Abstract

A new nondestructive characterization technique, based on a modified Maker fringe measurement, is reported that allows the complete determination of complex spatial distributions of the nonlinear χ(2)(z) coefficient in planar samples. Each sample under test was stacked together with a phase reference quartz plate to retrieve both amplitude and phase of the optical second-harmonic signal. The added phase information permits the precise determination of the location of the optically nonlinear region within the sample. Hemicylindrical lenses are used to obtain greater internal propagation angles, with an important increase in the information about the nonlinearity distribution. The technique is demonstrated for two Infrasil glass plates thermally poled in vacuum under the same temperature, voltage, and duration conditions. Very different distributions were obtained for these samples, one nonlinear layer being buried 4 µm under the anodic surface while the other was not, the latter exhibiting maximum χ(2) three times larger than the former. This difference in the χ(2)(z) distribution is explained in terms of charge injection during the poling process.

© 2004 Optical Society of America

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  1. U. Osterberg and W. Margulis, “Dye laser pumped by Nd:YAG laser pulses frequency doubled in a glass optical fiber,” Opt. Lett. 11, 516–518 (1986).
    [CrossRef] [PubMed]
  2. R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16, 1732–1734 (1991).
    [CrossRef] [PubMed]
  3. P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
    [CrossRef]
  4. T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectroscopy study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
    [CrossRef]
  5. Y. Quiquempois, G. Martinelli, P. Dutherage, P. Bernage, P. Niay, and M. Douay, “Localisation of the induced second-order non-linearity within Infrasil and Suprasil thermally poled glasses,” Opt. Commun. 176, 479–487 (2000).
    [CrossRef]
  6. V. Tréanton, N. Godbout, and S. Lacroix, “An interferometric Maker fringe experiment to reconstruct the χ(2) profile of poled silica plates,” in Proceedings of Bragg Gratings, Photosensitivity and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 510–512.
  7. A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Cylinder-assisted Maker-fringe technique,” Electron. Lett. 39, 1834–1835 (2003).
    [CrossRef]
  8. Y. Quiquempois, M. Lelek, A. Kudlinski, H. Zerglache, and G. Martinelli, “Non-linear distribution reconstruction in poled silica glasses with a sub-micron resolution,” in Proceedings of Bragg Gratings, Photosensitivity and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 256–258.
  9. A. L. C. Triques, C. M. B. Cordeiro, V. Balestrieri, B. Lesche, W. Margulis, and I. C. S. Carvalho, “Depletion region in thermally poled fused silica,” Appl. Phys. Lett. 76, 2496–2498 (2000).
    [CrossRef]
  10. D. Pureur, A. C. Liu, M. J. F. Digonnet, and G. S. Kino, “Absolute measurement of the second-order nonlinearity profile in poled silica,” Opt. Lett. 23, 588–590 (1998).
    [CrossRef]
  11. V. Rodriguez and C. Sourisseau, “General Maker-fringe ellipsometric analysis in multilayer nonlinear and linear anisotropic media,” J. Opt. Soc. Am. B 19, 2650–2664 (2002).
    [CrossRef]
  12. C. Corbari, O. Deparis, B. G. Klappauf, and P. G. Kazansky, “Practical technique for measurement of second-order nonlinearity in poled glass,” Electron. Lett. 39, 197–198 (2003).
    [CrossRef]
  13. A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Simplified inverse Fourier transform technique to measure optical nonlinearity profiles using a reference sample,” Electron. Lett. 40, 551–552 (2004).
    [CrossRef]
  14. A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Inverse Fourier transform technique to determine second-order optical nonlinearity spatial profiles,” Appl. Phys. Lett. 82, 1362–1364 (2003).
    [CrossRef]
  15. T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242, 165–176 (1998).
    [CrossRef]
  16. A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Phys. J. D 1, 223–226 (1998).
    [CrossRef]
  17. A. Kudlinski, G. Martinelli, Y. Quiquempois, and H. Zerglache, “Microscopic model for the second-order nonlinearity creation in thermally poled bulk silica glasses,” in Proceedings of Bragg Gratings, Photosensitivity and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 213–215.
  18. Y. Quiquempois, N. Godbout, and S. Lacroix, “Model of charge migration during thermal poling in silica glasses: evidence of a voltage threshold for the onset of a second-order nonlinearity,” Phys. Rev. A 65, 043816 (2002).
    [CrossRef]
  19. S. Kielich, “Optical second-harmonic generation by electrically polarized isotropic media,” IEEE J. Quantum Electron. QE-5, 562–568 (1969).
    [CrossRef]
  20. D. Wong, W. Xu, S. Fleming, M. Janos, and K. M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 65, 235–241 (1999).
    [CrossRef]
  21. R. Kashyap, F. C. Garcia, and L. Vogelaar, “Nonlinearity of the electro-optic effect in poled waveguides,” in Proceedings of Bragg Gratings, Photosensitivity and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 210–212.

2004

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Simplified inverse Fourier transform technique to measure optical nonlinearity profiles using a reference sample,” Electron. Lett. 40, 551–552 (2004).
[CrossRef]

2003

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Inverse Fourier transform technique to determine second-order optical nonlinearity spatial profiles,” Appl. Phys. Lett. 82, 1362–1364 (2003).
[CrossRef]

C. Corbari, O. Deparis, B. G. Klappauf, and P. G. Kazansky, “Practical technique for measurement of second-order nonlinearity in poled glass,” Electron. Lett. 39, 197–198 (2003).
[CrossRef]

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Cylinder-assisted Maker-fringe technique,” Electron. Lett. 39, 1834–1835 (2003).
[CrossRef]

2002

V. Rodriguez and C. Sourisseau, “General Maker-fringe ellipsometric analysis in multilayer nonlinear and linear anisotropic media,” J. Opt. Soc. Am. B 19, 2650–2664 (2002).
[CrossRef]

Y. Quiquempois, N. Godbout, and S. Lacroix, “Model of charge migration during thermal poling in silica glasses: evidence of a voltage threshold for the onset of a second-order nonlinearity,” Phys. Rev. A 65, 043816 (2002).
[CrossRef]

2000

Y. Quiquempois, G. Martinelli, P. Dutherage, P. Bernage, P. Niay, and M. Douay, “Localisation of the induced second-order non-linearity within Infrasil and Suprasil thermally poled glasses,” Opt. Commun. 176, 479–487 (2000).
[CrossRef]

A. L. C. Triques, C. M. B. Cordeiro, V. Balestrieri, B. Lesche, W. Margulis, and I. C. S. Carvalho, “Depletion region in thermally poled fused silica,” Appl. Phys. Lett. 76, 2496–2498 (2000).
[CrossRef]

1999

T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectroscopy study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
[CrossRef]

D. Wong, W. Xu, S. Fleming, M. Janos, and K. M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 65, 235–241 (1999).
[CrossRef]

1998

T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242, 165–176 (1998).
[CrossRef]

A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Phys. J. D 1, 223–226 (1998).
[CrossRef]

D. Pureur, A. C. Liu, M. J. F. Digonnet, and G. S. Kino, “Absolute measurement of the second-order nonlinearity profile in poled silica,” Opt. Lett. 23, 588–590 (1998).
[CrossRef]

1991

1986

1969

S. Kielich, “Optical second-harmonic generation by electrically polarized isotropic media,” IEEE J. Quantum Electron. QE-5, 562–568 (1969).
[CrossRef]

1962

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Alley, T. G.

T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectroscopy study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
[CrossRef]

T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242, 165–176 (1998).
[CrossRef]

Balestrieri, V.

A. L. C. Triques, C. M. B. Cordeiro, V. Balestrieri, B. Lesche, W. Margulis, and I. C. S. Carvalho, “Depletion region in thermally poled fused silica,” Appl. Phys. Lett. 76, 2496–2498 (2000).
[CrossRef]

Bernage, P.

Y. Quiquempois, G. Martinelli, P. Dutherage, P. Bernage, P. Niay, and M. Douay, “Localisation of the induced second-order non-linearity within Infrasil and Suprasil thermally poled glasses,” Opt. Commun. 176, 479–487 (2000).
[CrossRef]

Brueck, S. R. J.

T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectroscopy study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
[CrossRef]

T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242, 165–176 (1998).
[CrossRef]

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16, 1732–1734 (1991).
[CrossRef] [PubMed]

Carvalho, I. C. S.

A. L. C. Triques, C. M. B. Cordeiro, V. Balestrieri, B. Lesche, W. Margulis, and I. C. S. Carvalho, “Depletion region in thermally poled fused silica,” Appl. Phys. Lett. 76, 2496–2498 (2000).
[CrossRef]

Corbari, C.

C. Corbari, O. Deparis, B. G. Klappauf, and P. G. Kazansky, “Practical technique for measurement of second-order nonlinearity in poled glass,” Electron. Lett. 39, 197–198 (2003).
[CrossRef]

Cordeiro, C. M. B.

A. L. C. Triques, C. M. B. Cordeiro, V. Balestrieri, B. Lesche, W. Margulis, and I. C. S. Carvalho, “Depletion region in thermally poled fused silica,” Appl. Phys. Lett. 76, 2496–2498 (2000).
[CrossRef]

Deparis, O.

C. Corbari, O. Deparis, B. G. Klappauf, and P. G. Kazansky, “Practical technique for measurement of second-order nonlinearity in poled glass,” Electron. Lett. 39, 197–198 (2003).
[CrossRef]

Digonnet, M. J. F.

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Simplified inverse Fourier transform technique to measure optical nonlinearity profiles using a reference sample,” Electron. Lett. 40, 551–552 (2004).
[CrossRef]

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Inverse Fourier transform technique to determine second-order optical nonlinearity spatial profiles,” Appl. Phys. Lett. 82, 1362–1364 (2003).
[CrossRef]

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Cylinder-assisted Maker-fringe technique,” Electron. Lett. 39, 1834–1835 (2003).
[CrossRef]

D. Pureur, A. C. Liu, M. J. F. Digonnet, and G. S. Kino, “Absolute measurement of the second-order nonlinearity profile in poled silica,” Opt. Lett. 23, 588–590 (1998).
[CrossRef]

Douay, M.

Y. Quiquempois, G. Martinelli, P. Dutherage, P. Bernage, P. Niay, and M. Douay, “Localisation of the induced second-order non-linearity within Infrasil and Suprasil thermally poled glasses,” Opt. Commun. 176, 479–487 (2000).
[CrossRef]

Ducasse, A.

A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Phys. J. D 1, 223–226 (1998).
[CrossRef]

Dutherage, P.

Y. Quiquempois, G. Martinelli, P. Dutherage, P. Bernage, P. Niay, and M. Douay, “Localisation of the induced second-order non-linearity within Infrasil and Suprasil thermally poled glasses,” Opt. Commun. 176, 479–487 (2000).
[CrossRef]

Fleming, S.

D. Wong, W. Xu, S. Fleming, M. Janos, and K. M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 65, 235–241 (1999).
[CrossRef]

Freysz, E.

A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Phys. J. D 1, 223–226 (1998).
[CrossRef]

Godbout, N.

Y. Quiquempois, N. Godbout, and S. Lacroix, “Model of charge migration during thermal poling in silica glasses: evidence of a voltage threshold for the onset of a second-order nonlinearity,” Phys. Rev. A 65, 043816 (2002).
[CrossRef]

Janos, M.

D. Wong, W. Xu, S. Fleming, M. Janos, and K. M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 65, 235–241 (1999).
[CrossRef]

Kazansky, P. G.

C. Corbari, O. Deparis, B. G. Klappauf, and P. G. Kazansky, “Practical technique for measurement of second-order nonlinearity in poled glass,” Electron. Lett. 39, 197–198 (2003).
[CrossRef]

Kielich, S.

S. Kielich, “Optical second-harmonic generation by electrically polarized isotropic media,” IEEE J. Quantum Electron. QE-5, 562–568 (1969).
[CrossRef]

Kino, G. S.

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Simplified inverse Fourier transform technique to measure optical nonlinearity profiles using a reference sample,” Electron. Lett. 40, 551–552 (2004).
[CrossRef]

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Inverse Fourier transform technique to determine second-order optical nonlinearity spatial profiles,” Appl. Phys. Lett. 82, 1362–1364 (2003).
[CrossRef]

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Cylinder-assisted Maker-fringe technique,” Electron. Lett. 39, 1834–1835 (2003).
[CrossRef]

D. Pureur, A. C. Liu, M. J. F. Digonnet, and G. S. Kino, “Absolute measurement of the second-order nonlinearity profile in poled silica,” Opt. Lett. 23, 588–590 (1998).
[CrossRef]

Klappauf, B. G.

C. Corbari, O. Deparis, B. G. Klappauf, and P. G. Kazansky, “Practical technique for measurement of second-order nonlinearity in poled glass,” Electron. Lett. 39, 197–198 (2003).
[CrossRef]

Lacroix, S.

Y. Quiquempois, N. Godbout, and S. Lacroix, “Model of charge migration during thermal poling in silica glasses: evidence of a voltage threshold for the onset of a second-order nonlinearity,” Phys. Rev. A 65, 043816 (2002).
[CrossRef]

Le Calvez, A.

A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Phys. J. D 1, 223–226 (1998).
[CrossRef]

Lesche, B.

A. L. C. Triques, C. M. B. Cordeiro, V. Balestrieri, B. Lesche, W. Margulis, and I. C. S. Carvalho, “Depletion region in thermally poled fused silica,” Appl. Phys. Lett. 76, 2496–2498 (2000).
[CrossRef]

Liu, A. C.

Lo, K. M.

D. Wong, W. Xu, S. Fleming, M. Janos, and K. M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 65, 235–241 (1999).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Margulis, W.

A. L. C. Triques, C. M. B. Cordeiro, V. Balestrieri, B. Lesche, W. Margulis, and I. C. S. Carvalho, “Depletion region in thermally poled fused silica,” Appl. Phys. Lett. 76, 2496–2498 (2000).
[CrossRef]

U. Osterberg and W. Margulis, “Dye laser pumped by Nd:YAG laser pulses frequency doubled in a glass optical fiber,” Opt. Lett. 11, 516–518 (1986).
[CrossRef] [PubMed]

Martinelli, G.

Y. Quiquempois, G. Martinelli, P. Dutherage, P. Bernage, P. Niay, and M. Douay, “Localisation of the induced second-order non-linearity within Infrasil and Suprasil thermally poled glasses,” Opt. Commun. 176, 479–487 (2000).
[CrossRef]

Mukherjee, N.

Myers, R. A.

T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242, 165–176 (1998).
[CrossRef]

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16, 1732–1734 (1991).
[CrossRef] [PubMed]

Niay, P.

Y. Quiquempois, G. Martinelli, P. Dutherage, P. Bernage, P. Niay, and M. Douay, “Localisation of the induced second-order non-linearity within Infrasil and Suprasil thermally poled glasses,” Opt. Commun. 176, 479–487 (2000).
[CrossRef]

Nisenoff, M.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Osterberg, U.

Ozcan, A.

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Simplified inverse Fourier transform technique to measure optical nonlinearity profiles using a reference sample,” Electron. Lett. 40, 551–552 (2004).
[CrossRef]

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Cylinder-assisted Maker-fringe technique,” Electron. Lett. 39, 1834–1835 (2003).
[CrossRef]

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Inverse Fourier transform technique to determine second-order optical nonlinearity spatial profiles,” Appl. Phys. Lett. 82, 1362–1364 (2003).
[CrossRef]

Pureur, D.

Quiquempois, Y.

Y. Quiquempois, N. Godbout, and S. Lacroix, “Model of charge migration during thermal poling in silica glasses: evidence of a voltage threshold for the onset of a second-order nonlinearity,” Phys. Rev. A 65, 043816 (2002).
[CrossRef]

Y. Quiquempois, G. Martinelli, P. Dutherage, P. Bernage, P. Niay, and M. Douay, “Localisation of the induced second-order non-linearity within Infrasil and Suprasil thermally poled glasses,” Opt. Commun. 176, 479–487 (2000).
[CrossRef]

Rodriguez, V.

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Sourisseau, C.

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Triques, A. L. C.

A. L. C. Triques, C. M. B. Cordeiro, V. Balestrieri, B. Lesche, W. Margulis, and I. C. S. Carvalho, “Depletion region in thermally poled fused silica,” Appl. Phys. Lett. 76, 2496–2498 (2000).
[CrossRef]

Wiedenbeck, M.

T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectroscopy study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
[CrossRef]

Wong, D.

D. Wong, W. Xu, S. Fleming, M. Janos, and K. M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 65, 235–241 (1999).
[CrossRef]

Xu, W.

D. Wong, W. Xu, S. Fleming, M. Janos, and K. M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 65, 235–241 (1999).
[CrossRef]

Appl. Phys. Lett.

A. L. C. Triques, C. M. B. Cordeiro, V. Balestrieri, B. Lesche, W. Margulis, and I. C. S. Carvalho, “Depletion region in thermally poled fused silica,” Appl. Phys. Lett. 76, 2496–2498 (2000).
[CrossRef]

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Inverse Fourier transform technique to determine second-order optical nonlinearity spatial profiles,” Appl. Phys. Lett. 82, 1362–1364 (2003).
[CrossRef]

Electron. Lett.

C. Corbari, O. Deparis, B. G. Klappauf, and P. G. Kazansky, “Practical technique for measurement of second-order nonlinearity in poled glass,” Electron. Lett. 39, 197–198 (2003).
[CrossRef]

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Simplified inverse Fourier transform technique to measure optical nonlinearity profiles using a reference sample,” Electron. Lett. 40, 551–552 (2004).
[CrossRef]

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Cylinder-assisted Maker-fringe technique,” Electron. Lett. 39, 1834–1835 (2003).
[CrossRef]

Eur. Phys. J. D

A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Phys. J. D 1, 223–226 (1998).
[CrossRef]

IEEE J. Quantum Electron.

S. Kielich, “Optical second-harmonic generation by electrically polarized isotropic media,” IEEE J. Quantum Electron. QE-5, 562–568 (1969).
[CrossRef]

J. Appl. Phys.

T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectroscopy study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
[CrossRef]

J. Non-Cryst. Solids

T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242, 165–176 (1998).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

Y. Quiquempois, G. Martinelli, P. Dutherage, P. Bernage, P. Niay, and M. Douay, “Localisation of the induced second-order non-linearity within Infrasil and Suprasil thermally poled glasses,” Opt. Commun. 176, 479–487 (2000).
[CrossRef]

Opt. Fiber Technol.

D. Wong, W. Xu, S. Fleming, M. Janos, and K. M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 65, 235–241 (1999).
[CrossRef]

Opt. Lett.

Phys. Rev. A

Y. Quiquempois, N. Godbout, and S. Lacroix, “Model of charge migration during thermal poling in silica glasses: evidence of a voltage threshold for the onset of a second-order nonlinearity,” Phys. Rev. A 65, 043816 (2002).
[CrossRef]

Phys. Rev. Lett.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Other

V. Tréanton, N. Godbout, and S. Lacroix, “An interferometric Maker fringe experiment to reconstruct the χ(2) profile of poled silica plates,” in Proceedings of Bragg Gratings, Photosensitivity and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 510–512.

Y. Quiquempois, M. Lelek, A. Kudlinski, H. Zerglache, and G. Martinelli, “Non-linear distribution reconstruction in poled silica glasses with a sub-micron resolution,” in Proceedings of Bragg Gratings, Photosensitivity and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 256–258.

A. Kudlinski, G. Martinelli, Y. Quiquempois, and H. Zerglache, “Microscopic model for the second-order nonlinearity creation in thermally poled bulk silica glasses,” in Proceedings of Bragg Gratings, Photosensitivity and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 213–215.

R. Kashyap, F. C. Garcia, and L. Vogelaar, “Nonlinearity of the electro-optic effect in poled waveguides,” in Proceedings of Bragg Gratings, Photosensitivity and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 210–212.

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Figures (13)

Fig. 1
Fig. 1

(a) χ(2) spatial distribution profiles considered for simulation: Triangular (dashed curve) and Step (solid line) in a 550-mm-thick thermally poled silica glass plate, (b) their corresponding Maker fringe signal.

Fig. 2
Fig. 2

Schematic representation of the hemicylindral lens setup used.

Fig. 3
Fig. 3

(a) Theoretical Maker fringe signal and (b) normalized Fourier Maker signal for the profiles illustrated in Fig. 1(a) by use of hemicylindrical lenses. The nonlinearity thickness indicated in Fig. 1(a) can be deduced from the period of the signals on Fig. 3(b) using Eq. (6). For example, the solid-line profile has a 314-mm-1 period that leads to a 20-µm-thick layer. The gray rectangles mark the limits of the measured signal without the use of hemicylindrical lenses.

Fig. 4
Fig. 4

Schematic of the top view of the experimental configuration. An x-cut quartz is used as a phase reference plate. The small axes refer to the optical axes of the x-cut quartz plate; its y axis is in the plane of incidence, while its z-axis is directed out of plane. In our experiments, the quartz x axis is either directed toward the positive or the negative z axis of the setup; the latter case is what we refer to as flipped.

Fig. 5
Fig. 5

Schematic of the experimental setup used. It is composed of a Q-switched Nd:YAG laser, an attenuator, a collimating lens (CL), low-pass filters (F1), high-pass filters (F2), a beam splitter (BS), focusing lenses (L) and photomultiplier tubes (PMT) to measure the generated SHG. An x-cut quartz plate is placed in the reference arm to record the laser fluctuations. The sample arm consists in a thermally poled sample alone or stacked together with a phase reference plate, which is another x-cut quartz plate. The reference arm quartz plate is used at a fixed angle while the sample rotates from -80° to 80°.

Fig. 6
Fig. 6

Sample 1: (a) Experimental (solid curve) and theoretical (dashed curve) Maker fringe signal and (b) and normalized Fourier Maker signal.

Fig. 7
Fig. 7

Sample 2: (a) Experimental (solid curve) and theoretical (dashed curve) Maker fringe signal and (b) and normalized Fourier Maker signal.

Fig. 8
Fig. 8

Spatial distribution of χ(2)(z) determined for sample 1 and sample 2.

Fig. 9
Fig. 9

Experimental Maker fringe for sample 1 stacked with a 0.485-mm x-cut quartz plate with positive (solid curve) and negative (dashed curve) orientation with respect to the propagation direction. The internal angle is the angle inside the quartz phase reference plate.

Fig. 10
Fig. 10

Experimental Maker fringe for sample 2 stacked with a 0.485-mm x-cut quartz plate with positive (solid curve) and negative (dashed curve) orientation with respect to the propagation direction. The internal angle is the angle inside the quartz phase reference plate.

Fig. 11
Fig. 11

Difference of the two stacks signals (|A+B|2-|A-B|2) for sample 1: Experimental results (solid curve) and simulated results (dashed curve).

Fig. 12
Fig. 12

Difference of the two stacks signals (|A+B|2-|A-B|2) for sample 2: Experimental results (solid curve) and simulated results (dashed curve).

Fig. 13
Fig. 13

Summation of the two signals (|A+B|2+|A-B|2) for sample 1 (solid curve), twice the signal of the quartz plate (2|B|2 in dashed curve) and twice the signal of the sample (2|A|2 in dashed-dotted curve).

Tables (1)

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Table 1 Parameters for Sample 1 and 2, Poled in the Same Conditions

Equations (11)

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P2ω=hχ(2)(z)exp(ikz)dz2,
k=2ωc(nω cos θω-n2ω cos θ2ω)=2ωc(nω-n2ω)cos[(θω+θ2ω)/2] cos θω-θ2ω2,
k=4π(nω-n2ω)λ cos θ=Δkcos θ,
h(θ)=2ω2Pω2g(θ)2T(θ)0c3n2ωnω2πw02  cos2 θ,
P2ωh=4k2sin2 kL2.
L=2π/K.
|A+B|2=|A|2+|B|2+2|A||B|cos(ϕA-ϕB),
g(θ)=sin θ(1-4 sin θ cos2 θ).
|A+B|2-|A-B|2=4|A||B|cos(ϕA-ϕB).
χ(2)=3χ(3)EDC,
|A+B|2+|A-B|2=2|A|2+2|B|2.

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