Abstract

We show that the Talbot effect can be used to increase the gain of two-wave mixing in a stack of thin nonlinear media. We demonstrate that a large gain enhancement is achieved for a few nonlinear elements, provided that they are placed at distances that satisfy Talbot recurrences.

© 2006 Optical Society of America

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References

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  1. H. F. Talbot, Philos. Mag. 9, 401 (1836).
  2. Lord Rayleigh, Philos. Mag. 11, 196 (1881).
  3. See, e.g., M. Berry, I. Marzoli, and W. Schleich, Phys. World June 2001, 39 (2001).
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    [CrossRef]
  5. A. W. Lohman and D. E. Silva, Opt. Commun. 2, 413 (1971).
    [CrossRef]
  6. M. Wrage, P. Glas, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, Opt. Commun. 191, 149 (2001).
    [CrossRef]
  7. S. Minardi, G. Arrighi, P. Di Trapani, A. Varanavicius, and A. Piskarskas, Opt. Lett. 27, 2097 (2002).
    [CrossRef]
  8. M. Testorf, J. Jahns, N. A. Khilo, and A. Goncharenko, Opt. Commun. 129, 167 (1996).
    [CrossRef]
  9. S. Longhi, M. Marano, P. Laporta, O. Svelto, M. Belmonte, B. Agogliati, L. Arcangeli, V. Pruneri, M. N. Zervas, and M. Ibsen, Opt. Lett. 25, 1481 (2000).
    [CrossRef]
  10. H. Hamam and J. L. Bougrenet de la Tocnaye, Opt. Lett. 19, 1654 (2001).
    [CrossRef]
  11. R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
    [CrossRef] [PubMed]
  12. P. Gunter and J. P. Huignard, Photorefractive Crystals and Their Applications (Springer-Verlag, 1989).
  13. Z. Hu, D. Liu, A. Yan, X. Wan, and I. Liu, Presented at the Tenth International Conference on Photorefractive Effects, Materials, and Devices, Sanya Hainan, China, July 19-23, 2005.
  14. A. Brignon, I. Bongrand, B. Loiseaux, and J. P. Huignard, Opt. Lett. 22, 1855 (1997).
    [CrossRef]
  15. U. Bortolozzo, S. Residori, A. Petrosyan, and J. P. Huignard, Opt. Commun. doi: 10.1016/j.optcom.2006.01.038 (2006).

2006 (1)

U. Bortolozzo, S. Residori, A. Petrosyan, and J. P. Huignard, Opt. Commun. doi: 10.1016/j.optcom.2006.01.038 (2006).

2005 (1)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

2002 (1)

2001 (3)

M. Wrage, P. Glas, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, Opt. Commun. 191, 149 (2001).
[CrossRef]

See, e.g., M. Berry, I. Marzoli, and W. Schleich, Phys. World June 2001, 39 (2001).

H. Hamam and J. L. Bougrenet de la Tocnaye, Opt. Lett. 19, 1654 (2001).
[CrossRef]

2000 (1)

1997 (1)

1996 (2)

M. Testorf, J. Jahns, N. A. Khilo, and A. Goncharenko, Opt. Commun. 129, 167 (1996).
[CrossRef]

M. V. Berry and S. Klein, J. Mod. Opt. 43, 2139 (1996).
[CrossRef]

1971 (1)

A. W. Lohman and D. E. Silva, Opt. Commun. 2, 413 (1971).
[CrossRef]

1881 (1)

Lord Rayleigh, Philos. Mag. 11, 196 (1881).

1836 (1)

H. F. Talbot, Philos. Mag. 9, 401 (1836).

Agogliati, B.

Arcangeli, L.

Arrighi, G.

Belmonte, M.

Berry, M.

See, e.g., M. Berry, I. Marzoli, and W. Schleich, Phys. World June 2001, 39 (2001).

Berry, M. V.

M. V. Berry and S. Klein, J. Mod. Opt. 43, 2139 (1996).
[CrossRef]

Bongrand, I.

Bortolozzo, U.

U. Bortolozzo, S. Residori, A. Petrosyan, and J. P. Huignard, Opt. Commun. doi: 10.1016/j.optcom.2006.01.038 (2006).

Bougrenet de la Tocnaye, J. L.

Brignon, A.

Christodoulides, D. N.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Di Trapani, P.

Glas, P.

M. Wrage, P. Glas, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, Opt. Commun. 191, 149 (2001).
[CrossRef]

Goncharenko, A.

M. Testorf, J. Jahns, N. A. Khilo, and A. Goncharenko, Opt. Commun. 129, 167 (1996).
[CrossRef]

Gunter, P.

P. Gunter and J. P. Huignard, Photorefractive Crystals and Their Applications (Springer-Verlag, 1989).

Hamam, H.

Hu, Z.

Z. Hu, D. Liu, A. Yan, X. Wan, and I. Liu, Presented at the Tenth International Conference on Photorefractive Effects, Materials, and Devices, Sanya Hainan, China, July 19-23, 2005.

Huignard, J. P.

U. Bortolozzo, S. Residori, A. Petrosyan, and J. P. Huignard, Opt. Commun. doi: 10.1016/j.optcom.2006.01.038 (2006).

A. Brignon, I. Bongrand, B. Loiseaux, and J. P. Huignard, Opt. Lett. 22, 1855 (1997).
[CrossRef]

P. Gunter and J. P. Huignard, Photorefractive Crystals and Their Applications (Springer-Verlag, 1989).

Ibsen, M.

Iwanow, R.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Jahns, J.

M. Testorf, J. Jahns, N. A. Khilo, and A. Goncharenko, Opt. Commun. 129, 167 (1996).
[CrossRef]

Khilo, N. A.

M. Testorf, J. Jahns, N. A. Khilo, and A. Goncharenko, Opt. Commun. 129, 167 (1996).
[CrossRef]

Klein, S.

M. V. Berry and S. Klein, J. Mod. Opt. 43, 2139 (1996).
[CrossRef]

Laporta, P.

Leitner, M.

M. Wrage, P. Glas, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, Opt. Commun. 191, 149 (2001).
[CrossRef]

Liu, D.

Z. Hu, D. Liu, A. Yan, X. Wan, and I. Liu, Presented at the Tenth International Conference on Photorefractive Effects, Materials, and Devices, Sanya Hainan, China, July 19-23, 2005.

Liu, I.

Z. Hu, D. Liu, A. Yan, X. Wan, and I. Liu, Presented at the Tenth International Conference on Photorefractive Effects, Materials, and Devices, Sanya Hainan, China, July 19-23, 2005.

Lohman, A. W.

A. W. Lohman and D. E. Silva, Opt. Commun. 2, 413 (1971).
[CrossRef]

Loiseaux, B.

Longhi, S.

Marano, M.

Marzoli, I.

See, e.g., M. Berry, I. Marzoli, and W. Schleich, Phys. World June 2001, 39 (2001).

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Min, Y.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Minardi, S.

Napartovich, A. P.

M. Wrage, P. Glas, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, Opt. Commun. 191, 149 (2001).
[CrossRef]

Petrosyan, A.

U. Bortolozzo, S. Residori, A. Petrosyan, and J. P. Huignard, Opt. Commun. doi: 10.1016/j.optcom.2006.01.038 (2006).

Piskarskas, A.

Pruneri, V.

Rayleigh, Lord

Lord Rayleigh, Philos. Mag. 11, 196 (1881).

Residori, S.

U. Bortolozzo, S. Residori, A. Petrosyan, and J. P. Huignard, Opt. Commun. doi: 10.1016/j.optcom.2006.01.038 (2006).

Schleich, W.

See, e.g., M. Berry, I. Marzoli, and W. Schleich, Phys. World June 2001, 39 (2001).

Silva, D. E.

A. W. Lohman and D. E. Silva, Opt. Commun. 2, 413 (1971).
[CrossRef]

Sohler, W.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Stegeman, G. I.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Svelto, O.

Talbot, H. F.

H. F. Talbot, Philos. Mag. 9, 401 (1836).

Testorf, M.

M. Testorf, J. Jahns, N. A. Khilo, and A. Goncharenko, Opt. Commun. 129, 167 (1996).
[CrossRef]

Varanavicius, A.

Vysotsky, D. V.

M. Wrage, P. Glas, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, Opt. Commun. 191, 149 (2001).
[CrossRef]

Wan, X.

Z. Hu, D. Liu, A. Yan, X. Wan, and I. Liu, Presented at the Tenth International Conference on Photorefractive Effects, Materials, and Devices, Sanya Hainan, China, July 19-23, 2005.

Wrage, M.

M. Wrage, P. Glas, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, Opt. Commun. 191, 149 (2001).
[CrossRef]

Yan, A.

Z. Hu, D. Liu, A. Yan, X. Wan, and I. Liu, Presented at the Tenth International Conference on Photorefractive Effects, Materials, and Devices, Sanya Hainan, China, July 19-23, 2005.

Zervas, M. N.

J. Mod. Opt. (1)

M. V. Berry and S. Klein, J. Mod. Opt. 43, 2139 (1996).
[CrossRef]

Opt. Commun. (4)

A. W. Lohman and D. E. Silva, Opt. Commun. 2, 413 (1971).
[CrossRef]

M. Wrage, P. Glas, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, Opt. Commun. 191, 149 (2001).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, and A. Goncharenko, Opt. Commun. 129, 167 (1996).
[CrossRef]

U. Bortolozzo, S. Residori, A. Petrosyan, and J. P. Huignard, Opt. Commun. doi: 10.1016/j.optcom.2006.01.038 (2006).

Opt. Lett. (4)

Philos. Mag. (2)

H. F. Talbot, Philos. Mag. 9, 401 (1836).

Lord Rayleigh, Philos. Mag. 11, 196 (1881).

Phys. Rev. Lett. (1)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Phys. World (1)

See, e.g., M. Berry, I. Marzoli, and W. Schleich, Phys. World June 2001, 39 (2001).

Other (2)

P. Gunter and J. P. Huignard, Photorefractive Crystals and Their Applications (Springer-Verlag, 1989).

Z. Hu, D. Liu, A. Yan, X. Wan, and I. Liu, Presented at the Tenth International Conference on Photorefractive Effects, Materials, and Devices, Sanya Hainan, China, July 19-23, 2005.

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Figures (6)

Fig. 1
Fig. 1

Setup for 2WM with two valves.

Fig. 2
Fig. 2

(a) Measured 2WM gain as a function of δ, z T = 2.5 mm and β = 80 (circles) or 20 (triangles); z T = 1.9 mm and β = 80 (squares). (b) Gain for one valve (empty circles) and two valves (filled circles) as a function of β.

Fig. 3
Fig. 3

(a) Numerically calculated gain for N = 2 as a function of the distance L 1 between the two valves and (b) for N = 3 as a function of distances L 1 and L 2 .

Fig. 4
Fig. 4

(a) Numerical gain versus grating period p for N = 2 (dotted curve) and N = 3 (solid curve). (b) G versus N in the diffractionless limit (solid curve) and for optimized Talbot distances (dashed curve).

Fig. 5
Fig. 5

Talbot intensity carpets calculated for (a) N = 1 , (b) N = 2 , (c) N = 3 .

Fig. 6
Fig. 6

Refractive index grating for N = 1 , z = 0 (dashed curve); N = 2 , z = L 1 (black solid curve); N = 3 , z = L 1 + L 2 (gray solid curve).

Equations (2)

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E j ( x , z ) z = i 2 k 0 2 E j ( x , z ) x 2 ,
E j ( x , 0 ) = E j 1 exp [ i k 0 l ( n 1 + n 2 E j 1 2 ) ] ,

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