Abstract

We experimentally demonstrate a temporal imaging system based on a time pinhole. In accordance with the spatial pinhole-imaging counterpart, it consists of two sections of dispersion fibers connected by a temporal shutter, which is experimentally realized by a logic AND-gate with a short pulse. Both theoretical analysis and experimental results show that the output waveform is the scaled and broadened profile of the input waveform. Specifically, the output waveform is reversed if the signs of the dispersion on both sides of the time-gate are identical, otherwise it is non-reversed if the signs of the dispersion are opposite. Furthermore, we adjust the duration of the temporal shutter by changing the spectral width of the pulse, and investigate the effect of the shutter time on the performance of the output waveform.

© 2014 Optical Society of America

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References

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  1. R. Salem, M. A. Foster, and A. L. Gaeta, “Application of space-time duality to ultrahigh-speed optical signal processing,” Adv. Opt. Photon. 5(3), 274–317 (2013).
    [Crossref]
  2. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994).
    [Crossref]
  3. C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part I: System configurations,” IEEE J. Quantum Electron. 36(4), 430–437 (2000).
    [Crossref]
  4. C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part II: System performance,” IEEE J. Quantum Electron. 36(6), 649–655 (2000).
    [Crossref]
  5. J. Howe and C. Xu, “Ultrafast Optical Signal Processing Based Upon Space-Time Dualities,” J. Lightwave Technol. 24(7), 2649–2662 (2006).
    [Crossref]
  6. R. Salem, M. A. Foster, A. C. Turner-Foster, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “High-speed optical sampling using a silicon-chip temporal magnifier,” Opt. Express 17(6), 4324–4329 (2009).
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  7. O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Express 17(22), 20605–20614 (2009).
    [Crossref] [PubMed]
  8. Y. Okawachi, R. Salem, A. R. Johnson, K. Saha, J. S. Levy, M. Lipson, and A. L. Gaeta, “Asynchronous single-shot characterization of high-repetition-rate ultrafast waveforms using a time-lens-based temporal magnifier,” Opt. Lett. 37(23), 4892–4894 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  11. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33(10), 1047–1049 (2008).
    [Crossref] [PubMed]
  12. E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
  13. K. G. Petrillo and M. A. Foster, “Full 160-Gb/s OTDM to 16x10-Gb/s WDM conversion with a single nonlinear interaction,” Opt. Express 21(1), 508–518 (2013).
    [Crossref] [PubMed]
  14. C. Zhang, X. Wang, X. Xu, P. C. Chui, and K. K. Y. Wong, “Simultaneous Demultiplexing of OTDM Channels Based on Swept-Pump Fiber-Optical Parametric Amplifier,” in OFC, OSA Technical Digest (Optical Society of America, 2012), OM3B.2.
  15. K. G. Petrillo and M. A. Foster, “Scalable ultrahigh-speed optical transmultiplexer using a time lens,” Opt. Express 19(15), 14051–14059 (2011).
    [Crossref] [PubMed]
  16. B. H. Kolner, “The pinhole time camera,” J. Opt. Soc. Am. A 14(12), 3349–3357 (1997).
    [Crossref]
  17. H. Y. Jiang, L. S. Yan, Y. F. Sun, J. Ye, W. Pan, B. Luo, and X. H. Zou, “Photonic arbitrary waveform generation based on crossed frequency to time mapping,” Opt. Express 21(5), 6488–6496 (2013).
    [Crossref] [PubMed]
  18. V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, “20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping,” Opt. Express 16(26), 21564–21569 (2008).
    [Crossref] [PubMed]
  19. D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
    [Crossref]
  20. G. Agrawal, “Nonlinear fiber optics,” in Nonlinear Science at the Dawn of the 21st Century, (Springer, 2000), 195-211.
  21. D. Jianji, Y. Yuan, Z. Yin, L. Bowen, Y. Ting, and Z. Xinliang, “Arbitrary-Order Bandwidth-Tunable Temporal Differentiator Using a Programmable Optical Pulse Shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
    [Crossref]
  22. S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett. 5(1), 92–95 (1993).
    [Crossref]

2013 (3)

2012 (2)

E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).

Y. Okawachi, R. Salem, A. R. Johnson, K. Saha, J. S. Levy, M. Lipson, and A. L. Gaeta, “Asynchronous single-shot characterization of high-repetition-rate ultrafast waveforms using a time-lens-based temporal magnifier,” Opt. Lett. 37(23), 4892–4894 (2012).
[Crossref] [PubMed]

2011 (2)

K. G. Petrillo and M. A. Foster, “Scalable ultrahigh-speed optical transmultiplexer using a time lens,” Opt. Express 19(15), 14051–14059 (2011).
[Crossref] [PubMed]

D. Jianji, Y. Yuan, Z. Yin, L. Bowen, Y. Ting, and Z. Xinliang, “Arbitrary-Order Bandwidth-Tunable Temporal Differentiator Using a Programmable Optical Pulse Shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

2009 (3)

2008 (3)

2006 (1)

2000 (2)

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part I: System configurations,” IEEE J. Quantum Electron. 36(4), 430–437 (2000).
[Crossref]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part II: System performance,” IEEE J. Quantum Electron. 36(6), 649–655 (2000).
[Crossref]

1997 (1)

1994 (1)

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994).
[Crossref]

1993 (1)

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett. 5(1), 92–95 (1993).
[Crossref]

1989 (1)

Andrés, P.

Bennett, C. V.

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part I: System configurations,” IEEE J. Quantum Electron. 36(4), 430–437 (2000).
[Crossref]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part II: System performance,” IEEE J. Quantum Electron. 36(6), 649–655 (2000).
[Crossref]

Bowen, L.

D. Jianji, Y. Yuan, Z. Yin, L. Bowen, Y. Ting, and Z. Xinliang, “Arbitrary-Order Bandwidth-Tunable Temporal Differentiator Using a Programmable Optical Pulse Shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

Chen, L. R.

Chikama, T.

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett. 5(1), 92–95 (1993).
[Crossref]

Chou, J.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Clausen, A. T.

E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).

Foster, M. A.

Gaeta, A. L.

Galili, M.

E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).

Geraghty, D. F.

Howe, J.

Hu, H.

E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).

Jalali, B.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Jeppesen, P.

E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).

Jiang, H. Y.

Jianji, D.

D. Jianji, Y. Yuan, Z. Yin, L. Bowen, Y. Ting, and Z. Xinliang, “Arbitrary-Order Bandwidth-Tunable Temporal Differentiator Using a Programmable Optical Pulse Shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

Johnson, A. R.

Kolner, B. H.

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part II: System performance,” IEEE J. Quantum Electron. 36(6), 649–655 (2000).
[Crossref]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part I: System configurations,” IEEE J. Quantum Electron. 36(4), 430–437 (2000).
[Crossref]

B. H. Kolner, “The pinhole time camera,” J. Opt. Soc. Am. A 14(12), 3349–3357 (1997).
[Crossref]

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994).
[Crossref]

B. H. Kolner and M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett. 14(12), 630–632 (1989).
[Crossref] [PubMed]

Kuzucu, O.

Lancis, J.

Levy, J. S.

Lipson, M.

Luo, B.

Mulvad, H. C. H.

E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).

Naito, T.

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett. 5(1), 92–95 (1993).
[Crossref]

Nazarathy, M.

Okawachi, Y.

Oxenlowe, L. K.

E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).

Palushani, E.

E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).

Pan, W.

Petrillo, K. G.

Saha, K.

Salem, R.

Solli, D. R.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Sun, Y. F.

Ting, Y.

D. Jianji, Y. Yuan, Z. Yin, L. Bowen, Y. Ting, and Z. Xinliang, “Arbitrary-Order Bandwidth-Tunable Temporal Differentiator Using a Programmable Optical Pulse Shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

Torres-Company, V.

Turner, A. C.

Turner-Foster, A. C.

Watanabe, S.

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett. 5(1), 92–95 (1993).
[Crossref]

Xinliang, Z.

D. Jianji, Y. Yuan, Z. Yin, L. Bowen, Y. Ting, and Z. Xinliang, “Arbitrary-Order Bandwidth-Tunable Temporal Differentiator Using a Programmable Optical Pulse Shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

Xu, C.

Yan, L. S.

Ye, J.

Yin, Z.

D. Jianji, Y. Yuan, Z. Yin, L. Bowen, Y. Ting, and Z. Xinliang, “Arbitrary-Order Bandwidth-Tunable Temporal Differentiator Using a Programmable Optical Pulse Shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

Yuan, Y.

D. Jianji, Y. Yuan, Z. Yin, L. Bowen, Y. Ting, and Z. Xinliang, “Arbitrary-Order Bandwidth-Tunable Temporal Differentiator Using a Programmable Optical Pulse Shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

Zou, X. H.

Adv. Opt. Photon. (1)

IEEE J. Quantum Electron. (3)

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994).
[Crossref]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part I: System configurations,” IEEE J. Quantum Electron. 36(4), 430–437 (2000).
[Crossref]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging - Part II: System performance,” IEEE J. Quantum Electron. 36(6), 649–655 (2000).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenlowe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).

IEEE Photon. J. (1)

D. Jianji, Y. Yuan, Z. Yin, L. Bowen, Y. Ting, and Z. Xinliang, “Arbitrary-Order Bandwidth-Tunable Temporal Differentiator Using a Programmable Optical Pulse Shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (1)

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett. 5(1), 92–95 (1993).
[Crossref]

J. Lightwave Technol. (1)

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

Nat. Photonics (2)

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3(10), 581–585 (2009).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Other (2)

C. Zhang, X. Wang, X. Xu, P. C. Chui, and K. K. Y. Wong, “Simultaneous Demultiplexing of OTDM Channels Based on Swept-Pump Fiber-Optical Parametric Amplifier,” in OFC, OSA Technical Digest (Optical Society of America, 2012), OM3B.2.

G. Agrawal, “Nonlinear fiber optics,” in Nonlinear Science at the Dawn of the 21st Century, (Springer, 2000), 195-211.

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic diagram of the conventional pinhole camera. An object Ii placed at a distance di before an aperture is projected to an image Io at a distance do behind the aperture. (b) Temporal analog: an input waveform with pulse packet of “1101” propagates through a section of dispersion fiber, and then undergoes a short temporal shutter, which allows a small burst of the waveform to pass through. Finally, the waveform propagates in another dispersion fiber and forms the scaled profile of the input waveform.

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Fig. 2
Fig. 2

(a) Time-gate used to eliminate the effect of the quadratic phase term; (b) optimum width of the time-gate ΔTopt versus the output-to-input scale ratio M for a fixed input dispersion.

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Fig. 3
Fig. 3

Schematic setup for the proposed method.

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Fig. 4
Fig. 4

Waveform of the (a) data and (b) pump pulse.

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Fig. 5
Fig. 5

Spectrum at the output of HNLF2.

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Fig. 6
Fig. 6

The reversed waveforms from different length of DCF with opposite sign and same dispersion value of (a) 0.5 km; (b) 1 km; (c) 2 km; and (d) 4km SMF.

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Fig. 7
Fig. 7

The non-reversed waveforms from (a) 0.5 km; (b) 1km; (c) 2 km; and (d) 4 km SMF when the pump pulse is filtered by 1.6 nm BPF.

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Fig. 8
Fig. 8

(a) Output waveform from 2 km SMF when the pump pulse is filtered by 0.8 nm BPF; (b) output waveform from 4 km SMF when the pump pulse is filtered by 0.8 nm BPF (c) output waveform from 4 km SMF when the pump pulse is filtered by 0.32 nm BPF.

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Equations (5)

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

y(t)=[ x(t)⊗exp( ja t 2 )⋅g(t) ]⊗exp( jb t 2 )       = F b { F a { x(t) }⋅exp[ j(a+b) t 2 ]g(t) }⋅exp(jb t 2 )
F a { x(t) }= ∫ −∞ +∞ x(τ)exp(−j2atτ)dτ =X(f= a π t)
Δ T max = 2 | Δ φ a + b | = 2 | Δ φ 1 β 2 , a L a + 1 β 2 , b L b |
| y ( t ) | 2 ≈ | F b { F a { x ( t ) } ⋅ g ( t ) } | 2                   = | x ( − β 2 , a L a β 2 , b L b t ) ⊗ G ( f = − t 2 π β 2 , b L b ) | 2
Δ T opt =2 | Δφ⋅ β 2,a L a | ⋅ | M M−1 |

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