Abstract

We performed experiments to verify the theory of photorefractive pulse coupling in the frequency domain. In particular, we confirm that the phase added to the diffracted pulse depends quadratically on the relative delay between the two input pulses.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. X. S. Yao, V. G. Dominic, J. Feinberg, J. Opt. Soc. Am. B 7, 1295 (1990).
    [CrossRef]
  2. X. S. Yao, J. Feinberg, “Temporal shaping of optical pulses by beam coupling in a photorefractive crystal,”Opt. Lett. (to be published).
  3. X. S. Yao, “Optical pulse coupling in a photorefractive crystal, propagation of encoded pulses in an optical fiber, and phase conjugate optical interconnections,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1992).
  4. E. D. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
    [CrossRef]
  5. X. S. Yao, J. Feinberg, “A simple, in-line method to measure the dispersion of an optical system,”Appl. Phys. Lett. (to be published).
  6. R. Trebino, C. C. Hayden, A. M. Johnson, W. M. Simpson, A. M. Levine, Opt. Lett. 15, 1079 (1990).
    [CrossRef] [PubMed]

1990 (2)

1969 (1)

E. D. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Dominic, V. G.

X. S. Yao, V. G. Dominic, J. Feinberg, J. Opt. Soc. Am. B 7, 1295 (1990).
[CrossRef]

Feinberg, J.

X. S. Yao, V. G. Dominic, J. Feinberg, J. Opt. Soc. Am. B 7, 1295 (1990).
[CrossRef]

X. S. Yao, J. Feinberg, “Temporal shaping of optical pulses by beam coupling in a photorefractive crystal,”Opt. Lett. (to be published).

X. S. Yao, J. Feinberg, “A simple, in-line method to measure the dispersion of an optical system,”Appl. Phys. Lett. (to be published).

Hayden, C. C.

Johnson, A. M.

Levine, A. M.

Simpson, W. M.

Treacy, E. D.

E. D. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Trebino, R.

Yao, X. S.

X. S. Yao, V. G. Dominic, J. Feinberg, J. Opt. Soc. Am. B 7, 1295 (1990).
[CrossRef]

X. S. Yao, J. Feinberg, “A simple, in-line method to measure the dispersion of an optical system,”Appl. Phys. Lett. (to be published).

X. S. Yao, “Optical pulse coupling in a photorefractive crystal, propagation of encoded pulses in an optical fiber, and phase conjugate optical interconnections,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1992).

X. S. Yao, J. Feinberg, “Temporal shaping of optical pulses by beam coupling in a photorefractive crystal,”Opt. Lett. (to be published).

IEEE J. Quantum Electron. (1)

E. D. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

J. Opt. Soc. Am. B (1)

X. S. Yao, V. G. Dominic, J. Feinberg, J. Opt. Soc. Am. B 7, 1295 (1990).
[CrossRef]

Opt. Lett. (1)

Other (3)

X. S. Yao, J. Feinberg, “Temporal shaping of optical pulses by beam coupling in a photorefractive crystal,”Opt. Lett. (to be published).

X. S. Yao, “Optical pulse coupling in a photorefractive crystal, propagation of encoded pulses in an optical fiber, and phase conjugate optical interconnections,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1992).

X. S. Yao, J. Feinberg, “A simple, in-line method to measure the dispersion of an optical system,”Appl. Phys. Lett. (to be published).

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

Experimental setup for measuring the change in the optical spectrum of the signal pulses that is due to photorefractive pulse coupling. The grating pair chirps the signal pulses before they intersect with the pump pulses in the BaTiO3 crystal. Mirror Ml is tilted downward a bit so that the backward-going beam could be picked off by mirror M2, which lies below the incident beam in the plane of the figure. By opening and closing the shutter, we measure the spectra of the signal beam with and without beam coupling. The pump laser is not transform limited; it has a frequency-time product of ΔνΔτ = 1.

Fig. 2
Fig. 2

Power gain of the signal pulse as a function of optical frequency. (a) The crystal is oriented so that the signal beam loses energy, (b) the crystal is rotated 180° so that the signal pulse now gains energy. As predicted, the gain of the signal beam is a sinusoidal function of frequency with a varying periodicity. The solid curve is a fit to the data (circles). The roll-off in the wings is discussed in the text.

Fig. 3
Fig. 3

Spectral gain curve as a function of the relative delay τ between the pump and the signal pulses. Here the crystal is oriented so that the signal beam loses energy. The value of ϕdiff(τ) determines the position of the center lobe of each gain curve. We obtain a value of ϕdiff(τ) for each delay τ by curve fitting the corresponding gain curves.

Fig. 4
Fig. 4

Phase ϕdiff(τ) of the spectral gain as a function of delay τ, as determined by curve fits such as shown in Fig. 3. The crystal is oriented for the signal pulse (a) to gain energy and (b) to lose energy. The data (filled circles) are fitted to a quadratic function of the delay (solid curve). Both the data and the fits are in good agreement with the theoretical calculations (dotted curve).

Equations (5)

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

E shaped ( t ) = E signal ( t ) + G ( τ ) [ exp ( η L ) 1 ] E pump ( t ) ,
G ( τ ) = E signal ( t ) E pump ( t τ ) ¯ d t / I 0 | G ( τ ) | exp [ i ϕ diff ( τ ) ] .
E ( t ) = 1 2 π F ( ω ) exp ( i ω t ) d ω ,
| F shaped ( ω ) | 2 | F signal ( ω ) | 2 ¯ = a ( τ ) { 1 + b ( τ ) cos [ ϕ diff ( τ ) τ ω β ω 2 ] } ,
ϕ diff ( τ ) = 1 2 tan 1 β α β 4 ( α 2 + β 2 ) τ 2 .

Metrics