Abstract

The transmission of ultrashort (7 fs) broadband laser pulses through periodic gold nano-structures is studied. The distribution of the transmitted light intensity over wavelength and angle shows an efficient coupling of the incident p-polarized light to two counter-propagating surface plasmon (SP) modes. As a result of the mode interaction, the avoided crossing patterns exhibit energy and momentum gaps, which depend on the configuration of the nano-structure and the wavelength. Variations of the widths of the SP resonances and an abrupt change of the mode interaction in the vicinity of the avoided crossing region are observed. These features are explained by the model of two coupled modes and a coupling change due to switching from the higher frequency dark mode to the lower frequency bright mode for increasing wavelength of the excitation light.

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  47. A.-L. Fehrembach, S. Hernandez, and A. Sentenac, “k gaps for multimode waveguide gratings,” Phys. Rev. B 73(23), 233405 (2006).
    [CrossRef]

2010

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

2009

J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72(6), 064401 (2009).
[CrossRef]

P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photonics Rev. 3(6), 483–507 (2009).
[CrossRef]

J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80(20), 205417 (2009).
[CrossRef]

2008

Z. Chen, I. R. Hooper, and J. R. Sambles, “Strongly coupled surface plasmons on thin shallow metallic gratings,” Phys. Rev. B 77, 161405 (2008).
[CrossRef]

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77, 115437 (2008).
[CrossRef]

D. Noordegraaf, L. Scolari, J. Laegsgaard, T. Tanggaard Alkeskjold, G. Tartarini, E. Borelli, P. Bassi, J. Li, and S. T. Wu, “Avoided-crossing-based liquid-crystal photonic-bandgap notch filter,” Opt. Lett. 33(9), 986–988 (2008).
[CrossRef] [PubMed]

2007

2006

T. J. Davis, S. C. Mayo, and B. A. Sexton, “Optical absorption by surface plasmons in deep sub-wavelength channels,” Opt. Commun. 267, 253–259 (2006).
[CrossRef]

E. Altewischer, X. Ma, M. P. van Exter, and J. P. Woerdman, “Resonant Bragg scatter of surface plasmons on nanohole arrays,” N. J. Phys. 8(57), 1–14 (2006).
[CrossRef]

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through periodic arrays of sub-wavelength slits in metallic hosts,” Opt. Express 14(14), 6400–6413 (2006).
[CrossRef] [PubMed]

A.-L. Fehrembach, S. Hernandez, and A. Sentenac, “k gaps for multimode waveguide gratings,” Phys. Rev. B 73(23), 233405 (2006).
[CrossRef]

2005

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond light transmission and subradiant damping in plasmonic crystals,” Phys. Rev. Lett. 94(11), 113901 (2005).
[CrossRef] [PubMed]

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95(10), 103902 (2005).
[CrossRef] [PubMed]

P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A, Pure Appl. Opt. 7(8), 422–426 (2005).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

2002

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403 (2002).
[CrossRef] [PubMed]

2001

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
[CrossRef] [PubMed]

1999

D. C. Skigin and R. A. Depine, “Resonant enhancement of the field within a single ground-plane cavity: comparison of different rectangular shapes,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59, 3661–3668 (1999).
[CrossRef]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

1996

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[CrossRef] [PubMed]

H. Lochbihler, “Surface polaritons on metallic wire gratings studied via power losses,” Phys. Rev. B Condens. Matter 53(15), 10289–10295 (1996).
[CrossRef] [PubMed]

1994

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B Condens. Matter 50(7), 4795–4801 (1994).
[CrossRef] [PubMed]

1991

1990

R. J. C. Spreeuw, R. C. Neelen, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, “Mode coupling in a He-Ne ring laser with backscattering,” Phys. Rev. A 42(7), 4315–4324 (1990).
[CrossRef] [PubMed]

1989

P. Halevi and O. Mata-Méndez, “Electromagnetic modes of corrugated thin films and surfaces with a transition layer. II. Minigaps,” Phys. Rev. B Condens. Matter 39(9), 5694–5705 (1989).
[CrossRef] [PubMed]

E. Popov, “Plasmon interactions in metallic gratings: w- and k-minigaps and their connection with poles and zeros,” Surf. Sci. 222, 517–527 (1989).
[CrossRef]

1988

V. Celli, P. Tran, A. A. Maradudin, and D. L. Mills, “k gaps for surface polaritons on gratings,” Phys. Rev. B Condens. Matter 37(15), 9089–9092 (1988).
[CrossRef] [PubMed]

P. Tran, V. Celli, and A. A. Maradudin, “Conditions for the occurrence of k gaps for surface polaritons on gratings,” Opt. Lett. 13(6), 530–532 (1988).
[CrossRef] [PubMed]

1987

D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B Condens. Matter 35(6), 2660–2666 (1987).
[CrossRef] [PubMed]

1985

M. G. Weber and D. L. Mills, “Symmetry and the reflectivity of diffraction gratings at normal incidence,” Phys. Rev. B Condens. Matter 31(4), 2510–2513 (1985).
[CrossRef] [PubMed]

1983

M. Weber and D. L. Mills, “Interaction of electromagnetic waves with periodic gratings: enhanced fields and the reflectivity,” Phys. Rev. B 27, 2698–2709 (1983).
[CrossRef]

1981

N. Kroo, Z. Szentirmay, and J. Felszerfalvi, “Dispersion anomalies of surface plasma oscillations in MOM tunnel structures,” Phys. Lett. 86A, 445–448 (1981).

1976

I. Pockrand, “Resonance anomalies in the light intensity reflected at silver gratings with dielectric coatings,” J. Phys. D 9(17), 2423–2432 (1976).
[CrossRef]

1972

H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

1971

E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

1968

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

1965

B. R. Cooper, H. Ehrenreich, and H. R. Philipp, “Optical properties of noble metals,” Phys. Rev. 138(2A), A494–A507 (1965).
[CrossRef]

1961

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

1941

1902

R. W. Wood, “On the remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–408 (1902).

Alleyne, C. J.

Altewischer, E.

E. Altewischer, X. Ma, M. P. van Exter, and J. P. Woerdman, “Resonant Bragg scatter of surface plasmons on nanohole arrays,” N. J. Phys. 8(57), 1–14 (2006).
[CrossRef]

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[CrossRef] [PubMed]

Bassi, P.

Benahmed, A. J.

Borelli, E.

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
[CrossRef] [PubMed]

Brueck, S. R.

Cao, Q.

Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403 (2002).
[CrossRef] [PubMed]

Celli, V.

P. Tran, V. Celli, and A. A. Maradudin, “Conditions for the occurrence of k gaps for surface polaritons on gratings,” Opt. Lett. 13(6), 530–532 (1988).
[CrossRef] [PubMed]

V. Celli, P. Tran, A. A. Maradudin, and D. L. Mills, “k gaps for surface polaritons on gratings,” Phys. Rev. B Condens. Matter 37(15), 9089–9092 (1988).
[CrossRef] [PubMed]

Cerullo, G.

C. Ropers, T. Elsaesser, G. Cerullo, M. Zavelani-Rossi, and C. Lienau, “Ultrafast optical excitations of metallic nanostructures: from light confinement to a novel electron source,” N. J. Phys. 9(397), 1–32 (2007).
[CrossRef]

Chen, Z.

Z. Chen, I. R. Hooper, and J. R. Sambles, “Strongly coupled surface plasmons on thin shallow metallic gratings,” Phys. Rev. B 77, 161405 (2008).
[CrossRef]

Christ, A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

Cooper, B. R.

B. R. Cooper, H. Ehrenreich, and H. R. Philipp, “Optical properties of noble metals,” Phys. Rev. 138(2A), A494–A507 (1965).
[CrossRef]

Cowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Davis, T. J.

T. J. Davis, S. C. Mayo, and B. A. Sexton, “Optical absorption by surface plasmons in deep sub-wavelength channels,” Opt. Commun. 267, 253–259 (2006).
[CrossRef]

de Dood, M. J. A.

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77, 115437 (2008).
[CrossRef]

Depine, R. A.

D. C. Skigin and R. A. Depine, “Resonant enhancement of the field within a single ground-plane cavity: comparison of different rectangular shapes,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59, 3661–3668 (1999).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Driessen, E. F. C.

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77, 115437 (2008).
[CrossRef]

Ebbesen, T. W.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[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,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Ehrenreich, H.

B. R. Cooper, H. Ehrenreich, and H. R. Philipp, “Optical properties of noble metals,” Phys. Rev. 138(2A), A494–A507 (1965).
[CrossRef]

Eliel, E. R.

R. J. C. Spreeuw, R. C. Neelen, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, “Mode coupling in a He-Ne ring laser with backscattering,” Phys. Rev. A 42(7), 4315–4324 (1990).
[CrossRef] [PubMed]

Elsaesser, T.

C. Ropers, T. Elsaesser, G. Cerullo, M. Zavelani-Rossi, and C. Lienau, “Ultrafast optical excitations of metallic nanostructures: from light confinement to a novel electron source,” N. J. Phys. 9(397), 1–32 (2007).
[CrossRef]

Erland, J.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
[CrossRef] [PubMed]

Fano, U.

Fehrembach, A.-L.

A.-L. Fehrembach, S. Hernandez, and A. Sentenac, “k gaps for multimode waveguide gratings,” Phys. Rev. B 73(23), 233405 (2006).
[CrossRef]

Felszerfalvi, J.

N. Kroo, Z. Szentirmay, and J. Felszerfalvi, “Dispersion anomalies of surface plasma oscillations in MOM tunnel structures,” Phys. Lett. 86A, 445–448 (1981).

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[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,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Giessen, H.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

Gippius, N. A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
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P. Halevi and O. Mata-Méndez, “Electromagnetic modes of corrugated thin films and surfaces with a transition layer. II. Minigaps,” Phys. Rev. B Condens. Matter 39(9), 5694–5705 (1989).
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R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

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D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B Condens. Matter 35(6), 2660–2666 (1987).
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A.-L. Fehrembach, S. Hernandez, and A. Sentenac, “k gaps for multimode waveguide gratings,” Phys. Rev. B 73(23), 233405 (2006).
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Hooper, I. R.

Z. Chen, I. R. Hooper, and J. R. Sambles, “Strongly coupled surface plasmons on thin shallow metallic gratings,” Phys. Rev. B 77, 161405 (2008).
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P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A, Pure Appl. Opt. 7(8), 422–426 (2005).
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S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
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Kim, D. S.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond light transmission and subradiant damping in plasmonic crystals,” Phys. Rev. Lett. 94(11), 113901 (2005).
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Kim, J.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond light transmission and subradiant damping in plasmonic crystals,” Phys. Rev. Lett. 94(11), 113901 (2005).
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Kitson, S. C.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
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D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B Condens. Matter 35(6), 2660–2666 (1987).
[CrossRef] [PubMed]

N. Kroo, Z. Szentirmay, and J. Felszerfalvi, “Dispersion anomalies of surface plasma oscillations in MOM tunnel structures,” Phys. Lett. 86A, 445–448 (1981).

Kuhl, J.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

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F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
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Laegsgaard, J.

Lalanne, P.

P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A, Pure Appl. Opt. 7(8), 422–426 (2005).
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Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403 (2002).
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Lee, J. W.

J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80(20), 205417 (2009).
[CrossRef]

Lee, K. G.

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95(10), 103902 (2005).
[CrossRef] [PubMed]

Leosson, K.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
[CrossRef] [PubMed]

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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Li, J.

Lienau, C.

P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photonics Rev. 3(6), 483–507 (2009).
[CrossRef]

C. Ropers, T. Elsaesser, G. Cerullo, M. Zavelani-Rossi, and C. Lienau, “Ultrafast optical excitations of metallic nanostructures: from light confinement to a novel electron source,” N. J. Phys. 9(397), 1–32 (2007).
[CrossRef]

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond light transmission and subradiant damping in plasmonic crystals,” Phys. Rev. Lett. 94(11), 113901 (2005).
[CrossRef] [PubMed]

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H. Lochbihler, “Surface polaritons on metallic wire gratings studied via power losses,” Phys. Rev. B Condens. Matter 53(15), 10289–10295 (1996).
[CrossRef] [PubMed]

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B Condens. Matter 50(7), 4795–4801 (1994).
[CrossRef] [PubMed]

Ma, X.

E. Altewischer, X. Ma, M. P. van Exter, and J. P. Woerdman, “Resonant Bragg scatter of surface plasmons on nanohole arrays,” N. J. Phys. 8(57), 1–14 (2006).
[CrossRef]

Mansuripur, M.

Maradudin, A. A.

P. Tran, V. Celli, and A. A. Maradudin, “Conditions for the occurrence of k gaps for surface polaritons on gratings,” Opt. Lett. 13(6), 530–532 (1988).
[CrossRef] [PubMed]

V. Celli, P. Tran, A. A. Maradudin, and D. L. Mills, “k gaps for surface polaritons on gratings,” Phys. Rev. B Condens. Matter 37(15), 9089–9092 (1988).
[CrossRef] [PubMed]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

Mata-Méndez, O.

P. Halevi and O. Mata-Méndez, “Electromagnetic modes of corrugated thin films and surfaces with a transition layer. II. Minigaps,” Phys. Rev. B Condens. Matter 39(9), 5694–5705 (1989).
[CrossRef] [PubMed]

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T. J. Davis, S. C. Mayo, and B. A. Sexton, “Optical absorption by surface plasmons in deep sub-wavelength channels,” Opt. Commun. 267, 253–259 (2006).
[CrossRef]

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McPhedran, R. C.

Mills, D. L.

V. Celli, P. Tran, A. A. Maradudin, and D. L. Mills, “k gaps for surface polaritons on gratings,” Phys. Rev. B Condens. Matter 37(15), 9089–9092 (1988).
[CrossRef] [PubMed]

M. G. Weber and D. L. Mills, “Symmetry and the reflectivity of diffraction gratings at normal incidence,” Phys. Rev. B Condens. Matter 31(4), 2510–2513 (1985).
[CrossRef] [PubMed]

M. Weber and D. L. Mills, “Interaction of electromagnetic waves with periodic gratings: enhanced fields and the reflectivity,” Phys. Rev. B 27, 2698–2709 (1983).
[CrossRef]

Mittleman, D. M.

J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80(20), 205417 (2009).
[CrossRef]

Moloney, J. V.

Neelen, R. C.

R. J. C. Spreeuw, R. C. Neelen, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, “Mode coupling in a He-Ne ring laser with backscattering,” Phys. Rev. A 42(7), 4315–4324 (1990).
[CrossRef] [PubMed]

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Noordegraaf, D.

Nordlander, P.

J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80(20), 205417 (2009).
[CrossRef]

Park, D. J.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond light transmission and subradiant damping in plasmonic crystals,” Phys. Rev. Lett. 94(11), 113901 (2005).
[CrossRef] [PubMed]

Park, Q. H.

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95(10), 103902 (2005).
[CrossRef] [PubMed]

Park, T. H.

J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80(20), 205417 (2009).
[CrossRef]

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B. R. Cooper, H. Ehrenreich, and H. R. Philipp, “Optical properties of noble metals,” Phys. Rev. 138(2A), A494–A507 (1965).
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I. Pockrand, “Resonance anomalies in the light intensity reflected at silver gratings with dielectric coatings,” J. Phys. D 9(17), 2423–2432 (1976).
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P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photonics Rev. 3(6), 483–507 (2009).
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W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[CrossRef] [PubMed]

Ritchie, R. H.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

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P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A, Pure Appl. Opt. 7(8), 422–426 (2005).
[CrossRef]

Ropers, C.

P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photonics Rev. 3(6), 483–507 (2009).
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C. Ropers, T. Elsaesser, G. Cerullo, M. Zavelani-Rossi, and C. Lienau, “Ultrafast optical excitations of metallic nanostructures: from light confinement to a novel electron source,” N. J. Phys. 9(397), 1–32 (2007).
[CrossRef]

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond light transmission and subradiant damping in plasmonic crystals,” Phys. Rev. Lett. 94(11), 113901 (2005).
[CrossRef] [PubMed]

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Z. Chen, I. R. Hooper, and J. R. Sambles, “Strongly coupled surface plasmons on thin shallow metallic gratings,” Phys. Rev. B 77, 161405 (2008).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
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D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B Condens. Matter 35(6), 2660–2666 (1987).
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A.-L. Fehrembach, S. Hernandez, and A. Sentenac, “k gaps for multimode waveguide gratings,” Phys. Rev. B 73(23), 233405 (2006).
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T. J. Davis, S. C. Mayo, and B. A. Sexton, “Optical absorption by surface plasmons in deep sub-wavelength channels,” Opt. Commun. 267, 253–259 (2006).
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H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
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D. C. Skigin and R. A. Depine, “Resonant enhancement of the field within a single ground-plane cavity: comparison of different rectangular shapes,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59, 3661–3668 (1999).
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S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
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R. J. C. Spreeuw, R. C. Neelen, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, “Mode coupling in a He-Ne ring laser with backscattering,” Phys. Rev. A 42(7), 4315–4324 (1990).
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C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond light transmission and subradiant damping in plasmonic crystals,” Phys. Rev. Lett. 94(11), 113901 (2005).
[CrossRef] [PubMed]

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C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, “Femtosecond light transmission and subradiant damping in plasmonic crystals,” Phys. Rev. Lett. 94(11), 113901 (2005).
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M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77, 115437 (2008).
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D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B Condens. Matter 35(6), 2660–2666 (1987).
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N. Kroo, Z. Szentirmay, and J. Felszerfalvi, “Dispersion anomalies of surface plasma oscillations in MOM tunnel structures,” Phys. Lett. 86A, 445–448 (1981).

Tanggaard Alkeskjold, T.

Tartarini, G.

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,” Nature 391(6668), 667–669 (1998).
[CrossRef]

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A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[CrossRef] [PubMed]

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V. Celli, P. Tran, A. A. Maradudin, and D. L. Mills, “k gaps for surface polaritons on gratings,” Phys. Rev. B Condens. Matter 37(15), 9089–9092 (1988).
[CrossRef] [PubMed]

P. Tran, V. Celli, and A. A. Maradudin, “Conditions for the occurrence of k gaps for surface polaritons on gratings,” Opt. Lett. 13(6), 530–532 (1988).
[CrossRef] [PubMed]

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R. J. C. Spreeuw, R. C. Neelen, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, “Mode coupling in a He-Ne ring laser with backscattering,” Phys. Rev. A 42(7), 4315–4324 (1990).
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M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77, 115437 (2008).
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E. Altewischer, X. Ma, M. P. van Exter, and J. P. Woerdman, “Resonant Bragg scatter of surface plasmons on nanohole arrays,” N. J. Phys. 8(57), 1–14 (2006).
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P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photonics Rev. 3(6), 483–507 (2009).
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M. Weber and D. L. Mills, “Interaction of electromagnetic waves with periodic gratings: enhanced fields and the reflectivity,” Phys. Rev. B 27, 2698–2709 (1983).
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M. G. Weber and D. L. Mills, “Symmetry and the reflectivity of diffraction gratings at normal incidence,” Phys. Rev. B Condens. Matter 31(4), 2510–2513 (1985).
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E. Altewischer, X. Ma, M. P. van Exter, and J. P. Woerdman, “Resonant Bragg scatter of surface plasmons on nanohole arrays,” N. J. Phys. 8(57), 1–14 (2006).
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R. J. C. Spreeuw, R. C. Neelen, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, “Mode coupling in a He-Ne ring laser with backscattering,” Phys. Rev. A 42(7), 4315–4324 (1990).
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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
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R. W. Wood, “On the remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–408 (1902).

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Xie, Y.

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Zaidi, S. H.

Zakharian, A. R.

Zavelani-Rossi, M.

C. Ropers, T. Elsaesser, G. Cerullo, M. Zavelani-Rossi, and C. Lienau, “Ultrafast optical excitations of metallic nanostructures: from light confinement to a novel electron source,” N. J. Phys. 9(397), 1–32 (2007).
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Appl. Opt.

J. Appl. Phys.

H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
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P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A, Pure Appl. Opt. 7(8), 422–426 (2005).
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J. Opt. Soc. Am. B

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P. Vasa, C. Ropers, R. Pomraenke, and C. Lienau, “Ultra-fast nano-optics,” Laser Photonics Rev. 3(6), 483–507 (2009).
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E. Altewischer, X. Ma, M. P. van Exter, and J. P. Woerdman, “Resonant Bragg scatter of surface plasmons on nanohole arrays,” N. J. Phys. 8(57), 1–14 (2006).
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C. Ropers, T. Elsaesser, G. Cerullo, M. Zavelani-Rossi, and C. Lienau, “Ultrafast optical excitations of metallic nanostructures: from light confinement to a novel electron source,” N. J. Phys. 9(397), 1–32 (2007).
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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
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Opt. Express

Opt. Lett.

Philos. Mag.

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Phys. Lett.

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Phys. Rev. A

R. J. C. Spreeuw, R. C. Neelen, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, “Mode coupling in a He-Ne ring laser with backscattering,” Phys. Rev. A 42(7), 4315–4324 (1990).
[CrossRef] [PubMed]

Phys. Rev. B

Z. Chen, I. R. Hooper, and J. R. Sambles, “Strongly coupled surface plasmons on thin shallow metallic gratings,” Phys. Rev. B 77, 161405 (2008).
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M. Weber and D. L. Mills, “Interaction of electromagnetic waves with periodic gratings: enhanced fields and the reflectivity,” Phys. Rev. B 27, 2698–2709 (1983).
[CrossRef]

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77, 115437 (2008).
[CrossRef]

J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Antibonding plasmon mode coupling of an individual hole in a thin metallic film,” Phys. Rev. B 80(20), 205417 (2009).
[CrossRef]

A.-L. Fehrembach, S. Hernandez, and A. Sentenac, “k gaps for multimode waveguide gratings,” Phys. Rev. B 73(23), 233405 (2006).
[CrossRef]

Phys. Rev. B Condens. Matter

H. Lochbihler, “Surface polaritons on metallic wire gratings studied via power losses,” Phys. Rev. B Condens. Matter 53(15), 10289–10295 (1996).
[CrossRef] [PubMed]

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B Condens. Matter 50(7), 4795–4801 (1994).
[CrossRef] [PubMed]

D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B Condens. Matter 35(6), 2660–2666 (1987).
[CrossRef] [PubMed]

M. G. Weber and D. L. Mills, “Symmetry and the reflectivity of diffraction gratings at normal incidence,” Phys. Rev. B Condens. Matter 31(4), 2510–2513 (1985).
[CrossRef] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[CrossRef] [PubMed]

V. Celli, P. Tran, A. A. Maradudin, and D. L. Mills, “k gaps for surface polaritons on gratings,” Phys. Rev. B Condens. Matter 37(15), 9089–9092 (1988).
[CrossRef] [PubMed]

P. Halevi and O. Mata-Méndez, “Electromagnetic modes of corrugated thin films and surfaces with a transition layer. II. Minigaps,” Phys. Rev. B Condens. Matter 39(9), 5694–5705 (1989).
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Figures (5)

Fig. 1
Fig. 1

Measured samples: (a). Schematic of the sample profile and the geometry of the laser beam incidence (red arrows). The two samples had the following dimensions. Sample 1: d = 705   nm , d 1 = 390   nm , h = 27   nm , h 1 = 35   nm . Sample 2: d = 722   nm , d 1 = 395   nm , h = 50   nm , h 1 = 0 . (b). SEM image of sample 1.

Fig. 2
Fig. 2

Transmitted light intensity for different incidence angles and wavelengths: (a,b) sample 1, (c,d) sample 2. Figures (a, c) show false color density plots with the dark (blue) color corresponding to the reduction of the light transmission due to the SP excitation. Figures (b,d) depict the wavelength dependences of the intensity for a set of angles, showing that while in (b) the minimum at shorter wavelength becomes narrower for smaller angles, in (d) the similar minimum becomes slightly broader; in (b,d) the curves for different wavelengths are equidistantly shifted vertically for better viewing.

Fig. 3
Fig. 3

Dependence of coupling on polarization angleϕwith ϕ = 0 ° corresponding to polarization in the plane of incidence.

Fig. 4
Fig. 4

Angular dependences of the coupling for the lower and higher frequency SP branches for sample 1.

Fig. 5
Fig. 5

Observed and calculated SP modes in the avoided crossing region: (a, d) minima of the transmission from the experiment, (b,e) transmitted intensity vs. angle for a set of wavelengths and (c,f) calculation of the SP modes of n = ± 1 orders taking into account their interaction (Eqs. (3), details in the text). Crosses in (a,d) show the extension of the observed minima loci traceable also in (b,d) into the gap region. Dotted lines in (c,f) show the dispersion dependences of the SP modes without interaction. Transmission dependences in the band-gap regions, indicated by dashed boxes in (a,d) are plotted for different wavelengths with steps of 4 nm in (b) and with steps of 2 nm in (e) for samples 1 and 2, respectively.

Equations (3)

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k sin θ + n k g r = k s p ,
d d z A 1 ( z ) = i K 1 , 2 A 2 ( z ) exp [ i ( k s p ; 2 + 2 k g r k s p ; 1 ) ] , d d z A 2 ( z ) = i K 2 , 1 A 1 ( z ) exp [ i ( k s p ; 2 + 2 k g r k s p ; 1 ) ] ,
k ' s p ; 1 , 2 = ± ( k s p ; 1 + k s p ; 2 + 2 k g r ) / 2 q   for  ω < ω c   and k ' s p ; 1 , 2 = ± ( k s p ; 1 + k s p ; 2 + 2 k g r ) / 2 ± q   for  ω > ω c ,

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