Abstract

We measured the spectrum and energy of infrared triple photons generated in a phase-matched KTiOPO4 crystal pumped by picosecond beams at 532 and 1662 nm. The experimental data are in good agreement with our model, taking into account the spectral linewidths of the incident beams as well as a parasitic Kerr effect.

© 2012 Optical Society of America

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  1. D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).
    [CrossRef]
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  3. K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 8, 206 (2007).
  4. H. Hubel, D. Hamel, A. Fedrizzi, S. Ramelow, K. Resch, and T. Jennewein, Nature 466, 601 (2010).
    [CrossRef]
  5. J. Douady and B. Boulanger, Opt. Lett. 29, 2794 (2004).
    [CrossRef]
  6. F. Gravier and B. Boulanger, J. Opt. Soc. Am. B 25, 98 (2008).
    [CrossRef]
  7. A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, Phys. Rev. A 85, 023809 (2012).
    [CrossRef]
  8. K. Tarnowski, B. Kibler, and W. Urbanczyk, J. Opt. Soc. Am. B 28, 2075 (2011).
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  9. B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, Appl. Phys. B 91, 349 (2008).
    [CrossRef]
  10. M. Corona, K. Garay-Palmett, and A. B. U’Ren, Phys. Rev. A 84, 033823 (2011).
    [CrossRef]
  11. B. Boulanger, M. M. Fejer, R. Blachman, and P. Bordui, Appl. Phys. Lett. 65, 2401 (1994).
    [CrossRef]
  12. V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
    [CrossRef]
  13. http://www.cristal-laser.com/.
  14. W. Ji, P. Li, F. Zhou, and N. Zhai, Proc. SPIE 2897, 414 (1996).
    [CrossRef]

2012

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, Phys. Rev. A 85, 023809 (2012).
[CrossRef]

2011

K. Tarnowski, B. Kibler, and W. Urbanczyk, J. Opt. Soc. Am. B 28, 2075 (2011).
[CrossRef]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, Phys. Rev. A 84, 033823 (2011).
[CrossRef]

2010

H. Hubel, D. Hamel, A. Fedrizzi, S. Ramelow, K. Resch, and T. Jennewein, Nature 466, 601 (2010).
[CrossRef]

2008

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, Appl. Phys. B 91, 349 (2008).
[CrossRef]

F. Gravier and B. Boulanger, J. Opt. Soc. Am. B 25, 98 (2008).
[CrossRef]

2007

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 8, 206 (2007).

2004

1997

K. Banaszek and P. Knight, Phys. Rev. A 55, 2368 (1997).
[CrossRef]

1996

W. Ji, P. Li, F. Zhou, and N. Zhai, Proc. SPIE 2897, 414 (1996).
[CrossRef]

1994

B. Boulanger, M. M. Fejer, R. Blachman, and P. Bordui, Appl. Phys. Lett. 65, 2401 (1994).
[CrossRef]

1993

V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

1990

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).
[CrossRef]

Banaszek, K.

K. Banaszek and P. Knight, Phys. Rev. A 55, 2368 (1997).
[CrossRef]

Bencheikh, K.

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, Phys. Rev. A 85, 023809 (2012).
[CrossRef]

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 8, 206 (2007).

Blachman, R.

B. Boulanger, M. M. Fejer, R. Blachman, and P. Bordui, Appl. Phys. Lett. 65, 2401 (1994).
[CrossRef]

Bordui, P.

B. Boulanger, M. M. Fejer, R. Blachman, and P. Bordui, Appl. Phys. Lett. 65, 2401 (1994).
[CrossRef]

Borne, A.

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, Phys. Rev. A 85, 023809 (2012).
[CrossRef]

Boulanger, B.

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, Phys. Rev. A 85, 023809 (2012).
[CrossRef]

F. Gravier and B. Boulanger, J. Opt. Soc. Am. B 25, 98 (2008).
[CrossRef]

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 8, 206 (2007).

J. Douady and B. Boulanger, Opt. Lett. 29, 2794 (2004).
[CrossRef]

B. Boulanger, M. M. Fejer, R. Blachman, and P. Bordui, Appl. Phys. Lett. 65, 2401 (1994).
[CrossRef]

Cerullo, G.

V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

Corona, M.

M. Corona, K. Garay-Palmett, and A. B. U’Ren, Phys. Rev. A 84, 033823 (2011).
[CrossRef]

Dot, A.

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, Phys. Rev. A 85, 023809 (2012).
[CrossRef]

Douady, J.

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 8, 206 (2007).

J. Douady and B. Boulanger, Opt. Lett. 29, 2794 (2004).
[CrossRef]

Dudley, J. M.

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, Appl. Phys. B 91, 349 (2008).
[CrossRef]

Fedrizzi, A.

H. Hubel, D. Hamel, A. Fedrizzi, S. Ramelow, K. Resch, and T. Jennewein, Nature 466, 601 (2010).
[CrossRef]

Fejer, M. M.

B. Boulanger, M. M. Fejer, R. Blachman, and P. Bordui, Appl. Phys. Lett. 65, 2401 (1994).
[CrossRef]

Fischer, R.

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, Appl. Phys. B 91, 349 (2008).
[CrossRef]

Garay-Palmett, K.

M. Corona, K. Garay-Palmett, and A. B. U’Ren, Phys. Rev. A 84, 033823 (2011).
[CrossRef]

Genty, G.

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, Appl. Phys. B 91, 349 (2008).
[CrossRef]

Gravier, F.

F. Gravier and B. Boulanger, J. Opt. Soc. Am. B 25, 98 (2008).
[CrossRef]

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 8, 206 (2007).

Greenberger, D. M.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).
[CrossRef]

Hamel, D.

H. Hubel, D. Hamel, A. Fedrizzi, S. Ramelow, K. Resch, and T. Jennewein, Nature 466, 601 (2010).
[CrossRef]

Horne, M. A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).
[CrossRef]

Hubel, H.

H. Hubel, D. Hamel, A. Fedrizzi, S. Ramelow, K. Resch, and T. Jennewein, Nature 466, 601 (2010).
[CrossRef]

Jennewein, T.

H. Hubel, D. Hamel, A. Fedrizzi, S. Ramelow, K. Resch, and T. Jennewein, Nature 466, 601 (2010).
[CrossRef]

Ji, W.

W. Ji, P. Li, F. Zhou, and N. Zhai, Proc. SPIE 2897, 414 (1996).
[CrossRef]

Kibler, B.

K. Tarnowski, B. Kibler, and W. Urbanczyk, J. Opt. Soc. Am. B 28, 2075 (2011).
[CrossRef]

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, Appl. Phys. B 91, 349 (2008).
[CrossRef]

Knight, P.

K. Banaszek and P. Knight, Phys. Rev. A 55, 2368 (1997).
[CrossRef]

Levenson, J. A.

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, Phys. Rev. A 85, 023809 (2012).
[CrossRef]

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 8, 206 (2007).

Li, P.

W. Ji, P. Li, F. Zhou, and N. Zhai, Proc. SPIE 2897, 414 (1996).
[CrossRef]

Magni, V.

V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

Neshev, D. N.

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, Appl. Phys. B 91, 349 (2008).
[CrossRef]

Ramelow, S.

H. Hubel, D. Hamel, A. Fedrizzi, S. Ramelow, K. Resch, and T. Jennewein, Nature 466, 601 (2010).
[CrossRef]

Resch, K.

H. Hubel, D. Hamel, A. Fedrizzi, S. Ramelow, K. Resch, and T. Jennewein, Nature 466, 601 (2010).
[CrossRef]

Shimony, A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).
[CrossRef]

Silvestri, S. D.

V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

Tarnowski, K.

U’Ren, A. B.

M. Corona, K. Garay-Palmett, and A. B. U’Ren, Phys. Rev. A 84, 033823 (2011).
[CrossRef]

Urbanczyk, W.

Zeilinger, A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).
[CrossRef]

Zhai, N.

W. Ji, P. Li, F. Zhou, and N. Zhai, Proc. SPIE 2897, 414 (1996).
[CrossRef]

Zhou, F.

W. Ji, P. Li, F. Zhou, and N. Zhai, Proc. SPIE 2897, 414 (1996).
[CrossRef]

Am. J. Phys.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).
[CrossRef]

Appl. Phys. B

B. Kibler, R. Fischer, G. Genty, D. N. Neshev, and J. M. Dudley, Appl. Phys. B 91, 349 (2008).
[CrossRef]

Appl. Phys. Lett.

B. Boulanger, M. M. Fejer, R. Blachman, and P. Bordui, Appl. Phys. Lett. 65, 2401 (1994).
[CrossRef]

C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron.

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 8, 206 (2007).

J. Opt. Soc. Am. B

Nature

H. Hubel, D. Hamel, A. Fedrizzi, S. Ramelow, K. Resch, and T. Jennewein, Nature 466, 601 (2010).
[CrossRef]

Opt. Commun.

V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

Opt. Lett.

Phys. Rev. A

K. Banaszek and P. Knight, Phys. Rev. A 55, 2368 (1997).
[CrossRef]

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, Phys. Rev. A 85, 023809 (2012).
[CrossRef]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, Phys. Rev. A 84, 033823 (2011).
[CrossRef]

Proc. SPIE

W. Ji, P. Li, F. Zhou, and N. Zhai, Proc. SPIE 2897, 414 (1996).
[CrossRef]

Other

http://www.cristal-laser.com/.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Energy diagram of TPG where ω0, ω1, ω2, and ω3 are the circular frequencies; (b) experimental setup.

Fig. 2.
Fig. 2.

Spectra of the pump beam (field 0) (a) and stimulation beams (fields 2 and 3); (b) used for the TPG experiments.

Fig. 3.
Fig. 3.

Spectrum of field 1 generated by TPG in the KTP crystal. The incident pump energy is ξ0=52μJ and the incident stimulation energy is (ξ2+ξ3)=60μJ.

Fig. 4.
Fig. 4.

Generated energy in field 1 as a function of the energy of the stimulation fields 2 and 3. The incident pump energy is fixed at ξ0=14.5μJ. The fitting parameters are υ=0.375 and μ=0.6.

Fig. 5.
Fig. 5.

Generated energy in field 1 as a function of the energy of the pump field 0. The incident stimulation energy is fixed at (ξ2+ξ3)=63μJ. The fitting parameters are υ=0.388 and μ=0.6.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ξ1(ω1,L)=|dω0dω2F(ω0,ω1,ω2)ϕ(ω0,ω1,ω2,L)|2,
F(ω0,ω1,ω2)=ξ0(ω0)ξ2(ω2)ξ3(ω0ω1ω2)ny(ω0)ny(ω2)nz(ω0ω1ω2)
ϕ(ω0,ω1,ω2,L)=χ24(3)(ω1)8πε0c2ω1nz(ω1)0LdzeiΔk(ω0,ω1,ω2)zw2(z),
Δk(ω0,ω1,ω2)=1c[ω0ny(ω0)ω1nz(ω1)ω2nz(ω2)(ω0ω1ω2)ny(ω0ω1ω2)].
ξ1(L)=dω1ξ1(ω1,L),
neff(ω,z)=n(ω)+nKerr(ω)Itot(z).
w2(z)=[v2(went2wKerr2)][zμfKerrμfKerr]2+v2wKerr2.

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