Abstract

The roles of surface plasmon resonance and localized resonances in second-harmonic generation are investigated in a noncentrosymmetrical metallic film with a periodic subwavelength nanohole array. By using a recently developed microscopic classical theory and a three-dimensional finite-difference time-domain algorithm, numerical results show that the second-harmonic intensity is a function of the polarization and wavelength of incident waves. A peak of the second-harmonic intensity is achieved when the incident wave is along the direction perpendicular to the x-axis of nanoholes, which corresponds to the maximal extraordinary optical transmission. Meanwhile, the second harmonic is found to correlate with the group delay of incident waves.

© 2010 Optical Society of America

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2009 (2)

Y. Zeng, W. Hoyer, J. 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]

Y. Zeng and J. V. Moloney, “Volume electric dipole origin of second-harmonic generation from metallic membrane with non-centrosymmetry patterns,” Opt. Lett.  34, 2844–2846(2009).
[CrossRef] [PubMed]

2008 (3)

2007 (4)

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]

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B  75, 245421 (2007).
[CrossRef]

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “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 non-centrosymmetric nanodimers,” Nano Lett.  7, 1251–1255 (2007).
[CrossRef] [PubMed]

2006 (4)

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

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett.  96, 233901 (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]

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]

2005 (6)

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express  13, 1933–1938 (2005).
[CrossRef] [PubMed]

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanism of light transmission through metallic films,” Phys. Rev. Lett.  95, 067403 (2005).
[CrossRef]

E. Popov, M. Nevière, A. L. Fehrembach, and N. Bonod, “Enhanced transmission of light through a circularly structured aperture,” Appl. Opt.  44, 6898–6904 (2005).
[CrossRef] [PubMed]

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

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B  72, 045421 (2005).
[CrossRef]

2004 (1)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science  305, 847–848 (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]

1998 (1)

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

1944 (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev.  66, 163–182 (1944).
[CrossRef]

Adam, P. M.

M. R. Zavelani, 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 subwavelength metal apertures,” J. Opt. A: Pure Appl. Opt.  7, S118–S123 (2005).
[CrossRef]

Allegrini, M.

M. R. Zavelani, 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]

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 non-centrosymmetric nanodimers,” Nano Lett.  7, 1251–1255 (2007).
[CrossRef] [PubMed]

Baida, F. I.

Benichou, E.

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]

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev.  66, 163–182 (1944).
[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, 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 subwavelength metal apertures,” J. Opt. A: Pure Appl. Opt.  7, S118–S123 (2005).
[CrossRef]

Blanco, L. A.

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanism of light transmission through metallic films,” Phys. Rev. Lett.  95, 067403 (2005).
[CrossRef]

Bonod, N.

Borisov, A. G.

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanism of light transmission through metallic films,” Phys. Rev. Lett.  95, 067403 (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.

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]

Brolo, A. G.

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 non-centrosymmetric nanodimers,” Nano Lett.  7, 1251–1255 (2007).
[CrossRef] [PubMed]

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

Celebrano, M.

M. R. Zavelani, 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, 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]

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, 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.

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

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. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B  72, 045421 (2005).
[CrossRef]

Fehrembach, A. L.

Feth, N.

Finazzi, M.

M. R. Zavelani, 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]

Garcia de Abajo, F. J.

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanism of light transmission through metallic films,” Phys. Rev. Lett.  95, 067403 (2005).
[CrossRef]

Garcia-Vidal, F. J.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science  305, 847–848 (2004).
[CrossRef] [PubMed]

Ghaemi, H. F.

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

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]

Gomez-Santos, G.

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanism of light transmission through metallic films,” Phys. Rev. Lett.  95, 067403 (2005).
[CrossRef]

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]

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express  13, 1933–1938 (2005).
[CrossRef] [PubMed]

Grand, J.

M. R. Zavelani, 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]

Guizal, B.

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]

Hoyer, W.

Huang, C. P.

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B  75, 245421 (2007).
[CrossRef]

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 non-centrosymmetric nanodimers,” Nano Lett.  7, 1251–1255 (2007).
[CrossRef] [PubMed]

Ishi, T.

Jonin, C.

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]

Kauranen, 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 non-centrosymmetric nanodimers,” Nano Lett.  7, 1251–1255 (2007).
[CrossRef] [PubMed]

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

Klein, M. W.

Koch, S. W.

Koerkamp, K. J.

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B  72, 045421 (2005).
[CrossRef]

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. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B  72, 045421 (2005).
[CrossRef]

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 non-centrosymmetric nanodimers,” Nano Lett.  7, 1251–1255 (2007).
[CrossRef] [PubMed]

Kujala, S.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “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]

Labardi, M.

M. R. Zavelani, 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]

Labeke, D. V.

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 non-centrosymmetric nanodimers,” Nano Lett.  7, 1251–1255 (2007).
[CrossRef] [PubMed]

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]

Lezec, H. J.

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

Linden, S.

Linke, R. A.

Liu, J.

Liu, J. J.

Y. Zeng, W. Hoyer, J. 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]

Liu, Y.

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

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science  305, 847–848 (2004).
[CrossRef] [PubMed]

Moloney, J. 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]

Nevière, M.

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.

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science  305, 847–848 (2004).
[CrossRef] [PubMed]

Polli, D.

M. R. Zavelani, 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]

Popov, E.

Prangsma, J.

J. Prangsma, “Local and dynamic properties of light interacting with subwavelength holes” (Ipskamp, 2009), http://www-old.amolf.nl/publications/theses/prangsma/chap3.pdf.

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]

Qiu, M.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett.  96, 233901 (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]

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]

Ruan, Z.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett.  96, 233901 (2006).
[CrossRef] [PubMed]

Russier-Antoine, I.

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]

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. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B  72, 045421 (2005).
[CrossRef]

Shabanov, S. V.

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanism of light transmission through metallic films,” Phys. Rev. Lett.  95, 067403 (2005).
[CrossRef]

Svirko, Y.

S. Kujala, B. K. Canfield, M. Kauranen, Y. Svirko, and J. Turunen, “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).

Thio, T.

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

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 non-centrosymmetric nanodimers,” Nano Lett.  7, 1251–1255 (2007).
[CrossRef] [PubMed]

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

van der Molen, K. L.

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B  72, 045421 (2005).
[CrossRef]

van Hulst, N. F.

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B  72, 045421 (2005).
[CrossRef]

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]

Wang, Q. J.

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B  75, 245421 (2007).
[CrossRef]

Wegener, M.

Wokaun, A.

A. Wokaun, “Surface-enhanced electromagnetic processes,” in Solid State Physics, H.Ehrenreich, T.Thurnbull, and F.Seitz, eds. (Academic, 1984), Vol.  38, p. 223.
[CrossRef]

Wolff, P. A.

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

Zavelani, M. R.

M. R. Zavelani, 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. V.

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]

Zeng, Y.

Zhu, Y. Y.

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B  75, 245421 (2007).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

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]

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]

M. R. Zavelani, 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. Opt. A: Pure Appl. Opt. (1)

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

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 non-centrosymmetric nanodimers,” Nano Lett.  7, 1251–1255 (2007).
[CrossRef] [PubMed]

Nature (1)

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

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev.  66, 163–182 (1944).
[CrossRef]

Phys. Rev. B (4)

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B  75, 245421 (2007).
[CrossRef]

Y. Zeng, W. Hoyer, J. 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]

K. L. van der Molen, K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B  72, 045421 (2005).
[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]

Phys. Rev. Lett. (6)

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett.  96, 233901 (2006).
[CrossRef] [PubMed]

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

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]

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]

F. J. Garcia de Abajo, G. Gomez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, “Tunneling mechanism of light transmission through metallic films,” Phys. Rev. Lett.  95, 067403 (2005).
[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]

Science (2)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science  305, 847–848 (2004).
[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]

Other (3)

J. Prangsma, “Local and dynamic properties of light interacting with subwavelength holes” (Ipskamp, 2009), http://www-old.amolf.nl/publications/theses/prangsma/chap3.pdf.

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

A. Wokaun, “Surface-enhanced electromagnetic processes,” in Solid State Physics, H.Ehrenreich, T.Thurnbull, and F.Seitz, eds. (Academic, 1984), Vol.  38, p. 223.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) Structure in the x y plane of a unit cell of the periodic hole array with thickness h = 320 nm . (b) Cross section of the computational domain consisting of a single unit cell, where d = 750 nm . The detector plane is set to collect the fundamental light and second-harmonic signal. The color zone represents the gold.

Fig. 2
Fig. 2

Intensity of the SHG signal versus the intensity of the fundamental light. The incident wavelength is equal to 1300 nm , and the incident polarization is along the y-axis.

Fig. 3
Fig. 3

Second-harmonic emission from the metallic arrays at different incident polarization angles.

Fig. 4
Fig. 4

Transmission of the periodic hole array. θ represents the included angle between the electric polarization and the x-axis.

Fig. 5
Fig. 5

SHG efficiency for different incident wavelengths on the detector plane.

Fig. 6
Fig. 6

Group delay of the input pulse versus wavelength, which corresponds to the SHG efficiency for different wavelengths in Fig. 5.

Fig. 7
Fig. 7

Intensity distributions of the components E y and E z for an incident plane wave of 900 nm wavelength. The distribution in the x y plane is located at a distance of 7.5 nm above the gold film. a represents the size of the spatial cell and is equal to 7.5 nm . The distribution in the y z plane is calculated at the center points of the spatial cell, which corresponds to Fig. 1b.

Equations (9)

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

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 ) ] .
T ( w ) = F [ E out ( t ) ] / F [ E int ( t ) ] ,
τ g = d arg [ T ( w ) ] / d w ,

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