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 Optical Society of America

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References

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  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 (3)

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

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

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]

2009 (2)

2008 (3)

2007 (1)

2006 (2)

2000 (1)

1997 (1)

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

1995 (1)

Ahn, T. J.

Asghari, M. H.

Ayotte, N.

Azaña, J.

Binh, L. N.

Chériaux, G.

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.

Ding, Y.

Doucet, S.

Erdogan, T.

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

Feced, R.

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.

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.

LaRochelle, S.

Lepetit, L.

Ngo, N. Q.

Park, Y.

Quoc Ngo, N.

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.

Wang, C.

Yao, J.

Zervas, M. N.

Zhang, X.

Appl. Opt. (1)

IEEE Photon. J. (1)

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. (4)

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

Opt. Express (3)

Opt. Lett. (3)

Proc. SPIE (1)

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

Other (1)

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

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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.

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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).

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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).

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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.

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Fig. 2
Fig. 2 Conceptual diagram of the proposed temporal integrator design.

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Fig. 4
Fig. 4 Experimental setup for the proof-of-concept demonstration of the proposed photonic integration design.

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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.

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Equations (5)

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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 ,

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