Abstract

A newly developed method for the characterization of the optical nonlinearities and dynamics is applied to Kerr liquids. The time-resolved pump-probe system based on the 4f nonlinear imaging technique with phase object is used to obtain the diffraction pattern of the nonlinear filter induced in the liquid CS2 placed in the Fourier plane by a charge-coupled device at various delay times. A theory based on two-beam coupling in perpendicular linear polarizations is used to interpret the measurement results. Good agreement is obtained between theory and experiment, suggesting a new method for simultaneous measurements of both magnitude and sign of the intensity-dependent refractive index as well as the dynamics of the Kerr liquids.

© 2009 Optical Society of America

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References

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  1. S. Cherukulappurath, G. Boudebs, and A. Monteil, “4f coherent imager system and its application to nonlinear optical measurements,” J. Opt. Soc. Am. B 21, 273-279 (2004).
    [CrossRef]
  2. G. Boudebs and S. Cherukulappurath, “Nonlinear optical measurements using a 4f coherent imaging system with phase objects,” Phys. Rev. A 69, 053813 (2004).
    [CrossRef]
  3. Y. Li, G. Pan, K. Yang, X. Zhang, Y. Wang, T. Wei, and Y. Song, “Time-resolved pump-probe system based on a nonlinear imaging technique with phase object,” Opt. Express 16, 6251-6259 (2008).
    [CrossRef] [PubMed]
  4. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003), p. 350.
  5. A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland, and N. Bloembergen, “Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B 14, 796-803 (1997).
    [CrossRef]
  6. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), p. 69.
  7. R. Y. Chiao and J. Godine, “Polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect,” Phys. Rev. 185, 430-445 (1969).
    [CrossRef]
  8. W. E. Williams, M. J. Soileau, and E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256-260 (1984).
    [CrossRef]

2008

2004

S. Cherukulappurath, G. Boudebs, and A. Monteil, “4f coherent imager system and its application to nonlinear optical measurements,” J. Opt. Soc. Am. B 21, 273-279 (2004).
[CrossRef]

G. Boudebs and S. Cherukulappurath, “Nonlinear optical measurements using a 4f coherent imaging system with phase objects,” Phys. Rev. A 69, 053813 (2004).
[CrossRef]

1997

1984

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

1969

R. Y. Chiao and J. Godine, “Polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect,” Phys. Rev. 185, 430-445 (1969).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), p. 69.

Bloembergen, N.

Boudebs, G.

G. Boudebs and S. Cherukulappurath, “Nonlinear optical measurements using a 4f coherent imaging system with phase objects,” Phys. Rev. A 69, 053813 (2004).
[CrossRef]

S. Cherukulappurath, G. Boudebs, and A. Monteil, “4f coherent imager system and its application to nonlinear optical measurements,” J. Opt. Soc. Am. B 21, 273-279 (2004).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003), p. 350.

Cherukulappurath, S.

S. Cherukulappurath, G. Boudebs, and A. Monteil, “4f coherent imager system and its application to nonlinear optical measurements,” J. Opt. Soc. Am. B 21, 273-279 (2004).
[CrossRef]

G. Boudebs and S. Cherukulappurath, “Nonlinear optical measurements using a 4f coherent imaging system with phase objects,” Phys. Rev. A 69, 053813 (2004).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao and J. Godine, “Polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect,” Phys. Rev. 185, 430-445 (1969).
[CrossRef]

Dogariu, A.

Godine, J.

R. Y. Chiao and J. Godine, “Polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect,” Phys. Rev. 185, 430-445 (1969).
[CrossRef]

Hagan, D. J.

Li, Y.

Monteil, A.

Pan, G.

Said, A. A.

Soileau, M. J.

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

Song, Y.

Van Stryland, E. W.

Wang, Y.

Wei, T.

Williams, W. E.

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

Xia, T.

Yang, K.

Zhang, X.

J. Opt. Soc. Am. B

Opt. Commun.

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

Opt. Express

Phys. Rev.

R. Y. Chiao and J. Godine, “Polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect,” Phys. Rev. 185, 430-445 (1969).
[CrossRef]

Phys. Rev. A

G. Boudebs and S. Cherukulappurath, “Nonlinear optical measurements using a 4f coherent imaging system with phase objects,” Phys. Rev. A 69, 053813 (2004).
[CrossRef]

Other

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003), p. 350.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), p. 69.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the time-resolved pump-probe system based on the 4 f nonlinear imaging technique with phase object. BS is the beam splitter; M 1 M 3 are mirrors; L 1 L 3 are lenses. A is an aperture with phase object; t f is the neutral filter; NL is the nonlinear sample C S 2 .

Fig. 2
Fig. 2

Time-resolved picosecond pump-probe results based on the 4 f nonlinear imaging technique with phase object: (a) is the normalized transmitted energy N T ; (b) is the difference of the normalized fluence inside and outside the phase object Δ T . Both are plotted as a function of delay time τ. Solid squares are experimental data, and curves are theoretical fits.

Fig. 3
Fig. 3

Profiles of numerically simulated normalized fluence N F for (a) linear and (b) nonlinear images for C S 2 .

Equations (17)

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E ( r , r , t ) = Re [ A ( r , t ) exp ( i { k r [ ω + Δ ω ( t ) ] t } ) ] ,
E ( r , r , t , τ ) = A e ( r , t ) exp ( i { k e r [ ω + Δ ω ( t ) ] t } ) + A p ( r , t ) exp ( i { k p r [ ω + Δ ω ( t τ ) ] ( t τ ) } ) ,
A p 0 ( r , t ) = A 0 exp ( t 2 2 τ p 2 ) circ ( r R a ) exp [ i φ circ ( r L p ) ] ,
A p 0 ( ρ , t ) = 2 π λ f 1 0 R a r A p 0 ( r , t ) J 0 ( 2 π r ρ ) d r ,
A p L ( ρ , t ) = A p 0 ( ρ , t ) exp ( i Δ φ NL ) ,
A p L ( r , t ) = 2 π λ f 2 0 ρ A p L ( ρ , t ) J 0 ( 2 π r ρ ) d ρ ,
F L ( r ) = + A p L ( r , t ) 2 d t A 0 2 π 1 2 τ p ,
I = A e A e * + A p A p * + A e A p * exp ( i q r ) exp ( i ω τ ) exp ( i Ω t ) + c.c.
τ rot d n NL d t + n NL = n 2 I ,
d A p d z = i α n 2 k ( I e + I p + I e 1 + i Ω τ rot ) A p ,
d I p d z = α n 2 k 2 Ω τ rot 1 + ( Ω τ rot ) 2 I e I p ,
d φ p d z = α n 2 k ( I e + I p + I e 1 + ( Ω τ rot ) 2 ) .
I p L = I p 0 exp ( α g L ) ,
g = 2 n 2 k Ω τ rot I e 1 + ( Ω τ rot ) 2 ,
φ p L = α n 2 k [ I e ( 1 + 1 1 + ( Ω τ rot ) 2 ) L + I p 0 exp ( α g L ) 1 α g ] .
NT = E p E p 0 = 2 π d t 0 r I p L d r 2 π d t 0 r I p 0 d r ,
I e 0 ( z , r , t ) = I 0 ω 0 2 ω 2 ( z ) exp ( 2 r 2 ω 2 ( z ) ) exp ( t 2 τ p 2 ) ,

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