Abstract

We propose and experimentally prove a novel design for implementing photonic temporal integrators simultaneously offering a high processing bandwidth and a long operation time window, namely a large time-bandwidth product. The proposed scheme is based on concatenating in series a time-limited ultrafast photonic temporal integrator, e.g. implemented using a fiber Bragg grating (FBG), with a discrete-time (bandwidth limited) optical integrator, e.g. implemented using an optical resonant cavity. This design combines the advantages of these two previously demonstrated photonic integrator solutions, providing a processing speed as high as that of the time-limited ultrafast integrator and an operation time window fixed by the discrete-time integrator. Proof-of-concept experiments are reported using a uniform fiber Bragg grating (as the original time-limited integrator) connected in series with a bulk-optics coherent interferometers’ system (as a passive 4-points discrete-time photonic temporal integrator). Using this setup, we demonstrate accurate temporal integration of complex-field optical signals with time-features as fast as ~6 ps, only limited by the processing bandwidth of the FBG integrator, over time durations as long as ~200 ps, which represents a 4-fold improvement over the operation time window (~50 ps) of the original FBG integrator.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. V. Oppenheim, A. S. Willsky, and S. Hamid, Signals and Systems, 2nd ed. Upper Saddle River, (NJ: Prentice Hall, 1996).
  2. J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J. 2(3), 359–386 (2010).
    [CrossRef]
  3. N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006).
    [CrossRef] [PubMed]
  4. N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation,” J. Lightwave Technol. 24(1), 563–572 (2006).
    [CrossRef]
  5. 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 16(22), 18202–18214 (2008).
    [CrossRef] [PubMed]
  6. Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express 17(15), 12835–12848 (2009).
    [CrossRef] [PubMed]
  7. N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. 32(20), 3020–3022 (2007).
    [CrossRef] [PubMed]
  8. J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33(1), 4–6 (2008).
    [CrossRef]
  9. Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
    [CrossRef] [PubMed]
  10. M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings,” J. Lightwave Technol. 27(17), 3888–3895 (2009).
    [CrossRef]
  11. M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010).
    [CrossRef] [PubMed]
  12. Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE 7797, 1–8 (2010).
  13. R. Feced and M. N. Zervas, “Effects of random phase and amplitude errors in optical fiber Bragg gratings,” J. Lightwave Technol. 18(1), 90–101 (2000).
    [CrossRef]
  14. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
    [CrossRef]
  15. 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(12), 2467–2474 (1995).
    [CrossRef]

2010

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J. 2(3), 359–386 (2010).
[CrossRef]

M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010).
[CrossRef] [PubMed]

Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE 7797, 1–8 (2010).

2009

Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express 17(15), 12835–12848 (2009).
[CrossRef] [PubMed]

M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings,” J. Lightwave Technol. 27(17), 3888–3895 (2009).
[CrossRef]

2008

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 16(22), 18202–18214 (2008).
[CrossRef] [PubMed]

J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33(1), 4–6 (2008).
[CrossRef]

Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
[CrossRef] [PubMed]

2007

N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. 32(20), 3020–3022 (2007).
[CrossRef] [PubMed]

2006

N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006).
[CrossRef] [PubMed]

N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation,” J. Lightwave Technol. 24(1), 563–572 (2006).
[CrossRef]

2000

R. Feced and M. N. Zervas, “Effects of random phase and amplitude errors in optical fiber Bragg gratings,” J. Lightwave Technol. 18(1), 90–101 (2000).
[CrossRef]

1997

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[CrossRef]

1995

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(12), 2467–2474 (1995).
[CrossRef]

Ahn, T. J.

Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
[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 16(22), 18202–18214 (2008).
[CrossRef] [PubMed]

Asghari, M. H.

M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010).
[CrossRef] [PubMed]

M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings,” J. Lightwave Technol. 27(17), 3888–3895 (2009).
[CrossRef]

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 16(22), 18202–18214 (2008).
[CrossRef] [PubMed]

Azaña, J.

M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010).
[CrossRef] [PubMed]

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J. 2(3), 359–386 (2010).
[CrossRef]

M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings,” J. Lightwave Technol. 27(17), 3888–3895 (2009).
[CrossRef]

Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
[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 16(22), 18202–18214 (2008).
[CrossRef] [PubMed]

J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33(1), 4–6 (2008).
[CrossRef]

Binh, L. N.

N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation,” J. Lightwave Technol. 24(1), 563–572 (2006).
[CrossRef]

Chériaux, G.

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(12), 2467–2474 (1995).
[CrossRef]

Costanzo-Caso, P.

Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE 7797, 1–8 (2010).

Dai, Y.

Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
[CrossRef] [PubMed]

Ding, Y.

Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express 17(15), 12835–12848 (2009).
[CrossRef] [PubMed]

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 16(22), 18202–18214 (2008).
[CrossRef] [PubMed]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[CrossRef]

Feced, R.

R. Feced and M. N. Zervas, “Effects of random phase and amplitude errors in optical fiber Bragg gratings,” J. Lightwave Technol. 18(1), 90–101 (2000).
[CrossRef]

Granieri, S.

Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE 7797, 1–8 (2010).

Huang, D.

Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express 17(15), 12835–12848 (2009).
[CrossRef] [PubMed]

Jin, Y.

Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE 7797, 1–8 (2010).

Joffre, M.

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(12), 2467–2474 (1995).
[CrossRef]

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 16(22), 18202–18214 (2008).
[CrossRef] [PubMed]

Lepetit, L.

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(12), 2467–2474 (1995).
[CrossRef]

Ngo, N. Q.

N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006).
[CrossRef] [PubMed]

N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation,” J. Lightwave Technol. 24(1), 563–572 (2006).
[CrossRef]

Park, Y.

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 16(22), 18202–18214 (2008).
[CrossRef] [PubMed]

Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
[CrossRef] [PubMed]

Quoc Ngo, N.

N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. 32(20), 3020–3022 (2007).
[CrossRef] [PubMed]

Siahmakoun, A.

Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE 7797, 1–8 (2010).

Slavík, R.

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 16(22), 18202–18214 (2008).
[CrossRef] [PubMed]

Wang, C.

M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010).
[CrossRef] [PubMed]

Yao, J.

M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010).
[CrossRef] [PubMed]

Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
[CrossRef] [PubMed]

Zervas, M. N.

R. Feced and M. N. Zervas, “Effects of random phase and amplitude errors in optical fiber Bragg gratings,” J. Lightwave Technol. 18(1), 90–101 (2000).
[CrossRef]

Zhang, X.

Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express 17(15), 12835–12848 (2009).
[CrossRef] [PubMed]

Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express 17(15), 12835–12848 (2009).
[CrossRef] [PubMed]

Appl. Opt.

N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006).
[CrossRef] [PubMed]

IEEE Photon. J.

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photon. J. 2(3), 359–386 (2010).
[CrossRef]

J. Lightwave Technol.

M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber Bragg gratings,” J. Lightwave Technol. 27(17), 3888–3895 (2009).
[CrossRef]

N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-Based Integrators for Dark Soliton Generation,” J. Lightwave Technol. 24(1), 563–572 (2006).
[CrossRef]

R. Feced and M. N. Zervas, “Effects of random phase and amplitude errors in optical fiber Bragg gratings,” J. Lightwave Technol. 18(1), 90–101 (2000).
[CrossRef]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[CrossRef]

J. Opt. Soc. Am. B

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(12), 2467–2474 (1995).
[CrossRef]

Opt. Express

Y. Park, T. J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
[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 16(22), 18202–18214 (2008).
[CrossRef] [PubMed]

Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express 17(15), 12835–12848 (2009).
[CrossRef] [PubMed]

Opt. Lett.

N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. 32(20), 3020–3022 (2007).
[CrossRef] [PubMed]

J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33(1), 4–6 (2008).
[CrossRef]

M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010).
[CrossRef] [PubMed]

Proc. SPIE

Y. Jin, P. Costanzo-Caso, S. Granieri, and A. Siahmakoun, “Photonic integrator for A/D conversion,” Proc. SPIE 7797, 1–8 (2010).

Other

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

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 (7)

Fig. 1
Fig. 1

Effect of the limited spatial grating profile resolution on the reflection field spectrum (a) and temporal impulse response (b) of a 5 mm long weak-coupling FBG integrator. The ideal responses of the FBG integrator are plotted with red-solid lines and the results for the cases of grating spatial resolutions of 0.1 mm, 0.5 mm and 1 mm are plotted with blue-dotted, green-dashed and brown-dash-dotted lines, respectively. The plots are in normalized units (n.u.). The vertical axis in (a) is in logarithmic scale.

Fig. 6
Fig. 6

Experimentally obtained photonic integration (b-d) of a ~100 ps square-like input pulse (a) using the proposed scheme (c-d) compared to the integration using the original integrator (b). Results for the case of a 2-point discrete-time optical integrator (b) and a 4-point discrete-time optical integrator (c) are shown. For comparison, the numerical integral of the input waveform in (a) is also represented (dashed curves).

Fig. 7
Fig. 7

Experimentally obtained photonic integration of a complex-field optical signal using the proposed scheme (red-solid line). Input is an optical waveform consists of two π-phase shifted ultrafast Gaussian pulses each with FWHM duration of ~6 ps (blue-dotted line). For comparison, the numerical integral of the input waveform in is also represented (green-dashed line).

Fig. 3
Fig. 3

Spectral responses of the proposed configuration (green-solid lines) from concatenation of a time-limited integrator (red-dotted lines) and a discrete-time optical integrator (blue-dashed lines): (a) 4-point (N = 4) discrete-time integrator; (b) ideal active optical resonant cavity (N → ∞). The vertical axes are in logarithmic scale. A value of T = 50 ps was fixed for these representations.

Fig. 2
Fig. 2

Conceptual diagram of the proposed temporal integrator design.

Fig. 4
Fig. 4

Experimental setup for the proof-of-concept demonstration of the proposed photonic integration design.

Fig. 5
Fig. 5

Experimentally measured (solid curves) ultra-short temporal pulse response of the proposed photonic integrator (b-c) compared to that of the original integrator (a). Results for the case of a 2-point passive discrete-time optical integrator (b) and a 4-point passive discrete-time optical integrator (c) are shown. For comparison, the ultra-short temporal response of an ideal device is also represented (dashed curves). Input is a Gaussian pulse with FWHM ~6 ps, spectrally centered at the FBG resonance frequency.

Equations (5)

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

h ( t )           u ( t ) = { 1                   0 t 0                 o t h e r w i s e ,
h T ( t )           { 1                 0 t T 0                 o t h e r w i s e         = ( t T / 2 T ) ,
h ( t )           h D ( t )               h T ( t )                         n = 0 N 1 { ( t T / 2 n T T ) } = ( t N T / 2 N T ) ,
H ( f )                     H T ( f ) ×       H D ( f )                                   =         e j π f T e j π f T j 2 π f × e j π f T × n = 0 N 1 e j 2 π n f T                                     =         1 j 2 π f n = 0 N 1 ( e j 2 π n f T e j 2 π ( n + 1 ) f T )                                   =         1 j 2 π f ( 1 e j 2 π N f T )                                           s i n c ( f N T ) × e j π f N T ,
H ( f )                     H T ( f ) ×       H C ( f )                                   =           s i n c ( f T ) × e j π f T × 1 1 e j 2 π f T                                               1 e j 2 π f T j π f × 1 1 e j 2 π f T                                     =       1 j π f ,

Metrics