Abstract

We report the experimental realization of an ultrafast all-optical temporal differentiator. Differentiation is obtained via all-fiber filtering based on a simple diffraction grating-assisted mode coupler (uniform long-period fiber grating) that performs full energy conversion at the optical carrier frequency. Due to its high bandwidth, this device allows processing of arbitrary optical signals with sub-picosecond temporal features (down to 180-fs with the specific realizations reported here). Functionality of this device was tested by differentiating a 700-fs Gaussian optical pulse generated from a fiber laser (@ 1535nm). The derivative of this pulse is an odd-symmetry Hermite-Gaussian waveform, consisting of two linked 500-fs-long, π-phase-shifted temporal lobes. This waveform is noteworthy for its application in advanced ultrahigh-speed optical communication systems.

© 2006 Optical Society of America

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  1. C. K. Madsen, D. Dragoman, and J. Azaña, eds., Special Issue on "Signal Analysis Tools for Optical Signal Processing," in EURASIP J. Appl. Signal Proc. 2005, 1449-1623 (2005).
    [CrossRef]
  2. J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., Special Issue on "Optical Signal Processing," in IEEE/OSA J. Ligthwave Technol. 24, 2484-2767 (2006).
  3. R. Slavík, Y. Park, M. Kulishov, J. Azaña, and R. Morandotti, "Temporal differentiation of sub-picosecond optical pulses using a single long-period fiber grating," in Tech. Dig. of Conf. Lasers and Electro-Optics (CLEO/IQEC), Long Beach, CA, May 2006, Paper CTuBB5.
  4. N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115-129 (2004).
    [CrossRef]
  5. M. Kulishov and J. Azaña, "Long-period fiber gratings as ultrafast optical differentiators," Opt. Lett. 30, 2700-2702 (2005).
    [CrossRef] [PubMed]
  6. C. Paré, and P. A. Bélanger, "Antisymmetric soliton in a dispersion-managed system," Opt. Commun. 168, 103-109 (1999).
    [CrossRef]
  7. M. Stratmann, T. Pagel, and F. Mitschke, "Experimental observation of temporal soliton molecules," Phys. Rev. Lett. 95, 143902-1-3 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. A. Papoulis, The Fourier Integral and its Applications, (McGraw-Hill, New York, 1987).
  11. R. Kashyap, Fiber Bragg Gratings, (Academic Press, San Diego, 1999).
  12. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J.Lightwave Technol. 14, 58-65 (1996).
    [CrossRef]
  13. J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, "Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment," IEEE J. Sel. Top. Quantum Electron. 3, 1232-1245 (1997).
    [CrossRef]
  14. B. H. Kim, T. J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W. T. Han, "Effects of CO2 laser irradiation on the refractive-index change in optical fibers," Appl. Opt. 41, 3809-3815(2002).
    [CrossRef] [PubMed]
  15. R. Slavík, "Extremely deep long-period fiber grating made with CO2 laser," IEEE Photon. Technol. Lett. 18, 1705-1707 (2006).
    [CrossRef]
  16. C. Curatu, S. LaRochelle, C. Paré, and P. A. Bélanger, "Antisymmetric pulse generation using phase-shifted fibre Bragg grating," Electron. Lett. 38, 307-309 (2002).
    [CrossRef]
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    [CrossRef]
  19. J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, "Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset," J.Lightwave Technol. 23, 3282-3289 (2005).
    [CrossRef]
  20. M. Kulishov, Y. Park, J. Azaña, and R. Slavík, "(Sub-)Picosecond Flat-Top Waveform Generation using a Single Uniform Long-Period Fiber Grating," in Proc. of European Conference on Optical Communications (ECOC 2006), Cannes, France, September 2006. Paper We2.3.7.
    [CrossRef]

2006 (2)

R. Slavík, "Extremely deep long-period fiber grating made with CO2 laser," IEEE Photon. Technol. Lett. 18, 1705-1707 (2006).
[CrossRef]

Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
[CrossRef]

2005 (2)

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, "Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset," J.Lightwave Technol. 23, 3282-3289 (2005).
[CrossRef]

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

2004 (1)

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115-129 (2004).
[CrossRef]

2002 (2)

C. Curatu, S. LaRochelle, C. Paré, and P. A. Bélanger, "Antisymmetric pulse generation using phase-shifted fibre Bragg grating," Electron. Lett. 38, 307-309 (2002).
[CrossRef]

B. H. Kim, T. J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W. T. Han, "Effects of CO2 laser irradiation on the refractive-index change in optical fibers," Appl. Opt. 41, 3809-3815(2002).
[CrossRef] [PubMed]

2000 (1)

A. M. Weiner, "Femtosecond pulse processing," Opt. Quantum Electron. 32, 473-487 (2000).
[CrossRef]

1999 (1)

C. Paré, and P. A. Bélanger, "Antisymmetric soliton in a dispersion-managed system," Opt. Commun. 168, 103-109 (1999).
[CrossRef]

1997 (1)

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, "Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment," IEEE J. Sel. Top. Quantum Electron. 3, 1232-1245 (1997).
[CrossRef]

1996 (1)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J.Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

1995 (1)

1989 (1)

Ahn, T. J.

Azaña, J.

Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
[CrossRef]

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

Bélanger, P. A.

C. Curatu, S. LaRochelle, C. Paré, and P. A. Bélanger, "Antisymmetric pulse generation using phase-shifted fibre Bragg grating," Electron. Lett. 38, 307-309 (2002).
[CrossRef]

C. Paré, and P. A. Bélanger, "Antisymmetric soliton in a dispersion-managed system," Opt. Commun. 168, 103-109 (1999).
[CrossRef]

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J.Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Chériaux, G.

Chung, Y.

Curatu, C.

C. Curatu, S. LaRochelle, C. Paré, and P. A. Bélanger, "Antisymmetric pulse generation using phase-shifted fibre Bragg grating," Electron. Lett. 38, 307-309 (2002).
[CrossRef]

Da Silva, H. J. A.

Eggleton, B. J.

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, "Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment," IEEE J. Sel. Top. Quantum Electron. 3, 1232-1245 (1997).
[CrossRef]

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J.Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Han, W. T.

Joffre, M.

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J.Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Kam, C. H.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115-129 (2004).
[CrossRef]

Kim, B. H.

Kim, D. Y.

Kulishov, M.

Kumar, P. V.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, "Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset," J.Lightwave Technol. 23, 3282-3289 (2005).
[CrossRef]

Kutz, J. N.

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, "Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment," IEEE J. Sel. Top. Quantum Electron. 3, 1232-1245 (1997).
[CrossRef]

LaRochelle, S.

C. Curatu, S. LaRochelle, C. Paré, and P. A. Bélanger, "Antisymmetric pulse generation using phase-shifted fibre Bragg grating," Electron. Lett. 38, 307-309 (2002).
[CrossRef]

Lee, B. H.

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J.Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Lepetit, L.

Li, F.

Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
[CrossRef]

McGeehan, J. E.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, "Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset," J.Lightwave Technol. 23, 3282-3289 (2005).
[CrossRef]

Nezam, S. M. R. M.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, "Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset," J.Lightwave Technol. 23, 3282-3289 (2005).
[CrossRef]

Ngo, N. Q.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115-129 (2004).
[CrossRef]

O’Reilly, J. J.

Omrani, R.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, "Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset," J.Lightwave Technol. 23, 3282-3289 (2005).
[CrossRef]

Paek, U. C.

Paré, C.

C. Curatu, S. LaRochelle, C. Paré, and P. A. Bélanger, "Antisymmetric pulse generation using phase-shifted fibre Bragg grating," Electron. Lett. 38, 307-309 (2002).
[CrossRef]

C. Paré, and P. A. Bélanger, "Antisymmetric soliton in a dispersion-managed system," Opt. Commun. 168, 103-109 (1999).
[CrossRef]

Park, Y.

Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
[CrossRef]

Saghari, P.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, "Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset," J.Lightwave Technol. 23, 3282-3289 (2005).
[CrossRef]

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J.Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Slavík, R.

R. Slavík, "Extremely deep long-period fiber grating made with CO2 laser," IEEE Photon. Technol. Lett. 18, 1705-1707 (2006).
[CrossRef]

Slusher, R. E.

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, "Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment," IEEE J. Sel. Top. Quantum Electron. 3, 1232-1245 (1997).
[CrossRef]

Stark, J. B.

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, "Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment," IEEE J. Sel. Top. Quantum Electron. 3, 1232-1245 (1997).
[CrossRef]

Tjin, S. C.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115-129 (2004).
[CrossRef]

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J.Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Weiner, A. M.

A. M. Weiner, "Femtosecond pulse processing," Opt. Quantum Electron. 32, 473-487 (2000).
[CrossRef]

Willner, A. E.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, "Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset," J.Lightwave Technol. 23, 3282-3289 (2005).
[CrossRef]

Yu, S. F.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115-129 (2004).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (1)

C. Curatu, S. LaRochelle, C. Paré, and P. A. Bélanger, "Antisymmetric pulse generation using phase-shifted fibre Bragg grating," Electron. Lett. 38, 307-309 (2002).
[CrossRef]

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

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, "Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment," IEEE J. Sel. Top. Quantum Electron. 3, 1232-1245 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

R. Slavík, "Extremely deep long-period fiber grating made with CO2 laser," IEEE Photon. Technol. Lett. 18, 1705-1707 (2006).
[CrossRef]

Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006).
[CrossRef]

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

Lightwave Technol. (2)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J.Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, "Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset," J.Lightwave Technol. 23, 3282-3289 (2005).
[CrossRef]

Opt. Commun. (2)

C. Paré, and P. A. Bélanger, "Antisymmetric soliton in a dispersion-managed system," Opt. Commun. 168, 103-109 (1999).
[CrossRef]

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-derivative optical differentiators," Opt. Commun. 230, 115-129 (2004).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. M. Weiner, "Femtosecond pulse processing," Opt. Quantum Electron. 32, 473-487 (2000).
[CrossRef]

Other (7)

A. Papoulis, The Fourier Integral and its Applications, (McGraw-Hill, New York, 1987).

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

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

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., Special Issue on "Optical Signal Processing," in IEEE/OSA J. Ligthwave Technol. 24, 2484-2767 (2006).

R. Slavík, Y. Park, M. Kulishov, J. Azaña, and R. Morandotti, "Temporal differentiation of sub-picosecond optical pulses using a single long-period fiber grating," in Tech. Dig. of Conf. Lasers and Electro-Optics (CLEO/IQEC), Long Beach, CA, May 2006, Paper CTuBB5.

M. Stratmann, T. Pagel, and F. Mitschke, "Experimental observation of temporal soliton molecules," Phys. Rev. Lett. 95, 143902-1-3 (2005).
[CrossRef]

M. Kulishov, Y. Park, J. Azaña, and R. Slavík, "(Sub-)Picosecond Flat-Top Waveform Generation using a Single Uniform Long-Period Fiber Grating," in Proc. of European Conference on Optical Communications (ECOC 2006), Cannes, France, September 2006. Paper We2.3.7.
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Principle of the optical temporal differentiator.

Fig. 2.
Fig. 2.

Amplitude and phase characteristics of the fiber LPG filters. Measured field amplitude and phase characteristics of the realized long, S3 (red) and short S1 (blue) LPGs together with the theoretical characteristics of an ideal differentiator similar to S3 (green, dash-dotted lines). The S3 and S1 LPG operational bandwidths (highlighted in the figure) are 5.5 nm and 19 nm, respectively. The inset shows a fiber uniform LPG, where the level of green corresponds to the refractive index.

Fig. 3.
Fig. 3.

Results from numerical simulations. Expected field amplitude (blue solid line) and intensity (red dotted line) temporal profiles of the generated OS-HG waveform, and intensity profile of an ideal 700-fs (FWHM time-width) Gaussian input pulse (red dashed line).

Fig. 4.
Fig. 4.

Autocorrelation traces. Theoretical (dashed lines) and measured (solid lines) autocorrelation traces of the input pulse (blue, lower curves) and of the generated OS-HG waveform at the differentiator output (red, upper curves).

Fig. 5.
Fig. 5.

Fiber propagation results. Autocorrelation traces of the generated OS-HG waveform at the differentiator output (red solid line) and after additional propagation through 20 meters of SMF-28 fiber (green dashed line).

Fig. 6.
Fig. 6.

Results from Spectral Interferometry (SI) measurements. The phase (red) and intensity (blue) temporal profiles of the generated odd-symmetry HG waveform are retrieved from the experimental data obtained using Fourier-Transform SI (solid lines); the theoretical prediction (dashed lines) and considered input pulse waveform (dotted line) are also shown.

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