm) of the teardrop in water near the four resonances observed on the thin blue curve of Fig. 2.

Tables (2)

Tables Icon

Table 1 Scattering Cross-Section Parameters of Resonant Modes; Au Teardrop in Vacuum

Tables Icon

Table 2 Radar Cross-Section Parameters of Resonant Modes; Au Teardrop in Water.

Equations (3)

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

C scat ( λ 0 )=R | E scat ( λ 0 ) | 2 / | E inc ( λ 0 ) | 2 dδ
σ 2D =2πR | E scat ( λ 0 ) | 2 / | E inc ( λ 0 ) | 2
FoM= ( λ r / n d ) / FWHM

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