Abstract

We present a theoretical study on second harmonic generation from metallo-dielectric multilayered structures in the plasmonic regime. In particular we analyze the behavior of structures made of Ag (silver) and MgF2 (magnesium-fluoride) due to the straightforward procedure to grow these materials with standard sputtering or thermal evaporation techniques. A systematic study is performed which analyzes four different kinds of elementary cells- namely (Ag/MgF2)N, (MgF2/Ag)N, (Ag/MgF2/Ag)N and (MgF2/Ag/MgF2)N-as function of the number of periods (N) and the thickness of the layers. We predict the conversion efficiency to be up to three orders of magnitude greater than the conversion efficiency found in the non-plasmonic regime and we point out the best geometries to achieve these conversion efficiencies. We also underline the role played by the short-range/long-range plasmons and leaky waves in the generation process. We perform a statistical study to demonstrate the robustness of the SH process in the plasmonic regime against the inevitable variations in the thickness of the layers. Finally, we show that a proper choice of the output medium can further improve the conversion efficiency reaching an enhancement of almost five orders of magnitude with respect to the non plasmonic regime.

© 2010 OSA

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    [CrossRef] [PubMed]
  28. G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19(9), 2111 (2002).
    [CrossRef]
  29. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
    [CrossRef] [PubMed]

2010 (2)

N. Mattiucci, G. D’Aguanno, N. Akozbek, M. Scalora, and M. J. Bloemer, “Homogenization procedure for a metamaterial and local violation of the second principle of thermodynamics,” Opt. Commun. 283(8), 1613–1620 (2010).
[CrossRef]

G. D’Aguanno, M. C. Larciprete, N. Mattiucci, A. Belardini, M. J. Bloemer, E. Fazio, O. Buganov, M. Centini, and C. Sibilia, “Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems,” Phys. Rev. A 81(1), 013834 (2010).
[CrossRef]

2009 (1)

2006 (1)

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97(7), 073905 (2006).
[CrossRef] [PubMed]

2005 (2)

R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun. 248(1-3), 249–256 (2005).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, “Second-harmonic generation from a positive-negative index material heterostructure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066612 (2005).
[CrossRef]

2004 (1)

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: a comprehensive analysis,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016612 (2004).
[CrossRef] [PubMed]

2002 (1)

2000 (1)

T. A. Leskova, M. Leyva-Lucero, E. R. Mendez, A. A. Maradudin, and I. V. Novikov, “The surface enhanced second harmonic generation of light from a randomly rough metal surface in the Kretschmann geometry,” Opt. Commun. 183(5-6), 529–545 (2000).
[CrossRef]

1999 (1)

1996 (1)

1986 (2)

S. Ciraci and I. P. Batra, “Theory of the quantum size effect in simple metals,” Phys. Rev. B Condens. Matter 33(6), 4294–4297 (1986).
[CrossRef] [PubMed]

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[CrossRef] [PubMed]

1985 (1)

J. C. Quail and H. J. Simon, “Second-harmonic generation from silver and aluminum films in total internal reflection,” Phys. Rev. B Condens. Matter 31(8), 4900–4905 (1985).
[CrossRef] [PubMed]

1984 (1)

J. G. Rako, J. C. Quail, and H. J. Simon, “Optical second-harmonic generation with surface plasmons in noncentrosymmetric crystals,” Phys. Rev. B 30(10), 5552–5559 (1984).
[CrossRef]

1981 (2)

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981).
[CrossRef]

G. M. Wysin, H. J. Simon, and R. T. Deck, “Optical bistability with surface plasmons,” Opt. Lett. 6(1), 30–32 (1981).
[CrossRef] [PubMed]

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]

1979 (1)

1978 (1)

M. Fukui, J. E. Sipe, V. C. Y. So, and G. I. Stegeman, “Nonlinear mixing of opposite traveling surface plasmons,” Solid State Commun. 27(12), 1265–1267 (1978).
[CrossRef]

1974 (1)

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[CrossRef]

1971 (1)

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241(4), 313–324 (1971).
[CrossRef]

1968 (1)

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[CrossRef]

1965 (1)

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear Optical Reflection from a Metallic Boundary,” Phys. Rev. Lett. 14(25), 1029–1031 (1965).
[CrossRef]

Akozbek, N.

N. Mattiucci, G. D’Aguanno, N. Akozbek, M. Scalora, and M. J. Bloemer, “Homogenization procedure for a metamaterial and local violation of the second principle of thermodynamics,” Opt. Commun. 283(8), 1613–1620 (2010).
[CrossRef]

Batra, I. P.

S. Ciraci and I. P. Batra, “Theory of the quantum size effect in simple metals,” Phys. Rev. B Condens. Matter 33(6), 4294–4297 (1986).
[CrossRef] [PubMed]

Belardini, A.

G. D’Aguanno, M. C. Larciprete, N. Mattiucci, A. Belardini, M. J. Bloemer, E. Fazio, O. Buganov, M. Centini, and C. Sibilia, “Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems,” Phys. Rev. A 81(1), 013834 (2010).
[CrossRef]

Bertolotti, M.

Bloembergen, N.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[CrossRef]

Bloemer, M. J.

G. D’Aguanno, M. C. Larciprete, N. Mattiucci, A. Belardini, M. J. Bloemer, E. Fazio, O. Buganov, M. Centini, and C. Sibilia, “Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems,” Phys. Rev. A 81(1), 013834 (2010).
[CrossRef]

N. Mattiucci, G. D’Aguanno, N. Akozbek, M. Scalora, and M. J. Bloemer, “Homogenization procedure for a metamaterial and local violation of the second principle of thermodynamics,” Opt. Commun. 283(8), 1613–1620 (2010).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: application to super-resolution,” Opt. Express 17(20), 17517–17529 (2009).
[CrossRef] [PubMed]

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, “Second-harmonic generation from a positive-negative index material heterostructure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066612 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: a comprehensive analysis,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016612 (2004).
[CrossRef] [PubMed]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19(9), 2111 (2002).
[CrossRef]

Bowden, C. M.

Brown, F.

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear Optical Reflection from a Metallic Boundary,” Phys. Rev. Lett. 14(25), 1029–1031 (1965).
[CrossRef]

Buganov, O.

G. D’Aguanno, M. C. Larciprete, N. Mattiucci, A. Belardini, M. J. Bloemer, E. Fazio, O. Buganov, M. Centini, and C. Sibilia, “Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems,” Phys. Rev. A 81(1), 013834 (2010).
[CrossRef]

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[CrossRef] [PubMed]

Centini, M.

G. D’Aguanno, M. C. Larciprete, N. Mattiucci, A. Belardini, M. J. Bloemer, E. Fazio, O. Buganov, M. Centini, and C. Sibilia, “Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems,” Phys. Rev. A 81(1), 013834 (2010).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19(9), 2111 (2002).
[CrossRef]

Chang, R. K.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[CrossRef]

Chen, C. K.

Chen, Q.

Ciraci, S.

S. Ciraci and I. P. Batra, “Theory of the quantum size effect in simple metals,” Phys. Rev. B Condens. Matter 33(6), 4294–4297 (1986).
[CrossRef] [PubMed]

Coddington, I. R.

D’Aguanno, G.

N. Mattiucci, G. D’Aguanno, N. Akozbek, M. Scalora, and M. J. Bloemer, “Homogenization procedure for a metamaterial and local violation of the second principle of thermodynamics,” Opt. Commun. 283(8), 1613–1620 (2010).
[CrossRef]

G. D’Aguanno, M. C. Larciprete, N. Mattiucci, A. Belardini, M. J. Bloemer, E. Fazio, O. Buganov, M. Centini, and C. Sibilia, “Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems,” Phys. Rev. A 81(1), 013834 (2010).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: application to super-resolution,” Opt. Express 17(20), 17517–17529 (2009).
[CrossRef] [PubMed]

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, “Second-harmonic generation from a positive-negative index material heterostructure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066612 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: a comprehensive analysis,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016612 (2004).
[CrossRef] [PubMed]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19(9), 2111 (2002).
[CrossRef]

de Castro, A. R. B.

Deck, R. T.

Decoopman, T.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97(7), 073905 (2006).
[CrossRef] [PubMed]

Enoch, S.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97(7), 073905 (2006).
[CrossRef] [PubMed]

Fazio, E.

G. D’Aguanno, M. C. Larciprete, N. Mattiucci, A. Belardini, M. J. Bloemer, E. Fazio, O. Buganov, M. Centini, and C. Sibilia, “Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems,” Phys. Rev. A 81(1), 013834 (2010).
[CrossRef]

Fukui, M.

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]

M. Fukui, J. E. Sipe, V. C. Y. So, and G. I. Stegeman, “Nonlinear mixing of opposite traveling surface plasmons,” Solid State Commun. 27(12), 1265–1267 (1978).
[CrossRef]

Goetz, D. A.

Gralak, B.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97(7), 073905 (2006).
[CrossRef] [PubMed]

Hashimoto, K.

R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun. 248(1-3), 249–256 (2005).
[CrossRef]

Jha, S. S.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[CrossRef]

Kajikawa, K.

R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun. 248(1-3), 249–256 (2005).
[CrossRef]

Kretschmann, E.

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241(4), 313–324 (1971).
[CrossRef]

Larciprete, M. C.

G. D’Aguanno, M. C. Larciprete, N. Mattiucci, A. Belardini, M. J. Bloemer, E. Fazio, O. Buganov, M. Centini, and C. Sibilia, “Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems,” Phys. Rev. A 81(1), 013834 (2010).
[CrossRef]

Lee, C. H.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[CrossRef]

Leskova, T. A.

T. A. Leskova, M. Leyva-Lucero, E. R. Mendez, A. A. Maradudin, and I. V. Novikov, “The surface enhanced second harmonic generation of light from a randomly rough metal surface in the Kretschmann geometry,” Opt. Commun. 183(5-6), 529–545 (2000).
[CrossRef]

Leyva-Lucero, M.

T. A. Leskova, M. Leyva-Lucero, E. R. Mendez, A. A. Maradudin, and I. V. Novikov, “The surface enhanced second harmonic generation of light from a randomly rough metal surface in the Kretschmann geometry,” Opt. Commun. 183(5-6), 529–545 (2000).
[CrossRef]

Maradudin, A. A.

T. A. Leskova, M. Leyva-Lucero, E. R. Mendez, A. A. Maradudin, and I. V. Novikov, “The surface enhanced second harmonic generation of light from a randomly rough metal surface in the Kretschmann geometry,” Opt. Commun. 183(5-6), 529–545 (2000).
[CrossRef]

Mattiucci, N.

G. D’Aguanno, M. C. Larciprete, N. Mattiucci, A. Belardini, M. J. Bloemer, E. Fazio, O. Buganov, M. Centini, and C. Sibilia, “Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems,” Phys. Rev. A 81(1), 013834 (2010).
[CrossRef]

N. Mattiucci, G. D’Aguanno, N. Akozbek, M. Scalora, and M. J. Bloemer, “Homogenization procedure for a metamaterial and local violation of the second principle of thermodynamics,” Opt. Commun. 283(8), 1613–1620 (2010).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: application to super-resolution,” Opt. Express 17(20), 17517–17529 (2009).
[CrossRef] [PubMed]

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, “Second-harmonic generation from a positive-negative index material heterostructure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066612 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: a comprehensive analysis,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016612 (2004).
[CrossRef] [PubMed]

Maystre, D.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97(7), 073905 (2006).
[CrossRef] [PubMed]

Mendez, E. R.

T. A. Leskova, M. Leyva-Lucero, E. R. Mendez, A. A. Maradudin, and I. V. Novikov, “The surface enhanced second harmonic generation of light from a randomly rough metal surface in the Kretschmann geometry,” Opt. Commun. 183(5-6), 529–545 (2000).
[CrossRef]

Mitchell, D. E.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[CrossRef]

Naraoka, R.

R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun. 248(1-3), 249–256 (2005).
[CrossRef]

Novikov, I. V.

T. A. Leskova, M. Leyva-Lucero, E. R. Mendez, A. A. Maradudin, and I. V. Novikov, “The surface enhanced second harmonic generation of light from a randomly rough metal surface in the Kretschmann geometry,” Opt. Commun. 183(5-6), 529–545 (2000).
[CrossRef]

Okawa, H.

R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun. 248(1-3), 249–256 (2005).
[CrossRef]

Parks, R. E.

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear Optical Reflection from a Metallic Boundary,” Phys. Rev. Lett. 14(25), 1029–1031 (1965).
[CrossRef]

Quail, J. C.

J. C. Quail and H. J. Simon, “Second-harmonic generation from silver and aluminum films in total internal reflection,” Phys. Rev. B Condens. Matter 31(8), 4900–4905 (1985).
[CrossRef] [PubMed]

J. G. Rako, J. C. Quail, and H. J. Simon, “Optical second-harmonic generation with surface plasmons in noncentrosymmetric crystals,” Phys. Rev. B 30(10), 5552–5559 (1984).
[CrossRef]

Rako, J. G.

J. G. Rako, J. C. Quail, and H. J. Simon, “Optical second-harmonic generation with surface plasmons in noncentrosymmetric crystals,” Phys. Rev. B 30(10), 5552–5559 (1984).
[CrossRef]

Sarid, D.

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981).
[CrossRef]

Scalora, M.

N. Mattiucci, G. D’Aguanno, N. Akozbek, M. Scalora, and M. J. Bloemer, “Homogenization procedure for a metamaterial and local violation of the second principle of thermodynamics,” Opt. Commun. 283(8), 1613–1620 (2010).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: application to super-resolution,” Opt. Express 17(20), 17517–17529 (2009).
[CrossRef] [PubMed]

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, “Second-harmonic generation from a positive-negative index material heterostructure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066612 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: a comprehensive analysis,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016612 (2004).
[CrossRef] [PubMed]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19(9), 2111 (2002).
[CrossRef]

Shen, Y. R.

Sibilia, C.

Simon, H. J.

Q. Chen, X. Sun, I. R. Coddington, D. A. Goetz, and H. J. Simon, “Reflected second-harmonic generation with coupled surface-plasmon modes in Ag/liquid/Ag layers,” J. Opt. Soc. Am. B 16(6), 971–975 (1999).
[CrossRef]

J. C. Quail and H. J. Simon, “Second-harmonic generation from silver and aluminum films in total internal reflection,” Phys. Rev. B Condens. Matter 31(8), 4900–4905 (1985).
[CrossRef] [PubMed]

J. G. Rako, J. C. Quail, and H. J. Simon, “Optical second-harmonic generation with surface plasmons in noncentrosymmetric crystals,” Phys. Rev. B 30(10), 5552–5559 (1984).
[CrossRef]

G. M. Wysin, H. J. Simon, and R. T. Deck, “Optical bistability with surface plasmons,” Opt. Lett. 6(1), 30–32 (1981).
[CrossRef] [PubMed]

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[CrossRef]

Sipe, J. E.

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]

M. Fukui, J. E. Sipe, V. C. Y. So, and G. I. Stegeman, “Nonlinear mixing of opposite traveling surface plasmons,” Solid State Commun. 27(12), 1265–1267 (1978).
[CrossRef]

Sleeper, A. M.

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear Optical Reflection from a Metallic Boundary,” Phys. Rev. Lett. 14(25), 1029–1031 (1965).
[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]

M. Fukui, J. E. Sipe, V. C. Y. So, and G. I. Stegeman, “Nonlinear mixing of opposite traveling surface plasmons,” Solid State Commun. 27(12), 1265–1267 (1978).
[CrossRef]

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[CrossRef] [PubMed]

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]

M. Fukui, J. E. Sipe, V. C. Y. So, and G. I. Stegeman, “Nonlinear mixing of opposite traveling surface plasmons,” Solid State Commun. 27(12), 1265–1267 (1978).
[CrossRef]

Sun, X.

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[CrossRef] [PubMed]

Tayeb, G.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97(7), 073905 (2006).
[CrossRef] [PubMed]

Tsang, T. Y. F.

Watson, J. G.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[CrossRef]

Wysin, G. M.

Zheltikov, A. M.

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: a comprehensive analysis,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016612 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (2)

Opt. Commun. (3)

N. Mattiucci, G. D’Aguanno, N. Akozbek, M. Scalora, and M. J. Bloemer, “Homogenization procedure for a metamaterial and local violation of the second principle of thermodynamics,” Opt. Commun. 283(8), 1613–1620 (2010).
[CrossRef]

R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun. 248(1-3), 249–256 (2005).
[CrossRef]

T. A. Leskova, M. Leyva-Lucero, E. R. Mendez, A. A. Maradudin, and I. V. Novikov, “The surface enhanced second harmonic generation of light from a randomly rough metal surface in the Kretschmann geometry,” Opt. Commun. 183(5-6), 529–545 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. (1)

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[CrossRef]

Phys. Rev. A (1)

G. D’Aguanno, M. C. Larciprete, N. Mattiucci, A. Belardini, M. J. Bloemer, E. Fazio, O. Buganov, M. Centini, and C. Sibilia, “Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems,” Phys. Rev. A 81(1), 013834 (2010).
[CrossRef]

Phys. Rev. B (2)

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]

J. G. Rako, J. C. Quail, and H. J. Simon, “Optical second-harmonic generation with surface plasmons in noncentrosymmetric crystals,” Phys. Rev. B 30(10), 5552–5559 (1984).
[CrossRef]

Phys. Rev. B Condens. Matter (3)

J. C. Quail and H. J. Simon, “Second-harmonic generation from silver and aluminum films in total internal reflection,” Phys. Rev. B Condens. Matter 31(8), 4900–4905 (1985).
[CrossRef] [PubMed]

S. Ciraci and I. P. Batra, “Theory of the quantum size effect in simple metals,” Phys. Rev. B Condens. Matter 33(6), 4294–4297 (1986).
[CrossRef] [PubMed]

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, “Second-harmonic generation from a positive-negative index material heterostructure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066612 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: a comprehensive analysis,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016612 (2004).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981).
[CrossRef]

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear Optical Reflection from a Metallic Boundary,” Phys. Rev. Lett. 14(25), 1029–1031 (1965).
[CrossRef]

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[CrossRef]

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97(7), 073905 (2006).
[CrossRef] [PubMed]

Solid State Commun. (1)

M. Fukui, J. E. Sipe, V. C. Y. So, and G. I. Stegeman, “Nonlinear mixing of opposite traveling surface plasmons,” Solid State Commun. 27(12), 1265–1267 (1978).
[CrossRef]

Z. Phys. (1)

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241(4), 313–324 (1971).
[CrossRef]

Other (5)

Y. R. Shen, The Principles of Nonlinear Optics, (Wiley, 1984)

Handbook of Optical constants of solids, E. D. Palik ed., (Academic Press Inc., 1991).

H. A. Macleod, Thin film optical filters, (Institute of Physics Publishing, 2001)

H. Raether, “Surface Plasmons,” Springer Tracts in Modern Physics, (Berlin, 1988)

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 Nanostructures,” at http://arxiv.org/abs/1006.3841

Supplementary Material (4)

» Media 1: AVI (3720 KB)     
» Media 2: AVI (3720 KB)     
» Media 3: AVI (3720 KB)     
» Media 4: AVI (3720 KB)     

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Figures (7)

Fig. 1
Fig. 1

Scheme of the configurations studied: a hemi-cylindrical prism that acts as input medium, on which a periodic metal/dielectric multilayer is grown. The output medium is air. (a) The elementary cell is symmetric (MgF2/Ag/MgF2). (b) The elementary cell is asymmetric (MgF2/Ag). (c) The elementary cell is asymmetric (Ag/MgF2). (d) The elementary cell is symmetric (Ag/MgF2/Ag). The SHG is studied for a pump field tuned at 800nm and the SH generated at 400nm. The prism is made of fused silica whose refractive indices at 800nm and 400nm are respectively nin(800nm) = 1.53837 and nin(400nm) = 1.55774. The refractive indices of Ag and MgF2 are respectively, nAg(800nm) = 0.144 + 5.289i, nAg(400nm) = 0.173 + 1.95i, nMgF2(800nm) = 1.3751, nMgF2(400nm) = 1.3839 + 0.02i. In the figures are also represented the input fundamental frequency (FF) pump field and the reflected FF and SH fields.

Fig. 2
Fig. 2

Left side: Log(η) vs. Ag thickness and incident angle for the 1-period structures considered, η is the conversion efficiency. Right side: Schematic representation of the structures considered: Symmetric-1 (2a), Asymmetric-1 (2b), Asymmetric-2 (2c), Symmetric-2 (2d). In Fig. 2(a) the black dashed line superimposed represents the dispersion of the short-range/long-range plasmons for the structure MgF2/Ag/MgF2. For each figure, see also the multimedia material (Media 1, Media 2, Media 3, and Media 4) where the thickness of the MgF2 is varied.

Fig. 3
Fig. 3

Maximum conversion efficiency accessible as function of the thickness of the layers for a given number of periods and a given type of elementary cell. Superimposed an acronym that indicates the type of resonant mechanism: LR indicates that the enhanced SH generation is due to the excitation of long range plasmons; SR indicates that the enhanced SH generation is due to the excitation of short range plasmons; SPair indicates that the enhanced SH generation is due to the excitation of a plasmon at the Ag/Air interface; SPMgF2 indicates that the enhanced SH generation is due to the excitation of a plasmon at the Ag/MgF2 interface; LW indicates that the enhanced SH generation is due to the excitation of a leaky waveguide mode.

Fig. 4
Fig. 4

Angle at which the conversion efficiency reported in Fig. 3 is reached as a function of the thickness of the layers for a given number of periods and a given type of elementary cell.

Fig. 5
Fig. 5

(a) Histogram of the conversion efficiency and (b)angle at which it is obtained when each layer is randomly varied around its central value according to a Gaussian distribution having a standard deviation from the central value equal to 5%. The structure considered is N=5-periods Symmetric-1 for which the maximum conversion efficiency of η=4.9*10-8 is reached when dAg=15nm and dMgF2=101nm which represent our central values in the statistical study. The histograms have been obtained after 6318856 simulations.

Fig. 6
Fig. 6

(a) Classical Kretschmann geometry where the input medium is a fused silica prism, the metal is silver, and the output medium is a generic non absorptive non dispersive dielectric of index of refraction nout. (b) Maximum conversion efficiency achievable vs. the Ag layer thickness and the index of refraction of the output medium (nout). (c) Transmission as a function of the angle of incidence and of nout when dAg = 10nm. The transmission maxima correspond to the dispersion of the leaky wave in the fused silica. The white dashed line is the dispersion of the surface plasmon at the Ag/nout interface calculated according to the standard dispersion law: k S P = k 0 ε A g ε o u t / ( ε A g + ε o u t ) . The black dashed line represents instead the loci of the maxima of the SHG. Note how the loci of the maxima of the SHG follow exactly the dispersion of the leaky wave. Note also as the dispersion of the Ag/nout surface plasmon is similar to the dispersion of the leaky wave. (c) Angle at which the maximum conversion efficiency is obtained vs. dAg and nout.

Fig. 7
Fig. 7

(a) Scheme of the configuration studied. The 8-periods asymmetric-1 structure with dAg=9nm and dMgF2=52nm is grown on the base of a fused silica hemi-cylindrical prism, while the output medium is a generic non absorptive non dispersive dielectric of index of refraction nout. (b) Conversion efficiency vs. the index of refraction of the output medium (nout) and the angle of incidence ϑ.

Equations (2)

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d 2 H 2 ω d z 2 + 4 ω 2 c 2 ( n 2 ω 2 ( z ) n i n 2 sin 2 ϑ ) H 2 ω = 4 ω 2 n i n c sin ϑ ( ε 0 d s ( 2 ) k δ ( z z k ) E z , ω 2 )     .
k S P = k 0 ε 1 ε 2 ε 1 + ε 2 ,

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