Abstract

We introduce a new family of equivalent periodic phase-only filtering configurations that can be used for implementing the Talbot-based pulse rate multiplication technique. The introduced family of periodic Talbot filters allows one to design a desired pulse repetition rate multiplier with an unprecedented degree of freedom and flexibility. Moreover, these filters can be implemented using all-fiber technologies, and in particular (superimposed) linearly chirped fiber Bragg gratings. The design specifications and associated constraints of this new class of Talbot filters are discussed.

© 2006 Optical Society of America

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References

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  1. K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, "Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by modulation instability," Appl. Phys. Lett. 49, 236-238 (1986).
    [CrossRef]
  2. P. Petropoulos, M. Ibsen, M.N. Zervas and D.J. Richardson, "Generation of a 40 GHz pulse stream by pulse multiplication with a sampled fiber Bragg grating," Opt. Lett. 25, 521-523 (2000).
    [CrossRef]
  3. J. Azaña, and M. A. Muriel, "Technique for multiplying the repetition rates of periodic pulse trains of pulses by means of a temporal self-imaging effect in chirped fiber gratings," Opt. Lett. 24, 1672-1674 (1999).
    [CrossRef]
  4. J. Azaña and M. A. Muriel, "Temporal self-imaging effects: Theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum Electron. 7, 728-744 (2001).
    [CrossRef]
  5. S. Atkins and B. Fischer, "All-optical pulse rate multiplication using fractional Talbot effect and field-to-intensity conversion with cross-gain modulation," IEEE Photon. Technol. Lett. 15, 132-134 (2003).
    [CrossRef]
  6. J. Azaña, P. Kockaert, R. Slavík, L.R. Chen, and S. LaRochelle, "Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 413-415 (2003).
    [CrossRef]
  7. J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, J. Azaña, "4×100 GHz pulse train generation from a single wavelength 10 GHz mode-locked laser using superimposed fiber gratings and nonlinear conversion," J. Lightwave Technol. 24, 2006 (in press).
    [CrossRef]
  8. N. K. Berger, B. Levit, A. Bekker and B. Fischer, "Compression of periodic optical pulses using temporal fractional Talbot effect," IEEE Photon. Technol. Lett. 16, 1855-1857 (2004).
    [CrossRef]
  9. K. Miyamoto, "The phase Fresnel lens," J. Opt. Soc. Am. 51, 17-20 (1961).
    [CrossRef]
  10. L. Cohen, "Time-frequency distributions - A review," Proc. IEEE 77, 941-981 (1989)
    [CrossRef]
  11. S. Gupta, P. F. Ndione, J. Azaña, R. Morandotti, "A new insight into the problem of temporal Talbot phenomena in optical fibers," Proc. SPIE 5971, paper 59710O 1-12 (2005).

2006

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, J. Azaña, "4×100 GHz pulse train generation from a single wavelength 10 GHz mode-locked laser using superimposed fiber gratings and nonlinear conversion," J. Lightwave Technol. 24, 2006 (in press).
[CrossRef]

2004

N. K. Berger, B. Levit, A. Bekker and B. Fischer, "Compression of periodic optical pulses using temporal fractional Talbot effect," IEEE Photon. Technol. Lett. 16, 1855-1857 (2004).
[CrossRef]

2003

S. Atkins and B. Fischer, "All-optical pulse rate multiplication using fractional Talbot effect and field-to-intensity conversion with cross-gain modulation," IEEE Photon. Technol. Lett. 15, 132-134 (2003).
[CrossRef]

J. Azaña, P. Kockaert, R. Slavík, L.R. Chen, and S. LaRochelle, "Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 413-415 (2003).
[CrossRef]

2001

J. Azaña and M. A. Muriel, "Temporal self-imaging effects: Theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum Electron. 7, 728-744 (2001).
[CrossRef]

2000

1999

1989

L. Cohen, "Time-frequency distributions - A review," Proc. IEEE 77, 941-981 (1989)
[CrossRef]

1986

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, "Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by modulation instability," Appl. Phys. Lett. 49, 236-238 (1986).
[CrossRef]

1961

Atkins, S.

S. Atkins and B. Fischer, "All-optical pulse rate multiplication using fractional Talbot effect and field-to-intensity conversion with cross-gain modulation," IEEE Photon. Technol. Lett. 15, 132-134 (2003).
[CrossRef]

Azaña, J.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, J. Azaña, "4×100 GHz pulse train generation from a single wavelength 10 GHz mode-locked laser using superimposed fiber gratings and nonlinear conversion," J. Lightwave Technol. 24, 2006 (in press).
[CrossRef]

J. Azaña, P. Kockaert, R. Slavík, L.R. Chen, and S. LaRochelle, "Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 413-415 (2003).
[CrossRef]

J. Azaña and M. A. Muriel, "Temporal self-imaging effects: Theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum Electron. 7, 728-744 (2001).
[CrossRef]

J. Azaña, and M. A. Muriel, "Technique for multiplying the repetition rates of periodic pulse trains of pulses by means of a temporal self-imaging effect in chirped fiber gratings," Opt. Lett. 24, 1672-1674 (1999).
[CrossRef]

Bekker, A.

N. K. Berger, B. Levit, A. Bekker and B. Fischer, "Compression of periodic optical pulses using temporal fractional Talbot effect," IEEE Photon. Technol. Lett. 16, 1855-1857 (2004).
[CrossRef]

Berger, N. K.

N. K. Berger, B. Levit, A. Bekker and B. Fischer, "Compression of periodic optical pulses using temporal fractional Talbot effect," IEEE Photon. Technol. Lett. 16, 1855-1857 (2004).
[CrossRef]

Bolger, J.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, J. Azaña, "4×100 GHz pulse train generation from a single wavelength 10 GHz mode-locked laser using superimposed fiber gratings and nonlinear conversion," J. Lightwave Technol. 24, 2006 (in press).
[CrossRef]

Chen, L. R.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, J. Azaña, "4×100 GHz pulse train generation from a single wavelength 10 GHz mode-locked laser using superimposed fiber gratings and nonlinear conversion," J. Lightwave Technol. 24, 2006 (in press).
[CrossRef]

Chen, L.R.

J. Azaña, P. Kockaert, R. Slavík, L.R. Chen, and S. LaRochelle, "Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 413-415 (2003).
[CrossRef]

Cohen, L.

L. Cohen, "Time-frequency distributions - A review," Proc. IEEE 77, 941-981 (1989)
[CrossRef]

Eggleton, B. J.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, J. Azaña, "4×100 GHz pulse train generation from a single wavelength 10 GHz mode-locked laser using superimposed fiber gratings and nonlinear conversion," J. Lightwave Technol. 24, 2006 (in press).
[CrossRef]

Fischer, B.

N. K. Berger, B. Levit, A. Bekker and B. Fischer, "Compression of periodic optical pulses using temporal fractional Talbot effect," IEEE Photon. Technol. Lett. 16, 1855-1857 (2004).
[CrossRef]

S. Atkins and B. Fischer, "All-optical pulse rate multiplication using fractional Talbot effect and field-to-intensity conversion with cross-gain modulation," IEEE Photon. Technol. Lett. 15, 132-134 (2003).
[CrossRef]

Hasegawa, A.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, "Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by modulation instability," Appl. Phys. Lett. 49, 236-238 (1986).
[CrossRef]

Ibsen, M.

Jewell, J. L.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, "Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by modulation instability," Appl. Phys. Lett. 49, 236-238 (1986).
[CrossRef]

Kockaert, P.

J. Azaña, P. Kockaert, R. Slavík, L.R. Chen, and S. LaRochelle, "Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 413-415 (2003).
[CrossRef]

LaRochelle, S.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, J. Azaña, "4×100 GHz pulse train generation from a single wavelength 10 GHz mode-locked laser using superimposed fiber gratings and nonlinear conversion," J. Lightwave Technol. 24, 2006 (in press).
[CrossRef]

J. Azaña, P. Kockaert, R. Slavík, L.R. Chen, and S. LaRochelle, "Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 413-415 (2003).
[CrossRef]

Levit, B.

N. K. Berger, B. Levit, A. Bekker and B. Fischer, "Compression of periodic optical pulses using temporal fractional Talbot effect," IEEE Photon. Technol. Lett. 16, 1855-1857 (2004).
[CrossRef]

Magné, J.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, J. Azaña, "4×100 GHz pulse train generation from a single wavelength 10 GHz mode-locked laser using superimposed fiber gratings and nonlinear conversion," J. Lightwave Technol. 24, 2006 (in press).
[CrossRef]

Miyamoto, K.

Muriel, M. A.

J. Azaña and M. A. Muriel, "Temporal self-imaging effects: Theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum Electron. 7, 728-744 (2001).
[CrossRef]

J. Azaña, and M. A. Muriel, "Technique for multiplying the repetition rates of periodic pulse trains of pulses by means of a temporal self-imaging effect in chirped fiber gratings," Opt. Lett. 24, 1672-1674 (1999).
[CrossRef]

Petropoulos, P.

Richardson, D.J.

Rochette, M.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, J. Azaña, "4×100 GHz pulse train generation from a single wavelength 10 GHz mode-locked laser using superimposed fiber gratings and nonlinear conversion," J. Lightwave Technol. 24, 2006 (in press).
[CrossRef]

Slavík, R.

J. Azaña, P. Kockaert, R. Slavík, L.R. Chen, and S. LaRochelle, "Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 413-415 (2003).
[CrossRef]

Tai, K.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, "Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by modulation instability," Appl. Phys. Lett. 49, 236-238 (1986).
[CrossRef]

Tomita, A.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, "Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by modulation instability," Appl. Phys. Lett. 49, 236-238 (1986).
[CrossRef]

Zervas, M.N.

Appl. Phys. Lett.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, "Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by modulation instability," Appl. Phys. Lett. 49, 236-238 (1986).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. Azaña and M. A. Muriel, "Temporal self-imaging effects: Theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum Electron. 7, 728-744 (2001).
[CrossRef]

IEEE Photon. Technol. Lett.

S. Atkins and B. Fischer, "All-optical pulse rate multiplication using fractional Talbot effect and field-to-intensity conversion with cross-gain modulation," IEEE Photon. Technol. Lett. 15, 132-134 (2003).
[CrossRef]

J. Azaña, P. Kockaert, R. Slavík, L.R. Chen, and S. LaRochelle, "Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 413-415 (2003).
[CrossRef]

N. K. Berger, B. Levit, A. Bekker and B. Fischer, "Compression of periodic optical pulses using temporal fractional Talbot effect," IEEE Photon. Technol. Lett. 16, 1855-1857 (2004).
[CrossRef]

J. Lightwave Technol.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, J. Azaña, "4×100 GHz pulse train generation from a single wavelength 10 GHz mode-locked laser using superimposed fiber gratings and nonlinear conversion," J. Lightwave Technol. 24, 2006 (in press).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Proc. IEEE

L. Cohen, "Time-frequency distributions - A review," Proc. IEEE 77, 941-981 (1989)
[CrossRef]

Other

S. Gupta, P. F. Ndione, J. Azaña, R. Morandotti, "A new insight into the problem of temporal Talbot phenomena in optical fibers," Proc. SPIE 5971, paper 59710O 1-12 (2005).

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Figures (4)

Fig. 1.
Fig. 1.

Spectral phase and group delay responses of two equivalent Talbot filters, namely a single dispersive medium (top plot) and a periodic phase filter (bottom plot), for multiplying the repetition rate of an incoming optical pulse train by m=3, assuming a factor q=1. The solid red and blue curves in the plots represent the group delay and phase profile of the corresponding filter, respectively, while the small arrows in the top plot represent the discrete spectral components (modes) of the input periodic optical pulse train.

Fig. 2.
Fig. 2.

Group delay response of a periodic quadratic-phase filter for multiplying the repetition rate of an input pulse train by a factor of m=3 (periodic Talbot filter with p=2, assuming q=1). The red solid curve represents the filter’s group delay and the small arrows represent the discrete spectral components (modes) of the input periodic pulse train.

Fig. 3.
Fig. 3.

Joint time-frequency analysis of the multiplied-rate optical pulse train generated at the output of any of the Talbot filters described in the text. For comparison, the temporal waveform of the input pulse train is also shown in the bottom plot (dashed curve).

Fig. 4.
Fig. 4.

Joint time-frequency analysis of the output pulse train with multiplied rate by 4, generated by introducing a π phase shift over one spectral mode every 4 modes of the original input pulse train (for comparison, the temporal waveform of the input pulse train is also represented in the bottom plot with a dashed curve).

Equations (6)

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Φ 0 ( 2 ) = ( q m ) ( T r 2 2 π )
Φ p = p 2 ( q m ) π
Δ τ 0 = Φ 0 ( 2 ) Δ ω in = ( q m ) ( T r 2 2 π ) Δ ω in = q T r N
Δ τ 1 = Φ 0 ( 2 ) ω r , out = q T r
Δ τ p = Φ 0 ( 2 ) p ω r , out = p ( q T r )
N p = R { Δ ω in ( p ω r , out ) }

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