Abstract

We present an analysis of the occurrence of a frequency chirp on picosecond pump and signal pulses as a result of optical parametric amplification with a large phase mismatch in a medium with a large second-order susceptibility. When pump depletion and differences in the group velocity are neglected, a simple analytical formula shows that the signal pulse has a frequency chirp. The sign of the chirp is determined by the sign of Δk. Numerical calculations that account for changes in the pump and differences in the group velocity demonstrate that for higher intensities of the signal and the idler, the pump, the signal, and the idler develop a chirp. In all cases the chirp is large enough to increase the bandwidth of the pulses significantly.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. L. Shapiro, Appl. Phys. Lett. 13, 19 (1968).
    [Crossref]
  2. W. Kranitzky, K. Ding, A. Seilmeier, and W. Kaiser, Opt. Commun. 34, 483 (1980).
    [Crossref]
  3. H. Herrmann and W. Sohler, J. Opt. Soc. Am. B 5, 278 (1988).
    [Crossref]
  4. R. C. Eckardt and J. Reintjes, IEEE J. Quantum Electron. QE-20, 1178 (1984).
    [Crossref]
  5. J. T. Manassah, J. Opt. Soc. Am. B 4, 1235 (1987).
    [Crossref]
  6. Y. N. Karamzin and A. P. Sukhorukov, Sov. J. Quantum Electron. 5, 496 (1975).
    [Crossref]
  7. S. A. Akhmanov, A. S. Chirkin, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
    [Crossref]
  8. G. A. Bukauskas, V. I. Kabelka, A. S. Piskarskas, and A. Yu. Stabinis, Sov. J. Quantum Electron. 4, 290 (1974).
    [Crossref]
  9. R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, Sov. J. Quantum Electron. 7, 1360 (1977).
    [Crossref]
  10. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  11. N. C. Kothari and X. Carlotti, J. Opt. Soc. Am. B 5, 756 (1988).
    [Crossref]
  12. H. J. Bakker, P. C. M. Planken, and H. G. Muller, J. Opt. Soc. Am. B 6, 1665 (1989).
    [Crossref]
  13. F. T. Arecchi and E. O. Schulz-Dubois, Laser Handbook (North-Holland, Amsterdam, 1972), Vol. 1.
  14. R. Alfano, Q. X. Li, T. Jimbo, J. T. Manassah, and P. P. Ho, Opt. Lett. 11, 626 (1986).
    [Crossref] [PubMed]
  15. H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A (to be published).

1989 (1)

1988 (2)

1987 (1)

1986 (1)

1984 (1)

R. C. Eckardt and J. Reintjes, IEEE J. Quantum Electron. QE-20, 1178 (1984).
[Crossref]

1980 (1)

W. Kranitzky, K. Ding, A. Seilmeier, and W. Kaiser, Opt. Commun. 34, 483 (1980).
[Crossref]

1977 (1)

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, Sov. J. Quantum Electron. 7, 1360 (1977).
[Crossref]

1975 (1)

Y. N. Karamzin and A. P. Sukhorukov, Sov. J. Quantum Electron. 5, 496 (1975).
[Crossref]

1974 (1)

G. A. Bukauskas, V. I. Kabelka, A. S. Piskarskas, and A. Yu. Stabinis, Sov. J. Quantum Electron. 4, 290 (1974).
[Crossref]

1968 (2)

S. A. Akhmanov, A. S. Chirkin, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[Crossref]

S. L. Shapiro, Appl. Phys. Lett. 13, 19 (1968).
[Crossref]

Akhmanov, S. A.

S. A. Akhmanov, A. S. Chirkin, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[Crossref]

Alfano, R.

Arecchi, F. T.

F. T. Arecchi and E. O. Schulz-Dubois, Laser Handbook (North-Holland, Amsterdam, 1972), Vol. 1.

Bakker, H. J.

H. J. Bakker, P. C. M. Planken, and H. G. Muller, J. Opt. Soc. Am. B 6, 1665 (1989).
[Crossref]

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A (to be published).

Bukauskas, G. A.

G. A. Bukauskas, V. I. Kabelka, A. S. Piskarskas, and A. Yu. Stabinis, Sov. J. Quantum Electron. 4, 290 (1974).
[Crossref]

Carlotti, X.

Chirkin, A. S.

S. A. Akhmanov, A. S. Chirkin, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[Crossref]

Danelyus, R.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, Sov. J. Quantum Electron. 7, 1360 (1977).
[Crossref]

Dikchyus, G.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, Sov. J. Quantum Electron. 7, 1360 (1977).
[Crossref]

Ding, K.

W. Kranitzky, K. Ding, A. Seilmeier, and W. Kaiser, Opt. Commun. 34, 483 (1980).
[Crossref]

Eckardt, R. C.

R. C. Eckardt and J. Reintjes, IEEE J. Quantum Electron. QE-20, 1178 (1984).
[Crossref]

Herrmann, H.

Ho, P. P.

Jimbo, T.

Kabelka, V.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, Sov. J. Quantum Electron. 7, 1360 (1977).
[Crossref]

Kabelka, V. I.

G. A. Bukauskas, V. I. Kabelka, A. S. Piskarskas, and A. Yu. Stabinis, Sov. J. Quantum Electron. 4, 290 (1974).
[Crossref]

Kaiser, W.

W. Kranitzky, K. Ding, A. Seilmeier, and W. Kaiser, Opt. Commun. 34, 483 (1980).
[Crossref]

Karamzin, Y. N.

Y. N. Karamzin and A. P. Sukhorukov, Sov. J. Quantum Electron. 5, 496 (1975).
[Crossref]

Khokhlov, R. V.

S. A. Akhmanov, A. S. Chirkin, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[Crossref]

Kothari, N. C.

Kovrigin, A. I.

S. A. Akhmanov, A. S. Chirkin, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[Crossref]

Kranitzky, W.

W. Kranitzky, K. Ding, A. Seilmeier, and W. Kaiser, Opt. Commun. 34, 483 (1980).
[Crossref]

Kuipers, L.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A (to be published).

Lagendijk, A.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A (to be published).

Li, Q. X.

Manassah, J. T.

Muller, H. G.

Piskarskas, A.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, Sov. J. Quantum Electron. 7, 1360 (1977).
[Crossref]

Piskarskas, A. S.

G. A. Bukauskas, V. I. Kabelka, A. S. Piskarskas, and A. Yu. Stabinis, Sov. J. Quantum Electron. 4, 290 (1974).
[Crossref]

Planken, P. C. M.

H. J. Bakker, P. C. M. Planken, and H. G. Muller, J. Opt. Soc. Am. B 6, 1665 (1989).
[Crossref]

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A (to be published).

Reintjes, J.

R. C. Eckardt and J. Reintjes, IEEE J. Quantum Electron. QE-20, 1178 (1984).
[Crossref]

Schulz-Dubois, E. O.

F. T. Arecchi and E. O. Schulz-Dubois, Laser Handbook (North-Holland, Amsterdam, 1972), Vol. 1.

Seilmeier, A.

W. Kranitzky, K. Ding, A. Seilmeier, and W. Kaiser, Opt. Commun. 34, 483 (1980).
[Crossref]

Shapiro, S. L.

S. L. Shapiro, Appl. Phys. Lett. 13, 19 (1968).
[Crossref]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Sohler, W.

Stabinis, A.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, Sov. J. Quantum Electron. 7, 1360 (1977).
[Crossref]

Stabinis, A. Yu.

G. A. Bukauskas, V. I. Kabelka, A. S. Piskarskas, and A. Yu. Stabinis, Sov. J. Quantum Electron. 4, 290 (1974).
[Crossref]

Sukhorukov, A. P.

Y. N. Karamzin and A. P. Sukhorukov, Sov. J. Quantum Electron. 5, 496 (1975).
[Crossref]

S. A. Akhmanov, A. S. Chirkin, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[Crossref]

Yasevichyute, Ya.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, Sov. J. Quantum Electron. 7, 1360 (1977).
[Crossref]

Appl. Phys. Lett. (1)

S. L. Shapiro, Appl. Phys. Lett. 13, 19 (1968).
[Crossref]

IEEE J. Quantum Electron. (2)

R. C. Eckardt and J. Reintjes, IEEE J. Quantum Electron. QE-20, 1178 (1984).
[Crossref]

S. A. Akhmanov, A. S. Chirkin, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[Crossref]

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

W. Kranitzky, K. Ding, A. Seilmeier, and W. Kaiser, Opt. Commun. 34, 483 (1980).
[Crossref]

Opt. Lett. (1)

Sov. J. Quantum Electron. (3)

Y. N. Karamzin and A. P. Sukhorukov, Sov. J. Quantum Electron. 5, 496 (1975).
[Crossref]

G. A. Bukauskas, V. I. Kabelka, A. S. Piskarskas, and A. Yu. Stabinis, Sov. J. Quantum Electron. 4, 290 (1974).
[Crossref]

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, Sov. J. Quantum Electron. 7, 1360 (1977).
[Crossref]

Other (3)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear optical processes,” Phys. Rev. A (to be published).

F. T. Arecchi and E. O. Schulz-Dubois, Laser Handbook (North-Holland, Amsterdam, 1972), Vol. 1.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Calculated frequency chirp Δωc(z = 5, η) on a 900-nm 40-psec signal pulse at z = 5 cm in LiNbO3 for several values of Δk. The pump wavelength is 532 nm, and the intensity is 1 GW/cm2 in a 40-psec pulse. a, Weak signal [Eq. (7)]; b, strong signal, without differences in group velocities, beginning values of the signal and the idler intensities, 0.3 and 0.2 GW/cm2, respectively; c, as in b, but with differences in group velocities.

Fig. 2
Fig. 2

Calculated intensity of a 900-nm 40-psec signal pulse after 5 cm of LiNbO3 for several values of Δk. The pump wavelength is 532 nm, and the intensity is 1 GW/cm2 in a 40-psec pulse. a, Reduced intensity of a weak signal (analytical result); b, strong signal, without differences in group velocities, beginning values of the signal and the idler intensities, 0.3 and 0.2 GW/cm2, respectively; c, as in b, but with differences in group velocities.

Fig. 3
Fig. 3

Calculated frequency chirp Δωc(z = 5, η) on a 532-nm, 40-psec pump pulse after 5 cm of LiNbO3 for several values of Δk, beginning values of the signal and the idler intensities, 0.3 and 0.2 GW/cm2, respectively. a, Without differences in group velocities; b, with differences in group velocities.

Fig. 4
Fig. 4

Calculated intensity of a 532-nm, 40-psec pump pulse after 5 cm of LiNbO3 for several values of Δk; beginning values of the signal and the idler intensities, 0.3 and 0.2 GW/cm2, respectively. a, Without differences in group velocities; b, with differences in group velocities.

Equations (10)

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

E i ( z , t ) = E i ( z , t ) exp [ i ( k i z ω i t ) ] ,
( z + 1 υ 1 g t ) E 1 ( z , t ) = i ω 1 χ eff ( 2 ) 2 n 1 c E 2 * ( z , t ) E 3 ( z , t ) e i Δ k z , ( z + 1 υ 2 g t ) E 2 ( z , t ) = i ω 2 χ eff ( 2 ) 2 n 2 c E 1 * ( z , t ) E 3 ( z , t ) e i Δ k z , ( z + 1 υ 3 g t ) E 3 ( z , t ) = i ω 3 χ eff ( 2 ) 2 n 3 c E 1 ( z , t ) E 2 ( z , t ) e i Δ k z ,
z B 1 ( z , η ) = i ω 1 χ eff ( 2 ) 2 n 1 c B 2 * ( z , η ) B 3 ( η ) e i Δ k z , z B 2 ( z , η ) = i ω 2 χ eff ( 2 ) 2 n 2 c B 1 * ( z , η ) B 3 ( η ) e i Δ k z ,
B 1 ( z , η ) = B 1 ( 0 , η ) { g ( η ) + i Δ k 2 g ( η ) exp [ ( 1 / 2 ) g ( η ) z ] + g ( η ) i Δ k 2 g ( η ) exp [ ( 1 / 2 ) g ( η ) z ] } exp [ ( i / 2 ) Δ k z ] ,
g ( η ) = [ g 0 2 ( η ) Δ k 2 ] 1 / 2
g 0 2 ( η ) = ω 1 ω 2 χ eff 2 | B 3 ( η ) | 2 n 1 n 2 c 2 .
Z ( z , η ) = { cos 2 [ 1 2 Δ k z A ( η ) ] + sin 2 [ ( 1 / 2 ) Δ k z A ( η ) ] A 2 ( η ) } 1 / 2 ,
Φ c ( z , η ) = arctan { tan [ ( 1 / 2 ) Δ k z A ( η ) ] A ( η ) } ,
Δ ω c ( z , η ) = η A ( η ) τ 2 [ g 0 ( η ) Δ k ] 2 × ( 1 / 2 ) Δ k A ( η ) z ( 1 / 2 ) sin [ Δ k A ( η ) z ] 1 [ g 0 ( η ) / Δ k ] 2 cos 2 [ ( 1 / 2 ) Δ k A ( η ) z ] .
Δ ω c ( z , η ) 1 2 η τ 2 g 0 2 ( η ) Δ k z .

Metrics