Abstract

An ultrafast all-optical temporal integrator is experimentally demonstrated. The demonstrated integrator is based on a very simple and practical solution only requiring the use of a widely available all-fiber passive component, namely a reflection uniform fiber Bragg grating (FBG). This design allows overcoming the severe speed (bandwidth) limitations of the previously demonstrated photonic integrator designs. We demonstrate temporal integration of a variety of ultrafast optical waveforms, including Gaussian, odd-symmetry Hermite Gaussian, and (odd-)symmetry double pulses, with temporal features as fast as ~6-ps, which is about one order of magnitude faster than in previous photonic integration demonstrations. The developed device is potentially interesting for a multitude of applications in all-optical computing and information processing, ultrahigh-speed optical communications, ultrafast pulse (de-)coding, shaping and metrology.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  5. M. Kulishov and J. Azaña, "Long-period fiber gratings as ultrafast optical differentiators," Opt. Lett. 30, 2700-2702 (2005).
    [CrossRef] [PubMed]
  6. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators," Opt. Express 14, 10699-10707 (2006).
    [CrossRef] [PubMed]
  7. Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-712 (2007).
    [CrossRef] [PubMed]
  8. N. Q. Ngo and L. N. Binh, "Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation," IEEE/OSAJ. Lightwave Technol. 24, 563-572 (2006).
    [CrossRef]
  9. N. Q. Ngo "Optical integrator for optical dark-soliton detection and pulse shaping," Appl. Opt. 45, 6785-6791 (2006).
    [CrossRef] [PubMed]
  10. N. Q. Ngo "Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission," Opt. Lett. 32, 3020-3022 (2007).
    [CrossRef]
  11. N. Q. Ngo and L. N. Binh, "New approach for the design of an optical square pulse generator," Appl. Opt. 46, 3546-3560 (2007)
    [CrossRef] [PubMed]
  12. J. Azaña "Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator," Opt. Lett. 33, 4-6 (2008).
    [CrossRef]
  13. R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. -J. Ahn, S. LaRochelle, and J. Azaña, "Photonic Temporal Integrator for All-Optical Computing," Opt. Express (to be published).
    [PubMed]
  14. G. F. Simmons, Differential Equations with Applications and Historical Notes (McGraw-Hill, New York, 1991).
  15. R. Kashyap, Fiber Bragg Gratings (Academic Press, San Diego, 1999).
  16. L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, "Ultrashort pulse reflection from fiber gratings: A numerical investigation," J. Lightwave Technol. 15, 1503-1512 (1997).
    [CrossRef]
  17. Y. Park, M. H. Asghari, T. -J. Ahn, and J. Azaña, "Transform-limited picosecond pulse shaping based on coherence synthesization," Opt. Express 15, 9584-9599 (2007).
    [CrossRef] [PubMed]
  18. L. Lepetit, G. Chériaux, and M. Joffre, "Linear technique of phase measurement by femtosecond spectral interferometry for applications in spectroscopy," J. Opt. Soc. Am. B 12, 2467-2474 (1995).
    [CrossRef]
  19. Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
    [CrossRef]
  20. J. Yao, F. Zeng, and Q. Wang, "Photonic generation of Ultra-Wideband signals," IEEE/OSAJ. Lightwave Technol. 25, 3219-3235 (2007).
  21. J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, "High-speed all-optical differentiator based on a semiconductor optical amplifier and an optical filter," Opt. Lett. 32, 1872-1874 (2007).
    [CrossRef] [PubMed]
  22. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, "Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings," Opt. Express 14, 12670-12678 (2006).
    [CrossRef] [PubMed]
  23. R. Slavík, L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azaña, and P. Jeppesen, "Demultiplexing of 320 and 640 Gbit/s OTDM data using ultrashort flat-top pulses," IEEE Photon. Technol. Lett. 19, 1855-1857 (2007).
    [CrossRef]
  24. F. Li, Y. Park, and J. Azaña, "Complete temporal pulse characterization based on phase reconstruction using optical ultrafast differentiation (PROUD)," Opt. Lett. 32, 3364-3366 (2007).
    [CrossRef] [PubMed]
  25. F. Li, Y. Park, and J. Azaña, "Group delay characterization of dispersive devices using a pulse temporal intensity measurement setup," IEEE Photon. Technol. Lett. (to be published).
  26. F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-Optical Pulse Reshaping and Retiming Systems Incorporating Pulse Shaping Fiber Bragg Grating," IEEE/OSA J.Ligthwave Technol. 24, 357 (2006).
    [CrossRef]
  27. A. V. Oppenheim, A. S. Willsky, and S. Hamid Nawab, Signals & systems (Prentice-Hall, Upper Saddle River, NJ, 1996)
  28. K. Ogata, Modern Control Engineering (Prentice Hall, Upper Saddle River, NJ, USA, 2001).

2008 (1)

2007 (8)

2006 (7)

N. Q. Ngo and L. N. Binh, "Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation," IEEE/OSAJ. Lightwave Technol. 24, 563-572 (2006).
[CrossRef]

N. Q. Ngo "Optical integrator for optical dark-soliton detection and pulse shaping," Appl. Opt. 45, 6785-6791 (2006).
[CrossRef] [PubMed]

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., Special Issue on "Optical Signal Processing," IEEE/OSAJ. Lightwave Technol. 24, 2484-2767 (2006).
[CrossRef]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators," Opt. Express 14, 10699-10707 (2006).
[CrossRef] [PubMed]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-Optical Pulse Reshaping and Retiming Systems Incorporating Pulse Shaping Fiber Bragg Grating," IEEE/OSA J.Ligthwave Technol. 24, 357 (2006).
[CrossRef]

Y. Park, M. Kulishov, R. Slavík, and J. Azaña, "Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings," Opt. Express 14, 12670-12678 (2006).
[CrossRef] [PubMed]

Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
[CrossRef]

2005 (1)

2004 (1)

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115−129 (2004).
[CrossRef]

1997 (1)

L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, "Ultrashort pulse reflection from fiber gratings: A numerical investigation," J. Lightwave Technol. 15, 1503-1512 (1997).
[CrossRef]

1995 (1)

Ahn, T. -J.

Y. Park, M. H. Asghari, T. -J. Ahn, and J. Azaña, "Transform-limited picosecond pulse shaping based on coherence synthesization," Opt. Express 15, 9584-9599 (2007).
[CrossRef] [PubMed]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. -J. Ahn, S. LaRochelle, and J. Azaña, "Photonic Temporal Integrator for All-Optical Computing," Opt. Express (to be published).
[PubMed]

Asghari, M. H.

Ayotte, N.

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. -J. Ahn, S. LaRochelle, and J. Azaña, "Photonic Temporal Integrator for All-Optical Computing," Opt. Express (to be published).
[PubMed]

Azaña, J.

J. Azaña "Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator," Opt. Lett. 33, 4-6 (2008).
[CrossRef]

Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-712 (2007).
[CrossRef] [PubMed]

Y. Park, M. H. Asghari, T. -J. Ahn, and J. Azaña, "Transform-limited picosecond pulse shaping based on coherence synthesization," Opt. Express 15, 9584-9599 (2007).
[CrossRef] [PubMed]

R. Slavík, L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azaña, and P. Jeppesen, "Demultiplexing of 320 and 640 Gbit/s OTDM data using ultrashort flat-top pulses," IEEE Photon. Technol. Lett. 19, 1855-1857 (2007).
[CrossRef]

F. Li, Y. Park, and J. Azaña, "Complete temporal pulse characterization based on phase reconstruction using optical ultrafast differentiation (PROUD)," Opt. Lett. 32, 3364-3366 (2007).
[CrossRef] [PubMed]

Y. Park, M. Kulishov, R. Slavík, and J. Azaña, "Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings," Opt. Express 14, 12670-12678 (2006).
[CrossRef] [PubMed]

Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
[CrossRef]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators," Opt. Express 14, 10699-10707 (2006).
[CrossRef] [PubMed]

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., Special Issue on "Optical Signal Processing," IEEE/OSAJ. Lightwave Technol. 24, 2484-2767 (2006).
[CrossRef]

M. Kulishov and J. Azaña, "Long-period fiber gratings as ultrafast optical differentiators," Opt. Lett. 30, 2700-2702 (2005).
[CrossRef] [PubMed]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. -J. Ahn, S. LaRochelle, and J. Azaña, "Photonic Temporal Integrator for All-Optical Computing," Opt. Express (to be published).
[PubMed]

F. Li, Y. Park, and J. Azaña, "Group delay characterization of dispersive devices using a pulse temporal intensity measurement setup," IEEE Photon. Technol. Lett. (to be published).

Benjamin, S. D.

L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, "Ultrashort pulse reflection from fiber gratings: A numerical investigation," J. Lightwave Technol. 15, 1503-1512 (1997).
[CrossRef]

Binh, L. N.

Chen, L. R.

L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, "Ultrashort pulse reflection from fiber gratings: A numerical investigation," J. Lightwave Technol. 15, 1503-1512 (1997).
[CrossRef]

Chériaux, G.

Cincontti, G.

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., Special Issue on "Optical Signal Processing," IEEE/OSAJ. Lightwave Technol. 24, 2484-2767 (2006).
[CrossRef]

Dong, J.

Doucet, S.

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. -J. Ahn, S. LaRochelle, and J. Azaña, "Photonic Temporal Integrator for All-Optical Computing," Opt. Express (to be published).
[PubMed]

Galili, M.

R. Slavík, L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azaña, and P. Jeppesen, "Demultiplexing of 320 and 640 Gbit/s OTDM data using ultrashort flat-top pulses," IEEE Photon. Technol. Lett. 19, 1855-1857 (2007).
[CrossRef]

Huang, D.

Ibsen, M.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-Optical Pulse Reshaping and Retiming Systems Incorporating Pulse Shaping Fiber Bragg Grating," IEEE/OSA J.Ligthwave Technol. 24, 357 (2006).
[CrossRef]

Jeppesen, P.

R. Slavík, L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azaña, and P. Jeppesen, "Demultiplexing of 320 and 640 Gbit/s OTDM data using ultrashort flat-top pulses," IEEE Photon. Technol. Lett. 19, 1855-1857 (2007).
[CrossRef]

Joffre, M.

Kam, C. H.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115−129 (2004).
[CrossRef]

Kulishov, M.

LaRochelle, S.

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. -J. Ahn, S. LaRochelle, and J. Azaña, "Photonic Temporal Integrator for All-Optical Computing," Opt. Express (to be published).
[PubMed]

Lepetit, L.

Li, F.

F. Li, Y. Park, and J. Azaña, "Complete temporal pulse characterization based on phase reconstruction using optical ultrafast differentiation (PROUD)," Opt. Lett. 32, 3364-3366 (2007).
[CrossRef] [PubMed]

Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
[CrossRef]

F. Li, Y. Park, and J. Azaña, "Group delay characterization of dispersive devices using a pulse temporal intensity measurement setup," IEEE Photon. Technol. Lett. (to be published).

Liu, D.

Madsen, C. K.

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., Special Issue on "Optical Signal Processing," IEEE/OSAJ. Lightwave Technol. 24, 2484-2767 (2006).
[CrossRef]

Morandotti, R.

Mulvad, H. C. H.

R. Slavík, L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azaña, and P. Jeppesen, "Demultiplexing of 320 and 640 Gbit/s OTDM data using ultrashort flat-top pulses," IEEE Photon. Technol. Lett. 19, 1855-1857 (2007).
[CrossRef]

Ngo, N. Q.

Oxenløwe, L. K.

R. Slavík, L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azaña, and P. Jeppesen, "Demultiplexing of 320 and 640 Gbit/s OTDM data using ultrashort flat-top pulses," IEEE Photon. Technol. Lett. 19, 1855-1857 (2007).
[CrossRef]

Park, Y.

R. Slavík, L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azaña, and P. Jeppesen, "Demultiplexing of 320 and 640 Gbit/s OTDM data using ultrashort flat-top pulses," IEEE Photon. Technol. Lett. 19, 1855-1857 (2007).
[CrossRef]

F. Li, Y. Park, and J. Azaña, "Complete temporal pulse characterization based on phase reconstruction using optical ultrafast differentiation (PROUD)," Opt. Lett. 32, 3364-3366 (2007).
[CrossRef] [PubMed]

Y. Park, M. H. Asghari, T. -J. Ahn, and J. Azaña, "Transform-limited picosecond pulse shaping based on coherence synthesization," Opt. Express 15, 9584-9599 (2007).
[CrossRef] [PubMed]

Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-712 (2007).
[CrossRef] [PubMed]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators," Opt. Express 14, 10699-10707 (2006).
[CrossRef] [PubMed]

Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
[CrossRef]

Y. Park, M. Kulishov, R. Slavík, and J. Azaña, "Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings," Opt. Express 14, 12670-12678 (2006).
[CrossRef] [PubMed]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. -J. Ahn, S. LaRochelle, and J. Azaña, "Photonic Temporal Integrator for All-Optical Computing," Opt. Express (to be published).
[PubMed]

F. Li, Y. Park, and J. Azaña, "Group delay characterization of dispersive devices using a pulse temporal intensity measurement setup," IEEE Photon. Technol. Lett. (to be published).

Parmigiani, F.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-Optical Pulse Reshaping and Retiming Systems Incorporating Pulse Shaping Fiber Bragg Grating," IEEE/OSA J.Ligthwave Technol. 24, 357 (2006).
[CrossRef]

Petropoulos, P.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-Optical Pulse Reshaping and Retiming Systems Incorporating Pulse Shaping Fiber Bragg Grating," IEEE/OSA J.Ligthwave Technol. 24, 357 (2006).
[CrossRef]

Richardson, D. J.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-Optical Pulse Reshaping and Retiming Systems Incorporating Pulse Shaping Fiber Bragg Grating," IEEE/OSA J.Ligthwave Technol. 24, 357 (2006).
[CrossRef]

Sipe, J. E.

L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, "Ultrashort pulse reflection from fiber gratings: A numerical investigation," J. Lightwave Technol. 15, 1503-1512 (1997).
[CrossRef]

Slavík, R.

R. Slavík, L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azaña, and P. Jeppesen, "Demultiplexing of 320 and 640 Gbit/s OTDM data using ultrashort flat-top pulses," IEEE Photon. Technol. Lett. 19, 1855-1857 (2007).
[CrossRef]

Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-712 (2007).
[CrossRef] [PubMed]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators," Opt. Express 14, 10699-10707 (2006).
[CrossRef] [PubMed]

Y. Park, M. Kulishov, R. Slavík, and J. Azaña, "Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings," Opt. Express 14, 12670-12678 (2006).
[CrossRef] [PubMed]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. -J. Ahn, S. LaRochelle, and J. Azaña, "Photonic Temporal Integrator for All-Optical Computing," Opt. Express (to be published).
[PubMed]

Smith, P. W. E.

L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, "Ultrashort pulse reflection from fiber gratings: A numerical investigation," J. Lightwave Technol. 15, 1503-1512 (1997).
[CrossRef]

Takiguchi, K.

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., Special Issue on "Optical Signal Processing," IEEE/OSAJ. Lightwave Technol. 24, 2484-2767 (2006).
[CrossRef]

Tjin, S. C.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115−129 (2004).
[CrossRef]

Wang, Q.

Xu, J.

Yao, J.

Yu, S. F.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115−129 (2004).
[CrossRef]

Zeng, F.

Zhang, X.

Appl. Opt. (2)

IEEE Photon. Technol. Lett. (3)

Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
[CrossRef]

R. Slavík, L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azaña, and P. Jeppesen, "Demultiplexing of 320 and 640 Gbit/s OTDM data using ultrashort flat-top pulses," IEEE Photon. Technol. Lett. 19, 1855-1857 (2007).
[CrossRef]

F. Li, Y. Park, and J. Azaña, "Group delay characterization of dispersive devices using a pulse temporal intensity measurement setup," IEEE Photon. Technol. Lett. (to be published).

J. Lightwave Technol. (4)

J. Yao, F. Zeng, and Q. Wang, "Photonic generation of Ultra-Wideband signals," IEEE/OSAJ. Lightwave Technol. 25, 3219-3235 (2007).

L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, "Ultrashort pulse reflection from fiber gratings: A numerical investigation," J. Lightwave Technol. 15, 1503-1512 (1997).
[CrossRef]

N. Q. Ngo and L. N. Binh, "Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation," IEEE/OSAJ. Lightwave Technol. 24, 563-572 (2006).
[CrossRef]

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., Special Issue on "Optical Signal Processing," IEEE/OSAJ. Lightwave Technol. 24, 2484-2767 (2006).
[CrossRef]

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

Ligthwave Technol. (1)

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-Optical Pulse Reshaping and Retiming Systems Incorporating Pulse Shaping Fiber Bragg Grating," IEEE/OSA J.Ligthwave Technol. 24, 357 (2006).
[CrossRef]

Opt. Commun. (1)

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115−129 (2004).
[CrossRef]

Opt. Express (4)

Opt. Lett. (6)

Other (6)

Photonics Technologies. Nature Insight 424, (2003).

C. K. Madsen, D. Dragoman, and J. Azaña (editors), Special Issue on "Signal Analysis Tools for Optical Signal Processing," EURASIP J. Appl. Signal Proc. 2005, 1449-1623 (2005).
[CrossRef]

G. F. Simmons, Differential Equations with Applications and Historical Notes (McGraw-Hill, New York, 1991).

R. Kashyap, Fiber Bragg Gratings (Academic Press, San Diego, 1999).

A. V. Oppenheim, A. S. Willsky, and S. Hamid Nawab, Signals & systems (Prentice-Hall, Upper Saddle River, NJ, 1996)

K. Ogata, Modern Control Engineering (Prentice Hall, Upper Saddle River, NJ, USA, 2001).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic of a weak-coupling FBG and its reflection temporal impulse response. (b) Diagram describing the experimental procedure. (c) Schematic of an interferometer-based pulse shaper using free-space optics. L: collimating lens. B: beam splitter. M: mirror. (d) Proposed FBG-based integrator and the measured reflectivity of the FBG sample used in our experiments.

Fig. 2.
Fig. 2.

Theoretical input (left) and output (right) pulses from an ideal FBG-based temporal integrator for different input waveforms: (a) Gaussian pulse. (b) Odd-symmetry Hermite-Gaussian (OS-HG) pulse. (c) Symmetric and odd-symmetry double pulses.

Fig. 3.
Fig. 3.

Experimentally measured input and output temporal waveforms for different integration experiments: integration of an OS-HG input pulse (a), integration of odd-symmetry double-pulse waveforms with different input inter-pulse delays (b, c), and integration of a symmetric double pulse (d). In each plot, the top sub-plot (named by the suffix ‘-i’) shows the signal launched at the input of the FBG (integrator) whereas the bottom sub-plot (named by the suffix ‘-o’) shows the signal reflected from the FBG (integrator output), illustrating the integration time window with a gray box and also presenting the theoretical (numerical) time integral of the measured input complex envelope along the integration window (curve with red hollow circles). In each sub-plot, the measured temporal intensity profile is represented with a solid blue line and the measured temporal phase profile is represented with a dashed red line.

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