Abstract

The plasmonic nanogap antenna is an efficient radiating or receiving optical device. The resonance behavior of optical antennas is commonly attributed to the excitation of a localized surface plasmon resonance (LSPR), which can be theoretically defined as the quasi-normal mode (QNM). To clarify the physical origin of the LSPR, we build up an analytical model of the LSPR by considering a multiple scattering process of propagative surface plasmon polaritons (SPPs) on the antenna arms. The model can comprehensively reproduce the complex eigenfrequency and the field distribution of QNMs of the antenna, unveiling that the LSPR arises from a Fabry–Perot resonance of SPPs. By further applying the complex pole expansion theorem of meromorphic functions, the field of the antenna under illumination by a nearby dipole emitter can be analytically expanded with QNMs, which well predicts the frequency response of the enhancement factor of radiation. The present model establishes explicit relations between the concepts of the LSPR and the propagative SPP and integrates the advantages of the Fabry–Perot and QNM formalisms of nanogap antennas.

© 2016 Chinese Laser Press

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    [Crossref]

2016 (3)

H. Jia, P. Lalanne, and H. Liu, “Comprehensive surface-wave description for the nano-scale energy concentration with resonant dipole antennas,” Plasmonics 11, 1025–1033 (2016).
[Crossref]

X. Zhang, C. J. Chung, S. Wang, H. Subbaraman, Z. Pan, Q. Zhan, and R. T. Chen, “Integrated broadband bowtie antenna on transparent silica substrate,” IEEE Antennas Wireless Propag. Lett. 15, 1377–1381 (2016).
[Crossref]

F. Yang, H. Liu, H. Jia, and Y. Zhong, “Analytical description of quasi normal mode in resonant plasmonic nano-cavities,” J. Opt. 18, 035003 (2016).

2015 (5)

R. C. Ge, J. F. Young, and S. Hughes, “Quasi-normal mode approach to the local-field problem in quantum optics,” Optica 2, 246–249 (2015).

R. Esteban, G. Aguirregabiria, A. G. Borisov, Y. M. Wang, P. Nordlander, G. W. Bryant, and J. Aizpurua, “The morphology of narrow gaps modifies the plasmonic response,” ACS Photon. 2, 295–305 (2015).
[Crossref]

H. Jia, H. Liu, and Y. Zhong, “Role of surface plasmon polaritons and other waves in the radiation of resonant optical dipole antennas,” Sci. Rep. 5, 8456 (2015).
[Crossref]

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
[Crossref]

M. S. Eggleston, K. Messer, L. Zhang, E. Yablonovitch, and M. C. Wu, “Optical antenna enhanced spontaneous emission,” Proc. Natl. Acad. Sci. USA 112, 1704–1709 (2015).
[Crossref]

2014 (6)

M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant-state expansion applied to three-dimensional open optical systems,” Phys. Rev. A 90, 013834 (2014).
[Crossref]

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
[Crossref]

C. Sauvan, J. P. Hugonin, R. Carminati, and P. Lalanne, “Modal representation of spatial coherence in dissipative and resonant photonic systems,” Phys. Rev. A 89, 043825 (2014).
[Crossref]

C. Liu, H. Liu, and Y. Zhong, “Impact of surface plasmon polaritons and other waves on the radiation of a dipole emitter close to a metallic nanowire antenna,” Opt. Express 22, 25539–25549 (2014).
[Crossref]

Y. Li, H. Liu, H. Jia, F. Bo, G. Zhang, and J. Xu, “Fully-vectorial modeling of cylindrical microresonators with aperiodic Fourier modal method,” J. Opt. Soc. Am. A 31, 2459–2466 (2014).
[Crossref]

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G. B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).
[Crossref]

2013 (7)

M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant state expansion applied to two-dimensional open optical systems,” Phys. Rev. A 87, 043827 (2013).
[Crossref]

H. Liu, “Coherent-form energy conservation relation for the elastic scattering of a guided mode in a symmetric scattering system,” Opt. Express 21, 24093–24098 (2013).
[Crossref]

Q. Bai, M. Perrin, C. Sauvan, J. P. Hugonin, and P. Lalanne, “Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure,” Opt. Express 21, 27371–27382 (2013).
[Crossref]

Z. Pan and J. Guo, “Enhanced optical absorption and electric field resonance in diabolo metal bar optical antennas,” Opt. Express 21, 32491–32500 (2013).
[Crossref]

R. Adato and H. Altug, “In-situ ultra-sensitive infrared absorption spectroscopy of biomolecule interactions in real time with plasmonic nanoantennas,” Nat. Commun. 4, 2154 (2013).
[Crossref]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

X. W. Chen, V. Sandoghdar, and M. Agio, “Coherent interaction of light with a metallic structure coupled to a single quantum emitter: from superabsorption to cloaking,” Phys. Rev. Lett. 110, 153605 (2013).
[Crossref]

2012 (5)

Z. Liu, E. Li, V. M. Shalaev, and A. V. Kildishev, “Near field enhancement in silver nanoantenna–superlens systems,” Appl. Phys. Lett. 101, 021109 (2012).
[Crossref]

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the nonlinear optical response using multifrequency gold-nanowire antennas,” Phys. Rev. Lett. 108, 217403 (2012).
[Crossref]

K. Höflich, M. Becker, G. Leuchs, and S. Christiansen, “Plasmonic dimer antennas for surface enhanced Raman scattering,” Nanotechnology 23, 185303 (2012).
[Crossref]

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492, 411–414 (2012).
[Crossref]

M. Agio, “Optical antennas as nanoscale resonators,” Nanoscale 4, 692–706 (2012).
[Crossref]

2011 (4)

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett. 11, 1020–1024 (2011).
[Crossref]

J. Scheuer, “Ultra-high enhancement of the field concentration in split ring resonators by azimuthally polarized excitation,” Opt. Express 19, 25454–25464 (2011).
[Crossref]

L. Novotny and N. Van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[Crossref]

A. Artar, A. A. Yanik, and H. Altug, “Directional double Fano resonances in plasmonic hetero-oligomers,” Nano Lett. 11, 3694–3700 (2011).
[Crossref]

2010 (4)

E. A. Muljarov, W. Langbein, and R. Zimmermann, “Brillouin–Wigner perturbation theory in open electromagnetic systems,” Europhys. Lett. 92, 50010 (2010).
[Crossref]

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrichm, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
[Crossref]

J. S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
[Crossref]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Interaction between plasmonic nanoparticles revisited with transformation optics,” Phys. Rev. Lett. 105, 233901 (2010).
[Crossref]

2009 (7)

R. Gordon, “Reflection of cylindrical surface waves,” Opt. Express 17, 18621–18629 (2009).
[Crossref]

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
[Crossref]

W. Zhang, H. Fischer, T. Schmid, R. Zenobi, and O. J. Martin, “Mode-selective surface-enhanced Raman spectroscopy using nanofabricated plasmonic dipole antennas,” J. Phys. Chem. C 113, 14672–14675 (2009).
[Crossref]

T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103, 257404 (2009).
[Crossref]

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[Crossref]

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
[Crossref]

E. Cubukcu, S. Zhang, Y. S. Park, G. Bartal, and X. Zhang, “Split ring resonator sensors for infrared detection of single molecular monolayers,” Appl. Phys. Lett. 95, 043113 (2009).
[Crossref]

2008 (4)

A. Alù and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. 101, 043901 (2008).
[Crossref]

R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008).
[Crossref]

H. Fischer and O. J. Martin, “Polarization sensitivity of optical resonant dipole antennas,” J. Eur. Opt. Soc. 3, 08018 (2008).
[Crossref]

L. Douillard, F. Charra, Z. Korczak, R. Bachelot, S. Kostcheev, G. Lerondel, P. M. Adam, and P. Royer, “Short range plasmon resonators probed by photoemission electron microscopy,” Nano Lett. 8, 935–940 (2008).
[Crossref]

2007 (5)

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
[Crossref]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[Crossref]

F. Jäckel, A. A. Kinkhabwala, and W. E. Moerner, “Gold bowtie nanoantennas for surface-enhanced Raman scattering under controlled electrochemical potential,” Chem. Phys. Lett. 446, 339–343 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

2005 (2)

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hech, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[Crossref]

J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22, 1844–1849 (2005).
[Crossref]

2003 (1)

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A 5, 53–60 (2003).
[Crossref]

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

1998 (2)

E. S. C. Ching, P. T. Leung, A. M. van den Brink, W. M. Suen, S. S. Tong, and K. Young, “Quasinormal-mode expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545–1554 (1998).
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1996 (1)

1994 (1)

P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994).
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R. Adato and H. Altug, “In-situ ultra-sensitive infrared absorption spectroscopy of biomolecule interactions in real time with plasmonic nanoantennas,” Nat. Commun. 4, 2154 (2013).
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X. W. Chen, V. Sandoghdar, and M. Agio, “Coherent interaction of light with a metallic structure coupled to a single quantum emitter: from superabsorption to cloaking,” Phys. Rev. Lett. 110, 153605 (2013).
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R. Esteban, G. Aguirregabiria, A. G. Borisov, Y. M. Wang, P. Nordlander, G. W. Bryant, and J. Aizpurua, “The morphology of narrow gaps modifies the plasmonic response,” ACS Photon. 2, 295–305 (2015).
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R. Adato and H. Altug, “In-situ ultra-sensitive infrared absorption spectroscopy of biomolecule interactions in real time with plasmonic nanoantennas,” Nat. Commun. 4, 2154 (2013).
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A. Artar, A. A. Yanik, and H. Altug, “Directional double Fano resonances in plasmonic hetero-oligomers,” Nano Lett. 11, 3694–3700 (2011).
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L. Douillard, F. Charra, Z. Korczak, R. Bachelot, S. Kostcheev, G. Lerondel, P. M. Adam, and P. Royer, “Short range plasmon resonators probed by photoemission electron microscopy,” Nano Lett. 8, 935–940 (2008).
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Bai, Q.

Baida, F. I.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Bakker, R. M.

R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008).
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E. Cubukcu, S. Zhang, Y. S. Park, G. Bartal, and X. Zhang, “Split ring resonator sensors for infrared detection of single molecular monolayers,” Appl. Phys. Lett. 95, 043113 (2009).
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K. Höflich, M. Becker, G. Leuchs, and S. Christiansen, “Plasmonic dimer antennas for surface enhanced Raman scattering,” Nanotechnology 23, 185303 (2012).
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M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Biagioni, P.

J. S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
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P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
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M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Bo, F.

Boltasseva, A.

R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008).
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Borisov, A. G.

R. Esteban, G. Aguirregabiria, A. G. Borisov, Y. M. Wang, P. Nordlander, G. W. Bryant, and J. Aizpurua, “The morphology of narrow gaps modifies the plasmonic response,” ACS Photon. 2, 295–305 (2015).
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Bratschitsch, R.

T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103, 257404 (2009).
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Bryant, G. W.

R. Esteban, G. Aguirregabiria, A. G. Borisov, Y. M. Wang, P. Nordlander, G. W. Bryant, and J. Aizpurua, “The morphology of narrow gaps modifies the plasmonic response,” ACS Photon. 2, 295–305 (2015).
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C. Sauvan, J. P. Hugonin, R. Carminati, and P. Lalanne, “Modal representation of spatial coherence in dissipative and resonant photonic systems,” Phys. Rev. A 89, 043825 (2014).
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Chang, D. E.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
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D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
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Charra, F.

L. Douillard, F. Charra, Z. Korczak, R. Bachelot, S. Kostcheev, G. Lerondel, P. M. Adam, and P. Royer, “Short range plasmon resonators probed by photoemission electron microscopy,” Nano Lett. 8, 935–940 (2008).
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Chen, J. J.

R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008).
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Chen, R. T.

X. Zhang, C. J. Chung, S. Wang, H. Subbaraman, Z. Pan, Q. Zhan, and R. T. Chen, “Integrated broadband bowtie antenna on transparent silica substrate,” IEEE Antennas Wireless Propag. Lett. 15, 1377–1381 (2016).
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Chen, X. W.

X. W. Chen, V. Sandoghdar, and M. Agio, “Coherent interaction of light with a metallic structure coupled to a single quantum emitter: from superabsorption to cloaking,” Phys. Rev. Lett. 110, 153605 (2013).
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Ching, E. S. C.

E. S. C. Ching, P. T. Leung, A. M. van den Brink, W. M. Suen, S. S. Tong, and K. Young, “Quasinormal-mode expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545–1554 (1998).
[Crossref]

Christiansen, S.

K. Höflich, M. Becker, G. Leuchs, and S. Christiansen, “Plasmonic dimer antennas for surface enhanced Raman scattering,” Nanotechnology 23, 185303 (2012).
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Chung, C. J.

X. Zhang, C. J. Chung, S. Wang, H. Subbaraman, Z. Pan, Q. Zhan, and R. T. Chen, “Integrated broadband bowtie antenna on transparent silica substrate,” IEEE Antennas Wireless Propag. Lett. 15, 1377–1381 (2016).
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Cubukcu, E.

E. Cubukcu, S. Zhang, Y. S. Park, G. Bartal, and X. Zhang, “Split ring resonator sensors for infrared detection of single molecular monolayers,” Appl. Phys. Lett. 95, 043113 (2009).
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M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant-state expansion applied to three-dimensional open optical systems,” Phys. Rev. A 90, 013834 (2014).
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M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant state expansion applied to two-dimensional open optical systems,” Phys. Rev. A 87, 043827 (2013).
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Dorfmuller, J.

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrichm, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
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Douillard, L.

L. Douillard, F. Charra, Z. Korczak, R. Bachelot, S. Kostcheev, G. Lerondel, P. M. Adam, and P. Royer, “Short range plasmon resonators probed by photoemission electron microscopy,” Nano Lett. 8, 935–940 (2008).
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Drachev, V. P.

R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008).
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Duò, L.

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
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Eggleston, M. S.

M. S. Eggleston, K. Messer, L. Zhang, E. Yablonovitch, and M. C. Wu, “Optical antenna enhanced spontaneous emission,” Proc. Natl. Acad. Sci. USA 112, 1704–1709 (2015).
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Eisler, H. J.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hech, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
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Engheta, N.

A. Alù and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. 101, 043901 (2008).
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Esteban, R.

R. Esteban, G. Aguirregabiria, A. G. Borisov, Y. M. Wang, P. Nordlander, G. W. Bryant, and J. Aizpurua, “The morphology of narrow gaps modifies the plasmonic response,” ACS Photon. 2, 295–305 (2015).
[Crossref]

Etrichm, C.

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrichm, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
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Fan, S.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
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Finazzi, M.

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
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W. Zhang, H. Fischer, T. Schmid, R. Zenobi, and O. J. Martin, “Mode-selective surface-enhanced Raman spectroscopy using nanofabricated plasmonic dipole antennas,” J. Phys. Chem. C 113, 14672–14675 (2009).
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H. Fischer and O. J. Martin, “Polarization sensitivity of optical resonant dipole antennas,” J. Eur. Opt. Soc. 3, 08018 (2008).
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J. S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
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Ge, R. C.

R. C. Ge, J. F. Young, and S. Hughes, “Quasi-normal mode approach to the local-field problem in quantum optics,” Optica 2, 246–249 (2015).

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
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Geisler, P.

J. S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
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Giannini, V.

O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
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J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
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O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
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Gordon, R.

Granet, G.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Gray, S. K.

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
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Guizal, B.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Guo, J.

Guyot-Sionnest, P.

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
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Hanke, T.

T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103, 257404 (2009).
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H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the nonlinear optical response using multifrequency gold-nanowire antennas,” Phys. Rev. Lett. 108, 217403 (2012).
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Hech, B.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hech, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[Crossref]

Hecht, B.

J. S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
[Crossref]

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
[Crossref]

Helfert, S.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Hemmer, P. R.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[Crossref]

Höflich, K.

K. Höflich, M. Becker, G. Leuchs, and S. Christiansen, “Plasmonic dimer antennas for surface enhanced Raman scattering,” Nanotechnology 23, 185303 (2012).
[Crossref]

Hu, Y. H.

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G. B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).
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Hu, Y. S.

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G. B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).
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Huang, J. S.

J. S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
[Crossref]

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
[Crossref]

Hughes, S.

R. C. Ge, J. F. Young, and S. Hughes, “Quasi-normal mode approach to the local-field problem in quantum optics,” Optica 2, 246–249 (2015).

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
[Crossref]

Hugonin, J. P.

C. Sauvan, J. P. Hugonin, R. Carminati, and P. Lalanne, “Modal representation of spatial coherence in dissipative and resonant photonic systems,” Phys. Rev. A 89, 043825 (2014).
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Q. Bai, M. Perrin, C. Sauvan, J. P. Hugonin, and P. Lalanne, “Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure,” Opt. Express 21, 27371–27382 (2013).
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C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
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M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22, 1844–1849 (2005).
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Irudayaraj, J.

R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008).
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F. Jäckel, A. A. Kinkhabwala, and W. E. Moerner, “Gold bowtie nanoantennas for surface-enhanced Raman scattering under controlled electrochemical potential,” Chem. Phys. Lett. 446, 339–343 (2007).
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Janssen, O. T. A.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Jia, H.

F. Yang, H. Liu, H. Jia, and Y. Zhong, “Analytical description of quasi normal mode in resonant plasmonic nano-cavities,” J. Opt. 18, 035003 (2016).

H. Jia, P. Lalanne, and H. Liu, “Comprehensive surface-wave description for the nano-scale energy concentration with resonant dipole antennas,” Plasmonics 11, 1025–1033 (2016).
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H. Jia, H. Liu, and Y. Zhong, “Role of surface plasmon polaritons and other waves in the radiation of resonant optical dipole antennas,” Sci. Rep. 5, 8456 (2015).
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Y. Li, H. Liu, H. Jia, F. Bo, G. Zhang, and J. Xu, “Fully-vectorial modeling of cylindrical microresonators with aperiodic Fourier modal method,” J. Opt. Soc. Am. A 31, 2459–2466 (2014).
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Jiang, S. C.

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G. B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).
[Crossref]

Kamp, M.

J. S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
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Kern, J.

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Z. Liu, E. Li, V. M. Shalaev, and A. V. Kildishev, “Near field enhancement in silver nanoantenna–superlens systems,” Appl. Phys. Lett. 101, 021109 (2012).
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M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
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A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Interaction between plasmonic nanoparticles revisited with transformation optics,” Phys. Rev. Lett. 105, 233901 (2010).
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P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994).
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Z. Liu, E. Li, V. M. Shalaev, and A. V. Kildishev, “Near field enhancement in silver nanoantenna–superlens systems,” Appl. Phys. Lett. 101, 021109 (2012).
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A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Interaction between plasmonic nanoparticles revisited with transformation optics,” Phys. Rev. Lett. 105, 233901 (2010).
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C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
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A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
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M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant-state expansion applied to three-dimensional open optical systems,” Phys. Rev. A 90, 013834 (2014).
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E. A. Muljarov, W. Langbein, and R. Zimmermann, “Brillouin–Wigner perturbation theory in open electromagnetic systems,” Europhys. Lett. 92, 50010 (2010).
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A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
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M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
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A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Interaction between plasmonic nanoparticles revisited with transformation optics,” Phys. Rev. Lett. 105, 233901 (2010).
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S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G. B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).
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M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Perrin, M.

Pohl, D. W.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hech, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
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H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the nonlinear optical response using multifrequency gold-nanowire antennas,” Phys. Rev. Lett. 108, 217403 (2012).
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F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492, 411–414 (2012).
[Crossref]

Rockstuhl, C.

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrichm, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
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L. Douillard, F. Charra, Z. Korczak, R. Bachelot, S. Kostcheev, G. Lerondel, P. M. Adam, and P. Royer, “Short range plasmon resonators probed by photoemission electron microscopy,” Nano Lett. 8, 935–940 (2008).
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O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
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C. Sauvan, J. P. Hugonin, R. Carminati, and P. Lalanne, “Modal representation of spatial coherence in dissipative and resonant photonic systems,” Phys. Rev. A 89, 043825 (2014).
[Crossref]

Q. Bai, M. Perrin, C. Sauvan, J. P. Hugonin, and P. Lalanne, “Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure,” Opt. Express 21, 27371–27382 (2013).
[Crossref]

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[Crossref]

Scheuer, J.

Schmid, T.

W. Zhang, H. Fischer, T. Schmid, R. Zenobi, and O. J. Martin, “Mode-selective surface-enhanced Raman spectroscopy using nanofabricated plasmonic dipole antennas,” J. Phys. Chem. C 113, 14672–14675 (2009).
[Crossref]

Seideman, T.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Shalaev, V. M.

Z. Liu, E. Li, V. M. Shalaev, and A. V. Kildishev, “Near field enhancement in silver nanoantenna–superlens systems,” Appl. Phys. Lett. 101, 021109 (2012).
[Crossref]

R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008).
[Crossref]

Smiet, C. B.

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492, 411–414 (2012).
[Crossref]

Sørensen, A. S.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
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X. Zhang, C. J. Chung, S. Wang, H. Subbaraman, Z. Pan, Q. Zhan, and R. T. Chen, “Integrated broadband bowtie antenna on transparent silica substrate,” IEEE Antennas Wireless Propag. Lett. 15, 1377–1381 (2016).
[Crossref]

Suen, W. M.

E. S. C. Ching, P. T. Leung, A. M. van den Brink, W. M. Suen, S. S. Tong, and K. Young, “Quasinormal-mode expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545–1554 (1998).
[Crossref]

Sukharev, M.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Sun, C.

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G. B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).
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Tam, C. Y.

P. T. Leung, Y. T. Liu, C. Y. Tam, and K. Young, “Numerical solution for quasinormal modes for potentials with exponential tails,” Phys. Lett. A 247, 253–260 (1998).
[Crossref]

Taminiau, T. H.

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett. 11, 1020–1024 (2011).
[Crossref]

Tong, S. S.

E. S. C. Ching, P. T. Leung, A. M. van den Brink, W. M. Suen, S. S. Tong, and K. Young, “Quasinormal-mode expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545–1554 (1998).
[Crossref]

P. T. Leung, S. S. Tong, and K. Young, “Two-component eigenfunction expansion for open systems described by the wave equation II: linear space structure,” J. Phys. A 30, 2153–2162 (1997).
[Crossref]

P. T. Leung, S. S. Tong, and K. Young, “Two-component eigenfunction expansion for open systems described by the wave equation I: completeness of expansion,” J. Phys. A 30, 2139–2151 (1997).
[Crossref]

Träutlein, D.

T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103, 257404 (2009).
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Urbach, H. P.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

van Beijnum, F.

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492, 411–414 (2012).
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M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

van den Brink, A. M.

E. S. C. Ching, P. T. Leung, A. M. van den Brink, W. M. Suen, S. S. Tong, and K. Young, “Quasinormal-mode expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545–1554 (1998).
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F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492, 411–414 (2012).
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van Haver, S.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Van Hulst, N.

L. Novotny and N. Van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[Crossref]

van Hulst, N. F.

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett. 11, 1020–1024 (2011).
[Crossref]

Van Labeke, D.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Vassallo, C.

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

Vogelgesang, R.

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrichm, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
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Volpe, G.

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the nonlinear optical response using multifrequency gold-nanowire antennas,” Phys. Rev. Lett. 108, 217403 (2012).
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Wang, M.

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G. B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).
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Wang, S.

X. Zhang, C. J. Chung, S. Wang, H. Subbaraman, Z. Pan, Q. Zhan, and R. T. Chen, “Integrated broadband bowtie antenna on transparent silica substrate,” IEEE Antennas Wireless Propag. Lett. 15, 1377–1381 (2016).
[Crossref]

Wang, Y. M.

R. Esteban, G. Aguirregabiria, A. G. Borisov, Y. M. Wang, P. Nordlander, G. W. Bryant, and J. Aizpurua, “The morphology of narrow gaps modifies the plasmonic response,” ACS Photon. 2, 295–305 (2015).
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Weinmann, P.

J. S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
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Wiersig, J.

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A 5, 53–60 (2003).
[Crossref]

Wild, B.

T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103, 257404 (2009).
[Crossref]

Wu, M. C.

M. S. Eggleston, K. Messer, L. Zhang, E. Yablonovitch, and M. C. Wu, “Optical antenna enhanced spontaneous emission,” Proc. Natl. Acad. Sci. USA 112, 1704–1709 (2015).
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Xiong, X.

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G. B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).
[Crossref]

Xu, J.

Xu, M.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

Yablonovitch, E.

M. S. Eggleston, K. Messer, L. Zhang, E. Yablonovitch, and M. C. Wu, “Optical antenna enhanced spontaneous emission,” Proc. Natl. Acad. Sci. USA 112, 1704–1709 (2015).
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Yang, F.

F. Yang, H. Liu, H. Jia, and Y. Zhong, “Analytical description of quasi normal mode in resonant plasmonic nano-cavities,” J. Opt. 18, 035003 (2016).

Yang, J.

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
[Crossref]

Yanik, A. A.

A. Artar, A. A. Yanik, and H. Altug, “Directional double Fano resonances in plasmonic hetero-oligomers,” Nano Lett. 11, 3694–3700 (2011).
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Young, J. F.

R. C. Ge, J. F. Young, and S. Hughes, “Quasi-normal mode approach to the local-field problem in quantum optics,” Optica 2, 246–249 (2015).

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
[Crossref]

Young, K.

E. S. C. Ching, P. T. Leung, A. M. van den Brink, W. M. Suen, S. S. Tong, and K. Young, “Quasinormal-mode expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545–1554 (1998).
[Crossref]

P. T. Leung, Y. T. Liu, C. Y. Tam, and K. Young, “Numerical solution for quasinormal modes for potentials with exponential tails,” Phys. Lett. A 247, 253–260 (1998).
[Crossref]

P. T. Leung, S. S. Tong, and K. Young, “Two-component eigenfunction expansion for open systems described by the wave equation I: completeness of expansion,” J. Phys. A 30, 2139–2151 (1997).
[Crossref]

P. T. Leung, S. S. Tong, and K. Young, “Two-component eigenfunction expansion for open systems described by the wave equation II: linear space structure,” J. Phys. A 30, 2153–2162 (1997).
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P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994).
[Crossref]

Yu, C. L.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
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Yu, Z.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
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Yuan, H. K.

R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008).
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Zenobi, R.

W. Zhang, H. Fischer, T. Schmid, R. Zenobi, and O. J. Martin, “Mode-selective surface-enhanced Raman spectroscopy using nanofabricated plasmonic dipole antennas,” J. Phys. Chem. C 113, 14672–14675 (2009).
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Zhan, Q.

X. Zhang, C. J. Chung, S. Wang, H. Subbaraman, Z. Pan, Q. Zhan, and R. T. Chen, “Integrated broadband bowtie antenna on transparent silica substrate,” IEEE Antennas Wireless Propag. Lett. 15, 1377–1381 (2016).
[Crossref]

Zhang, G.

Zhang, L.

M. S. Eggleston, K. Messer, L. Zhang, E. Yablonovitch, and M. C. Wu, “Optical antenna enhanced spontaneous emission,” Proc. Natl. Acad. Sci. USA 112, 1704–1709 (2015).
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Zhang, S.

E. Cubukcu, S. Zhang, Y. S. Park, G. Bartal, and X. Zhang, “Split ring resonator sensors for infrared detection of single molecular monolayers,” Appl. Phys. Lett. 95, 043113 (2009).
[Crossref]

Zhang, W.

W. Zhang, H. Fischer, T. Schmid, R. Zenobi, and O. J. Martin, “Mode-selective surface-enhanced Raman spectroscopy using nanofabricated plasmonic dipole antennas,” J. Phys. Chem. C 113, 14672–14675 (2009).
[Crossref]

Zhang, X.

X. Zhang, C. J. Chung, S. Wang, H. Subbaraman, Z. Pan, Q. Zhan, and R. T. Chen, “Integrated broadband bowtie antenna on transparent silica substrate,” IEEE Antennas Wireless Propag. Lett. 15, 1377–1381 (2016).
[Crossref]

E. Cubukcu, S. Zhang, Y. S. Park, G. Bartal, and X. Zhang, “Split ring resonator sensors for infrared detection of single molecular monolayers,” Appl. Phys. Lett. 95, 043113 (2009).
[Crossref]

Zhong, Y.

F. Yang, H. Liu, H. Jia, and Y. Zhong, “Analytical description of quasi normal mode in resonant plasmonic nano-cavities,” J. Opt. 18, 035003 (2016).

H. Jia, H. Liu, and Y. Zhong, “Role of surface plasmon polaritons and other waves in the radiation of resonant optical dipole antennas,” Sci. Rep. 5, 8456 (2015).
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C. Liu, H. Liu, and Y. Zhong, “Impact of surface plasmon polaritons and other waves on the radiation of a dipole emitter close to a metallic nanowire antenna,” Opt. Express 22, 25539–25549 (2014).
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Zibrov, A. S.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
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Zimmermann, R.

E. A. Muljarov, W. Langbein, and R. Zimmermann, “Brillouin–Wigner perturbation theory in open electromagnetic systems,” Europhys. Lett. 92, 50010 (2010).
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ACS Photon. (1)

R. Esteban, G. Aguirregabiria, A. G. Borisov, Y. M. Wang, P. Nordlander, G. W. Bryant, and J. Aizpurua, “The morphology of narrow gaps modifies the plasmonic response,” ACS Photon. 2, 295–305 (2015).
[Crossref]

Appl. Phys. Lett. (2)

Z. Liu, E. Li, V. M. Shalaev, and A. V. Kildishev, “Near field enhancement in silver nanoantenna–superlens systems,” Appl. Phys. Lett. 101, 021109 (2012).
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E. Cubukcu, S. Zhang, Y. S. Park, G. Bartal, and X. Zhang, “Split ring resonator sensors for infrared detection of single molecular monolayers,” Appl. Phys. Lett. 95, 043113 (2009).
[Crossref]

Chem. Phys. Lett. (1)

F. Jäckel, A. A. Kinkhabwala, and W. E. Moerner, “Gold bowtie nanoantennas for surface-enhanced Raman scattering under controlled electrochemical potential,” Chem. Phys. Lett. 446, 339–343 (2007).
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Europhys. Lett. (1)

E. A. Muljarov, W. Langbein, and R. Zimmermann, “Brillouin–Wigner perturbation theory in open electromagnetic systems,” Europhys. Lett. 92, 50010 (2010).
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IEEE Antennas Wireless Propag. Lett. (1)

X. Zhang, C. J. Chung, S. Wang, H. Subbaraman, Z. Pan, Q. Zhan, and R. T. Chen, “Integrated broadband bowtie antenna on transparent silica substrate,” IEEE Antennas Wireless Propag. Lett. 15, 1377–1381 (2016).
[Crossref]

J. Eur. Opt. Soc. (2)

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. Van Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Eur. Opt. Soc. 2, 07022 (2007).

H. Fischer and O. J. Martin, “Polarization sensitivity of optical resonant dipole antennas,” J. Eur. Opt. Soc. 3, 08018 (2008).
[Crossref]

J. Opt. (1)

F. Yang, H. Liu, H. Jia, and Y. Zhong, “Analytical description of quasi normal mode in resonant plasmonic nano-cavities,” J. Opt. 18, 035003 (2016).

J. Opt. A (1)

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A 5, 53–60 (2003).
[Crossref]

J. Opt. Soc. Am. A (3)

J. Phys. A (2)

P. T. Leung, S. S. Tong, and K. Young, “Two-component eigenfunction expansion for open systems described by the wave equation I: completeness of expansion,” J. Phys. A 30, 2139–2151 (1997).
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P. T. Leung, S. S. Tong, and K. Young, “Two-component eigenfunction expansion for open systems described by the wave equation II: linear space structure,” J. Phys. A 30, 2153–2162 (1997).
[Crossref]

J. Phys. Chem. C (1)

W. Zhang, H. Fischer, T. Schmid, R. Zenobi, and O. J. Martin, “Mode-selective surface-enhanced Raman spectroscopy using nanofabricated plasmonic dipole antennas,” J. Phys. Chem. C 113, 14672–14675 (2009).
[Crossref]

Nano Lett. (7)

O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
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A. Artar, A. A. Yanik, and H. Altug, “Directional double Fano resonances in plasmonic hetero-oligomers,” Nano Lett. 11, 3694–3700 (2011).
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J. S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
[Crossref]

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
[Crossref]

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett. 11, 1020–1024 (2011).
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L. Douillard, F. Charra, Z. Korczak, R. Bachelot, S. Kostcheev, G. Lerondel, P. M. Adam, and P. Royer, “Short range plasmon resonators probed by photoemission electron microscopy,” Nano Lett. 8, 935–940 (2008).
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J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrichm, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
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Nanoscale (1)

M. Agio, “Optical antennas as nanoscale resonators,” Nanoscale 4, 692–706 (2012).
[Crossref]

Nanotechnology (1)

K. Höflich, M. Becker, G. Leuchs, and S. Christiansen, “Plasmonic dimer antennas for surface enhanced Raman scattering,” Nanotechnology 23, 185303 (2012).
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Nat. Commun. (1)

R. Adato and H. Altug, “In-situ ultra-sensitive infrared absorption spectroscopy of biomolecule interactions in real time with plasmonic nanoantennas,” Nat. Commun. 4, 2154 (2013).
[Crossref]

Nat. Photonics (2)

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[Crossref]

L. Novotny and N. Van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[Crossref]

Nature (3)

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

F. van Beijnum, C. Rétif, C. B. Smiet, H. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492, 411–414 (2012).
[Crossref]

New J. Phys. (2)

R. M. Bakker, V. P. Drachev, Z. Liu, H. K. Yuan, R. H. Pedersen, A. Boltasseva, J. J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantenna array-induced fluorescence enhancement and reduced lifetimes,” New J. Phys. 10, 125022 (2008).
[Crossref]

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
[Crossref]

Opt. Express (6)

Optica (1)

Phys. Lett. A (1)

P. T. Leung, Y. T. Liu, C. Y. Tam, and K. Young, “Numerical solution for quasinormal modes for potentials with exponential tails,” Phys. Lett. A 247, 253–260 (1998).
[Crossref]

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 37–38 (1946).
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Phys. Rev. A (4)

M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant state expansion applied to two-dimensional open optical systems,” Phys. Rev. A 87, 043827 (2013).
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C. Sauvan, J. P. Hugonin, R. Carminati, and P. Lalanne, “Modal representation of spatial coherence in dissipative and resonant photonic systems,” Phys. Rev. A 89, 043825 (2014).
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M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant-state expansion applied to three-dimensional open optical systems,” Phys. Rev. A 90, 013834 (2014).
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P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994).
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Phys. Rev. B (1)

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
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Phys. Rev. Lett. (8)

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
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A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Interaction between plasmonic nanoparticles revisited with transformation optics,” Phys. Rev. Lett. 105, 233901 (2010).
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A. Alù and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. 101, 043901 (2008).
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C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
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M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102, 107401 (2009).
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T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, and A. Leitenstorfer, “Efficient nonlinear light emission of single gold optical antennas driven by few-cycle near-infrared pulses,” Phys. Rev. Lett. 103, 257404 (2009).
[Crossref]

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the nonlinear optical response using multifrequency gold-nanowire antennas,” Phys. Rev. Lett. 108, 217403 (2012).
[Crossref]

X. W. Chen, V. Sandoghdar, and M. Agio, “Coherent interaction of light with a metallic structure coupled to a single quantum emitter: from superabsorption to cloaking,” Phys. Rev. Lett. 110, 153605 (2013).
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Phys. Rev. X (1)

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G. B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).
[Crossref]

Plasmonics (1)

H. Jia, P. Lalanne, and H. Liu, “Comprehensive surface-wave description for the nano-scale energy concentration with resonant dipole antennas,” Plasmonics 11, 1025–1033 (2016).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

M. S. Eggleston, K. Messer, L. Zhang, E. Yablonovitch, and M. C. Wu, “Optical antenna enhanced spontaneous emission,” Proc. Natl. Acad. Sci. USA 112, 1704–1709 (2015).
[Crossref]

Rev. Mod. Phys. (1)

E. S. C. Ching, P. T. Leung, A. M. van den Brink, W. M. Suen, S. S. Tong, and K. Young, “Quasinormal-mode expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545–1554 (1998).
[Crossref]

Sci. Rep. (1)

H. Jia, H. Liu, and Y. Zhong, “Role of surface plasmon polaritons and other waves in the radiation of resonant optical dipole antennas,” Sci. Rep. 5, 8456 (2015).
[Crossref]

Science (1)

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hech, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
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Other (4)

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

E. D. Palik, Handbook of Optical Constants of Solids Part II (Academic, 1985).

The calculation is performed with in-house software, H. Liu, DIF CODE for Modeling Light Diffraction in Nanostructures (Nankai University, 2010).

G. B. Arfken, Mathematical Methods for Physicists (Elsevier, 2005).

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Figures (10)

Fig. 1.
Fig. 1. (a) Sketch of the nanogap antenna. The antenna is composed of two gold nanowire arms of length L (with a square cross section of side length D = 40    nm ) separated by a nanogap (gap width w = 30    nm ). a 1 , a 2 , b 1 , and b 2 are the complex amplitude coefficients of SPPs at the complex eigenfrequency of QNMs. (b) and (c) definitions of SPP scattering coefficients ρ , τ , and r and scattered fields Ψ SPP , + G , s and Ψ SPP , + R , s used in the model.
Fig. 2.
Fig. 2. Field distributions of QNMs for antenna arm length L = 0.6    μm . The left and right columns show the results obtained with the full-wave a-FMM and with the SPP model, respectively. (a)–(c) show the bonding QNMs for M = 1 , 2, 3, respectively, where the electric-field amplitude is defined as | E | = | E x | 2 + | E y | 2 + | E z | 2 . (d)–(f) show the antibonding QNMs for N = 1 , 2, 3, respectively.
Fig. 3.
Fig. 3. (a) Definitions of the amplitude coefficients ( c 1 , c 2 , d 1 , and d 2 ) of SPPs excited by an x -polarized electric point source located at the center of the nanogap. (b) Definitions of the SPP excitation coefficient β and scattered field used in the model. (c) Enhancement factor F of radiation plotted as a function of illumination frequency ω / ( 2 π c ) . Results are obtained with the full-wave a-FMM (blue circles) and the SPP model (red solid curve) for antenna length L = 0.6    μm .
Fig. 4.
Fig. 4. (a) Definitions of the amplitude coefficients ( e 1 , e 2 , f 1 , and f 2 ) of SPPs excited by an x -polarized electric point source located near the antenna termination (with a distance of 15 nm). (b) Definitions of the SPP excitation coefficient α and scattered field Ψ Source T used in the model. (c) Enhancement factor F of radiation plotted as a function of illumination frequency ω / ( 2 π c ) . Results are obtained with the full-wave a-FMM (blue circles) and the SPP model (red-solid curve), with antenna length L = 0.6    μm .
Fig. 5.
Fig. 5. SPP field and the residual field on the surface of the antenna arms for different orders of QNMs. (a1) and (a2) correspond to M = 1 and M = 2 orders of bonding QNMs, respectively. (b1) and (b2) correspond to N = 1 and N = 2 orders of antibonding QNMs, respectively. The results are obtained for antenna length L = 0.6    μm .
Fig. 6.
Fig. 6. SPP field and the residual field on the surface of the antenna arms at different resonance peaks of the enhancement factor F of radiation plotted in Figs. 3(c) and 4(c). (a1) and (a2) show the results at resonances corresponding to the M = 1 and M = 2 orders of QNMs for the case that the source is located at the center of the nanogap [see Fig. 3(c)]. (b1), (b2), (c1), and (c2) show the results at the resonances corresponding to M = 1 , 2 and N = 1 , 2 orders of QNMs for the case that the source is located near the antenna termination [see Fig. 4(c)]. The results are obtained for antenna length L = 0.6    μm .
Fig. 7.
Fig. 7. Field distributions of QNMs for antenna length L = 0.2    μm . The left and right columns show the results obtained with the full-wave a-FMM and with the SPP model, respectively. (a) and (b) show the real part of E x component and the amplitude of the electric field ( | E | = | E x | 2 + | E y | 2 + | E z | 2 ) for the M = 1 order QNM. (c) and (d) show the results for the N = 1 order QNM.
Fig. 8.
Fig. 8. Enhancement factor F of radiation plotted as a function of illumination frequency ω / ( 2 π c ) for antenna length L = 0.2    μm . The results are obtained with the full-wave a-FMM (blue circles) and the SPP model (red solid curves). (a) is for the case that the point emitter is located at the gap center [as sketched in Fig. 3(a)]. (b) is for the case that the point emitter is located near the antenna termination [as sketched in Fig. 4(a)].
Fig. 9.
Fig. 9. Calculation of the SPP excitation coefficients β and α with the Lorentzian reciprocity theorem. (a) and (c) Definitions of the SPP excitation coefficients for the point emitter located in the nanogap and near the antenna termination, respectively. (b) and (d) Reciprocal scattering processes of (a) and (c) by sending an incident SPP toward the nanogap and toward the antenna termination, respectively. E SPP , + G , tot ( r 0 ) and E SPP , + R , tot ( r 0 ) in (b) and (d) denote the electric field at the source position r 0 excited by the incident SPP.
Fig. 10.
Fig. 10. (a) Total field Ψ SPP , + G , tot excited by a right-going SPP incident from the left arm of an infinitely long nanowire with a nanogap. (b) Incident right-going SPP field Ψ SPP , + G , inc in the absence of the scatterer of the nanogap. (c) Total field Ψ SPP , + R , tot excited by a right-going SPP at a right-terminated semi-infinitely long nanowire. (d) Incident right-going SPP field Ψ SPP , + R , inc at an infinitely long nanowire. (e)–(h) The same as (a)–(d) but for a left-going incident SPP.

Tables (1)

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Table 1. Complex Eigenfrequencies ω c ( λ c = 2 π c / ω c ) of QNMs

Equations (65)

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Ψ QNM = a 1 u Ψ SPP , L , s + a 2 u Ψ SPP , + R , s + b 1 u Ψ SPP , + G , s + b 2 u Ψ SPP , G , s ,
a 1 = b 1 u ρ + b 2 u τ ,
a 2 = b 1 u τ + b 2 u ρ ,
b 1 = a 1 u r ,
b 2 = a 2 u r ,
u 2 r ( ρ + τ ) = 1 ,
u 2 r ( ρ τ ) = 1 .
Ψ QNM b = Ψ SPP , L , s + Ψ SPP , + R , s + u r Ψ SPP , + G , s + u r Ψ SPP , G , s ,
Ψ QNM a = Ψ SPP , L , s Ψ SPP , + R , s + u r Ψ SPP , + G , s u r Ψ SPP , G , s .
k 0 , c = ln ( | r | | ρ + τ | ) + i [ arg ( r ) + arg ( ρ + τ ) 2 M π ] i 2 n eff L ,
k 0 , c = ln ( | r | | ρ τ | ) + i [ arg ( r ) + arg ( ρ τ ) 2 N π ] i 2 n eff L ,
2 Re ( k 0 , c n eff ) L + arg ( r ) + arg ( ρ + τ ) = 2 M π ,
2 Re ( k 0 , c n eff ) L + arg ( r ) + arg ( ρ τ ) = 2 N π .
c 1 = β + d 1 u ρ + d 2 u τ ,
c 2 = β + d 2 u ρ + d 1 u τ ,
d 1 = c 1 u r ,
d 2 = c 2 u r ,
c 1 = c 2 = β 1 u 2 r ( ρ + τ ) ,
d 1 = d 2 = β u r 1 u 2 r ( ρ + τ ) .
Ψ = Ψ Source G + c 1 u Ψ SPP , L , s + c 2 u Ψ SPP , + R , s + d 1 u Ψ SPP , + G , s + d 2 u Ψ SPP , G , s ,
Ψ ( ω ) = Ψ ( 0 ) + n ω / ω c , n ω ω c , n p n ,
p n = lim ω ω c , n β u ( ω ω c , n ) 1 u 2 r ( ρ + τ ) × ( Ψ SPP , L , s + Ψ SPP , + R , s + u r Ψ SPP , + G , s + u r Ψ SPP , G , s ) ,
lim ω ω c , M β u ( ω ω c , M ) 1 u 2 r ( ρ + τ ) = ( β u ) ω = ω c , M [ 4 π i ω n eff L c ( 1 ω + 1 n eff n eff ω ) 1 r r ω 1 ρ + τ ( ρ + τ ) ω ] ω = ω c , M .
Ψ ( ω ) = M η M ( ω ) Ψ QNM , M b ,
η M ( ω ) = ω / ω c , M ω ω c , M × ( β u ) ω = ω c , M [ 4 π i ω n eff L c ( 1 ω + 1 n eff n eff ω ) 1 r r ω 1 ρ + τ ( ρ + τ ) ω ] ω = ω c , M .
f 1 = e 1 u r ,
f 2 = α + e 2 u r ,
e 1 = f 1 u ρ + f 2 u τ ,
e 2 = f 2 u ρ + f 1 u τ ,
e + = α u ( ρ + τ ) / 2 1 u 2 r ( ρ + τ ) ,
e = α u ( ρ τ ) / 2 1 u 2 r ( ρ τ ) ,
f + = α / 2 1 u 2 r ( ρ + τ ) ,
f = α / 2 1 u 2 r ( ρ τ ) .
Ψ = Ψ Source T + e 1 u Ψ SPP , L , s + e 2 u Ψ SPP , + R , s + f 1 u Ψ SPP , + G , s + f 2 u Ψ SPP , G , s .
Ψ = Ψ Source T + α / ( 2 r ) 1 u 2 r ( ρ + τ ) [ u 2 r ( ρ + τ ) Ψ SPP , L , s + u 2 r ( ρ + τ ) Ψ SPP , + R , s + u r Ψ SPP , + G , s + u r Ψ SPP , G , s ] + α / ( 2 r ) 1 u 2 r ( ρ τ ) [ u 2 r ( ρ τ ) Ψ SPP , L , s u 2 r ( ρ τ ) Ψ SPP , + R , s + u r Ψ SPP , + G , s u r Ψ SPP , G , s ] .
Ψ ( ω ) = M ξ M ( ω ) Ψ QNM , M b + N ζ N ( ω ) Ψ QNM , N a ,
ξ M ( ω ) = ω / ω c , M ω ω c , M × ( α / 2 r ) ω = ω c , M [ 4 π i ω n eff L c ( 1 ω + 1 n eff n eff ω ) 1 r r ω 1 ρ + τ ( ρ + τ ) ω ] ω = ω c , M ,
ζ N ( ω ) = ω / ω c , N ω ω c , N × ( α / 2 r ) ω = ω c , N [ 4 π i ω n eff L c ( 1 ω + 1 n eff n eff ω ) + 1 r r ω + 1 ρ τ ( ρ τ ) ω ] ω = ω c , N .
Ψ SPP = a Ψ SPP , + b Ψ SPP , + ,
η M = ω / ω c , M ω ω c , M i u · E ˜ b ( r 0 ) [ E ˜ b · ( ω ϵ ) ω E ˜ b H ˜ b · ( ω μ ) ω H ˜ b ] ω = ω c , M d 3 r ,
[ E ˜ b · ( ω ϵ ) ω E ˜ b H ˜ b · ( ω μ ) ω H ˜ b ] ω = ω c , M d 3 r = i u · E ˜ b ( r 0 ) ( β u ) ω = ω c , M [ 4 π i ω n eff L c ( 1 ω + 1 n eff n eff ω ) 1 r r ω 1 ρ + τ ( ρ + τ ) ω ] ω = ω c , M ,
V b = [ E ˜ b · ( ω ϵ ) ω E ˜ b H ˜ b · ( ω μ ) ω H ˜ b ] ω = ω c , M d 3 r 2 ϵ 0 [ u · E ˜ b ( r 0 ) ] 2 .
V b = [ 4 π i ω n eff L c ( 1 ω + 1 n eff n eff ω ) 1 r r ω 1 ρ + τ ( ρ + τ ) ω ] ω = ω c , M 2 i ϵ 0 ( β u ) ω = ω c , M [ u · E ˜ b ( r 0 ) ] .
β = u · E SPP , + G , tot ( r 0 ) Ψ SPP , + | Ψ SPP , .
Ψ SPP , + | Ψ SPP , = + + [ E SPP , ( x 0 , y , z ) × H SPP , + ( x 0 , y , z ) E SPP , + ( x 0 , y , z ) × H SPP , ( x 0 , y , z ) ] · x d y d z ,
E ˜ b ( r 0 ) = 2 u r E SPP , + G , tot ( r 0 ) ,
V b = [ 4 π i ω n eff L c ( 1 ω + 1 n eff n eff ω ) 1 r r ω 1 ρ + τ ( ρ + τ ) ω ] ω = ω c , M 2 i ϵ 0 ( α / 2 r ) ω = ω c , M [ u · E ˜ b ( r 0 ) ] .
α = u · E SPP , + R , tot ( r 0 ) Ψ SPP + | Ψ SPP ,
E ˜ b ( r 0 ) = E SPP , + R , tot ( r 0 ) .
V a = [ 4 π i ω n eff L c ( 1 ω + 1 n eff n eff ω ) + 1 r r ω + 1 ρ τ ( ρ τ ) ω ] ω = ω c , M 2 i ϵ 0 ( α / 2 r ) ω = ω c , M [ u · E ˜ a ( r 0 ) ] .
E ˜ a ( r 0 ) = E SPP , + R , tot ( r 0 ) ,
u r Ψ SPP , + G , s = u r ( Ψ SPP , + G , tot Ψ SPP , + G , inc ) ,
Ψ SPP , L , s = Ψ SPP , L , tot Ψ SPP , L , inc = u r Ψ SPP , + G , inc ,
Ψ SPP , L , s + u r Ψ SPP , + G , s = u r Ψ SPP , + G , tot .
Ψ SPP , + R , s + u r Ψ SPP , G , s = u r Ψ SPP , G , tot .
Ψ QNM b = u r ( Ψ SPP , + G , tot + Ψ SPP , G , tot ) ,
Ψ QNM a = u r ( Ψ SPP , + G , tot Ψ SPP , G , tot ) .
Ψ SPP , + R , s = Ψ SPP , + R , tot Ψ SPP , + R , inc ,
Ψ SPP , L , s = Ψ SPP , L , tot Ψ SPP , L , inc = u 2 v r Ψ SPP , + R , inc ,
u r Ψ SPP , + G , s = u r ( Ψ SPP , + G , tot Ψ SPP , + G , inc ) = u r ( u τ u v ) Ψ SPP , + R , inc .
u r Ψ SPP , G , s = u r ( Ψ SPP , G , tot Ψ SPP , G , inc ) = u r ( u ρ Ψ SPP , + R , inc ) ,
Ψ QNM b = Ψ SPP , + R , tot .
Ψ QNM a = Ψ SPP , + R , tot .
Ψ QNM b = Ψ SPP , L , tot ,
Ψ QNM a = Ψ SPP , L , tot .

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