Abstract

We present a simple way to analytically predict the effect of the temporal Talbot self-imaging process on random amplitude noise and timing jitter in periodic optical pulse trains. The analysis is general and can be applied to any pulse shape; simulation results are in excellent agreement with the predicted values. In addition, the results clearly show that the temporal Talbot effect has an inherent property of mitigating the standard deviation of both pulse amplitude noise and timing jitter.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. J. Delfyett, S. Gee, S. Ozharar, F. Quinlan, K. Kim, S. Lee, and W. Lee, "Ultrafast modelocked semiconductor laser - techniques and applications in networking, instrumentation and signal processing," in Proceedings of the 18th Lasers and Electro-Optics Society Annual Meeting (2005).
  2. J. Azaña and M. A. Muriel, "Temporal self-imaging effects: theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum. Electron. 7, 728-744 (2001).
    [CrossRef]
  3. D. Pudo and L. R. Chen, "Tunable passive all-optical pulse repetition rate multiplier using fiber Bragg gratings," J. Lightwave Technol. 23, 1729-1733 (2005).
    [CrossRef]
  4. D. Pudo, M. Depa, and L. R. Chen, "All-optical clock recovery using the temporal Talbot effect," in Proceedings of the Optical Fiber Communications Conference (2007).
  5. C. R. Fernández-Pousa, F. Mateos, L. Chantada, M. T. Flores-Arias, C. Bao, M. V. Pérez, and C. Gómez-Reino, "Timing jitter smoothing by Talbot effect. I. Variance," J. Opt. Soc. Am. B 21, 1170-1177 (2004).
    [CrossRef]
  6. C. R. Fernández-Pousa, F. Mateos, L. Chantada, M. T. Flores-Arias, C. Bao, M. V. Pérez, and C. Gómez-Reino, "Timing jitter smoothing by Talbot effect. II. Intensity spectrum," J. Opt. Soc. Am. B 22, 753-763 (2005).
    [CrossRef]
  7. D. Pudo and L. R. Chen, "Estimating intensity fluctuations in high repetition rate pulse trains generated using the temporal Talbot effect," IEEE Photon. Technol. Lett. 18, 658-660 (2006).
    [CrossRef]
  8. J. T. Mok and B. J. Eggleton, "Impact of group delay ripple on repetition-rate multiplication through Talbot self-imaging effect," Opt. Commun. 232, 167-178 (2004).
    [CrossRef]
  9. J. Azaña, "Temporal self-imaging effects for periodic optical pulse sequences of finite duration," J. Opt. Soc. Am. B 20, 83-90 (2003).
    [CrossRef]
  10. D. Duchesne, R. Morandotti, and J. Azaña, "Temporal Talbot phenomena in high-order dispersive media," J. Opt. Soc. Am. B 24, 113-125 (2007).
    [CrossRef]

2007 (1)

2006 (1)

D. Pudo and L. R. Chen, "Estimating intensity fluctuations in high repetition rate pulse trains generated using the temporal Talbot effect," IEEE Photon. Technol. Lett. 18, 658-660 (2006).
[CrossRef]

2005 (2)

2004 (2)

C. R. Fernández-Pousa, F. Mateos, L. Chantada, M. T. Flores-Arias, C. Bao, M. V. Pérez, and C. Gómez-Reino, "Timing jitter smoothing by Talbot effect. I. Variance," J. Opt. Soc. Am. B 21, 1170-1177 (2004).
[CrossRef]

J. T. Mok and B. J. Eggleton, "Impact of group delay ripple on repetition-rate multiplication through Talbot self-imaging effect," Opt. Commun. 232, 167-178 (2004).
[CrossRef]

2003 (1)

2001 (1)

J. Azaña and M. A. Muriel, "Temporal self-imaging effects: theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum. Electron. 7, 728-744 (2001).
[CrossRef]

Azaña, J.

Bao, C.

Chantada, L.

Chen, L. R.

D. Pudo and L. R. Chen, "Estimating intensity fluctuations in high repetition rate pulse trains generated using the temporal Talbot effect," IEEE Photon. Technol. Lett. 18, 658-660 (2006).
[CrossRef]

D. Pudo and L. R. Chen, "Tunable passive all-optical pulse repetition rate multiplier using fiber Bragg gratings," J. Lightwave Technol. 23, 1729-1733 (2005).
[CrossRef]

Duchesne, D.

Eggleton, B. J.

J. T. Mok and B. J. Eggleton, "Impact of group delay ripple on repetition-rate multiplication through Talbot self-imaging effect," Opt. Commun. 232, 167-178 (2004).
[CrossRef]

Fernández-Pousa, C. R.

Flores-Arias, M. T.

Gómez-Reino, C.

Mateos, F.

Mok, J. T.

J. T. Mok and B. J. Eggleton, "Impact of group delay ripple on repetition-rate multiplication through Talbot self-imaging effect," Opt. Commun. 232, 167-178 (2004).
[CrossRef]

Morandotti, R.

Muriel, M. A.

J. Azaña and M. A. Muriel, "Temporal self-imaging effects: theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum. Electron. 7, 728-744 (2001).
[CrossRef]

Pérez, M. V.

Pudo, D.

D. Pudo and L. R. Chen, "Estimating intensity fluctuations in high repetition rate pulse trains generated using the temporal Talbot effect," IEEE Photon. Technol. Lett. 18, 658-660 (2006).
[CrossRef]

D. Pudo and L. R. Chen, "Tunable passive all-optical pulse repetition rate multiplier using fiber Bragg gratings," J. Lightwave Technol. 23, 1729-1733 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum. Electron. (1)

J. Azaña and M. A. Muriel, "Temporal self-imaging effects: theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum. Electron. 7, 728-744 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

D. Pudo and L. R. Chen, "Estimating intensity fluctuations in high repetition rate pulse trains generated using the temporal Talbot effect," IEEE Photon. Technol. Lett. 18, 658-660 (2006).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Commun. (1)

J. T. Mok and B. J. Eggleton, "Impact of group delay ripple on repetition-rate multiplication through Talbot self-imaging effect," Opt. Commun. 232, 167-178 (2004).
[CrossRef]

Other (2)

D. Pudo, M. Depa, and L. R. Chen, "All-optical clock recovery using the temporal Talbot effect," in Proceedings of the Optical Fiber Communications Conference (2007).

P. J. Delfyett, S. Gee, S. Ozharar, F. Quinlan, K. Kim, S. Lee, and W. Lee, "Ultrafast modelocked semiconductor laser - techniques and applications in networking, instrumentation and signal processing," in Proceedings of the 18th Lasers and Electro-Optics Society Annual Meeting (2005).

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.

Temporal Talbot self-imaging process: a) incident pulse amplitude profile, b) pulse-by-pulse decomposition, c) effect of dispersion, d) observed output pulse amplitude profile. The dots illustrate a particular point in time, e.g. t = 0, where successive dispersed pulses overlap contributing to an output pulse peak o(0).

Fig. 2.
Fig. 2.

Simulated and predicted values of Rnoise as a function of a) s, b) m, c) input repetition rate, and d) pulse width.

Fig. 3.
Fig. 3.

Simulated and predicted values of Rjitter as a function of a) s, b) m, c) input repetition rate, and d) pulse width.

Fig. 4.
Fig. 4.

Offset between the predicted and simulated output: a) timing jitter b) amplitude noise for increasing input jitter/noise standard deviation values. Note the different y-axis scales.

Equations (17)

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

a in ( t ) = p = + a 0 ( t pT )
o ( t ) = p = + d ( t pT )
o ( t ) = 1 m p = + a 0 ( t p m T ) ; ( m∙s ) even o ( t ) = 1 m p = + a 0 ( t p m T T 2 m ) ; ( m s ) odd ;
o ( t ) = p = + d ( t pT ) = 1 m p = + a 0 ( t p m T )
o ( 0 ) = p = + d ( pT ) = 1 m
a in ( t ) = p = + N p a 0 ( t pT )
o ( 0 ) = p = + N p d ( pT )
σ noise out = σ noise in m p = + d ( pT ) 2
d ( t ) = T 0 T 0 2 i ϕ e 1 2 t 2 T 0 2 = T 0 T 0 2 i∙ T 2 s∙ ( m∙ 2 π ) 1 e 1 2 t 2 T 0 2 i T 2 s∙ ( m∙ 2 π ) 1
σ noise out = σ noise in [ m∙ p = + T 0 T 0 2 i∙ T 2 s∙ ( m∙ 2 π ) 1 e 1 2 p 2 T 2 T 0 2 i∙ T 2 s∙ ( m∙ 2 π ) 1 2 ] 1 2
A 1 p ( t + δ 1 ) + A 2 p ( t + δ 2 ) + + A n p ( t + δ n ) ( A 1 + A 2 + + A n ) p ( t + δ out )
where δ out = A 1 δ 1 + A 2 δ 2 + + A n δ n A 1 + A 2 + + A n
a in ( t ) = p = + a 0 ( t pT D p )
o ( t ) = p = + d ( t pT D p )
o ( 0 ) = p = + d ( pT D p )
D out = p = + ( d ( pT ) D p ) p = + d ( pT )
σ jitter out = σ jitter in p = + d ( pT ) 2 ( 1 m ) 2 = σ jitter in m∙ p = + d ( pT ) 2

Metrics