Abstract

We study the influence of dispersive propagation on picosecond flat-top pulses, which are generated using long period fiber grating (LPG)-based optical differentiators. We suggest an extremely simple scheme to compensate for the dispersion-induced flat-top pulse distortion; this scheme is based on proper tuning the LPG coupling strength. As this coupling strength may be changed via LPG axial straining, the demonstrated device can be tuned to compensate for different levels of the dispersion in a very easy and straightforward fashion. This allows for very fine flat-top pulse shape adjustment, even after propagation through a relatively long section of dispersive optical fiber. In the experimental demonstration reported here, the dispersion tolerance of 1.8-ps flat-top pulses propagating through a standard telecom fiber (SMF-28) was increased from ≈2 m to ≈18 m, giving a 9-fold improvement.

© 2007 Optical Society of America

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References

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  1. J. H. Lee, P. C. The, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-optical modulation and demultiplexing systems with significant timing jitter tolerance through incorporation of pulse shaping fiber Bragg gratings," IEEE Photon. Technol. Lett. 14, 203-205 (2002).
    [CrossRef]
  2. F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-optical pulse reshaping and retiming systems incorporating pulse shaping fiber Bragg grating," J. Lightwave Technol. 19, 746-752 (2001).
  3. L. K. Oxenlowe, M. Galili, A. T. Clausen, and P. Jeppesen, "Generating a square switching window for timing jitter tolerant 160Gb/s demutiplexing by the optical Fourier transform technique," Proc. of the 32nd European Conference on Optical Communication (ECOC 2006), Cannes, France, September 2006. Paper We2.3.4.
  4. L.K. Oxenlowe, M. Galili, H.C.H. Mulvad, P. Jeppesen, R. Slavík, J. Azaña, Y. Park, "Using a newly developed long-period grating filter to improve the timing tolerance of a 320 Gb/s demultiplexer," Conference on Lasers and Electro-Optics (CLEO 2007), Baltimore, Maryland, USA, May 2007. Paper CMZ5.
    [CrossRef]
  5. P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, "Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating," J. Lightwave Technol. 19, 746-752 (2001).
    [CrossRef]
  6. L. Qian, A. M. H. Wong, S. A. Neata, and X. Gu, "Simple and efficient optical pulse shaping: new algorithm and experimental demonstration," Conference on Lasers and Electro-Optics (CLEO) 2006, Long Beach, CA, USA. Paper JWB-33.
  7. 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).
    [CrossRef]
  8. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators, " Opt. Express 14, 10699-10707 (2006).
    [CrossRef] [PubMed]
  9. M. Kulishov and J. Azaña, "Long-period fiber gratings as ultrafast optical differentiators," Opt. Lett. 30, 2700-2702 (2005).
    [CrossRef] [PubMed]
  10. R. Slavík, "Extremely deep long-period fiber grating made with CO2 laser," IEEE Photon. Technol. Lett. 18, 1705-1707 (2006).
    [CrossRef]
  11. I. Bralwish, B. L. Bachim, and T.K. Gaylord, "Prototype CO2 laser-induced long-period fiber grating variable optical attenuators and optical tunable filters," Appl. Opt. 43, 1789-1793 (2004).
    [CrossRef]
  12. 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, 2467-2474 (1995).
    [CrossRef]
  13. 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]
  14. R. Slavík and F. Todorov, "Tuning of long-period fibre gratings written by CO2 laser with the resonant transmission below -45 dB," Electron. Lett.,  43, 16-18 (2007).
    [CrossRef]
  15. Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-713 (2007).
    [CrossRef] [PubMed]

2007 (2)

R. Slavík and F. Todorov, "Tuning of long-period fibre gratings written by CO2 laser with the resonant transmission below -45 dB," Electron. Lett.,  43, 16-18 (2007).
[CrossRef]

Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-713 (2007).
[CrossRef] [PubMed]

2006 (4)

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators, " Opt. Express 14, 10699-10707 (2006).
[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).
[CrossRef]

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 (1)

2004 (1)

2002 (1)

J. H. Lee, P. C. The, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-optical modulation and demultiplexing systems with significant timing jitter tolerance through incorporation of pulse shaping fiber Bragg gratings," IEEE Photon. Technol. Lett. 14, 203-205 (2002).
[CrossRef]

2001 (2)

1995 (1)

Azaña, J.

Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-713 (2007).
[CrossRef] [PubMed]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators, " Opt. Express 14, 10699-10707 (2006).
[CrossRef] [PubMed]

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]

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).
[CrossRef]

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

Bachim, B. L.

Bralwish, I.

Chériaux, G.

Ellis, A. D.

Gaylord, T.K.

Ibsen, M.

Joffre, M.

Kulishov, M.

Lee, J. H.

J. H. Lee, P. C. The, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-optical modulation and demultiplexing systems with significant timing jitter tolerance through incorporation of pulse shaping fiber Bragg gratings," IEEE Photon. Technol. Lett. 14, 203-205 (2002).
[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]

Morandotti, R.

Park, Y.

Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-713 (2007).
[CrossRef] [PubMed]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators, " Opt. Express 14, 10699-10707 (2006).
[CrossRef] [PubMed]

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]

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).
[CrossRef]

Parmigiani, F.

Petropoulos, P.

Richardson, D. J.

Slavík, R.

Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-713 (2007).
[CrossRef] [PubMed]

R. Slavík and F. Todorov, "Tuning of long-period fibre gratings written by CO2 laser with the resonant transmission below -45 dB," Electron. Lett.,  43, 16-18 (2007).
[CrossRef]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators, " Opt. Express 14, 10699-10707 (2006).
[CrossRef] [PubMed]

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

The, P. C.

J. H. Lee, P. C. The, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-optical modulation and demultiplexing systems with significant timing jitter tolerance through incorporation of pulse shaping fiber Bragg gratings," IEEE Photon. Technol. Lett. 14, 203-205 (2002).
[CrossRef]

Todorov, F.

R. Slavík and F. Todorov, "Tuning of long-period fibre gratings written by CO2 laser with the resonant transmission below -45 dB," Electron. Lett.,  43, 16-18 (2007).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (1)

R. Slavík and F. Todorov, "Tuning of long-period fibre gratings written by CO2 laser with the resonant transmission below -45 dB," Electron. Lett.,  43, 16-18 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

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. H. Lee, P. C. The, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-optical modulation and demultiplexing systems with significant timing jitter tolerance through incorporation of pulse shaping fiber Bragg gratings," IEEE Photon. Technol. Lett. 14, 203-205 (2002).
[CrossRef]

J. Lightwave Technol. (2)

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

Opt. Express (2)

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators, " Opt. Express 14, 10699-10707 (2006).
[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).
[CrossRef]

Opt. Lett. (2)

Other (3)

L. K. Oxenlowe, M. Galili, A. T. Clausen, and P. Jeppesen, "Generating a square switching window for timing jitter tolerant 160Gb/s demutiplexing by the optical Fourier transform technique," Proc. of the 32nd European Conference on Optical Communication (ECOC 2006), Cannes, France, September 2006. Paper We2.3.4.

L.K. Oxenlowe, M. Galili, H.C.H. Mulvad, P. Jeppesen, R. Slavík, J. Azaña, Y. Park, "Using a newly developed long-period grating filter to improve the timing tolerance of a 320 Gb/s demultiplexer," Conference on Lasers and Electro-Optics (CLEO 2007), Baltimore, Maryland, USA, May 2007. Paper CMZ5.
[CrossRef]

L. Qian, A. M. H. Wong, S. A. Neata, and X. Gu, "Simple and efficient optical pulse shaping: new algorithm and experimental demonstration," Conference on Lasers and Electro-Optics (CLEO) 2006, Long Beach, CA, USA. Paper JWB-33.

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Figures (6)

Fig. 1.
Fig. 1.

Temporal characteristics of the generated flat-top pulse with an ideal differentiator, ωcar >ω0 , for different levels of dispersion experienced by the pulse (represented in lengths of the SMF-28 fiber of 0 m (black), 3 m (red), 6 m (blue), and 9 m (green)).

Fig. 2.
Fig. 2.

Phase (a) and magnitude (b) variation of the LPG spectral transfer function; LPG length: 70 mm, period 530 μm. The LPG coupling strength κ was adjusted to achieve LPGs resonant transmission (in intensity) of -30 dB (red), -20 dB (blue) and -16 dB (green). The dashed curves are for undercoupled and dotted for overcoupled LPGs. Situation for LPG in full coupling condition is shown as black, solid line. For simplicity, only the extreme values are shown in plot (b) – the characteristics of overcoupled and undercoupled LPGs of identical resonant transmission are almost identical.

Fig. 3.
Fig. 3.

Temporal characteristics of the input pulse that passed through the filter that has the ideal differentiator’s magnitude transfer response having various levels of the phase jump (shown in the Fig.) across the filter central frequency. The envelope of the beating signal is shown for illustration.

Fig. 4.
Fig. 4.

Temporal characteristics of the flat-top pulse generated with a filter that has magnitude response identical to an ideal differentiator and a constant phase response with a jump across its central frequency (π, black, 3/4π, blue, and π/2, red, respectively) (a) and with full-coupled/undercoupled LPG with characteristics shown in Fig. 2 (for -20 and -16 dB) (b). The dispersion experienced by the pulse (represented in lengths of the SMF-28 fiber) is adjusted to obtain the desired flat-top temporal waveform.

Fig. 5.
Fig. 5.

Calculated (dash red) and measured (solid blue) spectral characteristics of the used LPG that was 70 mm long with period of 530 μm when adjusted for full coupling. The solid, green line shows the spectral power density of the used short pulse (measured with resolution of 1 nm) with central wavelength adjusted for optimal flat-top pulse generation.

Fig. 6.
Fig. 6.

Waveforms at the output of the LPG filter adjusted to obtain flat-top waveform (a); situation shown in (a) after adding 18 meters of SMF-28 standard telecom fiber (b); and situation from (b) after re-adjusting the filter coupling strength and filter-input pulse detuning to recover the flat-top waveform (c). Calculated data shown as dashed red; measured as solid black.

Equations (11)

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v ( t ) u ( t ) t + j ( ω car ω 0 ) u ( t ) ,
v ( t ) 2 u ( t ) t 2 + ( ω car ω 0 ) 2 u ( t ) 2 ,
u ( t ) disp w ( t ) exp ( j D t 2 ) ,
v ( t ) disp ( w ( t ) exp ( j D t 2 ) ) t + j ( ω car ω 0 ) w ( t ) exp ( j D t 2 ) ,
v ( t ) disp 2 w ( t ) t 2 + w ( t ) 2 ( ( ω car ω 0 ) 2 Dt ) 2 .
H ( ω ) [ cos ( κL ) + ( ω ω 0 ) sin ( κL ) ] exp ( jβL ) ,
cos ( κL ) Δ κL , sin ( κL ) 1 ,
H ( ω ) [ Δ κL + ( ω ω 0 ) ] exp ( jβL ) .
v ( t ) α u ( t ) t + Δ κLu ( t ) .
v ( t ) 2 α 2 u ( t ) t 2 + Δ κLu ( t ) 2 + 2 α Δ κL u ( t ) t u ( t ) .
v ( t ) disp 2 α 2 w ( t ) t 2 + Δ κ 2 L 2 w ( t ) 2 + 2 α Δ κLw ( t ) w ( t ) t + α 2 ( ( ω car ω 0 ) 2 Dt ) 2 w ( t ) 2

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