Abstract

We present an analysis of optical phase conjugation with frequency doubling in terms of nondegenerate six-wave mixing fifth-order nonlinear susceptibility. We show how the Bragg phase-matching condition is achieved at small angles. The process under picosecond-pulse conditions in a polydiacetylene solution pumped at two-photon resonance and probed at one-photon resonance is experimentally demonstrated. Results are discussed in terms of a one-dimensional quantum three-level system. The proximity of one- and two-photon resonance in conjugated polymers makes these polymers efficient nonlinear-optical materials for this original application. The experiment permits artifact-free measurement of the two-photon state recovery time of the red form of polydiacetylene.

© 1991 Optical Society of America

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References

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  1. M. S. Malcuit, D. J. Gauthier, R. W. Boyd, Opt. Lett. 13, 663 (1988).
    [CrossRef]
  2. J. M. Nunzi, D. Grec, J. Appl. Phys. 62, 2198 (1987).
    [CrossRef]
  3. J. M. Nunzi, F. Charra, Opt. Commun. 73, 357 (1989).
    [CrossRef]
  4. R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
    [CrossRef]
  5. J. W. R. Tabosa, C. L. Cesar, M. Ducloy, J. R. Rios Leite, Opt. Commun. 67, 240 (1988).
    [CrossRef]
  6. L. H. Acioli, A. S. L. Gomez, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
    [CrossRef]
  7. J. P. Huignard, B. Ledu, Opt. Lett. 7, 310 (1982).
    [CrossRef] [PubMed]
  8. C. Bao, J. Zhang, S. Wang, Appl. Opt. 27, 4572 (1988).
    [CrossRef] [PubMed]
  9. M. Ducloy, Appl. Phys. Lett. 46, 1020 (1985).
    [CrossRef]
  10. U. Österberg, W. Margulis, Opt. Lett. 11, 516 (1986).
    [CrossRef] [PubMed]
  11. R. H. Stolen, H. W. K. Tom, Opt. Lett. 12, 585 (1987).
    [CrossRef] [PubMed]
  12. F. Kajzar, J. Messier, Polymer J. 19, 275 (1987).
    [CrossRef]
  13. F. Charra, J. M. Nunzi, in Nonlinear Optical Materials II, J. B. Grun, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1127, 173 (1989).
    [CrossRef]
  14. C. Cojan, G. P. Agrawal, C. Flytzanis, Phys. Rev. B 15, 909 (1977).
    [CrossRef]
  15. F. Ouellette, K. O. Hill, D. C. Johnson, Opt. Lett. 13, 515 (1988).
    [CrossRef] [PubMed]
  16. J. M. Nunzi, F. Charra, in Organic Materials for Nonlinear Optics, R. A. Hann, D. Bloor, eds., Spec. Pub. 69, (Royal Society of Chemistry, London, 1989), p. 301.
  17. B. I. Green, J. Orenstein, R. R. Millard, L. R. Williams, Chem. Phys. Lett. 139, 381 (1987).
    [CrossRef]
  18. F. H. M. Faisal, Theory of Multiphoton Processes (Plenum, New York, 1987).
  19. S. I. Chu, in Advances in Molecular Physics, D. Bates, B. Bederson, eds. (Academic, New York, 1985), Vol. 21, p. 197.
    [CrossRef]
  20. M. Schubert, B. Wilhelmi, Nonlinear Optics and Quantum Electronics (Wiley, New York, 1986).
  21. B. J. Orr, J. F. Ward, Mol. Phys. 20, 513 (1971).
    [CrossRef]

1989 (1)

J. M. Nunzi, F. Charra, Opt. Commun. 73, 357 (1989).
[CrossRef]

1988 (5)

1987 (4)

B. I. Green, J. Orenstein, R. R. Millard, L. R. Williams, Chem. Phys. Lett. 139, 381 (1987).
[CrossRef]

R. H. Stolen, H. W. K. Tom, Opt. Lett. 12, 585 (1987).
[CrossRef] [PubMed]

F. Kajzar, J. Messier, Polymer J. 19, 275 (1987).
[CrossRef]

J. M. Nunzi, D. Grec, J. Appl. Phys. 62, 2198 (1987).
[CrossRef]

1986 (1)

1985 (1)

M. Ducloy, Appl. Phys. Lett. 46, 1020 (1985).
[CrossRef]

1984 (1)

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

1982 (1)

1977 (1)

C. Cojan, G. P. Agrawal, C. Flytzanis, Phys. Rev. B 15, 909 (1977).
[CrossRef]

1971 (1)

B. J. Orr, J. F. Ward, Mol. Phys. 20, 513 (1971).
[CrossRef]

Acioli, L. H.

L. H. Acioli, A. S. L. Gomez, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

Agrawal, G. P.

C. Cojan, G. P. Agrawal, C. Flytzanis, Phys. Rev. B 15, 909 (1977).
[CrossRef]

Bao, C.

Bloch, D.

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

Boyd, R. W.

Cesar, C. L.

J. W. R. Tabosa, C. L. Cesar, M. Ducloy, J. R. Rios Leite, Opt. Commun. 67, 240 (1988).
[CrossRef]

Charra, F.

J. M. Nunzi, F. Charra, Opt. Commun. 73, 357 (1989).
[CrossRef]

F. Charra, J. M. Nunzi, in Nonlinear Optical Materials II, J. B. Grun, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1127, 173 (1989).
[CrossRef]

J. M. Nunzi, F. Charra, in Organic Materials for Nonlinear Optics, R. A. Hann, D. Bloor, eds., Spec. Pub. 69, (Royal Society of Chemistry, London, 1989), p. 301.

Chu, S. I.

S. I. Chu, in Advances in Molecular Physics, D. Bates, B. Bederson, eds. (Academic, New York, 1985), Vol. 21, p. 197.
[CrossRef]

Cojan, C.

C. Cojan, G. P. Agrawal, C. Flytzanis, Phys. Rev. B 15, 909 (1977).
[CrossRef]

Ducloy, M.

J. W. R. Tabosa, C. L. Cesar, M. Ducloy, J. R. Rios Leite, Opt. Commun. 67, 240 (1988).
[CrossRef]

M. Ducloy, Appl. Phys. Lett. 46, 1020 (1985).
[CrossRef]

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

Faisal, F. H. M.

F. H. M. Faisal, Theory of Multiphoton Processes (Plenum, New York, 1987).

Flytzanis, C.

C. Cojan, G. P. Agrawal, C. Flytzanis, Phys. Rev. B 15, 909 (1977).
[CrossRef]

Gao, Q. F.

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

Gauthier, D. J.

Gomez, A. S. L.

L. H. Acioli, A. S. L. Gomez, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

Grec, D.

J. M. Nunzi, D. Grec, J. Appl. Phys. 62, 2198 (1987).
[CrossRef]

Green, B. I.

B. I. Green, J. Orenstein, R. R. Millard, L. R. Williams, Chem. Phys. Lett. 139, 381 (1987).
[CrossRef]

Hill, K. O.

Huignard, J. P.

Johnson, D. C.

Kajzar, F.

F. Kajzar, J. Messier, Polymer J. 19, 275 (1987).
[CrossRef]

Ledu, B.

Malcuit, M. S.

Margulis, W.

Messier, J.

F. Kajzar, J. Messier, Polymer J. 19, 275 (1987).
[CrossRef]

Millard, R. R.

B. I. Green, J. Orenstein, R. R. Millard, L. R. Williams, Chem. Phys. Lett. 139, 381 (1987).
[CrossRef]

Nunzi, J. M.

J. M. Nunzi, F. Charra, Opt. Commun. 73, 357 (1989).
[CrossRef]

J. M. Nunzi, D. Grec, J. Appl. Phys. 62, 2198 (1987).
[CrossRef]

F. Charra, J. M. Nunzi, in Nonlinear Optical Materials II, J. B. Grun, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1127, 173 (1989).
[CrossRef]

J. M. Nunzi, F. Charra, in Organic Materials for Nonlinear Optics, R. A. Hann, D. Bloor, eds., Spec. Pub. 69, (Royal Society of Chemistry, London, 1989), p. 301.

Orenstein, J.

B. I. Green, J. Orenstein, R. R. Millard, L. R. Williams, Chem. Phys. Lett. 139, 381 (1987).
[CrossRef]

Orr, B. J.

B. J. Orr, J. F. Ward, Mol. Phys. 20, 513 (1971).
[CrossRef]

Österberg, U.

Ouellette, F.

Raj, R. K.

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

Rios Leite, J. R.

L. H. Acioli, A. S. L. Gomez, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

J. W. R. Tabosa, C. L. Cesar, M. Ducloy, J. R. Rios Leite, Opt. Commun. 67, 240 (1988).
[CrossRef]

Schubert, M.

M. Schubert, B. Wilhelmi, Nonlinear Optics and Quantum Electronics (Wiley, New York, 1986).

Stolen, R. H.

Tabosa, J. W. R.

J. W. R. Tabosa, C. L. Cesar, M. Ducloy, J. R. Rios Leite, Opt. Commun. 67, 240 (1988).
[CrossRef]

Tom, H. W. K.

Wang, S.

Ward, J. F.

B. J. Orr, J. F. Ward, Mol. Phys. 20, 513 (1971).
[CrossRef]

Wilhelmi, B.

M. Schubert, B. Wilhelmi, Nonlinear Optics and Quantum Electronics (Wiley, New York, 1986).

Williams, L. R.

B. I. Green, J. Orenstein, R. R. Millard, L. R. Williams, Chem. Phys. Lett. 139, 381 (1987).
[CrossRef]

Zhang, J.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. Ducloy, Appl. Phys. Lett. 46, 1020 (1985).
[CrossRef]

L. H. Acioli, A. S. L. Gomez, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

Chem. Phys. Lett. (1)

B. I. Green, J. Orenstein, R. R. Millard, L. R. Williams, Chem. Phys. Lett. 139, 381 (1987).
[CrossRef]

J. Appl. Phys. (1)

J. M. Nunzi, D. Grec, J. Appl. Phys. 62, 2198 (1987).
[CrossRef]

Mol. Phys. (1)

B. J. Orr, J. F. Ward, Mol. Phys. 20, 513 (1971).
[CrossRef]

Opt. Commun. (3)

J. M. Nunzi, F. Charra, Opt. Commun. 73, 357 (1989).
[CrossRef]

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

J. W. R. Tabosa, C. L. Cesar, M. Ducloy, J. R. Rios Leite, Opt. Commun. 67, 240 (1988).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. B (1)

C. Cojan, G. P. Agrawal, C. Flytzanis, Phys. Rev. B 15, 909 (1977).
[CrossRef]

Polymer J. (1)

F. Kajzar, J. Messier, Polymer J. 19, 275 (1987).
[CrossRef]

Other (5)

F. Charra, J. M. Nunzi, in Nonlinear Optical Materials II, J. B. Grun, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1127, 173 (1989).
[CrossRef]

F. H. M. Faisal, Theory of Multiphoton Processes (Plenum, New York, 1987).

S. I. Chu, in Advances in Molecular Physics, D. Bates, B. Bederson, eds. (Academic, New York, 1985), Vol. 21, p. 197.
[CrossRef]

M. Schubert, B. Wilhelmi, Nonlinear Optics and Quantum Electronics (Wiley, New York, 1986).

J. M. Nunzi, F. Charra, in Organic Materials for Nonlinear Optics, R. A. Hann, D. Bloor, eds., Spec. Pub. 69, (Royal Society of Chemistry, London, 1989), p. 301.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the nondegenerate six-wave mixing experiment. By delaying beam 3 we study the quadratic index modulation grating, and, by delaying beam 1, the induced noncentrosymmetry grating. For small angles θ and weak dispersion we have Δθ ≃ 0, and beam 4 is the phase conjugate of beam 2.

Fig. 2
Fig. 2

General chemical formula for the polydiacetylenes. The subsituent R corresponds to the so-called 4-BCMU. The molecule is centrosymmetric and belongs to the C2h symmetry group.

Fig. 3
Fig. 3

Spectrum of a 1-mm-thick solution of polydiacetylene 4-BCMU in 1-4-dichlorobutane used in the experiment. The concentration is 0.25 g/L.

Fig. 4
Fig. 4

Quantum three-level model for polydiacetylene. The one-photon-allowed transition 0Ag → 1Bu is nearly resonant at 2ω, and the two-photon transition 0Ag → 2Ag is nearly resonant at ω + ω. d01 and d12 are the transition dipole moments from ground state 0Ag to 1Bu and from 1Bu to 2Ag, respectively.

Fig. 5
Fig. 5

Block diagram of the experimental setup for phase conjugation with frequency doubling. PD’s, photodiodes; PM, photo-multiplier tube; Fs, colored filters. L1 is a nearly achromatic 40-mm focal-convergent lens with focal point F at 30 mm before the sample. Lens L2 with pinhole P forms a 10−3rd spatial filter. The phase-conjugate signal is normalized shot to shot on incident intensity 3 and on the squares of intensities 1 and 2. Delay lines are computer controlled.

Fig. 6
Fig. 6

Evolution of a quadratic index-modulation grating. The phase-conjugate signal at double frequency as a function of delay of beam 3 (delay line 2 in Fig. 5 in the range −70 to +270 psec). The grating lifetime is ≃250 psec. No fast response appears up to the accuracy shown by the error bars.

Fig. 7
Fig. 7

Phase-conjugate signal at frequency due to acoustic oscillation as a function of delay of beam 3. The period of oscillation is 1.3 nsec and is exactly half of that observed when beam 3 is at fundamental frequency under the same geometrical conditions.

Fig. 8
Fig. 8

Evolution of an induced noncentrosymmetric grating. The phase-conjugate signal at double frequency is given in logarithmic scale as a function of delay of beam 1 (delay line 1 in Fig. 5). The half-width of the response is 31 psec. No long-lived induced noncentrosymmetry is detected.

Equations (31)

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

I ( M ) = I 1 + I 2 + 2 E 1 E 2 cos [ ( k 1 - k 2 ) · M ] ,             I i = E i 2 .
Δ n ( I 1 + I 2 ) 2 + 2 I 1 I 2 + 2 E 1 E 2 ( I 1 + I 2 ) × cos [ ( k 1 - k 2 ) · M ] + 2 I 1 I 2 cos [ 2 ( k 1 - k 2 ) · M ] .
χ ( 5 ) ( 2 ω ; ω , ω , - ω , - ω , 2 ω ) .
k 4 = 2 π { n 2 ( 2 ω ) + 2 n ( ω ) [ n ( ω ) - n ( 2 ω ) ] × [ 1 - cos ( θ ) ] } 1 / 2 / λ 2 ω ,
l c = λ 2 ω / 2 π { n 2 ( 2 ω ) + 2 n ( ω ) [ n ( ω ) - n ( 2 ω ) ] [ 1 - cos ( θ ) } 1 / 2 - n ( 2 ω ) .
l c λ 2 ω / π n ( ω ) n ( 2 ω ) [ n ( ω ) - n ( 2 ω ) ] θ 2 .
Δ θ [ 1 - n ( 2 ω ) n ( ω ) ] θ ,
E 2 exp ( i y 2 2 λ R ) E 4 exp [ - i y 2 2 ( λ / 2 ) R ] ,
E 3 ( t ) = 3 4 E 2 2 E 3 cos [ ( 2 k 2 - k 3 ) · M ] .
χ ( 5 ) ( 2 ω ; - ω , - ω , 2 ω , ω , ω ) .
χ ( 5 ) ( 2 ω ; ω , ω , - ω , - ω , 2 ω ) = 1 ɛ 0 N K γ 1 D ( 5 ) ,
χ x x x x x x ( 5 ) :             K = 1 / 7 ,
χ y x x x x y ( 5 ) :             K = 1 / 35 ,
χ x x x y y x ( ) 5 :             K = 1 / 35.
γ 1 D ( 5 ) 1 5 { - d 01 2 ( ω 1 - 2 ω ) d 01 2 d 12 2 ( ω 1 - ω ) 2 ( ω 2 - 2 ω ) 2
- d 01 2 ( ω 1 - 2 ω ) 2 d 01 2 d 12 2 ( ω 1 - ω ) 2 ( ω 2 - 2 ω )
- d 01 2 ( ω 1 - 2 ω ) 3 [ 2 d 01 2 d 12 2 ( ω 1 - ω ) ( ω 2 - 3 ω ) + 2 d 01 2 d 12 2 ( ω 1 - ω ) ( ω 2 - ω ) - d 01 4 ( ω 1 - ω ) 2 ] } .
H ( t ) = H 0 - [ j E j cos ( ω j t + φ j ) ] D ,
Ψ α ( t ) = exp ( i e α t / ) φ α ( t ) ,
φ α ( t ) = Δ ω Ψ Δ ω α exp ( i Δ ω t ) .
Ψ α ( t ) = exp ( i e α t / ) Δ ω , r a Δ ω , r α Ψ Δ ω , r 0 , Ψ Δ ω , r 0 = Ψ r 0 exp ( i Δ ω t ) .
Ψ Δ ω , r 0 H F Ψ Δ ω , r 0 = ω r + Δ ω ,
Ψ Δ ω + ω j , s 0 H F Ψ Δ ω , r 0 = d r , s E j ,
Ψ α | H F x | Ψ α = e α x .
D j = - e α E j * .
D σ = γ ( n ) ( ω σ ; ω 1 , ω 2 , ) E 1 E 2 .
- 1 3 [ d o . r d r , s d s , t d t , o ( ω r + ω k ) ( ω s + ω k + ω l ) ( ω t - ω n ) ,
- d o , r d r , o d o , s d s , o ( ω r + ω k ) ( ω r - ω l ) ( ω s + ω m ) ] E k E l E m E n .
- 1 5 [ d o , r d r , s d s , t d t , u d u , v d v , o ( ω r + ω k ) ( ω s + ω k + ω l ) ( ω t + ω k + ω l + ω m ) ( ω u + ω k + ω l + ω m + ω n ) ( ω v - ω q ) ,
- d o , r d r , o d o , s d s , t d t , u d u , o ( ω r + ω k ) ( ω r - ω l ) ( ω s + ω m ) ( ω t + ω m + ω n ) ( ω u + ω m + ω n + ω p ) , - d o , r d r , o d o , s d s , t d t , u d u , o ( ω r + ω k ) ( ω s + ω k + ω l + ω m ) ( ω s + ω m ) ( ω t + ω m + ω n ) ( ω u + ω m + ω n + ω p ) , - d o , r d r , o d o , s d s , t d t , u d u , o ( ω r + ω k ) ( ω s + ω k + ω l + ω m ) ( ω t + ω k + ω l + ω m + ω n ) ( ω t + ω m + ω n ) ( ω u + ω m + ω n + ω p ) , - d o , r d r , o d o , s d s , t d t , u d u , o ( ω r + ω k ) ( ω s + ω k + ω l + ω m ) ( ω t + ω k + ω l + ω m + ω n ) ( ω u - ω q ) ( ω u + ω m + ω n + ω p ) ,
+ d o , r d r , o d o , s d s , o d o , t d t , o ( ω r + ω k ) ( ω s + ω k + ω l + ω m ) ( ω s + ω m ) ( ω t + ω m + ω n + ω p ) ( ω t + ω p ) , + d o , r d r , o d o , s d s , o d o , t d t , o ( ω r + ω k ) ( ω s + ω k + ω l + ω m ) ( ω t - ω q ) ( ω t + ω m + ω n + ω p ) ( ω t + ω p ) ] E k E l E m E n E p E q .

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