Abstract

A model of energy transfer by nearly degenerate two-beam coupling in media exhibiting two-photon and excited state absorption is presented and discussed. The two beams include an incident laser, which has a nonlinear time dependent phase, and an elastically backscattered wave derived from the incident laser. Superposition of these two waves creates an index modulation, arising from a spatially modulated, two-photon-created excited-state population, which couples the forward and backward propagating waves. Reflectance of the stimulated wave and transmittance of the incident laser are computed, including the effects of two-photon absorption and excited state absorption as well as energy transfer between the two beams, and the relevance of the results to experimental measurements is discussed. The backscattered wave has a frequency that is unshifted with respect to that of the incident laser, and the small signal gain is proportional to the square of the incident laser intensity. The different effects due to multimode and chirped waves are also discussed.

©2005 Optical Society of America

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References

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  1. Y. Silberberg and I. Bar Joseph , “ Optical instabilities in a nonlinear Kerr medium ,” J. Opt. Soc. Am. B   1 , 662 – 670 ( 1984 ).
    [Crossref]
  2. Y. Silberberg and I. Bar Joseph , “ Instabilities, self-oscillation, and chaos in simple nonlinear optical interaction ,” Phys. Rev. Lett.   48 , 1541 – 1543 ( 1982 ).
    [Crossref]
  3. P. Yeh , “ Exact solution of a nonlinear model of two-wave mixing in Kerr media ,” J. Opt. Soc. Am. B   3 , 747 – 750 ( 1986 ).
    [Crossref]
  4. R. Boyd , Nonlinear Optics ( Academic Press, New York , 1992 ).
  5. G. S. He , T. -C. Lin , and P. N. Prasad , “ Stimulated Rayleigh-Bragg scattering enhanced by two-photon excitation ,” Opt. Express   12 , 5952 – 5961 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5952 .
    [Crossref] [PubMed]
  6. G. S. He , C. Lu , Q. Zheng , P. N. Prasad , P. Zerom , R. W. Boyd , and M. Samoc , “ Stimulated Rayleigh-Bragg scattering in two-photon absorbing media ,” Phys. Rev. A   71 , 063810 ( 2005 ).
    [Crossref]
  7. R. L. Sutherland , M. C. Brant , J. Heinrichs , J. E. Rogers , J. E. Slagle , D. G. McLean , and P. A. Fleitz “ Excited state characterization and effective three-photon absorption model of two-photon-induced excited state absorption in organic push-pull charge-transfer chromophores ,” J. Opt. Soc. Am. B   22 , 1939 – 1948 ( 2005 ).
    [Crossref]
  8. J. E. Rogers , J. E. Slagle , D. G. McLean , R. L. Sutherland , B. Sankaran , R. Kannan , L. -S. Tan , and P. A. Fleitz , “ Understanding the one-photon photophysical properties of a two-photon absorbing chromophore ,” J. Phys. Chem. A   108 , 5514 – 5520 ( 2004 ).
    [Crossref]
  9. N. Tang and R. L. Sutherland , “ Time-domain theory for pump-probe experiments with chirped pulses ,” J. Opt. Soc. Am. B   14 , 3412 – 3423 ( 1997 ).
    [Crossref]
  10. 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]
  11. A. Dogariu and D. J. Hagan , “ Low frequency Raman gain measurements using chirped pulses , Opt. Express   1 , 73 – 76 ( 1997 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-1-3-73 .
    [Crossref] [PubMed]
  12. A. Yariv , Quantum Electronics, Third Ed. ( John Wiley & Sons, New York , 1989 ).

2005 (2)

2004 (2)

G. S. He , T. -C. Lin , and P. N. Prasad , “ Stimulated Rayleigh-Bragg scattering enhanced by two-photon excitation ,” Opt. Express   12 , 5952 – 5961 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5952 .
[Crossref] [PubMed]

J. E. Rogers , J. E. Slagle , D. G. McLean , R. L. Sutherland , B. Sankaran , R. Kannan , L. -S. Tan , and P. A. Fleitz , “ Understanding the one-photon photophysical properties of a two-photon absorbing chromophore ,” J. Phys. Chem. A   108 , 5514 – 5520 ( 2004 ).
[Crossref]

1997 (3)

1986 (1)

1984 (1)

1982 (1)

Y. Silberberg and I. Bar Joseph , “ Instabilities, self-oscillation, and chaos in simple nonlinear optical interaction ,” Phys. Rev. Lett.   48 , 1541 – 1543 ( 1982 ).
[Crossref]

Bar Joseph, I.

Y. Silberberg and I. Bar Joseph , “ Optical instabilities in a nonlinear Kerr medium ,” J. Opt. Soc. Am. B   1 , 662 – 670 ( 1984 ).
[Crossref]

Y. Silberberg and I. Bar Joseph , “ Instabilities, self-oscillation, and chaos in simple nonlinear optical interaction ,” Phys. Rev. Lett.   48 , 1541 – 1543 ( 1982 ).
[Crossref]

Bloembergen, N.

Boyd, R.

R. Boyd , Nonlinear Optics ( Academic Press, New York , 1992 ).

Boyd, R. W.

G. S. He , C. Lu , Q. Zheng , P. N. Prasad , P. Zerom , R. W. Boyd , and M. Samoc , “ Stimulated Rayleigh-Bragg scattering in two-photon absorbing media ,” Phys. Rev. A   71 , 063810 ( 2005 ).
[Crossref]

Brant, M. C.

Dogariu, A.

Fleitz, P. A.

R. L. Sutherland , M. C. Brant , J. Heinrichs , J. E. Rogers , J. E. Slagle , D. G. McLean , and P. A. Fleitz “ Excited state characterization and effective three-photon absorption model of two-photon-induced excited state absorption in organic push-pull charge-transfer chromophores ,” J. Opt. Soc. Am. B   22 , 1939 – 1948 ( 2005 ).
[Crossref]

J. E. Rogers , J. E. Slagle , D. G. McLean , R. L. Sutherland , B. Sankaran , R. Kannan , L. -S. Tan , and P. A. Fleitz , “ Understanding the one-photon photophysical properties of a two-photon absorbing chromophore ,” J. Phys. Chem. A   108 , 5514 – 5520 ( 2004 ).
[Crossref]

Hagan, D. J.

He, G. S.

G. S. He , C. Lu , Q. Zheng , P. N. Prasad , P. Zerom , R. W. Boyd , and M. Samoc , “ Stimulated Rayleigh-Bragg scattering in two-photon absorbing media ,” Phys. Rev. A   71 , 063810 ( 2005 ).
[Crossref]

G. S. He , T. -C. Lin , and P. N. Prasad , “ Stimulated Rayleigh-Bragg scattering enhanced by two-photon excitation ,” Opt. Express   12 , 5952 – 5961 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5952 .
[Crossref] [PubMed]

Heinrichs, J.

Kannan, R.

J. E. Rogers , J. E. Slagle , D. G. McLean , R. L. Sutherland , B. Sankaran , R. Kannan , L. -S. Tan , and P. A. Fleitz , “ Understanding the one-photon photophysical properties of a two-photon absorbing chromophore ,” J. Phys. Chem. A   108 , 5514 – 5520 ( 2004 ).
[Crossref]

Lin, T. -C.

Lu, C.

G. S. He , C. Lu , Q. Zheng , P. N. Prasad , P. Zerom , R. W. Boyd , and M. Samoc , “ Stimulated Rayleigh-Bragg scattering in two-photon absorbing media ,” Phys. Rev. A   71 , 063810 ( 2005 ).
[Crossref]

McLean, D. G.

R. L. Sutherland , M. C. Brant , J. Heinrichs , J. E. Rogers , J. E. Slagle , D. G. McLean , and P. A. Fleitz “ Excited state characterization and effective three-photon absorption model of two-photon-induced excited state absorption in organic push-pull charge-transfer chromophores ,” J. Opt. Soc. Am. B   22 , 1939 – 1948 ( 2005 ).
[Crossref]

J. E. Rogers , J. E. Slagle , D. G. McLean , R. L. Sutherland , B. Sankaran , R. Kannan , L. -S. Tan , and P. A. Fleitz , “ Understanding the one-photon photophysical properties of a two-photon absorbing chromophore ,” J. Phys. Chem. A   108 , 5514 – 5520 ( 2004 ).
[Crossref]

Prasad, P. N.

G. S. He , C. Lu , Q. Zheng , P. N. Prasad , P. Zerom , R. W. Boyd , and M. Samoc , “ Stimulated Rayleigh-Bragg scattering in two-photon absorbing media ,” Phys. Rev. A   71 , 063810 ( 2005 ).
[Crossref]

G. S. He , T. -C. Lin , and P. N. Prasad , “ Stimulated Rayleigh-Bragg scattering enhanced by two-photon excitation ,” Opt. Express   12 , 5952 – 5961 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5952 .
[Crossref] [PubMed]

Rogers, J. E.

R. L. Sutherland , M. C. Brant , J. Heinrichs , J. E. Rogers , J. E. Slagle , D. G. McLean , and P. A. Fleitz “ Excited state characterization and effective three-photon absorption model of two-photon-induced excited state absorption in organic push-pull charge-transfer chromophores ,” J. Opt. Soc. Am. B   22 , 1939 – 1948 ( 2005 ).
[Crossref]

J. E. Rogers , J. E. Slagle , D. G. McLean , R. L. Sutherland , B. Sankaran , R. Kannan , L. -S. Tan , and P. A. Fleitz , “ Understanding the one-photon photophysical properties of a two-photon absorbing chromophore ,” J. Phys. Chem. A   108 , 5514 – 5520 ( 2004 ).
[Crossref]

Said, A. A.

Samoc, M.

G. S. He , C. Lu , Q. Zheng , P. N. Prasad , P. Zerom , R. W. Boyd , and M. Samoc , “ Stimulated Rayleigh-Bragg scattering in two-photon absorbing media ,” Phys. Rev. A   71 , 063810 ( 2005 ).
[Crossref]

Sankaran, B.

J. E. Rogers , J. E. Slagle , D. G. McLean , R. L. Sutherland , B. Sankaran , R. Kannan , L. -S. Tan , and P. A. Fleitz , “ Understanding the one-photon photophysical properties of a two-photon absorbing chromophore ,” J. Phys. Chem. A   108 , 5514 – 5520 ( 2004 ).
[Crossref]

Silberberg, Y.

Y. Silberberg and I. Bar Joseph , “ Optical instabilities in a nonlinear Kerr medium ,” J. Opt. Soc. Am. B   1 , 662 – 670 ( 1984 ).
[Crossref]

Y. Silberberg and I. Bar Joseph , “ Instabilities, self-oscillation, and chaos in simple nonlinear optical interaction ,” Phys. Rev. Lett.   48 , 1541 – 1543 ( 1982 ).
[Crossref]

Slagle, J. E.

R. L. Sutherland , M. C. Brant , J. Heinrichs , J. E. Rogers , J. E. Slagle , D. G. McLean , and P. A. Fleitz “ Excited state characterization and effective three-photon absorption model of two-photon-induced excited state absorption in organic push-pull charge-transfer chromophores ,” J. Opt. Soc. Am. B   22 , 1939 – 1948 ( 2005 ).
[Crossref]

J. E. Rogers , J. E. Slagle , D. G. McLean , R. L. Sutherland , B. Sankaran , R. Kannan , L. -S. Tan , and P. A. Fleitz , “ Understanding the one-photon photophysical properties of a two-photon absorbing chromophore ,” J. Phys. Chem. A   108 , 5514 – 5520 ( 2004 ).
[Crossref]

Sutherland, R. L.

Tan, L. -S.

J. E. Rogers , J. E. Slagle , D. G. McLean , R. L. Sutherland , B. Sankaran , R. Kannan , L. -S. Tan , and P. A. Fleitz , “ Understanding the one-photon photophysical properties of a two-photon absorbing chromophore ,” J. Phys. Chem. A   108 , 5514 – 5520 ( 2004 ).
[Crossref]

Tang, N.

Van Stryland, E. W.

Xia, T.

Yariv, A.

A. Yariv , Quantum Electronics, Third Ed. ( John Wiley & Sons, New York , 1989 ).

Yeh, P.

Zerom, P.

G. S. He , C. Lu , Q. Zheng , P. N. Prasad , P. Zerom , R. W. Boyd , and M. Samoc , “ Stimulated Rayleigh-Bragg scattering in two-photon absorbing media ,” Phys. Rev. A   71 , 063810 ( 2005 ).
[Crossref]

Zheng, Q.

G. S. He , C. Lu , Q. Zheng , P. N. Prasad , P. Zerom , R. W. Boyd , and M. Samoc , “ Stimulated Rayleigh-Bragg scattering in two-photon absorbing media ,” Phys. Rev. A   71 , 063810 ( 2005 ).
[Crossref]

J. Opt. Soc. Am. B (5)

J. Phys. Chem. A (1)

J. E. Rogers , J. E. Slagle , D. G. McLean , R. L. Sutherland , B. Sankaran , R. Kannan , L. -S. Tan , and P. A. Fleitz , “ Understanding the one-photon photophysical properties of a two-photon absorbing chromophore ,” J. Phys. Chem. A   108 , 5514 – 5520 ( 2004 ).
[Crossref]

Opt. Express (2)

Phys. Rev. A (1)

G. S. He , C. Lu , Q. Zheng , P. N. Prasad , P. Zerom , R. W. Boyd , and M. Samoc , “ Stimulated Rayleigh-Bragg scattering in two-photon absorbing media ,” Phys. Rev. A   71 , 063810 ( 2005 ).
[Crossref]

Phys. Rev. Lett. (1)

Y. Silberberg and I. Bar Joseph , “ Instabilities, self-oscillation, and chaos in simple nonlinear optical interaction ,” Phys. Rev. Lett.   48 , 1541 – 1543 ( 1982 ).
[Crossref]

Other (2)

R. Boyd , Nonlinear Optics ( Academic Press, New York , 1992 ).

A. Yariv , Quantum Electronics, Third Ed. ( John Wiley & Sons, New York , 1989 ).

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Figures (4)

Fig. 1.
Fig. 1. Schematic diagram of the chirped pulse interaction in a nonlinear medium. The backscattered pulse is assumed to be derived from the incident laser pulse at the back of the medium where it has the same frequency as the incident pulse. The color schematically indicates the frequency chirp, with blue representing higher frequencies and red representing lower frequencies.

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Fig. 2.
Fig. 2. Backscattered reflectance as a function of exponential gain factor for various values of nonlinear absorption coefficients. IS (d)/IL (0) = 10-2 in all cases. Circles give values for R calculated by the approximation in Eq. (10).

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Fig. 3.
Fig. 3. Backscattered intensity as a function of incident laser intensity.

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Fig. 4.
Fig. 4. Nonlinear transmittance of the incident laser as a function of incident intensity.

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Equations (15)

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

E z t = A L ( z , t + τ ) exp { i [ kz − ωt − b ( t + τ ) 2 ] }
+ A S ( z , t − τ ) exp { i [ − kz − ωt − b ( t − τ ) 2 ] } + c . c .
P = ε 0 ( χ g ( 1 ) + ( N e N ) Δ χ ( 1 ) + 3 χ ( 3 ) 〈 E 2 〉 ) E
∂ N e ∂ t = σ 2 N I 2 2 ħ ω − N e T e
N e N = C 0 + { C 1 exp [ i ( 2 kz − 4 bτt ) ] + C 2 exp [ i ( 4 kz − 8 bτt ) ] + c . c . } ,
C 0 = σ 2 T e 2 ħ ω ( I L 2 + I S 2 + 4 I L I S ) ,
C 1 = σ 2 T e 2 ħ ω ( I L + I S ) ( 4 ε 0 nc A L A S * 1 − i 4 bτ T e ) ,
C 2 = σ 2 T e 2 ħω ( 2 ε 0 nc A L A S * ) 2 1 − i 8 bτ T e ,
d I L dz = − g ( 1 − z d ) ( I L + I S ) I L I S − γ eff ( I L 2 + 3 I S 2 + 6 I L I S ) I L − β ( I L + 2 I S ) I L
d I S dz = − g ( 1 − z d ) ( I L + I S ) I L I S + γ eff ( 3 I L 2 + I S 2 + 6 I L I S ) I S + β ( 2 I L + I S ) I S
g = 8 b T e ω Δ χ R ( 1 ) d c 2 I sat 2 ,
γ eff = N Δ σ I sat 2 ,
η 0 = R [ ( 1 − R ) ( 1 − R + η 0 ) + 2 η 0 2 ] 1 2 ( 1 + R ) 2 exp ( Γ ) ( 1 − R + 2 η 0 1 − R + η 0 ) 3 2 ,
Γ = 1 2 ( 1 − R ) 2 g I L 2 ( 0 ) d .
η 0 ≈ R ( 1 − R ) ( 1 + R ) 2 exp ( Γ ) .

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