Abstract

Second-harmonic generation (SHG) through a proposed thin gold film with a periodic array of subwavelength nanoholes is numerically investigated. By using a recently developed microscopic classical theory and a full-vectorial three-dimensional finite-difference time-domain method, we demonstrate that the mirror symmetry of nanoholes in one direction restricts the polarization state of second-harmonic emission in the same direction. Numerical results show that the second-order nonlinear susceptibility χ(2)yyy dominates in the process of SHG when the nanoholes possess mirror symmetry in the x-axis direction. It is also found that the surface plasmon resonance can result in the enhancement of SHG from metallic nanoholes.

© 2010 Optical Society of America

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2009 (2)

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79, 235109 (2009).
[CrossRef]

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

2008 (4)

W. L. Schaich, “Second harmonic generation by periodically-structured metal surfaces,” Phys. Rev. B 78, 195416 (2008).
[CrossRef]

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25, 955–960 (2008).
[CrossRef]

N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, and M. Wegener, “Second-harmonic generation from complementary split-ring resonators,” Opt. Lett. 33, 1975–1977 (2008).
[CrossRef] [PubMed]

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

2007 (4)

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Tu-runen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98, 167403 (2007).
[CrossRef] [PubMed]

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007).
[CrossRef] [PubMed]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

2006 (3)

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006).
[CrossRef] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).
[CrossRef] [PubMed]

A. Lesuffleur, L. K. S. Kumar, and R. Gordon, “Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film,” Appl. Phys. Lett. 88, 261104 (2006).
[CrossRef]

2005 (4)

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71, 165407 (2005).
[CrossRef]

O. A. Aktsipetrov, T. V. Murzina, E. M. Kim, R. V. Kapra, A. A. Fedyanin, M. Inoue, A. F. Kravets, S. V. Kuznetsova, M. V. Ivanchenko, and V. G. Lifshits, “Magnetization-induced second- and third-harmonic generation in magnetic thin films and nanoparticles,” J. Opt. Soc. Am. B 22, 138–147 (2005).
[CrossRef]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

M. Airola, Y. Liu, and S. Blair, “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A, Pure Appl. Opt. 7, S118–S123 (2005).
[CrossRef]

2004 (2)

A. V. Zayats and I. I. Smolyaninov, “Near-field second-harmonic generation,” Philos. Trans. R. Soc. London, Ser. A 362, 843–860 (2004).
[CrossRef]

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. Van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

2003 (3)

2001 (1)

L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001).
[CrossRef] [PubMed]

1999 (3)

A. V. Zayats, I. Smolyaninov, and C. C. Davis, “Near-field microscopy of second-harmonic generation,” Proc. SPIE 3732, 81–92 (1999).
[CrossRef]

A. V. Zayats, I. I. Smolyaninov, and C. C. Davis, “Observation of localized plasmonic excitations in thin metal films with near-field second-harmonic microscopy,” Opt. Commun. 169, 93–96 (1999).
[CrossRef]

I. I. Smolyaninov, C. H. Lee, C. C. Davis, and S. Rudin, “Near-field imaging of surface-enhanced second harmonic generation,” J. Microsc. 194, 532–536 (1999).
[CrossRef]

1998 (1)

J. A. Maytorena, W. L. Mochán, and B. S. Mendoza, “Hydrodynamic model for sum and difference frequency generation at metal surfaces,” Phys. Rev. B 57, 2580–2585 (1998).
[CrossRef]

1997 (1)

I. Smolyaninov, A. Zayats, and C. Davis, “Near-field second harmonic generation from a rough metal surface,” Phys. Rev. B 56, 9290–9293 (1997).
[CrossRef]

1987 (1)

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centerosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[CrossRef]

1983 (1)

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhancement of second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

1981 (1)

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhancement of second-harmonic generation,” Phys. Rev. Lett. 46, 145–148 (1981).
[CrossRef]

1965 (2)

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[CrossRef]

S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev. 140, A2020–A2030 (1965).
[CrossRef]

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Adam, P. M.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

Airola, M.

M. Airola, Y. Liu, and S. Blair, “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A, Pure Appl. Opt. 7, S118–S123 (2005).
[CrossRef]

Aktsipetrov, O. A.

Allegrini, M.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

Bachelier, G.

Bachelot, R.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

Bai, B.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007).
[CrossRef] [PubMed]

Bailey, W. A.

Baumann, F.

Benichou, E.

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25, 955–960 (2008).
[CrossRef]

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71, 165407 (2005).
[CrossRef]

Beversluis, M.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef] [PubMed]

Biagioni, P.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

Billot, L.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

Blair, S.

M. Airola, Y. Liu, and S. Blair, “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A, Pure Appl. Opt. 7, S118–S123 (2005).
[CrossRef]

Bouhelier, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef] [PubMed]

Brevet, P. F.

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25, 955–960 (2008).
[CrossRef]

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71, 165407 (2005).
[CrossRef]

Brown, F.

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[CrossRef]

Canfield, B. K.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007).
[CrossRef] [PubMed]

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Tu-runen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98, 167403 (2007).
[CrossRef] [PubMed]

Celebrano, M.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

Cerullo, G.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

Chen, C. K.

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhancement of second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhancement of second-harmonic generation,” Phys. Rev. Lett. 46, 145–148 (1981).
[CrossRef]

Davis, C.

I. Smolyaninov, A. Zayats, and C. Davis, “Near-field second harmonic generation from a rough metal surface,” Phys. Rev. B 56, 9290–9293 (1997).
[CrossRef]

Davis, C. C.

A. V. Zayats, I. Smolyaninov, and C. C. Davis, “Near-field microscopy of second-harmonic generation,” Proc. SPIE 3732, 81–92 (1999).
[CrossRef]

A. V. Zayats, I. I. Smolyaninov, and C. C. Davis, “Observation of localized plasmonic excitations in thin metal films with near-field second-harmonic microscopy,” Opt. Commun. 169, 93–96 (1999).
[CrossRef]

I. I. Smolyaninov, C. H. Lee, C. C. Davis, and S. Rudin, “Near-field imaging of surface-enhanced second harmonic generation,” J. Microsc. 194, 532–536 (1999).
[CrossRef]

de Castro, A. R. B.

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhancement of second-harmonic generation,” Phys. Rev. Lett. 46, 145–148 (1981).
[CrossRef]

de Fornel, F.

L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001).
[CrossRef] [PubMed]

Decker, M.

Dorkenoo, K. D.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

Duò, L.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

Enkrich, C.

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).
[CrossRef] [PubMed]

Enoch, S.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006).
[CrossRef] [PubMed]

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. Van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Fedyanin, A. A.

Feth, N.

Finazzi, M.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

Fort, A.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

García-Meca, C.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

Gindre, D.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

Goodhue, W. D.

Gordon, R.

A. Lesuffleur, L. K. S. Kumar, and R. Gordon, “Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film,” Appl. Phys. Lett. 88, 261104 (2006).
[CrossRef]

Grand, J.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

Grillot, F.

L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001).
[CrossRef] [PubMed]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Harmsen, R. H.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006).
[CrossRef] [PubMed]

Hartschuh, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef] [PubMed]

Heinz, T. F.

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhancement of second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, H.Ponath and G.Stegeman, eds. (Elsevier, 1991).

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Hoyer, W.

Hubert, C.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

Husu, H.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007).
[CrossRef] [PubMed]

Inoue, M.

Ishi, T.

Ivanchenko, M. V.

Jha, S. S.

S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev. 140, A2020–A2030 (1965).
[CrossRef]

Jonin, C.

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25, 955–960 (2008).
[CrossRef]

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71, 165407 (2005).
[CrossRef]

Kapra, R. V.

Karakashian, A. S.

Kauranen, M.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Tu-runen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98, 167403 (2007).
[CrossRef] [PubMed]

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007).
[CrossRef] [PubMed]

Kim, E. M.

Klein, M. W.

Koch, S. W.

Koerkamp, K. J.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. Van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Kravets, A. F.

Kuipers, L.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006).
[CrossRef] [PubMed]

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. Van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Kuittinen, M.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007).
[CrossRef] [PubMed]

Kujala, S.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Tu-runen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98, 167403 (2007).
[CrossRef] [PubMed]

Kumar, L. K. S.

A. Lesuffleur, L. K. S. Kumar, and R. Gordon, “Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film,” Appl. Phys. Lett. 88, 261104 (2006).
[CrossRef]

Kuznetsova, S. V.

Labardi, M.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

Laukkanen, J.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007).
[CrossRef] [PubMed]

Lee, C. H.

I. I. Smolyaninov, C. H. Lee, C. C. Davis, and S. Rudin, “Near-field imaging of surface-enhanced second harmonic generation,” J. Microsc. 194, 532–536 (1999).
[CrossRef]

Lesuffleur, A.

A. Lesuffleur, L. K. S. Kumar, and R. Gordon, “Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film,” Appl. Phys. Lett. 88, 261104 (2006).
[CrossRef]

Lifshits, V. G.

Linden, S.

Linke, R. A.

Liu, J.

Liu, Y.

M. Airola, Y. Liu, and S. Blair, “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A, Pure Appl. Opt. 7, S118–S123 (2005).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

Martí, J.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

Martínez, A.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

Maytorena, J. A.

J. A. Maytorena, W. L. Mochán, and B. S. Mendoza, “Hydrodynamic model for sum and difference frequency generation at metal surfaces,” Phys. Rev. B 57, 2580–2585 (1998).
[CrossRef]

Mendoza, B. S.

J. A. Maytorena, W. L. Mochán, and B. S. Mendoza, “Hydrodynamic model for sum and difference frequency generation at metal surfaces,” Phys. Rev. B 57, 2580–2585 (1998).
[CrossRef]

Mochán, W. L.

J. A. Maytorena, W. L. Mochán, and B. S. Mendoza, “Hydrodynamic model for sum and difference frequency generation at metal surfaces,” Phys. Rev. B 57, 2580–2585 (1998).
[CrossRef]

Moloney, J. V.

Moss, D. J.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centerosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[CrossRef]

Murzina, T. V.

Nahata, A.

Nappa, J.

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71, 165407 (2005).
[CrossRef]

Naweed, A.

Niesler, F. B. P.

Novotny, L.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef] [PubMed]

Ohashi, K.

Ortuño, R.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

Parks, R. E.

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[CrossRef]

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Polli, D.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

Prangsma, J. C.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006).
[CrossRef] [PubMed]

Revillod, G.

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71, 165407 (2005).
[CrossRef]

Ricard, D.

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhancement of second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

Rodríguez-Fortuño, F. J.

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

Royer, P.

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

Rudin, S.

I. I. Smolyaninov, C. H. Lee, C. C. Davis, and S. Rudin, “Near-field imaging of surface-enhanced second harmonic generation,” J. Microsc. 194, 532–536 (1999).
[CrossRef]

Russier-Antoine, I.

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B 25, 955–960 (2008).
[CrossRef]

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71, 165407 (2005).
[CrossRef]

Salomon, L.

L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001).
[CrossRef] [PubMed]

Sandtke, M.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006).
[CrossRef] [PubMed]

Schaich, W. L.

W. L. Schaich, “Second harmonic generation by periodically-structured metal surfaces,” Phys. Rev. B 78, 195416 (2008).
[CrossRef]

Segerink, F. B.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006).
[CrossRef] [PubMed]

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. Van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Shen, Y. R.

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhancement of second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhancement of second-harmonic generation,” Phys. Rev. Lett. 46, 145–148 (1981).
[CrossRef]

Sipe, J. E.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centerosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[CrossRef]

J. E. Sipe and G. I. Stegeman, in Surface Polaritons: Electro-magnetic Waves at Surfaces and Interfaces, V.M.Agranovich and D.L.Mills, eds. (North-Holland, 1982).

Sleeper, A. M.

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[CrossRef]

Smolyaninov, I.

A. V. Zayats, I. Smolyaninov, and C. C. Davis, “Near-field microscopy of second-harmonic generation,” Proc. SPIE 3732, 81–92 (1999).
[CrossRef]

I. Smolyaninov, A. Zayats, and C. Davis, “Near-field second harmonic generation from a rough metal surface,” Phys. Rev. B 56, 9290–9293 (1997).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

A. V. Zayats and I. I. Smolyaninov, “Near-field second-harmonic generation,” Philos. Trans. R. Soc. London, Ser. A 362, 843–860 (2004).
[CrossRef]

I. I. Smolyaninov, C. H. Lee, C. C. Davis, and S. Rudin, “Near-field imaging of surface-enhanced second harmonic generation,” J. Microsc. 194, 532–536 (1999).
[CrossRef]

A. V. Zayats, I. I. Smolyaninov, and C. C. Davis, “Observation of localized plasmonic excitations in thin metal films with near-field second-harmonic microscopy,” Opt. Commun. 169, 93–96 (1999).
[CrossRef]

Stegeman, G. I.

J. E. Sipe and G. I. Stegeman, in Surface Polaritons: Electro-magnetic Waves at Surfaces and Interfaces, V.M.Agranovich and D.L.Mills, eds. (North-Holland, 1982).

Svirko, Y.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Tu-runen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98, 167403 (2007).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Turunen, J.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007).
[CrossRef] [PubMed]

Tu-runen, J.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Tu-runen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98, 167403 (2007).
[CrossRef] [PubMed]

van Driel, H. M.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centerosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[CrossRef]

Van Hulst, N. F.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. Van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

van Nieuwstadt, J. A. H.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006).
[CrossRef] [PubMed]

Wegener, M.

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[CrossRef]

Zavelani-Rossi, M. R.

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

Zayats, A.

I. Smolyaninov, A. Zayats, and C. Davis, “Near-field second harmonic generation from a rough metal surface,” Phys. Rev. B 56, 9290–9293 (1997).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

A. V. Zayats and I. I. Smolyaninov, “Near-field second-harmonic generation,” Philos. Trans. R. Soc. London, Ser. A 362, 843–860 (2004).
[CrossRef]

L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001).
[CrossRef] [PubMed]

A. V. Zayats, I. I. Smolyaninov, and C. C. Davis, “Observation of localized plasmonic excitations in thin metal films with near-field second-harmonic microscopy,” Opt. Commun. 169, 93–96 (1999).
[CrossRef]

A. V. Zayats, I. Smolyaninov, and C. C. Davis, “Near-field microscopy of second-harmonic generation,” Proc. SPIE 3732, 81–92 (1999).
[CrossRef]

Zeng, Y.

Appl. Phys. Lett. (3)

C. Hubert, L. Billot, P. M. Adam, R. Bachelot, P. Royer, J. Grand, D. Gindre, K. D. Dorkenoo, and A. Fort, “Role of surface plasmon in second harmonic generation from gold nanorods,” Appl. Phys. Lett. 90, 181105 (2007).
[CrossRef]

A. Lesuffleur, L. K. S. Kumar, and R. Gordon, “Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film,” Appl. Phys. Lett. 88, 261104 (2006).
[CrossRef]

M. R. Zavelani-Rossi, M. Celebrano, P. Biagioni, D. Polli, M. Finazzi, L. Duò, G. Cerullo, M. Labardi, M. Allegrini, J. Grand, and P. M. Adam, “Near-field second-harmonic generation in single gold nanoparticles,” Appl. Phys. Lett. 92, 093119 (2008).
[CrossRef]

J. Microsc. (1)

I. I. Smolyaninov, C. H. Lee, C. C. Davis, and S. Rudin, “Near-field imaging of surface-enhanced second harmonic generation,” J. Microsc. 194, 532–536 (1999).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

M. Airola, Y. Liu, and S. Blair, “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A, Pure Appl. Opt. 7, S118–S123 (2005).
[CrossRef]

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

Nano Lett. (1)

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007).
[CrossRef] [PubMed]

Nature (1)

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

Opt. Commun. (1)

A. V. Zayats, I. I. Smolyaninov, and C. C. Davis, “Observation of localized plasmonic excitations in thin metal films with near-field second-harmonic microscopy,” Opt. Commun. 169, 93–96 (1999).
[CrossRef]

Opt. Lett. (2)

Philos. Trans. R. Soc. London, Ser. A (1)

A. V. Zayats and I. I. Smolyaninov, “Near-field second-harmonic generation,” Philos. Trans. R. Soc. London, Ser. A 362, 843–860 (2004).
[CrossRef]

Phys. Rep. (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

Phys. Rev. (1)

S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev. 140, A2020–A2030 (1965).
[CrossRef]

Phys. Rev. B (8)

J. A. Maytorena, W. L. Mochán, and B. S. Mendoza, “Hydrodynamic model for sum and difference frequency generation at metal surfaces,” Phys. Rev. B 57, 2580–2585 (1998).
[CrossRef]

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centerosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[CrossRef]

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhancement of second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

I. Smolyaninov, A. Zayats, and C. Davis, “Near-field second harmonic generation from a rough metal surface,” Phys. Rev. B 56, 9290–9293 (1997).
[CrossRef]

W. L. Schaich, “Second harmonic generation by periodically-structured metal surfaces,” Phys. Rev. B 78, 195416 (2008).
[CrossRef]

R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009).
[CrossRef]

J. Nappa, G. Revillod, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Electric dipole origin of the second harmonic generation of small metallic particles,” Phys. Rev. B 71, 165407 (2005).
[CrossRef]

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79, 235109 (2009).
[CrossRef]

Phys. Rev. Lett. (8)

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Tu-runen, “Multipole interference in the second-harmonic optical radiation from gold nanoparticles,” Phys. Rev. Lett. 98, 167403 (2007).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of our gold film with periodical nanoapertures in the x y plane. A single unit cell is drawn in the top right-hand corner. The z-axis direction is perpendicular to the x y plane.

Fig. 2
Fig. 2

Cross section of the computational space in the y z plane in FDTD simulations. Periodic boundary conditions are employed on the four boundaries perpendicular to the gold film. Perfect matched layers are used at the left and right boundaries. The incident field propagates from the left to the right side of gold film with a thickness of h = 320   nm .

Fig. 3
Fig. 3

Transmission spectra with y- and x-polarized incident waves.

Fig. 4
Fig. 4

(a) Normalized spectra of the y-polarized incident pulse with 1067 nm wavelength. (b) The excited y-polarized SH signal and (c) x-polarized SH signal.

Fig. 5
Fig. 5

(a) Normalized spectra of the x-polarized incident pulse with 874 nm wavelength. (b) The excited y-polarized SH signal and (c) x-polarized SH signal.

Fig. 6
Fig. 6

Field ( | E y | 2 ) distributions of the (a) FF and (b) second-order nonlinear fields at a distance of 7.5 nm above the gold film.

Tables (1)

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Table 1 Different Incident FF Polarizations and the Corresponding Excited SH Intensities a

Equations (9)

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B ( 1 ) t = × E ( 1 ) ,
E ( 1 ) t = c 2 × B ( 1 ) 1 ε 0 j ( 1 ) ,
j ( 1 ) t = γ j ( 1 ) + e 2 n 0 m e E ( 1 ) .
B ( 2 ) t = × E ( 2 ) ,
E ( 2 ) t = c 2 × B ( 2 ) 1 ε 0 j ( 2 ) ,
j ( 2 ) t = γ j ( 2 ) + e 2 n 0 m e E ( 2 ) + S ( 2 ) ,
S ( 2 ) = k r k ( j ( 1 ) j ( 1 ) k e n 0 ) e m e [ ε 0 ( E ( 1 ) ) E ( 1 ) + j ( 1 ) × B ( 1 ) ] .
ε ( w ) = 1.0 w p 2 w ( w + i γ ) .
η = | E i ( 2 ) ( 2 w 0 ) / E j ( 1 ) ( w 0 ) | 2 ,

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