Abstract

A simple and efficient optical pulse re-shaper based on the concept of temporal coherence synthesization is proposed and analyzed in detail. Specifically, we demonstrate that an arbitrary chirp-free (transform-limited) optical pulse waveform can be synthesized from a given transform-limited Gaussian-like input optical pulse by coherently superposing a set of properly delayed replicas of this input pulse, e.g. using a conventional multi-arm interferometer. A practical implementation of this general concept based on the use of conventional concatenated two-arm interferometers is also suggested and demonstrated. This specific implementation allows the synthesis of any desired temporally-symmetric optical waveform with time features only limited by the input pulse bandwidth. A general optimization algorithm has been developed and applied for designing the system specifications (number of interferometers and relative time delays in these interferometers) that are required to achieve a desired optical pulse re-shaping operation. The required tolerances in this system have been also estimated and confirmed by numerical simulations. The proposed technique has been experimentally demonstrated by reshaping an ≈1-ps Gaussian-like optical pulse into various temporal shapes of practical interest, i.e. picosecond transform-limited flat-top, parabolic and triangular pulses (all centered at a wavelength of ≈ 1550nm), using a simple two-stage interferometer setup. A remarkable synthesis accuracy and high energetic efficiency have been achieved for all these pulse re-shaping operations.

© 2007 Optical Society of America

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

2006

2004

M. Shen, R. A. Minasian, “Toward a high-speed arbitrary waveform generation by a novel photonic processing structure,” IEEE Photon. Technol. Lett. 16, 1155–1157 (2004).
[CrossRef]

2001

2000

T. Otani, T. Miyajaki, S. Yamamoto, “Optical 3R Regenerator using wavelength converters based on electroabsorption modulator for all-optical network applications,” IEEE Photon. Technol. Lett. 12, 431–433 (2000).
[CrossRef]

1997

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, M. Ishii, “Time-space conversion optical signal processing using arrayed-waveguide grating,” Electron. Lett. 33, 1890–1891 (1997).
[CrossRef]

1995

1993

V. Narayan, D. L. MacFarlane, “Bursts and codes of ultrashort pulses,” IEEE Photon. Technol. Lett. 5, 1465–1467 (1993).
[CrossRef]

Azaña, J.

Y. Park, F. Li, 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, J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings,” Opt. Express 14, 12670–12678 (2006).
[CrossRef] [PubMed]

Y. Park, J. Azaña, “Optical pulse shaping technique based on a simple interferometry setup,” in Proc. of IEEE LEOS 2006 Annual Meeting. Paper TuN2, pp. 274–275.

L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, R. Slavík, Y. Park, J. Azaña, P. Jeppesen, “Flat-top pulse enabling 640 Gb/s OTDM demultiplexing,” Conference on Lasers and Electro-Optics Europe (CLEO-Europe) Munich, Germany, June 2007, Paper CI8-1.

Chériaux, G.

Ellis, A. D.

Finot, C.

Galili, M.

L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, R. Slavík, Y. Park, J. Azaña, P. Jeppesen, “Flat-top pulse enabling 640 Gb/s OTDM demultiplexing,” Conference on Lasers and Electro-Optics Europe (CLEO-Europe) Munich, Germany, June 2007, Paper CI8-1.

Glover, I.

I. Glover, P. Grant, Digital Communications (Pearson Education Ltd., 2004).

Grant, P.

I. Glover, P. Grant, Digital Communications (Pearson Education Ltd., 2004).

Ibsen, M.

Inoue, Y.

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, M. Ishii, “Time-space conversion optical signal processing using arrayed-waveguide grating,” Electron. Lett. 33, 1890–1891 (1997).
[CrossRef]

Ishii, M.

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, M. Ishii, “Time-space conversion optical signal processing using arrayed-waveguide grating,” Electron. Lett. 33, 1890–1891 (1997).
[CrossRef]

Jeppesen, P.

L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, R. Slavík, Y. Park, J. Azaña, P. Jeppesen, “Flat-top pulse enabling 640 Gb/s OTDM demultiplexing,” Conference on Lasers and Electro-Optics Europe (CLEO-Europe) Munich, Germany, June 2007, Paper CI8-1.

Joffre, M.

Kulishov, M.

Kurokawa, T.

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, M. Ishii, “Time-space conversion optical signal processing using arrayed-waveguide grating,” Electron. Lett. 33, 1890–1891 (1997).
[CrossRef]

Lepetit, L.

Li, F.

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

MacFarlane, D. L.

V. Narayan, D. L. MacFarlane, “Bursts and codes of ultrashort pulses,” IEEE Photon. Technol. Lett. 5, 1465–1467 (1993).
[CrossRef]

Madsen, C. K.

C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, (John Wiley & Sons, New York, 1999).

Minasian, R. A.

M. Shen, R. A. Minasian, “Toward a high-speed arbitrary waveform generation by a novel photonic processing structure,” IEEE Photon. Technol. Lett. 16, 1155–1157 (2004).
[CrossRef]

Miyajaki, T.

T. Otani, T. Miyajaki, S. Yamamoto, “Optical 3R Regenerator using wavelength converters based on electroabsorption modulator for all-optical network applications,” IEEE Photon. Technol. Lett. 12, 431–433 (2000).
[CrossRef]

Mukasa, K.

Mulvad, H. C. H.

L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, R. Slavík, Y. Park, J. Azaña, P. Jeppesen, “Flat-top pulse enabling 640 Gb/s OTDM demultiplexing,” Conference on Lasers and Electro-Optics Europe (CLEO-Europe) Munich, Germany, June 2007, Paper CI8-1.

Naganuma, K.

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, M. Ishii, “Time-space conversion optical signal processing using arrayed-waveguide grating,” Electron. Lett. 33, 1890–1891 (1997).
[CrossRef]

Narayan, V.

V. Narayan, D. L. MacFarlane, “Bursts and codes of ultrashort pulses,” IEEE Photon. Technol. Lett. 5, 1465–1467 (1993).
[CrossRef]

Okamoto, K.

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, M. Ishii, “Time-space conversion optical signal processing using arrayed-waveguide grating,” Electron. Lett. 33, 1890–1891 (1997).
[CrossRef]

Otani, T.

T. Otani, T. Miyajaki, S. Yamamoto, “Optical 3R Regenerator using wavelength converters based on electroabsorption modulator for all-optical network applications,” IEEE Photon. Technol. Lett. 12, 431–433 (2000).
[CrossRef]

Oxenløwe, L. K.

L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, R. Slavík, Y. Park, J. Azaña, P. Jeppesen, “Flat-top pulse enabling 640 Gb/s OTDM demultiplexing,” Conference on Lasers and Electro-Optics Europe (CLEO-Europe) Munich, Germany, June 2007, Paper CI8-1.

Park, Y.

Y. Park, F. Li, 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, J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings,” Opt. Express 14, 12670–12678 (2006).
[CrossRef] [PubMed]

L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, R. Slavík, Y. Park, J. Azaña, P. Jeppesen, “Flat-top pulse enabling 640 Gb/s OTDM demultiplexing,” Conference on Lasers and Electro-Optics Europe (CLEO-Europe) Munich, Germany, June 2007, Paper CI8-1.

Y. Park, J. Azaña, “Optical pulse shaping technique based on a simple interferometry setup,” in Proc. of IEEE LEOS 2006 Annual Meeting. Paper TuN2, pp. 274–275.

Parmigiani, F.

Petropoulos, P.

Richardson, D. J.

Roelens, M. A.

Shen, M.

M. Shen, R. A. Minasian, “Toward a high-speed arbitrary waveform generation by a novel photonic processing structure,” IEEE Photon. Technol. Lett. 16, 1155–1157 (2004).
[CrossRef]

Slavík, R.

Y. Park, M. Kulishov, R. Slavík, J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings,” Opt. Express 14, 12670–12678 (2006).
[CrossRef] [PubMed]

L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, R. Slavík, Y. Park, J. Azaña, P. Jeppesen, “Flat-top pulse enabling 640 Gb/s OTDM demultiplexing,” Conference on Lasers and Electro-Optics Europe (CLEO-Europe) Munich, Germany, June 2007, Paper CI8-1.

Takenouchi, H.

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, M. Ishii, “Time-space conversion optical signal processing using arrayed-waveguide grating,” Electron. Lett. 33, 1890–1891 (1997).
[CrossRef]

Tsuda, H.

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, M. Ishii, “Time-space conversion optical signal processing using arrayed-waveguide grating,” Electron. Lett. 33, 1890–1891 (1997).
[CrossRef]

Weiner, A. M.

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

Yamamoto, S.

T. Otani, T. Miyajaki, S. Yamamoto, “Optical 3R Regenerator using wavelength converters based on electroabsorption modulator for all-optical network applications,” IEEE Photon. Technol. Lett. 12, 431–433 (2000).
[CrossRef]

Zhao, J. H.

C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, (John Wiley & Sons, New York, 1999).

Electron. Lett.

T. Kurokawa, H. Tsuda, K. Okamoto, K. Naganuma, H. Takenouchi, Y. Inoue, M. Ishii, “Time-space conversion optical signal processing using arrayed-waveguide grating,” Electron. Lett. 33, 1890–1891 (1997).
[CrossRef]

IEEE Photon. Technol. Lett.

T. Otani, T. Miyajaki, S. Yamamoto, “Optical 3R Regenerator using wavelength converters based on electroabsorption modulator for all-optical network applications,” IEEE Photon. Technol. Lett. 12, 431–433 (2000).
[CrossRef]

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

V. Narayan, D. L. MacFarlane, “Bursts and codes of ultrashort pulses,” IEEE Photon. Technol. Lett. 5, 1465–1467 (1993).
[CrossRef]

M. Shen, R. A. Minasian, “Toward a high-speed arbitrary waveform generation by a novel photonic processing structure,” IEEE Photon. Technol. Lett. 16, 1155–1157 (2004).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Express

Prog. Quantum Electron.

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

Other

Y. Park, J. Azaña, “Optical pulse shaping technique based on a simple interferometry setup,” in Proc. of IEEE LEOS 2006 Annual Meeting. Paper TuN2, pp. 274–275.

C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, (John Wiley & Sons, New York, 1999).

I. Glover, P. Grant, Digital Communications (Pearson Education Ltd., 2004).

L. K. Oxenløwe, M. Galili, H. C. H. Mulvad, R. Slavík, Y. Park, J. Azaña, P. Jeppesen, “Flat-top pulse enabling 640 Gb/s OTDM demultiplexing,” Conference on Lasers and Electro-Optics Europe (CLEO-Europe) Munich, Germany, June 2007, Paper CI8-1.

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Figures (9)

Fig. 1.
Fig. 1.

Conceptual diagram of the proposed pulse shaping technique (temporal coherence synthesization) and examples of synthesized time waveforms: flat-top, parabolic, triangular, and trapezoidal pulse.

Fig. 2.
Fig. 2.

Schematic of the proposed multi-stage interferometric setup for pulse shaping based on temporal coherent synthesization. B: Beam splitter(50:50) M: Mirror I1: First interferometer I2: Second interferometer I3: Third interferometer

Fig. 3.
Fig. 3.

(a).Time domain and (b) frequency domain parametric representations of the raised cosine function

Fig. 4.
Fig. 4.

Results corresponding to the synthesis of (a) a 2-ps (FWHM) flat-top optical pulse and (b) a 3.1-ps (FWHM) flat-top optical pulse, by use of two cascaded interferometers. The inset of Fig. 4(a) shows the input pulse intensity profile. The inset of Fig. 4(b) shows the measured spectrum profiles of the synthesized 2- and 3.1-ps flat-top pulses in log scale.

Fig. 5.
Fig. 5.

Results corresponding to the synthesis of a 2-ps (FWHM) triangular optical pulse by use of two cascaded interferometers.

Fig. 6.
Fig. 6.

Results corresponding to the synthesis of a 2-ps (FWHM) parabolic optical pulse by use of two cascaded interferometers.

Fig. 7.
Fig. 7.

Results corresponding to the synthesis of a 3-ps (FWHM) triangular optical pulse by use of (a) two cascaded interferometers, and (b) three cascaded interferometers.

Fig. 8.
Fig. 8.

Output pulse shape in the case of variations in (a) the longer relative time delay, and (b) the shorter relative time delay, with respect to their optimal values.

Fig. 9.
Fig. 9.

Experimental setup for retrieving the amplitude and phase temporal profiles of the shaped output pulse using FTSI. The grayed box shows the pulse shaper based on two cascaded Michelson interferometers FFL: Femtosecond Fiber Laser. B: Beam Splitter. M: Mirror. PC: Polarization Controller. L: Lens. P: Primary output. S: Secondary output. The inset shows the measured input pulse spectrum.

Equations (11)

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A ( ω ) E ( ω ) j = 1 M ( 1 + exp [ i ( ω + ω c ) τ j ] )
a ( t ) e ( t ) ( δ ( t ) + δ ( t τ 1 ) exp [ i ω c τ 1 ] ) ( δ ( t ) + δ ( t τ 2 ) exp [ i ω c τ 2 ] )
( δ ( t ) + δ ( t τ M ) exp [ i ω c τ M ] )
a ( t ) e ( t ) ( δ ( t ) + δ ( t τ 1 ) ) ( δ ( t ) + δ ( t τ 2 ) ) ( δ ( t ) + δ ( t τ M ) )
Error = n = 1 N W ( t n ) I targ ( t n ) I calc ( t n ) 2
a t arg ( t ) = { 1 , t 1 α 2 T , 1 2 [ 1 + cos ( π α T [ t 1 α 2 T ] ) ] , 1 α 2 T < t < 1 + α 2 T , 0 , otherwise ,
A t arg ( ω ) = 4 π 2 sinc ( T ω 2 π ) cos ( π α T ω 2 π ) 4 π 2 4 α 2 T 2 ω 2
a t arg ( t ) = { P P 1 2 t 2 T P 2 if t T P 2 0 otherwise ,
a ( t ) e ( t ) ( δ ( t ) + δ ( t ( τ 1 + Δ τ 1 ) ) exp [ i ω c ( τ 1 + Δ τ 1 ) ] )
( δ ( t ) + δ ( t ( τ 2 + Δ τ 2 ) ) exp [ i ω c ( τ 2 + Δ τ 2 ) ] )
( δ ( t ) + δ ( t ( τ M + Δ τ M ) ) exp [ i ω c ( τ M + Δ τ M ) ] )

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