Abstract

We present a powerful but simple technique based on a 4f coherent imager system with top-hat beams to characterize nonlinear optical properties. We describe the theoretical model and the experimental details of the measurement for materials having nonlinear refraction with or without nonlinear absorption. We show that it is possible to characterize the nonlinearities by analyzing the intensity profile of the image after nonlinear filtering through the material placed in the Fourier plane of the setup. We will show that, as in the Z-scan technique, the use of top-hat beams instead of Gaussian beams increases the sensitivity of the measurement. Intensity-dependent nonlinearities can be studied by use of this single laser-shot technique. We validate this nonlinear imaging technique by measuring the absolute value of the n2 coefficient for CS2 and some well-known chalcogenide glasses (As2S3, As2Se3, GeSe4, and Ge10As10Se80). Our values are in good agreement with those obtained by other techniques.

© 2004 Optical Society of America

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  1. G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
    [CrossRef]
  2. G. Boudebs, M. Chis, and X. Nguyen Phu, “Third-order sus- ceptibility measurement by a new Mach–Zehnder interferometry technique,” J. Opt. Soc. Am. B 18, 623–627 (2001).
    [CrossRef]
  3. G. Boudebs, F. Sanchez, C. Duverger, and B. Boulard, “Improvement of Mach–Zehnder interferometry technique for third-order susceptibility measurement,” Opt. Commun. 199, 257–265 (2001).
    [CrossRef]
  4. G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, “Non- linear optical properties of chalcogenide glasses: comparison between Mach–Zehnder interferometry and Z-scan techniques,” Opt. Commun. 199, 425–433 (2001).
    [CrossRef]
  5. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
  6. F. Smektala, C. Quemard, V. Couderc, and A. Barthélémy, “Non-linear optical properties of chalcogenide glasses measured by Z-scan,” J. Non-Cryst. Solids 274, 232–237 (2000).
    [CrossRef]
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    [CrossRef]
  9. C. Quémard, F. Smektala, V. Couderc, A. Barthélémy, and J. Lucas, “Chalcogenide glasses with high non linear optical properties for telecommunications,” J. Phys. Chem. Solids 62, 1435–1440 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. G. Boudebs, M. Chis, and A. Monteil, “Contrast increasing by third-order nonlinear image processing: a numerical study for microscopic rectangular objects,” Opt. Commun. 150, 287–296 (1998).
    [CrossRef]
  14. N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
    [CrossRef]
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    [CrossRef]
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2003 (1)

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[CrossRef]

2002 (1)

2001 (4)

G. Boudebs, M. Chis, and X. Nguyen Phu, “Third-order sus- ceptibility measurement by a new Mach–Zehnder interferometry technique,” J. Opt. Soc. Am. B 18, 623–627 (2001).
[CrossRef]

G. Boudebs, F. Sanchez, C. Duverger, and B. Boulard, “Improvement of Mach–Zehnder interferometry technique for third-order susceptibility measurement,” Opt. Commun. 199, 257–265 (2001).
[CrossRef]

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, “Non- linear optical properties of chalcogenide glasses: comparison between Mach–Zehnder interferometry and Z-scan techniques,” Opt. Commun. 199, 425–433 (2001).
[CrossRef]

C. Quémard, F. Smektala, V. Couderc, A. Barthélémy, and J. Lucas, “Chalcogenide glasses with high non linear optical properties for telecommunications,” J. Phys. Chem. Solids 62, 1435–1440 (2001).
[CrossRef]

2000 (1)

F. Smektala, C. Quemard, V. Couderc, and A. Barthélémy, “Non-linear optical properties of chalcogenide glasses measured by Z-scan,” J. Non-Cryst. Solids 274, 232–237 (2000).
[CrossRef]

1998 (2)

F. Smektala, C. Quémard, L. LeNeindre, J. Lucas, A. Barthélémy, and C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

G. Boudebs, M. Chis, and A. Monteil, “Contrast increasing by third-order nonlinear image processing: a numerical study for microscopic rectangular objects,” Opt. Commun. 150, 287–296 (1998).
[CrossRef]

1997 (1)

1996 (2)

1993 (1)

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

1988 (1)

N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
[CrossRef]

1987 (1)

1984 (2)

J. A. Hermann, “Beam propagation and optical power limiting with nonlinear media,” J. Opt. Soc. Am. B 1, 729–736 (1984).
[CrossRef]

W. E. Williams, M. J. Soileau, and E. W. Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[CrossRef]

1964 (1)

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Adair, R.

Aggarwal, I. D.

Barthélémy, A.

C. Quémard, F. Smektala, V. Couderc, A. Barthélémy, and J. Lucas, “Chalcogenide glasses with high non linear optical properties for telecommunications,” J. Phys. Chem. Solids 62, 1435–1440 (2001).
[CrossRef]

F. Smektala, C. Quemard, V. Couderc, and A. Barthélémy, “Non-linear optical properties of chalcogenide glasses measured by Z-scan,” J. Non-Cryst. Solids 274, 232–237 (2000).
[CrossRef]

F. Smektala, C. Quémard, L. LeNeindre, J. Lucas, A. Barthélémy, and C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

Boudebs, G.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[CrossRef]

G. Boudebs, M. Chis, and X. Nguyen Phu, “Third-order sus- ceptibility measurement by a new Mach–Zehnder interferometry technique,” J. Opt. Soc. Am. B 18, 623–627 (2001).
[CrossRef]

G. Boudebs, F. Sanchez, C. Duverger, and B. Boulard, “Improvement of Mach–Zehnder interferometry technique for third-order susceptibility measurement,” Opt. Commun. 199, 257–265 (2001).
[CrossRef]

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, “Non- linear optical properties of chalcogenide glasses: comparison between Mach–Zehnder interferometry and Z-scan techniques,” Opt. Commun. 199, 425–433 (2001).
[CrossRef]

G. Boudebs, M. Chis, and A. Monteil, “Contrast increasing by third-order nonlinear image processing: a numerical study for microscopic rectangular objects,” Opt. Commun. 150, 287–296 (1998).
[CrossRef]

G. Boudebs, M. Chis, and J. P. Bourdin, “Third-order susceptibility measurements by nonlinear image processing,” J. Opt. Soc. Am. B 13, 1450–1456 (1996).
[CrossRef]

Boulard, B.

G. Boudebs, F. Sanchez, C. Duverger, and B. Boulard, “Improvement of Mach–Zehnder interferometry technique for third-order susceptibility measurement,” Opt. Commun. 199, 257–265 (2001).
[CrossRef]

Bourdin, J. P.

Brekhovskhikh, G. L.

N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
[CrossRef]

Chase, L. L.

Cherukulappurath, S.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[CrossRef]

Chis, M.

Couderc, V.

C. Quémard, F. Smektala, V. Couderc, A. Barthélémy, and J. Lucas, “Chalcogenide glasses with high non linear optical properties for telecommunications,” J. Phys. Chem. Solids 62, 1435–1440 (2001).
[CrossRef]

F. Smektala, C. Quemard, V. Couderc, and A. Barthélémy, “Non-linear optical properties of chalcogenide glasses measured by Z-scan,” J. Non-Cryst. Solids 274, 232–237 (2000).
[CrossRef]

De Angelis, C.

F. Smektala, C. Quémard, L. LeNeindre, J. Lucas, A. Barthélémy, and C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

Duverger, C.

G. Boudebs, F. Sanchez, C. Duverger, and B. Boulard, “Improvement of Mach–Zehnder interferometry technique for third-order susceptibility measurement,” Opt. Commun. 199, 257–265 (2001).
[CrossRef]

Ferrier, J. L.

N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
[CrossRef]

Gazengel, J.

N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
[CrossRef]

Gindre, D.

Hagan, D.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Harbold, J. M.

Hermann, J. A.

Ilday, F. Ö.

Krauss, F. T.

Kudriavtseva, A. D.

N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
[CrossRef]

Kung, I.

Leblond, H.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[CrossRef]

LeNeindre, L.

F. Smektala, C. Quémard, L. LeNeindre, J. Lucas, A. Barthélémy, and C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

Lucas, J.

C. Quémard, F. Smektala, V. Couderc, A. Barthélémy, and J. Lucas, “Chalcogenide glasses with high non linear optical properties for telecommunications,” J. Phys. Chem. Solids 62, 1435–1440 (2001).
[CrossRef]

F. Smektala, C. Quémard, L. LeNeindre, J. Lucas, A. Barthélémy, and C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

Maillote, H.

Maker, P. D.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Marcano, A.

Métin, D.

Monteil, A.

G. Boudebs, M. Chis, and A. Monteil, “Contrast increasing by third-order nonlinear image processing: a numerical study for microscopic rectangular objects,” Opt. Commun. 150, 287–296 (1998).
[CrossRef]

Nguyen, V. Q.

Nguyen Phu, X.

Palffy-Muhoray, P.

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

Payne, S. A.

Quemard, C.

F. Smektala, C. Quemard, V. Couderc, and A. Barthélémy, “Non-linear optical properties of chalcogenide glasses measured by Z-scan,” J. Non-Cryst. Solids 274, 232–237 (2000).
[CrossRef]

Quémard, C.

C. Quémard, F. Smektala, V. Couderc, A. Barthélémy, and J. Lucas, “Chalcogenide glasses with high non linear optical properties for telecommunications,” J. Phys. Chem. Solids 62, 1435–1440 (2001).
[CrossRef]

F. Smektala, C. Quémard, L. LeNeindre, J. Lucas, A. Barthélémy, and C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

Rivoire, G.

N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Sanchez, F.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[CrossRef]

G. Boudebs, F. Sanchez, C. Duverger, and B. Boulard, “Improvement of Mach–Zehnder interferometry technique for third-order susceptibility measurement,” Opt. Commun. 199, 257–265 (2001).
[CrossRef]

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, “Non- linear optical properties of chalcogenide glasses: comparison between Mach–Zehnder interferometry and Z-scan techniques,” Opt. Commun. 199, 425–433 (2001).
[CrossRef]

Sanghera, J. S.

Savage, C. M.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Shaw, L. B.

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Smektala, F.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[CrossRef]

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, “Non- linear optical properties of chalcogenide glasses: comparison between Mach–Zehnder interferometry and Z-scan techniques,” Opt. Commun. 199, 425–433 (2001).
[CrossRef]

C. Quémard, F. Smektala, V. Couderc, A. Barthélémy, and J. Lucas, “Chalcogenide glasses with high non linear optical properties for telecommunications,” J. Phys. Chem. Solids 62, 1435–1440 (2001).
[CrossRef]

F. Smektala, C. Quemard, V. Couderc, and A. Barthélémy, “Non-linear optical properties of chalcogenide glasses measured by Z-scan,” J. Non-Cryst. Solids 274, 232–237 (2000).
[CrossRef]

F. Smektala, C. Quémard, L. LeNeindre, J. Lucas, A. Barthélémy, and C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

Soileau, M. J.

W. E. Williams, M. J. Soileau, and E. W. Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[CrossRef]

Sokolovskaia, A. I.

N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
[CrossRef]

Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

W. E. Williams, M. J. Soileau, and E. W. Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[CrossRef]

Tcherniega, N. V.

N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Troles, J.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[CrossRef]

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, “Non- linear optical properties of chalcogenide glasses: comparison between Mach–Zehnder interferometry and Z-scan techniques,” Opt. Commun. 199, 425–433 (2001).
[CrossRef]

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Williams, W. E.

W. E. Williams, M. J. Soileau, and E. W. Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[CrossRef]

Wise, F.

Wise, F. W.

Xuan, N. P.

N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
[CrossRef]

Zhao, W.

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

Appl. Phys. Lett. (1)

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

J. Non-Cryst. Solids (2)

F. Smektala, C. Quemard, V. Couderc, and A. Barthélémy, “Non-linear optical properties of chalcogenide glasses measured by Z-scan,” J. Non-Cryst. Solids 274, 232–237 (2000).
[CrossRef]

F. Smektala, C. Quémard, L. LeNeindre, J. Lucas, A. Barthélémy, and C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. Chem. Solids (1)

C. Quémard, F. Smektala, V. Couderc, A. Barthélémy, and J. Lucas, “Chalcogenide glasses with high non linear optical properties for telecommunications,” J. Phys. Chem. Solids 62, 1435–1440 (2001).
[CrossRef]

Opt. Commun. (6)

G. Boudebs, F. Sanchez, C. Duverger, and B. Boulard, “Improvement of Mach–Zehnder interferometry technique for third-order susceptibility measurement,” Opt. Commun. 199, 257–265 (2001).
[CrossRef]

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, “Non- linear optical properties of chalcogenide glasses: comparison between Mach–Zehnder interferometry and Z-scan techniques,” Opt. Commun. 199, 425–433 (2001).
[CrossRef]

W. E. Williams, M. J. Soileau, and E. W. Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[CrossRef]

G. Boudebs, M. Chis, and A. Monteil, “Contrast increasing by third-order nonlinear image processing: a numerical study for microscopic rectangular objects,” Opt. Commun. 150, 287–296 (1998).
[CrossRef]

N. P. Xuan, J. L. Ferrier, J. Gazengel, G. Rivoire, G. L. Brekhovskhikh, A. D. Kudriavtseva, A. I. Sokolovskaia, and N. V. Tcherniega, “Changes in the space structures of light beams induced by nonlinear optical phenomena: application to phase contrast and image processing,” Opt. Commun. 68, 244–250 (1988).
[CrossRef]

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Other (3)

C. Quémard, “Propriétés optiques non linéaires de verres de chalcogénures en vue de leur application dans les technologies de commutation optique en télécommunications,” thèse (l’Université de Rennes 1, France, 2000).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Y. R. Shen, Nonlinear Optics (Wiley, New York, 1984), Chap. 3, pp. 42–50.

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Figures (4)

Fig. 1
Fig. 1

Schematic of a 4f coherent system imager. The nonlinear material (NL) is placed in the Fourier plane. L1L3, lenses; M1, M2, mirrors; BS1, BS2, beam splitters; tf, neutral filter.

Fig. 2
Fig. 2

(a) Numerical simulation of the Gaussian beam image profiles at the output of the 4f setup after transmission through CS2: The solid curve (1) is obtained with low intensity (insignificant nonlinear dephasing), and the dotted curve (2) is obtained with higher intensity, producing nonlinear phase filtering. The numerical parameters are I0=2.3 GW/cm2, λ=1.06 µm, L=5 mm, n2=3.4×10-18 m2/W, β=0, α=0, G=1, and NA=0.1. (b) Numerical simulation showing only the positive part of image subtractions. The left image corresponds to profile (2) (with nonlinearities) minus that corresponding to profile (1) (without nonlinearities). The right image is the inverse subtraction. The numerical parameters are the same as those used in (a). Note the loss of energy in the center of the right image, which is diffracted in a ring pattern on the wing of the left image. The x and y coordinates are in pixels, and the dimensions of a pixel is 12 µm×12 µm.

Fig. 3
Fig. 3

(a) Numerical simulation of the top-hat-beam image profiles at the output of the 4f setup after transmission through CS2: The solid curve (1) is obtained with low intensity (insignificant nonlinear dephasing), and the dotted curve (2) is obtained with higher intensity, producing nonlinear phase filtering. The numerical parameters are the same than those used in Fig. 2(a). (b) Numerical simulation showing only the positive part of the image after subtractions. The left image corresponds to profile (2) (with nonlinearities) minus that corresponding to profile (1) (without nonlinearities). The right image is the inverse subtraction. The numerical parameters are the same as those used in Fig. 2(a). Note the loss of energy in the center in the right image, which is diffracted in a ring pattern on the wing in the left image. As before, the x and y coordinates are in pixels, and the dimensions of a pixel is 12 µm×12 µm.

Fig. 4
Fig. 4

(a) Spatial profiles of the image of the diaphragm with the NL material: profile (1) with low I0 (negligible nonlinearities), profile (2) is a theoretical simulation of the image of the diaphragm with the measured optimized n2 value (n2=4.5×10-18 m2/W), and profile (3) is experimental acquisitions showing nonlinearities. (b) Zoomed profile of the image found in (a). Note the significant diffracted light outside the geometrical image of the border [profile (1), dashed points] in both experimental (3) and simulated (1) profiles.

Tables (2)

Tables Icon

Table 1 Measured Values of n2 by Use of Our Technique (NIT) for Different Nonlinear Materialsa

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Table 2 Comparison of the Nonlinear Coefficient Measurements of Different Infrared Glasses Obtained by Use of the NIT, MZT,4 and Z Scan6 at 1.06 µm in the Picosecond Range

Equations (5)

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S(u, v)=1λf1 FT[O(x, y)]=1λf1 O(x, y)exp[-2πj(ux+vy)]dxdy,
Iim(x, y)=|U(x, y)|2=|FT-1[S(u, v)T(u, v)H(u, v)]|2,
SL(u, v)=S(u, v)×exp(-αL/2)[1+q(u, v)]jkn2β-12,
T(u, v)=SL(u, v)S(u, v)={exp(αL)[1+q(u, v)]}-1/2×exp[jϕNL(u, v)],
ϕNL(u, v)=kn2β ln[1+q(u, v)].

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