Abstract

In this paper, we propose and numerically investigate a simple and practical all-fiber design for implementing first-order and higher order all-optical passive temporal integrators with optimized energetic efficiencies. The proposed solution is based on a high-reflectivity fiber Bragg grating (FBG) providing a reflection spectral response that approaches the frequency transfer function of a time-limited $N{\rm th}$-order optical integrator ($ N = 1, 2, 3 \ldots $). A closed-form analytical expression has been derived for the frequency response to be targeted for implementing an optical integrator of any given integration order operating over a prescribed limited time window. The required grating profile can then be designed using a layer-peeling FBG synthesis algorithm. Our simulations show that for a sufficiently long FBG, a relatively smooth amplitude-only apodization profile is required for any desired integration order even when an FBG peak reflectivity $ > 99\%$ is targeted. The resulting FBG integrators can provide at least a sixfold increase in energetic efficiency as compared with previously proposed FBG designs while offering a similar or superior performance in terms of processing accuracy. We estimate that ultrafast highly efficient arbitrary-order all-optical temporal integrators capable of accurate operation over nanosecond time windows could be implemented using readily feasible, centimeters-long FBGs.

© 2009 IEEE

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  1. A. V. Oppenheim, A. S. Willsky, S. N. Nawab, S. H. Nawab, Signals and Systems (Prentice Hall, 1996).
  2. N. Q. Ngo, "Optical integrator for optical dark-soliton detection and pulse shaping," Appl. Opt. 45, 6785-6791 (2006).
  3. N. Q. Ngo, L. N. Binh, "Optical realization of Newton-Cotes-based integrators for dark soliton generation," J. Lightw. Technol. 24, 563-572 (2006).
  4. N. Q. Ngo, L. N. Binh, "New approach for the design of an optical square pulse generator," Appl. Opt. 46, 3546-3560 (2007).
  5. Y. Ding, X.-B. Zhang, X.-L. Zhang, D. Huang, "Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators," Opt. Commun. 281, 5315-5321 (2008).
  6. 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).
  7. J. Azaña, "Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator," Opt. Lett. 33, 4-6 (2008).
  8. M. A. Preciado, M. A. Muriel, "Ultrafast all-optical integrator based on a fiber Bragg grating: Proposal and design," Opt. Lett. 33, 1348-1350 (2008).
  9. R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. –J. Ahn, S. LaRochelle, J. Azaña, "Photonic temporal integrator for all-optical computing," Opt. Exp. 16, 18202-18214 (2008).
  10. Y. Park, T.-J. Ahn, Y. Dai, J. Yao, J. Azaña, "All-optical temporal integration of ultrafast pulse waveforms," Opt. Exp. 16, 17817-17825 (2008).
  11. M. H. Asghari, J. Azaña, "Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings," Opt. Exp. 16, 11459-11469 (2008).
  12. M. H. Asghari, J. Azaña, "Proposal for arbitrary-order temporal integration of ultrafast optical signals using a single uniform-period fiber Bragg grating," Opt. Lett. 33, 1548-1550 (2008).
  13. J. Azaña, L. R. Chen, "Synthesis of temporal optical waveforms by fiber Bragg gratings: A new approach based on space-to-frequency-to-time mapping," J. Opt. Soc. Am. B 19, 2758-2769 (2002).
  14. J. Skaar, W. Ligang, T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
  15. T. Erdogan, "Fiber grating spectra," J. Lightw. Technol. 15, 1277-1294 (1997).
  16. A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill, 1962).
  17. A. W. F. Edwards, Pascal's Arithmetical Triangle: The Story of a Mathematical Idea (Johns Hopkins University Press, 2002).

2008 (7)

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

M. A. Preciado, M. A. Muriel, "Ultrafast all-optical integrator based on a fiber Bragg grating: Proposal and design," Opt. Lett. 33, 1348-1350 (2008).

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. –J. Ahn, S. LaRochelle, J. Azaña, "Photonic temporal integrator for all-optical computing," Opt. Exp. 16, 18202-18214 (2008).

Y. Park, T.-J. Ahn, Y. Dai, J. Yao, J. Azaña, "All-optical temporal integration of ultrafast pulse waveforms," Opt. Exp. 16, 17817-17825 (2008).

M. H. Asghari, J. Azaña, "Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings," Opt. Exp. 16, 11459-11469 (2008).

M. H. Asghari, J. Azaña, "Proposal for arbitrary-order temporal integration of ultrafast optical signals using a single uniform-period fiber Bragg grating," Opt. Lett. 33, 1548-1550 (2008).

Y. Ding, X.-B. Zhang, X.-L. Zhang, D. Huang, "Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators," Opt. Commun. 281, 5315-5321 (2008).

2007 (2)

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).

N. Q. Ngo, L. N. Binh, "New approach for the design of an optical square pulse generator," Appl. Opt. 46, 3546-3560 (2007).

2006 (2)

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

N. Q. Ngo, L. N. Binh, "Optical realization of Newton-Cotes-based integrators for dark soliton generation," J. Lightw. Technol. 24, 563-572 (2006).

2002 (1)

2001 (1)

J. Skaar, W. Ligang, T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).

1997 (1)

T. Erdogan, "Fiber grating spectra," J. Lightw. Technol. 15, 1277-1294 (1997).

Appl. Opt. (2)

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

N. Q. Ngo, L. N. Binh, "New approach for the design of an optical square pulse generator," Appl. Opt. 46, 3546-3560 (2007).

IEEE J. Quantum Electron. (1)

J. Skaar, W. Ligang, T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).

J. Lightw. Technol. (1)

N. Q. Ngo, L. N. Binh, "Optical realization of Newton-Cotes-based integrators for dark soliton generation," J. Lightw. Technol. 24, 563-572 (2006).

J. Lightw. Technol. (1)

T. Erdogan, "Fiber grating spectra," J. Lightw. Technol. 15, 1277-1294 (1997).

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

Opt. Lett. (2)

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

M. A. Preciado, M. A. Muriel, "Ultrafast all-optical integrator based on a fiber Bragg grating: Proposal and design," Opt. Lett. 33, 1348-1350 (2008).

Opt. Commun. (1)

Y. Ding, X.-B. Zhang, X.-L. Zhang, D. Huang, "Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators," Opt. Commun. 281, 5315-5321 (2008).

Opt. Exp. (3)

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. –J. Ahn, S. LaRochelle, J. Azaña, "Photonic temporal integrator for all-optical computing," Opt. Exp. 16, 18202-18214 (2008).

Y. Park, T.-J. Ahn, Y. Dai, J. Yao, J. Azaña, "All-optical temporal integration of ultrafast pulse waveforms," Opt. Exp. 16, 17817-17825 (2008).

M. H. Asghari, J. Azaña, "Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings," Opt. Exp. 16, 11459-11469 (2008).

Opt. Lett. (2)

Other (3)

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, S. H. Nawab, Signals and Systems (Prentice Hall, 1996).

A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill, 1962).

A. W. F. Edwards, Pascal's Arithmetical Triangle: The Story of a Mathematical Idea (Johns Hopkins University Press, 2002).

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