Abstract

We provide a modified Fano resonance formula applicable to dissipative two-port resonance systems. Based on a generic coupled-resonator model, the formula embodies loss-related correction terms and fundamental resonance parameters that can be determined by an analytic method or experimentally as opposed to finding phenomenological parameters by fitting to numerical results. The theory applies physically meaningful resonance parameters including resonance frequency, total decay rates, and partial radiation probabilities. For example, it shows that the classic Fano shape parameter q is given directly in terms of the phase difference between the resonant and non-resonant transmission pathways. Our new resonance formula quantitatively expresses the resonance spectra pertaining to modal nanophotonic and surface-plasmonic thin-film structures as verified by comparing with exact numerical models.

© 2013 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2013 (2)

M. Rahmani, B. Luk’yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photon. Rev.7(3), 329–349 (2013).
[CrossRef]

I. Avrusky, R. Gibson, J. Sears, G. Khitrova, H. M. Gibbs, and J. Hendrickson, “Linear systems approach to describing and classifying Fano resonances,” Phys. Rev. B87, 128118 (2013).

2012 (1)

J. W. Yoon, M. J. Jung, S. H. Song, and R. Magnusson, “Analytic theory of the resonance properties of metallic nanoslit arrays,” IEEE J. Quantum Electron.48(7), 852–861 (2012).
[CrossRef]

2011 (4)

B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano5(11), 8999–9008 (2011).
[CrossRef] [PubMed]

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011).
[CrossRef] [PubMed]

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
[CrossRef] [PubMed]

B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011).
[CrossRef]

2010 (4)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonance in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010).
[CrossRef]

R. Esteban, M. Laroche, and J. J. Greffet, “Dielectric gratings for wide-angle, broadband absorption by thin film photovoltaic cells,” Appl. Phys. Lett.97(22), 221111 (2010).
[CrossRef]

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C114(16), 7324–7329 (2010).
[CrossRef]

J. Yoon, K. H. Seol, S. H. Song, and R. Magnusson, “Critical coupling in dissipative surface-plasmon resonators with multiple ports,” Opt. Express18(25), 25702–25711 (2010).
[CrossRef] [PubMed]

2009 (2)

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron.15(5), 1485–1499 (2009).
[CrossRef]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009).
[CrossRef] [PubMed]

2008 (3)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

J. Yoon, S. H. Song, and J.-H. Kim, “Extraction efficiency of highly confined surface plasmon-polaritons to far-field radiation: an upper limit,” Opt. Express16(2), 1269–1279 (2008).
[CrossRef] [PubMed]

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
[CrossRef] [PubMed]

2006 (1)

D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguides,” Appl. Phys. Lett.89(4), 041111 (2006).
[CrossRef]

2004 (1)

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett.92(10), 107401 (2004).
[CrossRef] [PubMed]

2003 (2)

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Nonreciprocal reflection of a subwavelength hole array,” Opt. Lett.28(20), 1906–1908 (2003).
[CrossRef] [PubMed]

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun.225(4-6), 331–336 (2003).
[CrossRef]

2001 (1)

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

1992 (1)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett.61(9), 1022–1024 (1992).
[CrossRef]

1982 (1)

1981 (1)

Altewischer, E.

Amrania, H.

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
[CrossRef] [PubMed]

Avrusky, I.

I. Avrusky, R. Gibson, J. Sears, G. Khitrova, H. M. Gibbs, and J. Hendrickson, “Linear systems approach to describing and classifying Fano resonances,” Phys. Rev. B87, 128118 (2013).

Barnes, W. L.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett.92(10), 107401 (2004).
[CrossRef] [PubMed]

Chandezon, J.

Chang, W. S.

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011).
[CrossRef] [PubMed]

Chang-Hasnain, C. J.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron.15(5), 1485–1499 (2009).
[CrossRef]

Chase, C.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron.15(5), 1485–1499 (2009).
[CrossRef]

Cornet, G.

Devaux, E.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett.92(10), 107401 (2004).
[CrossRef] [PubMed]

Dintinger, J.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett.92(10), 107401 (2004).
[CrossRef] [PubMed]

Dupuis, M.

Ebbesen, T. W.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett.92(10), 107401 (2004).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Esteban, R.

R. Esteban, M. Laroche, and J. J. Greffet, “Dielectric gratings for wide-angle, broadband absorption by thin film photovoltaic cells,” Appl. Phys. Lett.97(22), 221111 (2010).
[CrossRef]

Fan, S.

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C114(16), 7324–7329 (2010).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonance in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010).
[CrossRef]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009).
[CrossRef] [PubMed]

Francescato, Y.

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
[CrossRef] [PubMed]

Gallinet, B.

B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011).
[CrossRef]

B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano5(11), 8999–9008 (2011).
[CrossRef] [PubMed]

Gaylord, T. K.

Genet, C.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun.225(4-6), 331–336 (2003).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Giannini, V.

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
[CrossRef] [PubMed]

Gibbs, H. M.

I. Avrusky, R. Gibson, J. Sears, G. Khitrova, H. M. Gibbs, and J. Hendrickson, “Linear systems approach to describing and classifying Fano resonances,” Phys. Rev. B87, 128118 (2013).

Gibson, R.

I. Avrusky, R. Gibson, J. Sears, G. Khitrova, H. M. Gibbs, and J. Hendrickson, “Linear systems approach to describing and classifying Fano resonances,” Phys. Rev. B87, 128118 (2013).

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009).
[CrossRef] [PubMed]

Gramotnev, D. K.

D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguides,” Appl. Phys. Lett.89(4), 041111 (2006).
[CrossRef]

Greffet, J. J.

R. Esteban, M. Laroche, and J. J. Greffet, “Dielectric gratings for wide-angle, broadband absorption by thin film photovoltaic cells,” Appl. Phys. Lett.97(22), 221111 (2010).
[CrossRef]

Halas, N. J.

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011).
[CrossRef] [PubMed]

Hendrickson, J.

I. Avrusky, R. Gibson, J. Sears, G. Khitrova, H. M. Gibbs, and J. Hendrickson, “Linear systems approach to describing and classifying Fano resonances,” Phys. Rev. B87, 128118 (2013).

Hong, M.

M. Rahmani, B. Luk’yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photon. Rev.7(3), 329–349 (2013).
[CrossRef]

Huang, M. C. Y.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron.15(5), 1485–1499 (2009).
[CrossRef]

Jin, J.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Jung, M. J.

J. W. Yoon, M. J. Jung, S. H. Song, and R. Magnusson, “Analytic theory of the resonance properties of metallic nanoslit arrays,” IEEE J. Quantum Electron.48(7), 852–861 (2012).
[CrossRef]

Karagodsky, V.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron.15(5), 1485–1499 (2009).
[CrossRef]

Kästel, J.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009).
[CrossRef] [PubMed]

Khitrova, G.

I. Avrusky, R. Gibson, J. Sears, G. Khitrova, H. M. Gibbs, and J. Hendrickson, “Linear systems approach to describing and classifying Fano resonances,” Phys. Rev. B87, 128118 (2013).

Kim, J.-H.

Kim, S.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Kim, S.-W.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Kim, Y.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Kim, Y.-J.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonance in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010).
[CrossRef]

Lal, S.

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011).
[CrossRef] [PubMed]

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

Langguth, L.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009).
[CrossRef] [PubMed]

Laroche, M.

R. Esteban, M. Laroche, and J. J. Greffet, “Dielectric gratings for wide-angle, broadband absorption by thin film photovoltaic cells,” Appl. Phys. Lett.97(22), 221111 (2010).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Link, S.

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011).
[CrossRef] [PubMed]

Liu, N.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009).
[CrossRef] [PubMed]

Luk’yanchuk, B.

M. Rahmani, B. Luk’yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photon. Rev.7(3), 329–349 (2013).
[CrossRef]

Magnusson, R.

J. W. Yoon, M. J. Jung, S. H. Song, and R. Magnusson, “Analytic theory of the resonance properties of metallic nanoslit arrays,” IEEE J. Quantum Electron.48(7), 852–861 (2012).
[CrossRef]

J. Yoon, K. H. Seol, S. H. Song, and R. Magnusson, “Critical coupling in dissipative surface-plasmon resonators with multiple ports,” Opt. Express18(25), 25702–25711 (2010).
[CrossRef] [PubMed]

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett.61(9), 1022–1024 (1992).
[CrossRef]

Maier, S. A.

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
[CrossRef] [PubMed]

Martin, O. J. F.

B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011).
[CrossRef]

B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano5(11), 8999–9008 (2011).
[CrossRef] [PubMed]

Maystre, D.

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonance in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010).
[CrossRef]

Mock, J. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

Moewe, M.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron.15(5), 1485–1499 (2009).
[CrossRef]

Moharam, M. G.

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett.92(10), 107401 (2004).
[CrossRef] [PubMed]

Nordlander, P.

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011).
[CrossRef] [PubMed]

Padilla, W. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

Park, I.-Y.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Pesala, B.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron.15(5), 1485–1499 (2009).
[CrossRef]

Pfau, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009).
[CrossRef] [PubMed]

Phillips, C. C.

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
[CrossRef] [PubMed]

Pile, D. F. P.

D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguides,” Appl. Phys. Lett.89(4), 041111 (2006).
[CrossRef]

Pottage, J. M.

Rahmani, M.

M. Rahmani, B. Luk’yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photon. Rev.7(3), 329–349 (2013).
[CrossRef]

Ruan, Z.

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C114(16), 7324–7329 (2010).
[CrossRef]

Russell, P. St. J.

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

Sears, J.

I. Avrusky, R. Gibson, J. Sears, G. Khitrova, H. M. Gibbs, and J. Hendrickson, “Linear systems approach to describing and classifying Fano resonances,” Phys. Rev. B87, 128118 (2013).

Sedgwick, F. G.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron.15(5), 1485–1499 (2009).
[CrossRef]

Seol, K. H.

Silvestre, E.

Smith, D. R.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

Song, S. H.

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

van Exter, M. P.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun.225(4-6), 331–336 (2003).
[CrossRef]

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Nonreciprocal reflection of a subwavelength hole array,” Opt. Lett.28(20), 1906–1908 (2003).
[CrossRef] [PubMed]

Wang, S. S.

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett.61(9), 1022–1024 (1992).
[CrossRef]

Weiss, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009).
[CrossRef] [PubMed]

Woerdman, J. P.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun.225(4-6), 331–336 (2003).
[CrossRef]

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Nonreciprocal reflection of a subwavelength hole array,” Opt. Lett.28(20), 1906–1908 (2003).
[CrossRef] [PubMed]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Yoon, J.

Yoon, J. W.

J. W. Yoon, M. J. Jung, S. H. Song, and R. Magnusson, “Analytic theory of the resonance properties of metallic nanoslit arrays,” IEEE J. Quantum Electron.48(7), 852–861 (2012).
[CrossRef]

Zhou, Y.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron.15(5), 1485–1499 (2009).
[CrossRef]

ACS Nano (1)

B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano5(11), 8999–9008 (2011).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

R. Esteban, M. Laroche, and J. J. Greffet, “Dielectric gratings for wide-angle, broadband absorption by thin film photovoltaic cells,” Appl. Phys. Lett.97(22), 221111 (2010).
[CrossRef]

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett.61(9), 1022–1024 (1992).
[CrossRef]

D. F. P. Pile and D. K. Gramotnev, “Adiabatic and nonadiabatic nanofocusing of plasmons by tapered gap plasmon waveguides,” Appl. Phys. Lett.89(4), 041111 (2006).
[CrossRef]

Chem. Rev. (1)

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

J. W. Yoon, M. J. Jung, S. H. Song, and R. Magnusson, “Analytic theory of the resonance properties of metallic nanoslit arrays,” IEEE J. Quantum Electron.48(7), 852–861 (2012).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-Index-Contrast Grating (HCG) and Its Applications in Optoelectronic Devices,” IEEE J. Sel. Top. Quantum Electron.15(5), 1485–1499 (2009).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Phys. Chem. C (1)

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C114(16), 7324–7329 (2010).
[CrossRef]

Laser Photon. Rev. (1)

M. Rahmani, B. Luk’yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photon. Rev.7(3), 329–349 (2013).
[CrossRef]

Nano Lett. (1)

V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier, “Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach,” Nano Lett.11(7), 2835–2840 (2011).
[CrossRef] [PubMed]

Nat. Mater. (1)

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009).
[CrossRef] [PubMed]

Nature (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Opt. Commun. (1)

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun.225(4-6), 331–336 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (2)

B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011).
[CrossRef]

I. Avrusky, R. Gibson, J. Sears, G. Khitrova, H. M. Gibbs, and J. Hendrickson, “Linear systems approach to describing and classifying Fano resonances,” Phys. Rev. B87, 128118 (2013).

Phys. Rev. Lett. (2)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett.92(10), 107401 (2004).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonance in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010).
[CrossRef]

Other (1)

E. D. Palik, Handbook of Optical Constants of Solids II (Academic, 1998).

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Figures (6)

Fig. 1
Fig. 1

Coupled-resonator model of Fano resonance. Here, η1 and η2 denote the fraction of radiation that the localized mode emits to the reflection and transmission sides, respectively. Symbols rD and tD denote the non-resonant reflection and transmission amplitudes, respectively. ηabs represents the absorption probability associated with the localized mode.

Fig. 2
Fig. 2

Dependence of (a) the transmittance T(δ) and (b) the Lorentzian correction term βηradηabs/(1 + δ2) on the absorption probability ηabs. (c) The coupling-symmetry factor β versus normalized difference in ηn.

Fig. 3
Fig. 3

(a) Zero-order transmittance (blue solid curve) and reflectance (red dotted curve) of a thin-film Si grating under surface-normal incidence of TE-polarized light. The thin-film Si grating has thickness 220 nm, grating depth 20 nm, period 450 nm, and fill factor 0.7. The cover medium is air, and the substrate is SiO2. The inset shows electric field distribution of a resonant mode at 0.912 μm.

Fig. 4
Fig. 4

Comparison of transmission and reflection spectra calculated by the RCWA (symbols) and our analytic theory (solid curves) for a GMR device. (a) Transmittance. (b) Reflectance under cover-side (air) incidence. (c) Reflectance under substrate-side (SiO2) incidence.

Fig. 5
Fig. 5

Zero-order transmittance spectrum calculated by the C-method for absorption factor fabs = 0. The inset shows the magnetic field distribution associated with the resonance at 1.124 μm.

Fig. 6
Fig. 6

Comparison of transmission and reflection spectra found with numerical C-method calculations (symbols) with our analytic theory (solid curves) for an SP resonance. (a) Transmittance. (b) Reflectance under cover-side (air) incidence. (c) Reflectance under substrate-side (SiO2) incidence.

Tables (2)

Tables Icon

Table 1 Resonance Parameters for the TE1 Mode at 0.912 μm

Tables Icon

Table 2 Resonance Parameters for the SP Mode at 1.124 μm

Equations (7)

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

T Fano (δ)=| t D | 2 (q+δ) 2 1+ δ 2 ,
T(δ)=| t D | 2 + 4 η 1 η 2 1+ δ 2 + 4| t D | η 1 η 2 ( δsinΔ+cosΔ ) 1+ δ 2 interference ,
Δ=p cos 1 (| t D |/ β 1/2 ),
q= tanΔ.
T(δ)= η rad T Fano (δ)β η rad η abs 1+ δ 2 + η abs | t D | 2 ,
R(δ)=1T(δ) 4 η 1 η abs 1+ δ 2 ,
F(δ)=a (q+δ) 2 +b 1+ δ 2 .

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