Abstract

We conceived an optical generator leading to the production of 3×1013 triple photons per pulse with a full-width duration of 88ps at 1e2, by using a third-order optical parametric interaction phase-matched in a KTP crystal and pumped at 532nm. The triple photon generation is stimulated by two photons orthogonally polarized emitted by a homemade optical parametric oscillator emitting at 1665nm. The energy generated at 1474nm is well modelized by an analytical model based on Jacobi elliptic functions. These results open the way to new quantum measurement relative to Greenberger–Horne–Zeilinger state of light.

© 2008 Optical Society of America

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References

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  1. D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, "Bell's theorem without inequalities," Am. J. Phys. 58, 1131-1143 (1990).
    [CrossRef]
  2. K. Banaszek and P. L. Knight, "Quantum interference in three-photon down-conversion," Phys. Rev. A 55, 2368-2375 (1997).
    [CrossRef]
  3. K. Bencheick, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, "Triple photons: a challenge in nonlinear and quantum optics," C. R. Phys. 8, 206-220 (2007).
    [CrossRef]
  4. J. Douady and B. Boulanger, "Experimental demonstration of a pure third-order optical parametric downconversion process," Opt. Lett. 29, 2794-2796 (2004).
    [CrossRef] [PubMed]
  5. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 117, 1918-1939 (1962).
    [CrossRef]
  6. Y. Chen, "Four-wave mixing in optical fibers: exact solution," J. Opt. Soc. Am. B 6, 1986-1993 (1989).
    [CrossRef]
  7. J. P. Fève, B. Boulanger, and J. Douady, "Specific properties of cubic optical parametric interactions compared to quadratic interaction," Phys. Rev. A 66, 1-11 (2002).
    [CrossRef]
  8. P. F. Bird and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists (Springer, 1954).
  9. P. F. Bordui and M. M. Fejer, "Inorganic crystals for nonlinear optical frequency conversion," Annu. Rev. Mater. Sci. 23, 321-379 (1993).
    [CrossRef]
  10. L. R. Marshall and A. Kaz, "Eye-safe output from noncritically phase-matched parametric oscillators," J. Opt. Soc. Am. B 10, 1730-1736 (1993).
    [CrossRef]
  11. B. Boulanger, J. P. Fève, P. Delarue, I. Rousseau, and G. Marnier, "Cubic optical nonlinearity of KTiOPO4," J. Phys. B 32, 475-488 (1999).
    [CrossRef]
  12. J. Douady and B. Boulanger, "Calculation of quadratic cascading contributions associated with a phase-matched cubic frequency difference generation in a KTiOPO4 crystal," J. Opt. A, Pure Appl. Opt. 7, 467-471 (2005).
    [CrossRef]
  13. I. Abram, R. K. Raj, J. L. Oudar, and G. Dolique, "Direct observation of the second-order coherence of parametrically generated light," Phys. Rev. Lett. 57, 2516-2519 (1986).
    [CrossRef] [PubMed]

2007 (1)

K. Bencheick, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, "Triple photons: a challenge in nonlinear and quantum optics," C. R. Phys. 8, 206-220 (2007).
[CrossRef]

2005 (1)

J. Douady and B. Boulanger, "Calculation of quadratic cascading contributions associated with a phase-matched cubic frequency difference generation in a KTiOPO4 crystal," J. Opt. A, Pure Appl. Opt. 7, 467-471 (2005).
[CrossRef]

2004 (1)

2002 (1)

J. P. Fève, B. Boulanger, and J. Douady, "Specific properties of cubic optical parametric interactions compared to quadratic interaction," Phys. Rev. A 66, 1-11 (2002).
[CrossRef]

1999 (1)

B. Boulanger, J. P. Fève, P. Delarue, I. Rousseau, and G. Marnier, "Cubic optical nonlinearity of KTiOPO4," J. Phys. B 32, 475-488 (1999).
[CrossRef]

1997 (1)

K. Banaszek and P. L. Knight, "Quantum interference in three-photon down-conversion," Phys. Rev. A 55, 2368-2375 (1997).
[CrossRef]

1993 (2)

P. F. Bordui and M. M. Fejer, "Inorganic crystals for nonlinear optical frequency conversion," Annu. Rev. Mater. Sci. 23, 321-379 (1993).
[CrossRef]

L. R. Marshall and A. Kaz, "Eye-safe output from noncritically phase-matched parametric oscillators," J. Opt. Soc. Am. B 10, 1730-1736 (1993).
[CrossRef]

1990 (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, "Bell's theorem without inequalities," Am. J. Phys. 58, 1131-1143 (1990).
[CrossRef]

1989 (1)

1986 (1)

I. Abram, R. K. Raj, J. L. Oudar, and G. Dolique, "Direct observation of the second-order coherence of parametrically generated light," Phys. Rev. Lett. 57, 2516-2519 (1986).
[CrossRef] [PubMed]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 117, 1918-1939 (1962).
[CrossRef]

Am. J. Phys. (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, "Bell's theorem without inequalities," Am. J. Phys. 58, 1131-1143 (1990).
[CrossRef]

Annu. Rev. Mater. Sci. (1)

P. F. Bordui and M. M. Fejer, "Inorganic crystals for nonlinear optical frequency conversion," Annu. Rev. Mater. Sci. 23, 321-379 (1993).
[CrossRef]

C. R. Phys. (1)

K. Bencheick, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, "Triple photons: a challenge in nonlinear and quantum optics," C. R. Phys. 8, 206-220 (2007).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

J. Douady and B. Boulanger, "Calculation of quadratic cascading contributions associated with a phase-matched cubic frequency difference generation in a KTiOPO4 crystal," J. Opt. A, Pure Appl. Opt. 7, 467-471 (2005).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

B. Boulanger, J. P. Fève, P. Delarue, I. Rousseau, and G. Marnier, "Cubic optical nonlinearity of KTiOPO4," J. Phys. B 32, 475-488 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 117, 1918-1939 (1962).
[CrossRef]

Phys. Rev. A (2)

K. Banaszek and P. L. Knight, "Quantum interference in three-photon down-conversion," Phys. Rev. A 55, 2368-2375 (1997).
[CrossRef]

J. P. Fève, B. Boulanger, and J. Douady, "Specific properties of cubic optical parametric interactions compared to quadratic interaction," Phys. Rev. A 66, 1-11 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

I. Abram, R. K. Raj, J. L. Oudar, and G. Dolique, "Direct observation of the second-order coherence of parametrically generated light," Phys. Rev. Lett. 57, 2516-2519 (1986).
[CrossRef] [PubMed]

Other (1)

P. F. Bird and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists (Springer, 1954).

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Figures (4)

Fig. 1
Fig. 1

TPG experimental setup. ξ 0 , ξ 1 , ξ 2 , and ξ 3 are the energy of the beams at λ 0 , λ 1 , λ 2 , and λ 3 , respectively.

Fig. 2
Fig. 2

DFG energy ξ 1 as a function of pump energy ξ 0 with a stimulation energy ξ S = 182 μ J and a KTP crystal length L = 13 mm . The squares are the experimental data, and the straight lines correspond to the calculation.

Fig. 3
Fig. 3

DFG energy ξ 1 as a function of the stimulation energy ξ S , with a pump energy ξ 0 = 4.5 mJ and a KTP crystal length L = 13 mm . The squares are the experimental data, and the straight lines correspond to the calculation.

Fig. 4
Fig. 4

DFG energy ξ 1 as a function of the interaction length L, with a pump energy ξ 0 = 4.5 mJ and an stimulation energy ξ S = 182 μ J . The squares are the experimental data and the straight lines correspond to the calculation.

Equations (17)

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N T P G = N 1 = ξ 1 ω 1 .
E 0 X = j π n 0 λ 0 cos 2 ( ρ 0 ) χ e f f ( 3 ) E 1 E 2 E 3 e j Δ k X ,
E 1 X = j π n 1 λ 1 cos 2 ( ρ 1 ) χ e f f ( 3 ) E 0 E 2 * E 3 * e j Δ k X ,
E 2 X = j π n 2 λ 2 cos 2 ( ρ 2 ) χ e f f ( 3 ) E 0 E 1 * E 3 * e j Δ k X ,
E 3 X = j π n 3 λ 3 cos 2 ( ρ 3 ) χ e f f ( 3 ) E 0 E 1 * E 2 * e j Δ k X ,
ξ i = I i ( π 2 ) 3 2 τ i 2 w i 2 ,
ξ 1 ( L ) μ 0 ε 0 32 π λ 1 n 0 n 1 n 2 n 3 ( w 1 w 0 w 2 w 3 ) 2 ( τ 1 τ 0 τ 2 τ 3 ) ( χ e f f ( 3 ) ) 2 L 2 ξ 0 ( 0 ) ξ 2 ( 0 ) ξ 3 ( 0 ) .
w 1 2 = w 0 2 + w 2 2 + w 3 2 ,
τ 1 2 = τ 0 2 + τ 2 2 + τ 3 2 .
ξ 1 ( L ) = ( π 2 ) 3 2 ( w 1 2 τ 1 2 ) γ 3 γ 0 s n 2 ( a 1 L 1 m 1 ) Γ ,
Γ = γ 3 m 1 s n 2 ( a 1 L 1 m 1 ) + ( γ 3 + γ 0 ) c n 2 ( a 1 L 1 m 1 ) ,
γ k = λ k λ 1 ( 2 π ) 3 2 2 w k 2 τ k ξ k ,
m 1 = γ 2 ( γ 0 + γ 3 ) γ 3 ( γ 0 + γ 2 ) ,
a 1 = Λ 1 2 γ 3 ( γ 0 + γ 2 ) ,
where Λ 1 = μ 0 ε 0 4 π χ e f f ( 3 ) n 0 n 1 n 2 n 3 λ 1 λ 0 λ 2 λ 3 .
F = ( t 1 p 0 ( t ) d t + t 1 + t 1 p 2 , 3 ( t ) d t + + t 1 + p 0 ( t ) d t ) + p 2 , 3 ( t ) d t = 1 e r f ( 2 t 1 2 τ 2 , 3 ) + ξ 0 ( 0 ) ξ 2 , 3 ( 0 ) e r f ( 2 t 1 2 τ 0 ) ,
t 1 = ln ( ξ 0 ( 0 ) ξ 2 , 3 ( 0 ) τ 0 τ 2 , 3 ) 2 τ 0 2 2 τ 2 , 3 2 ,

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