Abstract

A new configuration of sub-wavelength silver coaxial apertures filled with Lithium Niobate (LN) is proposed to enhance the Second Harmonic Generation (SHG) in transmission mode. The chosen geometrical parameters allows having both TE11 guided mode excitation for local field confinement of the fundamental signal and Fabry-Perot high transmission of the SH wave. Furthermore, an implementation of the three-dimensional Finite Difference Time Domain (3D-FDTD) method for nonlinear optical simulation is described. This method provides a direct calculation of the nonlinear polarizations before calculating the nonlinear electric and magnetic fields. FDTD studies shows that by embedding metallic nano-structures, for exciting TE11 like-mode inside a nonlinear material (LN), we achieve a SH signal 27 times higher than that generated on unpatterned LN.

© 2012 OSA

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  1. R. Raad, E. Inaty, P. Fortier, and H. M. H. Shalaby, “Optical S-ALOHA/CDMA Systems for Multirate Applications: Architecture, Performance Evaluation, and System Stability,” J. Lightwave Technol. 24, 1968–1977 (2006).
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    [CrossRef]
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    [CrossRef]
  7. F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67, 155314–155317 (2003).
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  8. F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419–205426 (2006).
    [CrossRef]
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    [CrossRef]
  17. E. 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, 6530–6536 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  20. Y. R. Shen, The Principles of Nonlinear Optics (Wiley Interscience, 1984).
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    [CrossRef]
  22. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [CrossRef]
  23. J. Dahdah, J. Hoblos, and F. I. Baida, “Nano-coaxial waveguide grating as quarter-wave plates in the visible range,” IEEE Photon. J. 4, 87–94 (2011).
    [CrossRef]
  24. W. Sellmeier, “Zur Erklrung der abnormen Farbenfolge im Spectrum einiger Substanzen,” Ann. Phys. Chem. 219, 272–282 (1981).
  25. 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, 1027–1030 (2006).
    [CrossRef]

2012 (1)

S. Park, J. W. Hahn, and J. Y. Lee, “Doubly resonant metallic nanostructure for high conversion efficiency of second harmonic generation,” Opt. Express 4, 4856–4871 (2012).
[CrossRef]

2011 (2)

2010 (2)

2009 (1)

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79, 235109–235118 (2009).
[CrossRef]

2008 (1)

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature (London) 452, 728–731 (2008).
[CrossRef]

2007 (1)

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local Field Asymmetry Drives Second-Harmonic Generation in Noncentrosymmetric Nanodimers,” Nano Lett. 20, 1251–1255 (2007).
[CrossRef]

2006 (4)

R. Raad, E. Inaty, P. Fortier, and H. M. H. Shalaby, “Optical S-ALOHA/CDMA Systems for Multirate Applications: Architecture, Performance Evaluation, and System Stability,” J. Lightwave Technol. 24, 1968–1977 (2006).
[CrossRef]

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, 1027–1030 (2006).
[CrossRef]

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419–205426 (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. B 97, 146102–146106 (2006).
[CrossRef]

2005 (1)

M. Roussey, M.-P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101–241104 (2005).
[CrossRef]

2003 (2)

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second-Harmonic Generation Induced by Local Field Enhancement,” Phys. Rev. Lett. 90, 13903–13907 (2003).
[CrossRef]

F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67, 155314–155317 (2003).
[CrossRef]

2002 (1)

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

1998 (1)

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

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

1981 (1)

W. Sellmeier, “Zur Erklrung der abnormen Farbenfolge im Spectrum einiger Substanzen,” Ann. Phys. Chem. 219, 272–282 (1981).

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

1961 (1)

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

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, 1027–1030 (2006).
[CrossRef]

Aktsipetrov, O. A.

Bai, B.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local Field Asymmetry Drives Second-Harmonic Generation in Noncentrosymmetric Nanodimers,” Nano Lett. 20, 1251–1255 (2007).
[CrossRef]

Baida, F. I.

J. Dahdah, J. Hoblos, and F. I. Baida, “Nano-coaxial waveguide grating as quarter-wave plates in the visible range,” IEEE Photon. J. 4, 87–94 (2011).
[CrossRef]

E. 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, 6530–6536 (2010).
[CrossRef] [PubMed]

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419–205426 (2006).
[CrossRef]

M. Roussey, M.-P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101–241104 (2005).
[CrossRef]

F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67, 155314–155317 (2003).
[CrossRef]

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

Barakat, E.

Belkhir, A.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419–205426 (2006).
[CrossRef]

Bernal, M.-P.

E. 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, 6530–6536 (2010).
[CrossRef] [PubMed]

M. Roussey, M.-P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101–241104 (2005).
[CrossRef]

Beversluis, M.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second-Harmonic Generation Induced by Local Field Enhancement,” Phys. Rev. Lett. 90, 13903–13907 (2003).
[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, 13903–13907 (2003).
[CrossRef]

Bratkovsky, A.

Brueck, S. R. J.

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, 1027–1030 (2006).
[CrossRef]

Canfield, B. K.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local Field Asymmetry Drives Second-Harmonic Generation in Noncentrosymmetric Nanodimers,” Nano Lett. 20, 1251–1255 (2007).
[CrossRef]

Courjal, N.

M. Roussey, M.-P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101–241104 (2005).
[CrossRef]

Dahdah, J.

J. Dahdah, J. Hoblos, and F. I. Baida, “Nano-coaxial waveguide grating as quarter-wave plates in the visible range,” IEEE Photon. J. 4, 87–94 (2011).
[CrossRef]

Ebbesen, T. W.

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

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. B 97, 146102–146106 (2006).
[CrossRef]

Fan, W.

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, 1027–1030 (2006).
[CrossRef]

Fortier, P.

Franken, P. A.

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

Ghaemi, H. F.

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

Gong, Y.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2005).

Hahn, J. W.

S. Park, J. W. Hahn, and J. Y. Lee, “Doubly resonant metallic nanostructure for high conversion efficiency of second harmonic generation,” Opt. Express 4, 4856–4871 (2012).
[CrossRef]

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. B 97, 146102–146106 (2006).
[CrossRef]

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, 13903–13907 (2003).
[CrossRef]

Hill, A. E.

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

Hoblos, J.

J. Dahdah, J. Hoblos, and F. I. Baida, “Nano-coaxial waveguide grating as quarter-wave plates in the visible range,” IEEE Photon. J. 4, 87–94 (2011).
[CrossRef]

Hoyer, W.

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79, 235109–235118 (2009).
[CrossRef]

Husu, H.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local Field Asymmetry Drives Second-Harmonic Generation in Noncentrosymmetric Nanodimers,” Nano Lett. 20, 1251–1255 (2007).
[CrossRef]

Inaty, E.

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

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 Noncentrosymmetric Nanodimers,” Nano Lett. 20, 1251–1255 (2007).
[CrossRef]

Koch, S. W.

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79, 235109–235118 (2009).
[CrossRef]

Kolmychek, I. A.

Krishna, S.

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, 1027–1030 (2006).
[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. B 97, 146102–146106 (2006).
[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 Noncentrosymmetric Nanodimers,” Nano Lett. 20, 1251–1255 (2007).
[CrossRef]

Lalanne, P.

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature (London) 452, 728–731 (2008).
[CrossRef]

Lamrous, O.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419–205426 (2006).
[CrossRef]

Laukkanen, J.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen, “Local Field Asymmetry Drives Second-Harmonic Generation in Noncentrosymmetric Nanodimers,” Nano Lett. 20, 1251–1255 (2007).
[CrossRef]

Lee, J. Y.

S. Park, J. W. Hahn, and J. Y. Lee, “Doubly resonant metallic nanostructure for high conversion efficiency of second harmonic generation,” Opt. Express 4, 4856–4871 (2012).
[CrossRef]

Lezec, H. J.

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

Liu, H.

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature (London) 452, 728–731 (2008).
[CrossRef]

Liu, J.

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79, 235109–235118 (2009).
[CrossRef]

Liu, X.

Lu, H.

Malloy, K. J.

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, 1027–1030 (2006).
[CrossRef]

Mamonov, E. A.

Mao, D.

Maydykovsky, A. I.

Moloney, J. V.

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79, 235109–235118 (2009).
[CrossRef]

Moshchalkov, V. V.

Murzina, T. V.

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, 13903–13907 (2003).
[CrossRef]

Osgood, R. M.

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, 1027–1030 (2006).
[CrossRef]

Panoiu, N.-C.

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, 1027–1030 (2006).
[CrossRef]

Park, S.

S. Park, J. W. Hahn, and J. Y. Lee, “Doubly resonant metallic nanostructure for high conversion efficiency of second harmonic generation,” Opt. Express 4, 4856–4871 (2012).
[CrossRef]

Peters, C. W.

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

Ponizovskaya, E.

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. B 97, 146102–146106 (2006).
[CrossRef]

Raad, R.

Roussey, M.

M. Roussey, M.-P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101–241104 (2005).
[CrossRef]

Sadiku, M. N.O.

M. N.O. Sadiku, Numerical Techniques in Electromagnetics (CRC Press, 2000).
[CrossRef]

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. B 97, 146102–146106 (2006).
[CrossRef]

Segerink, F. B.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays,” Phys. Rev. B 97, 146102–146106 (2006).
[CrossRef]

Sellmeier, W.

W. Sellmeier, “Zur Erklrung der abnormen Farbenfolge im Spectrum einiger Substanzen,” Ann. Phys. Chem. 219, 272–282 (1981).

Shalaby, H. M. H.

Shen, Y. R.

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

Silhanek, A. V.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2005).

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 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 Noncentrosymmetric Nanodimers,” Nano Lett. 20, 1251–1255 (2007).
[CrossRef]

Valev, V. K.

Van Labeke, D.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74, 205419–205426 (2006).
[CrossRef]

F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67, 155314–155317 (2003).
[CrossRef]

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[CrossRef]

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J. Dahdah, J. Hoblos, and F. I. Baida, “Nano-coaxial waveguide grating as quarter-wave plates in the visible range,” IEEE Photon. J. 4, 87–94 (2011).
[CrossRef]

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[CrossRef]

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[CrossRef]

Nature (London) (2)

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[CrossRef]

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Opt. Lett. (1)

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F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67, 155314–155317 (2003).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic showing embedded coaxial apertures into silver and filled by lithium niobate. (a) Geometry of one aperture of inner radius Ri = 65 nm and outer radius Ro = 135 nm. (b) Grating of squared array of apertures with periodicity p = 300 nm and thickness h = 120 nm = deposited on the same material.

Fig. 2
Fig. 2

(a) Zero order transmission spectrum of the Metallo-Dielectric Photonic Crystal. (b) Nonlinear enhancement factor (blue solid curve) versus the harmonic wavelength compared to the linear transmission (green solid line) of the embedded structure. For both spectra, the geometrical parameters are Ri = 65 nm, Ro = 135 nm, h = 120 nm and p = 300 nm.

Fig. 3
Fig. 3

(a): Normalized transmission and reflection spectra of the generated nonlinear signals inside the annular apertures. (b) and (c): Spatial distributions of the nonlinear electric field nearby one cavity at λ T N L max = 750 n m and at λSPRNL = 810 nm respectively.

Fig. 4
Fig. 4

The fifth root of the electric intensity distribution (|E|0.4). (a),(c) are the linear distributions at ω, (d) is the linear distribution at 2ω. (b),(e) show the nonlinear distribution at 2ω.

Fig. 5
Fig. 5

Linear (a,c) and nonlinear (b,d) distributions of the Poynting vector in the (zy) and (xz) planes respectively. The incident field is Z–polarized.

Fig. 6
Fig. 6

(a) Schematic of the geometry employed for polarization. In (b) and (c) we plot the normalized SHG signal generated from an x-cut and z-cut nano-patterned PhC respectively versus the polarization angle.

Equations (9)

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D ( ω ) = ε 0 E ( ω ) + P ( ω )
P = P L + P N L = χ ( 1 ) E + χ ( 2 ) E E + χ ( 3 ) E E E +
rot ( E ) = B t
rot ( B ) = D t
E x n + 1 ( i , j , k ) = E x n ( i , j , k ) + Δ t ε ( i , j , k ) [ H z ( n + 1 / 2 ) ( i , j , k ) H z ( n + 1 / 2 ) ( i , j 1 , k ) Δ y H y ( n + 1 / 2 ) ( i , j , k ) H y ( n + 1 / 2 ) ( i , j , k 1 ) Δ z ]
P ( 2 ω ) = 2 ε 0 χ ( 2 ) E ( ω ) E ( ω )
P N L ( 2 ) ( r , t ) = ε 0 χ ( 2 ) ( t t 1 , t t 2 ) E ( r , t 1 ) E ( r , t 2 ) d t 1 d t 2
E x N L t = 1 ε 0 ε N L [ ( H z N L y H y N L z ) P x N L t ]
( P x P y P z ) = 2 ε 0 ( 0 0 0 0 d 31 d 22 d 22 d 22 0 d 31 0 0 d 31 d 31 d 33 0 0 0 ) ( E x 2 E y 2 E z 2 2 E y E z 2 E x E z 2 E x E y )

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