Abstract

We have conducted a theoretical study of harmonic generation from a silver grating having slits filled with GaAs. By working in the enhanced transmission regime, and by exploiting phase-locking between the pump and its harmonics, we guarantee strong field localization and enhanced harmonic generation under conditions of high absorption at visible and UV wavelengths. Silver is treated using the hydrodynamic model, which includes Coulomb and Lorentz forces, convection, electron gas pressure, plus bulk χ(3) contributions. For GaAs we use nonlinear Lorentz oscillators, with characteristic χ(2) and χ(3) and nonlinear sources that arise from symmetry breaking and Lorentz forces. We find that: (i) electron pressure in the metal contributes to linear and nonlinear processes by shifting/reshaping the band structure; (ii) TE- and TM-polarized harmonics can be generated efficiently; (iii) the χ(2) tensor of GaAs couples TE- and TM-polarized harmonics that create phase-locked pump photons having polarization orthogonal compared to incident pump photons; (iv) Fabry-Perot resonances yield more efficient harmonic generation compared to plasmonic transmission peaks, where most of the light propagates along external metal surfaces with little penetration inside its volume. We predict conversion efficiencies that range from 10−6 for second harmonic generation to 10−3 for the third harmonic signal, when pump power is 2GW/cm2.

© 2011 OSA

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    [CrossRef]
  50. J. Olivares, J. Requejo-Isidro, R. del Coso, R. de Nalda, J. Solis, C. N. Afonso, A. L. Stepanov, D. Hole, P. D. Townsend, and A. Naudon, “Large enhancement of the third-order optical susceptibility in Cu-silica composites produced by low-energy high-current ion implantation,” J. Appl. Phys. 90(2), 1064 (2001).
    [CrossRef]
  51. J. M. Ballesteros, R. Serna, J Soli's, C. N Afonso, A. K Petford-Long, D. H Osborne, and R. F Haglund, “Pulsed laser deposition of Cu:Al2O3 nanocrystal thin films with high third-order optical susceptibility,” Appl. Phys. Lett. 71, 2445 (1997).
    [CrossRef]

2010 (3)

D. T. Owens, C. Fuentes-Hernandez, J. M. Hales, J. W. Perry, and B. Kippelen, “A comprehensive analysis of the contributions to the nonlinear optical properties of thin Ag films,” J. Appl. Phys. 107(12), 123114 (2010).
[CrossRef]

E. H. Barakat, M. P. Bernal, and F. I. Baida, “Second harmonic generation enhancement by use of annular aperture arrays embedded into silver and filled by lithium niobate,” Opt. Express 18(7), 6530–6536 (2010).
[CrossRef] [PubMed]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and Third Harmonic Generation in Metal-Based Structures,” Phys. Rev. A 82(4), 043828 (2010).
[CrossRef]

2009 (4)

T. Xu, X. Jiao, and S. Blair, “Third-harmonic generation from arrays of sub-wavelength metal apertures,” Opt. Express 17(26), 23582–23588 (2009).
[CrossRef]

F. Xiang Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[CrossRef]

D. J. Park, S. B. Choi, Y. H. Ahn, F. Rotermund, I. B. Sohn, C. Kang, M. S. Jeong, and D. S. Kim, “Terahertz near-field enhancement in narrow rectangular apertures on metal film,” Opt. Express 17(15), 12493–12501 (2009).
[CrossRef] [PubMed]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[CrossRef]

2008 (5)

M. A. Vincenti, M. De Sario, V. Petruzzelli, A. D’Orazio, F. Prudenzano, D. de Ceglia, N. Akozbek, M. J. Bloemer, P. Ashley, and M. Scalora, “Enhanced transmission and second harmonic generation from subwavelength slits on metal substrates,” Proc. SPIE 6987, 69870O, 69870O-9 (2008).
[CrossRef]

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative Determination of Optical Transmission through Subwavelength Slit Arrays in Ag films: The Essential role of Surface Wave Interference and Local Coupling between Adjacent Slits,” Phys. Rev. B 77(11), 115411 (2008).
[CrossRef]

M. A. Vincenti, V. Petruzzelli, A. D'Orazio, F. Prudenzano, M. J. Bloemer, N. Aközbek, and M. Scalora, “Second harmonic generation from nanoslits in metal substrates: applications to palladium-based H2 sensor,” J. Nanophotonics 2(1), 021851 (2008).
[CrossRef]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections, and negative refraction of phase-locked, second-harmonic pulses,” Metamaterials (Amst.) 2(2-3), 135–144 (2008).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[CrossRef] [PubMed]

2007 (1)

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[CrossRef]

2006 (4)

W. Fan, S. Zhang, K. J. S. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Second harmonic generation from patterned GaAs inside a subwavelength metallic hole array,” Opt. Express 14(21), 9570–9575 (2006).
[CrossRef] [PubMed]

W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second Harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
[CrossRef]

A. Lesuffler, L. K. S Kumar, and R. Gordon, “Enhanced second harmonic generation from Nanoscale double-hole arrays in gold film,” Appl. Phys. Lett. 88(26), 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(14), 146102 (2006).
[CrossRef] [PubMed]

2005 (2)

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(2), S118–S123 (2005).
[CrossRef]

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through a periodic array of slits in a thick metallic film,” Opt. Express 13(12), 4485–4491 (2005).
[CrossRef] [PubMed]

2004 (3)

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, “Enhanced nonlinear optical response of one-dimensional metal-dielectric photonic crystals,” Phys. Rev. Lett. 93(12), 123902 (2004).
[CrossRef] [PubMed]

D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. 96(7), 3626 (2004).
[CrossRef]

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B 79(1), 1–8 (2004).
[CrossRef]

2003 (4)

Y. Liu and S. Blair, “Fluorescence enhancement from an array of subwavelength metal apertures,” Opt. Lett. 28(7), 507–509 (2003).
[CrossRef] [PubMed]

N. Rakov, F. E. Ramos, and M. Xiao, “Strong second-harmonic radiation from a thin silver film with randomly distributed small holes,” J. Phys. Condens. Matter 15(23), L349–L352 (2003).
[CrossRef]

A. Nahata, R. A. Linke, T. Ishi, and K. Ohashi, “Enhanced nonlinear optical conversion from a periodically nanostructured metal film,” Opt. Lett. 28(6), 423–425 (2003).
[CrossRef] [PubMed]

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68(12), 125404 (2003).
[CrossRef]

2002 (2)

Q. Cao and Ph. 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]

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209(1-3), 17–22 (2002).
[CrossRef]

2001 (2)

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(6), 1110–1113 (2001).
[CrossRef] [PubMed]

J. Olivares, J. Requejo-Isidro, R. del Coso, R. de Nalda, J. Solis, C. N. Afonso, A. L. Stepanov, D. Hole, P. D. Townsend, and A. Naudon, “Large enhancement of the third-order optical susceptibility in Cu-silica composites produced by low-energy high-current ion implantation,” J. Appl. Phys. 90(2), 1064 (2001).
[CrossRef]

1999 (2)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[CrossRef]

R. S. Bennink, Y. K. Yoon, R. W. Boyd, and J. E. Sipe, “Accessing the optical nonlinearity of metals with metal- dielectric photonic bandgap structures,” Opt. Lett. 24(20), 1416–1418 (1999).
[CrossRef]

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(6668), 667–669 (1998).
[CrossRef]

1997 (1)

J. M. Ballesteros, R. Serna, J Soli's, C. N Afonso, A. K Petford-Long, D. H Osborne, and R. F Haglund, “Pulsed laser deposition of Cu:Al2O3 nanocrystal thin films with high third-order optical susceptibility,” Appl. Phys. Lett. 71, 2445 (1997).
[CrossRef]

1990 (1)

L. D. Noordam, H. J. Bakker, M. P. de Boer, and H. B. van Linden van den Heuvell, “Second-harmonic generation of femtosecond pulses: observation of phase-mismatch effects,” Opt. Lett. 15(24), 1464 (1990).
[CrossRef] [PubMed]

1988 (1)

N. C. Kothari and X. Carlotti, “Transient second-harmonic generation: influence of effective group-velocity dispersion,” J. Opt. Soc. Am. B 5(4), 756 (1988).
[CrossRef]

1987 (1)

J. T. Manassah and O. R. Cockings, “Induced phase modulation of a generated second-harmonic signal,” Opt. Lett. 12(12), 1005–1007 (1987).
[CrossRef] [PubMed]

1986 (2)

M. Corvi and W. L. Schaich, “Hydrodynamics model calculation of second harmonic generation at a metal surface,” Phys. Rev. B 33(6), 3688–3695 (1986).
[CrossRef]

D. Maystre, M. Neviere, and R. Reinisch, “Nonlinear polarization inside metals: a mathematical study of the free electron model,” Appl. Phys., A Mater. Sci. Process. 39(2), 115–121 (1986).
[CrossRef]

1980 (1)

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[CrossRef]

1976 (1)

A. Eguiluz and J. J. Quinn, “Hydrodynamic model for surface plasmon in metals and degenerate semiconductors,” Phys. Rev. B 14(4), 1347–1361 (1976).
[CrossRef]

1969 (1)

W. Glenn, “Second-harmonic generation by picosecond optical pulses,” IEEE J. Quantum Electron. 5(6), 284–290 (1969).
[CrossRef]

1968 (2)

S. L. Shapiro, “Second harmonic generation in LiNbO3 by picosecond pulses,” Appl. Phys. Lett. 13(1), 19 (1968).
[CrossRef]

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[CrossRef]

1962 (1)

N. Bloembergen and P. S. Pershan, “Light Waves at the Boundary of Nonlinear Media,” Phys. Rev. 128(2), 606–622 (1962).
[CrossRef]

Kumar, L. K. S

A. Lesuffler, L. K. S Kumar, and R. Gordon, “Enhanced second harmonic generation from Nanoscale double-hole arrays in gold film,” Appl. Phys. Lett. 88(26), 261104 (2006).
[CrossRef]

Abdenour, A.

W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second Harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
[CrossRef]

Afonso, C. N

J. M. Ballesteros, R. Serna, J Soli's, C. N Afonso, A. K Petford-Long, D. H Osborne, and R. F Haglund, “Pulsed laser deposition of Cu:Al2O3 nanocrystal thin films with high third-order optical susceptibility,” Appl. Phys. Lett. 71, 2445 (1997).
[CrossRef]

Afonso, C. N.

J. Olivares, J. Requejo-Isidro, R. del Coso, R. de Nalda, J. Solis, C. N. Afonso, A. L. Stepanov, D. Hole, P. D. Townsend, and A. Naudon, “Large enhancement of the third-order optical susceptibility in Cu-silica composites produced by low-energy high-current ion implantation,” J. Appl. Phys. 90(2), 1064 (2001).
[CrossRef]

Ahn, Y. H.

D. J. Park, S. B. Choi, Y. H. Ahn, F. Rotermund, I. B. Sohn, C. Kang, M. S. Jeong, and D. S. Kim, “Terahertz near-field enhancement in narrow rectangular apertures on metal film,” Opt. Express 17(15), 12493–12501 (2009).
[CrossRef] [PubMed]

Ahorinta, R.

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F. Xiang Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[CrossRef]

R. S. Bennink, Y. K. Yoon, R. W. Boyd, and J. E. Sipe, “Accessing the optical nonlinearity of metals with metal- dielectric photonic bandgap structures,” Opt. Lett. 24(20), 1416–1418 (1999).
[CrossRef]

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[CrossRef]

So, V. C. Y.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[CrossRef]

Sohn, I. B.

D. J. Park, S. B. Choi, Y. H. Ahn, F. Rotermund, I. B. Sohn, C. Kang, M. S. Jeong, and D. S. Kim, “Terahertz near-field enhancement in narrow rectangular apertures on metal film,” Opt. Express 17(15), 12493–12501 (2009).
[CrossRef] [PubMed]

Solis, J.

J. Olivares, J. Requejo-Isidro, R. del Coso, R. de Nalda, J. Solis, C. N. Afonso, A. L. Stepanov, D. Hole, P. D. Townsend, and A. Naudon, “Large enhancement of the third-order optical susceptibility in Cu-silica composites produced by low-energy high-current ion implantation,” J. Appl. Phys. 90(2), 1064 (2001).
[CrossRef]

Soli's, J

J. M. Ballesteros, R. Serna, J Soli's, C. N Afonso, A. K Petford-Long, D. H Osborne, and R. F Haglund, “Pulsed laser deposition of Cu:Al2O3 nanocrystal thin films with high third-order optical susceptibility,” Appl. Phys. Lett. 71, 2445 (1997).
[CrossRef]

Stegeman, G. I.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21(10), 4389–4402 (1980).
[CrossRef]

Stepanov, A. L.

J. Olivares, J. Requejo-Isidro, R. del Coso, R. de Nalda, J. Solis, C. N. Afonso, A. L. Stepanov, D. Hole, P. D. Townsend, and A. Naudon, “Large enhancement of the third-order optical susceptibility in Cu-silica composites produced by low-energy high-current ion implantation,” J. Appl. Phys. 90(2), 1064 (2001).
[CrossRef]

Teplin, C. W.

D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. 96(7), 3626 (2004).
[CrossRef]

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(6668), 667–669 (1998).
[CrossRef]

Townsend, P. D.

J. Olivares, J. Requejo-Isidro, R. del Coso, R. de Nalda, J. Solis, C. N. Afonso, A. L. Stepanov, D. Hole, P. D. Townsend, and A. Naudon, “Large enhancement of the third-order optical susceptibility in Cu-silica composites produced by low-energy high-current ion implantation,” J. Appl. Phys. 90(2), 1064 (2001).
[CrossRef]

Trull, J.

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[CrossRef]

Van Labeke, D.

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B 79(1), 1–8 (2004).
[CrossRef]

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209(1-3), 17–22 (2002).
[CrossRef]

van Linden van den Heuvell, H. B.

L. D. Noordam, H. J. Bakker, M. P. de Boer, and H. B. van Linden van den Heuvell, “Second-harmonic generation of femtosecond pulses: observation of phase-mismatch effects,” Opt. Lett. 15(24), 1464 (1990).
[CrossRef] [PubMed]

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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(14), 146102 (2006).
[CrossRef] [PubMed]

Vilaseca, R.

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[CrossRef]

Vincenti, M. A.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and Third Harmonic Generation in Metal-Based Structures,” Phys. Rev. A 82(4), 043828 (2010).
[CrossRef]

M. A. Vincenti, V. Petruzzelli, A. D'Orazio, F. Prudenzano, M. J. Bloemer, N. Aközbek, and M. Scalora, “Second harmonic generation from nanoslits in metal substrates: applications to palladium-based H2 sensor,” J. Nanophotonics 2(1), 021851 (2008).
[CrossRef]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections, and negative refraction of phase-locked, second-harmonic pulses,” Metamaterials (Amst.) 2(2-3), 135–144 (2008).
[CrossRef]

M. A. Vincenti, M. De Sario, V. Petruzzelli, A. D’Orazio, F. Prudenzano, D. de Ceglia, N. Akozbek, M. J. Bloemer, P. Ashley, and M. Scalora, “Enhanced transmission and second harmonic generation from subwavelength slits on metal substrates,” Proc. SPIE 6987, 69870O, 69870O-9 (2008).
[CrossRef]

Weiner, J.

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative Determination of Optical Transmission through Subwavelength Slit Arrays in Ag films: The Essential role of Surface Wave Interference and Local Coupling between Adjacent Slits,” Phys. Rev. B 77(11), 115411 (2008).
[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(6668), 667–669 (1998).
[CrossRef]

Xiang Wang, F.

F. Xiang Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[CrossRef]

Xiao, M.

N. Rakov, F. E. Ramos, and M. Xiao, “Strong second-harmonic radiation from a thin silver film with randomly distributed small holes,” J. Phys. Condens. Matter 15(23), L349–L352 (2003).
[CrossRef]

Xie, Y.

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through a periodic array of slits in a thick metallic film,” Opt. Express 13(12), 4485–4491 (2005).
[CrossRef] [PubMed]

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T. Xu, X. Jiao, and S. Blair, “Third-harmonic generation from arrays of sub-wavelength metal apertures,” Opt. Express 17(26), 23582–23588 (2009).
[CrossRef]

Yoon, Y. K.

R. S. Bennink, Y. K. Yoon, R. W. Boyd, and J. E. Sipe, “Accessing the optical nonlinearity of metals with metal- dielectric photonic bandgap structures,” Opt. Lett. 24(20), 1416–1418 (1999).
[CrossRef]

Zakharian, A. R.

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through a periodic array of slits in a thick metallic film,” Opt. Express 13(12), 4485–4491 (2005).
[CrossRef] [PubMed]

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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(6), 1110–1113 (2001).
[CrossRef] [PubMed]

Zhang, S.

W. Fan, S. Zhang, K. J. S. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Second harmonic generation from patterned GaAs inside a subwavelength metallic hole array,” Opt. Express 14(21), 9570–9575 (2006).
[CrossRef] [PubMed]

W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second Harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
[CrossRef]

Appl. Phys. B (1)

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B 79(1), 1–8 (2004).
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[CrossRef]

J. Olivares, J. Requejo-Isidro, R. del Coso, R. de Nalda, J. Solis, C. N. Afonso, A. L. Stepanov, D. Hole, P. D. Townsend, and A. Naudon, “Large enhancement of the third-order optical susceptibility in Cu-silica composites produced by low-energy high-current ion implantation,” J. Appl. Phys. 90(2), 1064 (2001).
[CrossRef]

J. Nanophotonics (1)

M. A. Vincenti, V. Petruzzelli, A. D'Orazio, F. Prudenzano, M. J. Bloemer, N. Aközbek, and M. Scalora, “Second harmonic generation from nanoslits in metal substrates: applications to palladium-based H2 sensor,” J. Nanophotonics 2(1), 021851 (2008).
[CrossRef]

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N. Rakov, F. E. Ramos, and M. Xiao, “Strong second-harmonic radiation from a thin silver film with randomly distributed small holes,” J. Phys. Condens. Matter 15(23), L349–L352 (2003).
[CrossRef]

Metamaterials (Amst.) (1)

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections, and negative refraction of phase-locked, second-harmonic pulses,” Metamaterials (Amst.) 2(2-3), 135–144 (2008).
[CrossRef]

Nano Lett. (1)

W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second Harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6(5), 1027–1030 (2006).
[CrossRef]

Nature (1)

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[CrossRef]

Opt. Commun. (1)

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209(1-3), 17–22 (2002).
[CrossRef]

Opt. Express (5)

T. Xu, X. Jiao, and S. Blair, “Third-harmonic generation from arrays of sub-wavelength metal apertures,” Opt. Express 17(26), 23582–23588 (2009).
[CrossRef]

D. J. Park, S. B. Choi, Y. H. Ahn, F. Rotermund, I. B. Sohn, C. Kang, M. S. Jeong, and D. S. Kim, “Terahertz near-field enhancement in narrow rectangular apertures on metal film,” Opt. Express 17(15), 12493–12501 (2009).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

W. Fan, S. Zhang, K. J. S. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Second harmonic generation from patterned GaAs inside a subwavelength metallic hole array,” Opt. Express 14(21), 9570–9575 (2006).
[CrossRef] [PubMed]

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through a periodic array of slits in a thick metallic film,” Opt. Express 13(12), 4485–4491 (2005).
[CrossRef] [PubMed]

Opt. Lett. (5)

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Phys. Rev. A (3)

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and Third Harmonic Generation in Metal-Based Structures,” Phys. Rev. A 82(4), 043828 (2010).
[CrossRef]

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V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[CrossRef]

Phys. Rev. B (6)

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative Determination of Optical Transmission through Subwavelength Slit Arrays in Ag films: The Essential role of Surface Wave Interference and Local Coupling between Adjacent Slits,” Phys. Rev. B 77(11), 115411 (2008).
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[CrossRef]

F. Xiang Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
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Supplementary Material (2)

» Media 1: MOV (364 KB)     
» Media 2: MOV (171 KB)     

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Figures (10)

Fig. 1
Fig. 1

(a) Sketch of a single slit of size a filled with GaAs and milled in a silver film of thickness w; (b) Transmission map at λ = 1064nm for a single slit on a silver substrate. We assume the fields are incident normal to the grating.

Fig. 2
Fig. 2

(a) Transmission versus pitch size p at 1064nm for TM (red line–square markers, right axis) and TE (blue line–circle markers, left axis) polarizations. Transmission minima occur when p matches a multiple of the plasmon wavelength; (b) Transmission vs. wavelength when p = 540nm. Inset: plasmonic gap and resonances.

Fig. 3
Fig. 3

TM-polarized (a) SH and (b) TH transmitted (blue line–circle markers), reflected (red line–square markers) conversion efficiencies. SH energies are comparable for p>500nm and p<500nm. However, for p>500nm SH light immediately leaves the grating; for p<500nm the fields linger near the grating and are re-absorbed by the metal.

Fig. 4
Fig. 4

TE-polarized (a) second and (b) third harmonic transmitted (blue line–circle markers), reflected (red line– square markers) total conversion efficiencies. The account of the dynamics that we provided in Figs. 3 for TM-polarized SH fields also applies to the TE-polarized SH signal.

Fig. 5
Fig. 5

TM-polarized SH (a) and TH (b) transmitted and reflected conversion efficiency spectra, normalized with respect to the spectrum of the transmitted pump field. (c) and (d): same as (a) and (b) but for TE-polarized fields. Predicted conversion efficiency of the TM-polarized TH signal is remarkably high.

Fig. 6
Fig. 6

Spectra of the transmitted, TM-polarized pump field (black line – triangle markers), and TE-polarized, transmitted (blue line – circle markers) and reflected (red line – square markers) down-converted pump photons. Conversion efficiencies are relatively small, but are nevertheless similar to those of TE-polarized THG.

Fig. 7
Fig. 7

Pump and harmonic field intensities inside and near the nano-cavities. The magnetic field intensities are depicted for TM-polarization; the transverse electric field is shown for TE-polarization. The pump magnetic field intensity (a) is amplified 250 times; the transverse pump electric field (not shown) is amplified by approximately two orders of magnitude. This combination gives way to TH conversion efficiencies that are unusually large (~10−5). Fields’ dynamics is shown in Media 1.

Fig. 8
Fig. 8

SH (a) and TH (b) conversion efficiencies vs. pulse duration. A diagonal χ(2) tensor boosts SHG by at least three orders of magnitude compared to GaAs thanks to the full exploitation of field localization properties. Allowing a non-zero χ(3) in the metal improves THG well in excess of one order of magnitude compared to GaAs alone.

Fig. 9
Fig. 9

Typical pump (a), SH (b) and TH (c) magnetic field intensities when the peak of a 50fs pulse reaches the grating. One should compare the field with the corresponding harmonics in Fig. 7. While the entire metal surface has a non-zero χ(3), only nonlinear sources on the metal walls inside the cavity matter to the process. Fields’ dynamics is shown in Media 2.

Fig. 10
Fig. 10

Transmission (solid lines) and reflection (dashed lines) vs. wavelength for the GaAs-filled array of Fig. 1, for different values of EF/m*c2 . The incident field spectrum (purple, circled line) is also shown. Shifts due to χ(3) in either GaAs and/or the metal may be of the same order of magnitude and could counteract the shifts depicted in this figure.

Equations (17)

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P ¨ f + γ ˜ P ˙ f = n 0 , f e 2 m f * ( λ 0 c ) 2 E e λ 0 m f * c 2 E ( P f ) + e λ 0 m f * c 2 P ˙ f × H 1 n 0 , f e λ 0 [ ( P ˙ f ) P ˙ f + ( P ˙ f ) P ˙ f ]                                                                       + 5 E F 3 m f * c 2 ( P f ) 10 9 E F / m f * c 2 n 0 f e λ 0 ( P f ) ( P f )
E = ( E x E y E z ) = ( i ( E T E x ω e i ω t + ( E T E x ω ) * e i ω t + E T E x 2 ω e 2 i ω t + ( E T E x 2 ω ) * e 2 i ω t + E T E x 3 ω e 3 i ω t + ( E T E x 3 ω ) * e 3 i ω t ) + j ( E T M y ω e i ω t + ( E T M y ω ) * e i ω t + E T M y 2 ω e 2 i ω t + ( E T M y 2 ω ) * e 2 i ω t + E T M y 3 ω e 3 i ω t + ( E T M y 3 ω ) * e 3 i ω t ) + k ( E T M z ω e i ω t + ( E T M z ω ) * e i ω t + E T M z 2 ω e 2 i ω t + ( E T M z 2 ω ) * e 2 i ω t + E T M z 3 ω e 3 i ω t + ( E T M z 3 ω ) * e 3 i ω t ) )
H = ( H x H y H z ) = ( i ( H T M x ω e i ω t + ( H T M x ω ) * e i ω t + H T M x 2 ω e 2 i ω t + ( H T M x 2 ω ) * e 2 i ω t + H T M x 3 ω e 3 i ω t + ( H T M x 3 ω ) * e 3 i ω t ) + j ( H T E y ω e i ω t + ( H T E y ω ) * e i ω t + H T E y 2 ω e 2 i ω t + ( H T E y 2 ω ) * e 2 i ω t + H T E y 3 ω e 3 i ω t + ( H T E y 3 ω ) * e 3 i ω t ) + k ( H T E z ω e i ω t + ( H T E z ω ) * e i ω t + H T E z 2 ω e 2 i ω t + ( H T E z 2 ω ) * e 2 i ω t + H T E z 3 ω e 3 i ω t + ( H T E z 3 ω ) * e 3 i ω t ) )
P ¨ b , ω + γ ˜ b , ω P ˙ b , ω + ω ˜ 0 , b , ω 2 P b , ω n 0 , b e 2 λ 0 2 m b * c 2 E ω + e λ 0 m b * c 2     ( 1 2 E ω * P b , 2 ω + 2 E 2 ω P b , ω * 2 3 E 2 ω * P b , 3 ω 3 2 E 3 ω P b , 2 ω * ) + e λ 0 m b * c 2 ( ( P ˙ b , ω * + i ω P b , ω * ) × H 2 ω + ( P ˙ b , 2 ω 2 i ω P b , 2 ω ) × H ω * + ( P ˙ b , 2 ω * + 2 i ω P b , 2 ω * ) × H 3 ω + ( P ˙ b , 3 ω 3 i ω P b , 3 ω ) × H 2 ω * )
P ¨ b , 2 ω + γ ˜ b , 2 ω P ˙ b , 2 ω + ω ˜ 0 , b , 2 ω 2 P b , 2 ω n 0 , b e 2 λ 0 2 m b * c 2 E 2 ω + e λ 0 m b * c 2 ( E ω P b , ω 1 3 E ω * P b , 3 ω 3 E 3 ω P b , ω * ) + e λ 0 m b * c 2 ( ( P ˙ b , ω i ω P b , ω ) × H ω + ( P ˙ b , ω * + i ω P b , ω * ) × H 3 ω + ( P ˙ b , 3 ω 3 i ω P b , 3 ω ) × H ω * )
P ¨ b , 3 ω + γ ˜ b , 3 ω P ˙ b , 3 ω + ω ˜ 0 , b , 3 ω 2 P b , 3 ω n 0 , b e 2 λ 0 2 m b * c 2 E 3 ω + e λ 0 m b * c 2 ( 1 2 E ω P b , 2 ω + 2 E 2 ω P b , ω     ) + e λ 0 m b * c 2 ( ( P ˙ b , 2 ω 2 i ω P b , 2 ω ) × H ω + ( P ˙ b , ω i ω P b , ω ) × H 2 ω )
( P N L , x ( 2 ) P N L , y ( 2 ) P N L , z ( 2 ) ) = 2d 14 ( E y E z   E x E z      E x E y )
P N L , x ( 2 ) = 2 d 14 ( ( E T M y 2 ω ( E T M z ω ) * + ( E T M y ω ) *     E T M z 2 ω + E T M y 3 ω ( E T M z 2 ω ) * + ( E T M y 2 ω ) * E T M z 3 ω ) e i ω t + ( E T M y ω E T M z ω + E T M y 3 ω ( E T M z ω ) * + ( E T M y ω ) * E T M z 3 ω ) e 2 i ω t + ( E T M y 2 ω E T M z ω + E T M y ω E T M z 2 ω ) e 3 i ω t )
P N L , y ( 2 ) =2d 14 ( ( E T E x 2 ω ( E T M z ω ) * + ( E T E x ω ) *     E T M z 2 ω + E T E x 3 ω ( E T M z 2 ω ) * + ( E T E x 2 ω ) * E T M z 3 ω ) e i ω t + ( E T E x ω E T M z ω + E T E x 3 ω ( E T M z ω ) * + ( E T E x ω ) * E T M z 3 ω ) e 2 i ω t + ( E T E x 2 ω E T M z ω + E T E x ω E T M z 2 ω ) e 3 i ω t )
P N L , z ( 2 ) = 2d 14 ( ( E T E x 2 ω ( E T M y ω ) * + ( E T E x ω ) *     E T M y 2 ω + E T E x 3 ω ( E T M y 2 ω ) * + ( E T E x 2 ω ) * E T M y 3 ω ) e i ω t + ( E T E x ω E T M y ω + E T E x 3 ω ( E T M y ω ) * + ( E T E x ω ) * E T M y 3 ω ) e 2 i ω t + ( E T E x 2 ω E T M y ω + E T E x ω E T M y 2 ω ) e 3 i ω t )
P N L , i ( 3 ) = j = 1 , 3 k = 1 , 3 l = 1 , 3 χ i , j , k , l E j E k E l
P N L , x ( 3 ) = χ x x x x ( 3 ) E x 3 + 3 χ x x y y ( 3 ) E y 2 E x + 3 χ x x z     z ( 3 ) E z 2 E x P N L , y ( 3 ) = χ y y y y ( 3 ) E y 3 + 3 χ x x y y ( 3 ) E x 2 E y + 3 χ y y z z ( 3 ) E z 2 E y P N L , z ( 3 ) = χ z z z z ( 3 ) E z 3 + 3 χ z z x x ( 3 ) E x 2 E z + 3 χ z z y y ( 3 ) E y 2 E z
P N L , x ( 3 ) = χ A g ( 3 ) ( E x 3 + E y 2 E x + E z 2 E x ) P N L , y ( 3 ) = χ A g ( 3 ) ( E y 3 + E x 2 E y + E z 2 E y ) P N L , z ( 3 ) = χ A g ( 3 ) ( E z 3 + E x 2 E z + E y 2 E z )
( P N L , x ( 2 ) P N L , y ( 2 ) P N L , z ( 2 ) ) = d 11 ( E x 2   E y 2      E z 2 ) .
P ¨ f + γ ˜ P ˙ f = n 0 f e 2 m f * ( λ 0 c ) 2 E ​ ​ ​ ​ ​ ​ ​   + 5 3 E F m f * c 2 ( P f ) .
P f ( ω , k ) = α E ( ω , k ) ​ ​ ​ ​ ​ ​ ​   + β K [ K P f ( ω , k ) ] ,
P f , y = α ( [ ( 1 β ( k y 2 + k z 2 ) + β 2 k y 2 k z 2 ) ] E y + β k y k z [ ( 1 β k y 2 ) E z ] ( 1 β k y 2 ) ( 1 β ( k y 2 + k z 2 ) ) ) P f , z = α [ ( 1 β k y 2 ) E z + β k z k y E y ( 1 β ( k y 2 + k z 2 ) ) ]

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