Abstract

We report the first experimental realization of an all-optical temporal integrator. The integrator is implemented using an all-fiber active (gain-assisted) filter based on superimposed fiber Bragg gratings made in an Er-Yb co-doped optical fiber that behaves like an ‘optical capacitor’. Functionality of this device was tested by integrating different optical pulses, with time duration down to 60 ps, and by integration of two consecutive pulses that had different relative phases, separated by up to 1 ns. The potential of the developed device for implementing all-optical computing systems for solving ordinary differential equations was also experimentally tested.

© 2008 Optical Society of America

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  5. N. Q. Ngo, "Optical integrator for optical dark-soliton detection and pulse shaping," Appl. Opt. 45, 6785-6791 (2006).
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    [CrossRef]
  8. M. A. Preciado and M. A. Muriel, "Ultrafast all-optical integrator based on a fiber Bragg grating: proposal and design," Opt. Lett. 33, 1348-1350 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  15. 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]
  16. 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]
  17. F. Li, Y. Park, and J. Azaña, "Precise and simple group delay measurement of dispersive devices based on ultrafast optical differentiation," in Proc. of OFC/NFOEC’08, Paper OWD5, 2008.
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  19. K. Ogata, Modern Control Engineering, 4th ed. (Prentice Hall, Upper Saddle River, NJ, USA 2001).
  20. G.F. SimmonsDifferential Equations with Applications and Historical Notes, 2nd ed. (McGraw-Hill, New York, USA 1991).
  21. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (John Wiley & Sons, New York, USA 1999).
  22. G. Brochu, S. LaRochelle, and R. Slavík, "Modeling and experimental demonstration of ultracompact multiwavelength distributed Fabry-Perot fiber lasers," J. Lightwave Technol. 23, 44-53 (2005).
    [CrossRef]
  23. Y. Barbarin, S. Anantathanasarn, E. A. J. M. Bente, Y. S. Oei, M. K. Smit, and R. Notzel, "1.55 µm range InAs-InP (100) quantum-dot Fabry-Perot and ring lasers using narrow deeply etched ridge waveguides," IEEE Photon. Technol. Lett. 18, 2644-2646 (2006).
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    [CrossRef]

2008 (2)

2007 (5)

2006 (6)

Y. Park, M. Kulishov, R. Slavík, and J. Azaña, "Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating," Opt. Express,  14, 12671-12678 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670.
[CrossRef]

Y. Barbarin, S. Anantathanasarn, E. A. J. M. Bente, Y. S. Oei, M. K. Smit, and R. Notzel, "1.55 µm range InAs-InP (100) quantum-dot Fabry-Perot and ring lasers using narrow deeply etched ridge waveguides," IEEE Photon. Technol. Lett. 18, 2644-2646 (2006).
[CrossRef]

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

N. Q. Ngo and L. N. Binh, "Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation," IEEE/OSA J. 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]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators, " Opt. Express 14, 10699-10707 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699.
[CrossRef] [PubMed]

2005 (2)

2004 (1)

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

2003 (1)

L. Venema, "Photonics Technologies," Nature Insight 424,No. 6950 (2003).

1995 (1)

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, "Wide-band Fabry-Perot-like filters in optical fiber," IEEE Photon. Technol. Lett. 7, 78-80 (1995).
[CrossRef]

Anantathanasarn, S.

Y. Barbarin, S. Anantathanasarn, E. A. J. M. Bente, Y. S. Oei, M. K. Smit, and R. Notzel, "1.55 µm range InAs-InP (100) quantum-dot Fabry-Perot and ring lasers using narrow deeply etched ridge waveguides," IEEE Photon. Technol. Lett. 18, 2644-2646 (2006).
[CrossRef]

Azaña, J.

J. Azaña, "Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator," Opt. Lett. 33, 4-6 (2008).
[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, "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 grating," Opt. Express,  14, 12671-12678 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670.
[CrossRef]

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti (editors), Special Issue on "Optical Signal Processing," IEEE/OSA J. 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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699.
[CrossRef] [PubMed]

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

Barbarin, Y.

Y. Barbarin, S. Anantathanasarn, E. A. J. M. Bente, Y. S. Oei, M. K. Smit, and R. Notzel, "1.55 µm range InAs-InP (100) quantum-dot Fabry-Perot and ring lasers using narrow deeply etched ridge waveguides," IEEE Photon. Technol. Lett. 18, 2644-2646 (2006).
[CrossRef]

Bennion, I.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, "Wide-band Fabry-Perot-like filters in optical fiber," IEEE Photon. Technol. Lett. 7, 78-80 (1995).
[CrossRef]

Bente, E. A. J. M.

Y. Barbarin, S. Anantathanasarn, E. A. J. M. Bente, Y. S. Oei, M. K. Smit, and R. Notzel, "1.55 µm range InAs-InP (100) quantum-dot Fabry-Perot and ring lasers using narrow deeply etched ridge waveguides," IEEE Photon. Technol. Lett. 18, 2644-2646 (2006).
[CrossRef]

Binh, L. N.

Binsma, H.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Brochu, G.

Cincontti, G.

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

De Vries, T.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Den Besten, J. H.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Dong, J.

Dorren, H. J. S.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [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]

Hill, M. T.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Huang, D.

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]

Khoe, G.-D.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Kulishov, M.

LaRochelle, S.

Leijtens, X. J. M.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Li, F.

Liu, D.

Madsen, C. K.

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti (editors), Special Issue on "Optical Signal Processing," IEEE/OSA J. 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]

Muriel, M. A.

Ngo, N. Q.

Notzel, R.

Y. Barbarin, S. Anantathanasarn, E. A. J. M. Bente, Y. S. Oei, M. K. Smit, and R. Notzel, "1.55 µm range InAs-InP (100) quantum-dot Fabry-Perot and ring lasers using narrow deeply etched ridge waveguides," IEEE Photon. Technol. Lett. 18, 2644-2646 (2006).
[CrossRef]

Oei, Y. S.

Y. Barbarin, S. Anantathanasarn, E. A. J. M. Bente, Y. S. Oei, M. K. Smit, and R. Notzel, "1.55 µm range InAs-InP (100) quantum-dot Fabry-Perot and ring lasers using narrow deeply etched ridge waveguides," IEEE Photon. Technol. Lett. 18, 2644-2646 (2006).
[CrossRef]

Oel, Y.-S.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

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. Kulishov, R. Slavík, and J. Azaña, "Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating," Opt. Express,  14, 12671-12678 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670.
[CrossRef]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators, " Opt. Express 14, 10699-10707 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699.
[CrossRef] [PubMed]

Poole, S. B.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, "Wide-band Fabry-Perot-like filters in optical fiber," IEEE Photon. Technol. Lett. 7, 78-80 (1995).
[CrossRef]

Preciado, M. A.

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, M. Kulishov, R. Slavík, and J. Azaña, "Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating," Opt. Express,  14, 12671-12678 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670.
[CrossRef]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators, " Opt. Express 14, 10699-10707 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699.
[CrossRef] [PubMed]

G. Brochu, S. LaRochelle, and R. Slavík, "Modeling and experimental demonstration of ultracompact multiwavelength distributed Fabry-Perot fiber lasers," J. Lightwave Technol. 23, 44-53 (2005).
[CrossRef]

Smalbrugge, B.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Smit, M. K.

Y. Barbarin, S. Anantathanasarn, E. A. J. M. Bente, Y. S. Oei, M. K. Smit, and R. Notzel, "1.55 µm range InAs-InP (100) quantum-dot Fabry-Perot and ring lasers using narrow deeply etched ridge waveguides," IEEE Photon. Technol. Lett. 18, 2644-2646 (2006).
[CrossRef]

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Sugden, K.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, "Wide-band Fabry-Perot-like filters in optical fiber," IEEE Photon. Technol. Lett. 7, 78-80 (1995).
[CrossRef]

Takiguchi, K.

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

Town, G. E.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, "Wide-band Fabry-Perot-like filters in optical fiber," IEEE Photon. Technol. Lett. 7, 78-80 (1995).
[CrossRef]

Venema, L.

L. Venema, "Photonics Technologies," Nature Insight 424,No. 6950 (2003).

Wang, Q.

Williams, J. A. R.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, "Wide-band Fabry-Perot-like filters in optical fiber," IEEE Photon. Technol. Lett. 7, 78-80 (1995).
[CrossRef]

Xu, J.

Yao, P.

Zeng, F.

Zhang, X.

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (3)

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. Barbarin, S. Anantathanasarn, E. A. J. M. Bente, Y. S. Oei, M. K. Smit, and R. Notzel, "1.55 µm range InAs-InP (100) quantum-dot Fabry-Perot and ring lasers using narrow deeply etched ridge waveguides," IEEE Photon. Technol. Lett. 18, 2644-2646 (2006).
[CrossRef]

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, and S. B. Poole, "Wide-band Fabry-Perot-like filters in optical fiber," IEEE Photon. Technol. Lett. 7, 78-80 (1995).
[CrossRef]

J. Lightwave Technol. (4)

Nature (1)

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004).
[CrossRef] [PubMed]

Nature Insight (1)

L. Venema, "Photonics Technologies," Nature Insight 424,No. 6950 (2003).

Opt. Express (2)

Opt. Lett. (6)

Other (7)

F. Li, Y. Park, and J. Azaña, "Precise and simple group delay measurement of dispersive devices based on ultrafast optical differentiation," in Proc. of OFC/NFOEC’08, Paper OWD5, 2008.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, Upper Saddle River, NJ, USA 1996).

K. Ogata, Modern Control Engineering, 4th ed. (Prentice Hall, Upper Saddle River, NJ, USA 2001).

G.F. SimmonsDifferential Equations with Applications and Historical Notes, 2nd ed. (McGraw-Hill, New York, USA 1991).

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (John Wiley & Sons, New York, USA 1999).

C. K. Madsen, D. Dragoman, and J. Azaña (editors), Special Issue on "Signal Analysis Tools for Optical Signal Processing," EURASIP J. Appl. Signal Proc. 10, 1449-1623 (2005).
[CrossRef]

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

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Figures (7)

Fig. 1.
Fig. 1.

Concept diagram of the proposed photonic temporal integrator. The integrator is implemented using two superimposed fiber Bragg gratings (acting as a resonant cavity) permanently photo-inscribed in an Er-Yb co-doped optical fiber that provides optical gain. The gain level is controlled via power of the optical pump (980-nm laser diode). The inset shows the measured (circles) and numerically calculated (solid, blue curve) integrator spectral transfer function. For comparison, the spectral transfer function of an ideal integrator is also shown (solid, red curve).

Fig. 2.
Fig. 2.

Experimental setup for the integration of pulses generated using electro-optically modulated signal. TL: Tunable laser, ISO: optical isolator, PC: polarization controller, IMOD: Optical intensity modulator, PPG: Picosecond electric pulse generator with 70 ps FWHM time width, AWG: Electric arbitrary waveform generator with 500 MHz bandwidth, Pump: 980-nm semiconductor pump laser, Amp: Erbium-doped fiber amplifier, OS: Optical sampler (photoreceiver).

Fig. 3.
Fig. 3.

Experimental results demonstrating time-domain integration of a single optical Gaussian pulse for two different input pulse FWHM time widths ((a) 140 ps and (b) 60 ps). The temporal optical intensity of the input pulse (orange curve) and the integrator output (green curve) are captured using a 20-GHz photoreceiver. For comparison, the square of the numerically calculated time cumulative integral of the measured input pulse field (square root of the measured temporal intensity profile) is also shown (yellow curve).

Fig. 4.
Fig. 4.

(a) Diagram showing all-optical integration of two consecutive optical pulses with different relative phases. For relative phases of 0 (in-phase – the field amplitudes are of the same sign, red curves) and π (out-of-phase – the field amplitudes are of opposite signs, blue curves), the time integral is expected to be a double step-rising waveform, and a flat-top waveform, respectively. (b) Experimental setup for the double pulse integration. 14-ps pulses are generated from the FFL followed by an optical bandpass filter (0.4 nm 3dB-bandwidth). Time-delayed pulse replicas are made by using a fiber-coupled Michelson interferometer. For the shortest time delay (170 ps), we confirmed the relative phase of the two pulses measuring the optical spectrum of the double-pulse structure, which is shown in the inset: for in-phase pulses (red line), the spectrum has a maximum at the integrator central frequency, while for the out-of-phase pulses (blue line), there is a minimum. The output spectrum is shown as green line.

Fig. 5.
Fig. 5.

Experimental results demonstrating time-domain integration of double optical pulses. (a) Time-domain optical intensity of the input signal - two 14-ps consecutive optical pulse with various inter-pulse delays (170 ps, 500 ps, and 1000ps). The integrated output depends on the relative phase of the two pulses: (b) integration for in-phase pulses; (c) integration for out-ofphase pulses.

Fig. 6.
Fig. 6.

Experimental results for the optical integration of two flat-top pulses set in-phase and out-of-phase. Left: in-phase; Right: out-of-phase. The input electric waveform: blue; the modulated optical intensity waveform: red, and the output optical intensity waveform: yellow.

Fig. 7.
Fig. 7.

(a) Schematic diagram of an integrator-based optical computing system designed for solving the first-order linear ordinary differential equation (ODE) defined in the figure. The two graphs at the bottom show the experimental (solid curves) and numerical (circles) solutions of the ODE for two different input optical signals: (b) an input ultrashort temporal impulse (FWHM time-width=60 ps) and (c) a constant excitation over a limited temporal window (2.9-ns long square-like pulse). In each case, the ODE is solved for different positive values of the parameter k.

Equations (3)

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h ( t ) u ( t ) ; u ( t ) = 0 for t < 0 , u ( t ) = 1 for t 0 .
h ( t ) exp ( k t ) u ( t ) ,
dy ( t ) dt + ky ( t ) = x ( t )

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