Abstract

Abstract

We propose an all-fiber method for the generation of ultrafast shaped pulse train bursts from a single pulse based on Fourier Series Developments (FDSs). The implementation of the FSD based filter only requires the use of a very simple non apodized Superimposed Fiber Bragg Grating (S-FBG) for the generation of the Shaped Output Pulse Train Burst (SOPTB). In this approach, the shape, the period and the temporal length of the generated SOPTB have no dependency on the input pulse rate.

© 2007 Optical Society of America

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References

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  1. A. M. Weiner, "Femtosecond optical pulse shaping and processing," Prog. Quantum Electron. 19, 161-235 (1995).
    [CrossRef]
  2. J. Azaña, R. Slavík, P. Kockaert, L. R. Chen, and S. LaRochelle, "Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings," J. Lightwave. Technol. 21, 1490-1498 (2003).
    [CrossRef]
  3. J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, "4x100 GHz pulse train generation from a single-wavelength 10 GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion," J. Lightwave. Technol. 24, 2091-2099 (2006).
    [CrossRef]
  4. J. Azaña and M. A. Muriel, "Technique for multiplying the repetition rates of periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber Bragg gratings," Opt. Lett. 24, 1672-1764 (1999).
    [CrossRef]
  5. P. Petropoulos, M. Ibsen, A. D. Ellis, 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. N. K. Berger, B. Levit, aand B. Fischer, "Reshaping periodic light pulses using cascaded uniform fiber Bragg gratings," J. Lightwave Technol. 24, 2746- 2751 (2006).
    [CrossRef]
  7. J. Azaña and L. R. Chen, "Synthesis of temporal optical waveforms by fiber Bragg gratings: a new approach based on space-to-frequency-to-time mapping," J. Opt. Soc. Am. B 19, 2758-2769 (2002).
    [CrossRef]
  8. I. Littler, M. Rochette, and B. Eggleton, "Adjustable bandwidth dispersionless bandpass FBG optical filter," Opt. Express 13, 3397-3407 (2005).
    [CrossRef] [PubMed]
  9. M. A. Preciado, V. García-Muñoz, and M. A. Muriel "Grating design of oppositely chirped FBGs for pulse shaping," IEEE Photon. Technol. Lett. 19, 435-437 (2007).
    [CrossRef]
  10. S. Longhi, M. Marano, P. Laporta, O. Svelto, "Propagation, manipulation, and control of picosecond optical pulses at 1.5 ?m in fiber Bragg gratings," J. Opt. Soc. Am. B 19, 2742-2757 (2002).
    [CrossRef]
  11. J. A. Bolger, I. C. M. Littler and B. J. Eggleton, "Optimisation of superimposed chirped fibre Bragg gratings for the generation of ultra-high speed optical pulse bursts," Opt. Commun. 271, 524-531 (2007).
    [CrossRef]
  12. T. Erdogan, "Fiber Grating Spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]

2007

M. A. Preciado, V. García-Muñoz, and M. A. Muriel "Grating design of oppositely chirped FBGs for pulse shaping," IEEE Photon. Technol. Lett. 19, 435-437 (2007).
[CrossRef]

J. A. Bolger, I. C. M. Littler and B. J. Eggleton, "Optimisation of superimposed chirped fibre Bragg gratings for the generation of ultra-high speed optical pulse bursts," Opt. Commun. 271, 524-531 (2007).
[CrossRef]

2006

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, "4x100 GHz pulse train generation from a single-wavelength 10 GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion," J. Lightwave. Technol. 24, 2091-2099 (2006).
[CrossRef]

N. K. Berger, B. Levit, aand B. Fischer, "Reshaping periodic light pulses using cascaded uniform fiber Bragg gratings," J. Lightwave Technol. 24, 2746- 2751 (2006).
[CrossRef]

2005

2003

J. Azaña, R. Slavík, P. Kockaert, L. R. Chen, and S. LaRochelle, "Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings," J. Lightwave. Technol. 21, 1490-1498 (2003).
[CrossRef]

2002

2001

1999

1997

T. Erdogan, "Fiber Grating Spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

1995

A. M. Weiner, "Femtosecond optical pulse shaping and processing," Prog. Quantum Electron. 19, 161-235 (1995).
[CrossRef]

Azaña, J.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, "4x100 GHz pulse train generation from a single-wavelength 10 GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion," J. Lightwave. Technol. 24, 2091-2099 (2006).
[CrossRef]

J. Azaña, R. Slavík, P. Kockaert, L. R. Chen, and S. LaRochelle, "Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings," J. Lightwave. Technol. 21, 1490-1498 (2003).
[CrossRef]

J. Azaña and L. R. Chen, "Synthesis of temporal optical waveforms by fiber Bragg gratings: a new approach based on space-to-frequency-to-time mapping," J. Opt. Soc. Am. B 19, 2758-2769 (2002).
[CrossRef]

J. Azaña and M. A. Muriel, "Technique for multiplying the repetition rates of periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber Bragg gratings," Opt. Lett. 24, 1672-1764 (1999).
[CrossRef]

Berger, N. K.

Bolger, J.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, "4x100 GHz pulse train generation from a single-wavelength 10 GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion," J. Lightwave. Technol. 24, 2091-2099 (2006).
[CrossRef]

Bolger, J. A.

J. A. Bolger, I. C. M. Littler and B. J. Eggleton, "Optimisation of superimposed chirped fibre Bragg gratings for the generation of ultra-high speed optical pulse bursts," Opt. Commun. 271, 524-531 (2007).
[CrossRef]

Chen, L. R.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, "4x100 GHz pulse train generation from a single-wavelength 10 GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion," J. Lightwave. Technol. 24, 2091-2099 (2006).
[CrossRef]

J. Azaña, R. Slavík, P. Kockaert, L. R. Chen, and S. LaRochelle, "Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings," J. Lightwave. Technol. 21, 1490-1498 (2003).
[CrossRef]

J. Azaña and L. R. Chen, "Synthesis of temporal optical waveforms by fiber Bragg gratings: a new approach based on space-to-frequency-to-time mapping," J. Opt. Soc. Am. B 19, 2758-2769 (2002).
[CrossRef]

Eggleton, B.

Eggleton, B. J.

J. A. Bolger, I. C. M. Littler and B. J. Eggleton, "Optimisation of superimposed chirped fibre Bragg gratings for the generation of ultra-high speed optical pulse bursts," Opt. Commun. 271, 524-531 (2007).
[CrossRef]

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, "4x100 GHz pulse train generation from a single-wavelength 10 GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion," J. Lightwave. Technol. 24, 2091-2099 (2006).
[CrossRef]

Ellis, A. D.

Erdogan, T.

T. Erdogan, "Fiber Grating Spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

García-Muñoz, V.

M. A. Preciado, V. García-Muñoz, and M. A. Muriel "Grating design of oppositely chirped FBGs for pulse shaping," IEEE Photon. Technol. Lett. 19, 435-437 (2007).
[CrossRef]

Ibsen, M.

Kockaert, P.

J. Azaña, R. Slavík, P. Kockaert, L. R. Chen, and S. LaRochelle, "Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings," J. Lightwave. Technol. 21, 1490-1498 (2003).
[CrossRef]

Laporta, P.

LaRochelle, S.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, "4x100 GHz pulse train generation from a single-wavelength 10 GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion," J. Lightwave. Technol. 24, 2091-2099 (2006).
[CrossRef]

J. Azaña, R. Slavík, P. Kockaert, L. R. Chen, and S. LaRochelle, "Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings," J. Lightwave. Technol. 21, 1490-1498 (2003).
[CrossRef]

Levit, B.

Littler, I.

Littler, I. C. M.

J. A. Bolger, I. C. M. Littler and B. J. Eggleton, "Optimisation of superimposed chirped fibre Bragg gratings for the generation of ultra-high speed optical pulse bursts," Opt. Commun. 271, 524-531 (2007).
[CrossRef]

Longhi, S.

Magné, J.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, "4x100 GHz pulse train generation from a single-wavelength 10 GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion," J. Lightwave. Technol. 24, 2091-2099 (2006).
[CrossRef]

Marano, M.

Muriel, M. A.

M. A. Preciado, V. García-Muñoz, and M. A. Muriel "Grating design of oppositely chirped FBGs for pulse shaping," IEEE Photon. Technol. Lett. 19, 435-437 (2007).
[CrossRef]

J. Azaña and M. A. Muriel, "Technique for multiplying the repetition rates of periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber Bragg gratings," Opt. Lett. 24, 1672-1764 (1999).
[CrossRef]

Petropoulos, P.

Preciado, M. A.

M. A. Preciado, V. García-Muñoz, and M. A. Muriel "Grating design of oppositely chirped FBGs for pulse shaping," IEEE Photon. Technol. Lett. 19, 435-437 (2007).
[CrossRef]

Richardson, D. J.

Rochette, M.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, "4x100 GHz pulse train generation from a single-wavelength 10 GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion," J. Lightwave. Technol. 24, 2091-2099 (2006).
[CrossRef]

I. Littler, M. Rochette, and B. Eggleton, "Adjustable bandwidth dispersionless bandpass FBG optical filter," Opt. Express 13, 3397-3407 (2005).
[CrossRef] [PubMed]

Slavík, R.

J. Azaña, R. Slavík, P. Kockaert, L. R. Chen, and S. LaRochelle, "Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings," J. Lightwave. Technol. 21, 1490-1498 (2003).
[CrossRef]

Svelto, O.

Weiner, A. M.

A. M. Weiner, "Femtosecond optical pulse shaping and processing," Prog. Quantum Electron. 19, 161-235 (1995).
[CrossRef]

IEEE Photon. Technol. Lett.

M. A. Preciado, V. García-Muñoz, and M. A. Muriel "Grating design of oppositely chirped FBGs for pulse shaping," IEEE Photon. Technol. Lett. 19, 435-437 (2007).
[CrossRef]

J. Lightwave Technol.

J. Lightwave. Technol.

J. Azaña, R. Slavík, P. Kockaert, L. R. Chen, and S. LaRochelle, "Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings," J. Lightwave. Technol. 21, 1490-1498 (2003).
[CrossRef]

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, "4x100 GHz pulse train generation from a single-wavelength 10 GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion," J. Lightwave. Technol. 24, 2091-2099 (2006).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

J. A. Bolger, I. C. M. Littler and B. J. Eggleton, "Optimisation of superimposed chirped fibre Bragg gratings for the generation of ultra-high speed optical pulse bursts," Opt. Commun. 271, 524-531 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Prog. Quantum Electron.

A. M. Weiner, "Femtosecond optical pulse shaping and processing," Prog. Quantum Electron. 19, 161-235 (1995).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(color online) Schematic diagram of the pulse shaper with chirped filters. Amplitude response (blue) and group delay (red). In the case where uniform filters are used, the group delay remains constant.

Fig. 2.
Fig. 2.

Generation of a square SOPTB with a uniform S-FBG. (a) Amplitude response of the filter. (b) Temporal amplitude envelope of the SOPTB.

Fig. 3.
Fig. 3.

Generation of a square SOPTB with S-LCFBG considering dc term. (a) Amplitude Response of the filter. (b) Group Delay. (c) Temporal amplitude envelope of the SOPTB.

Fig. 4.
Fig. 4.

Generation of a square SOPTB with S-LCFBG without dc term. (a) Amplitude response of the filter. (b) Group delay. (c) Temporal amplitude envelope of the SOPTB.

Fig. 5.
Fig. 5.

(color online) Effect of the variations on the S-FBG imperfections in the temporal amplitude envelope of the SOPTB. (a) Uniform S-FBG: ideal structure (blue), noisy structure (red). (b) S-LCFBG with dc term: ideal structure (blue), noisy structure (red). (c) S-LCFBG without dc term: ideal structure (blue), noisy structure (red).

Fig. 6.
Fig. 6.

(color online) Effect of the variations on the input pulse width in the temporal amplitude envelope of the SOPTB. (a) Uniform S-FBG: tFWHM =0.5 ps (blue), tFWHM =0.7 ps (red). (b) S-LCFBG with dc term: tFWHM =0.5 ps (blue), tFWHM =0.7 ps l (red). (c) S-LCFBG without dc term: tFWHM =0.5 ps l (blue), tFWHM =0.7 ps (red)

Equations (20)

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

H ( ω ) = p = p min p max H p ( ω ) = p = p min p max c p H 0 ( ω p Δ ω )
h ( t ) = h 0 ( t ) p = p min p max c p exp ( jp Δ ω t )
y ( t ) = h ( t ) * x ( t )
Y ( ω ) = H ( ω ) X ( ω )
y ( t ) = h 0 ( t ) s p = p min p max c p exp ( jp Δ ω t )
Y ( ω ) = p = p min p max X p c p H 0 ( ω p Δ ω )
y ( t ) = h 0 ( t ) p = p min p max X p c p exp ( jp Δ ω t )
R p , max = max ( H p ( ω ) 2 ) = c p 2 max ( H 0 ( ω ) 2 )
R p , max = ( d p X p ) 2 R 0 , max
n ( z ) = n av + p = p min p max Δ n p cos ( 2 π Λ 0 p z + φ p ) L 2 z L 2
Λ 0 p = π c n av ( ω 0 + p Δ ω )
Δ n p = 2c L( ω 0 +pΔω) atanh( R p,max )
n ( z ) = n av + p = p min p max Δ n p cos ( 2 π Λ 0 p z + C Kp 2 z 2 + φ p ) L 2 z L 2
C K = 4 n av 2 δ ω ( c 2 t h )
ϕ ̈ 1 δ ω 2
ϕ ̈ = t h δ ω
t h T 2 π
Δ n p = 2 n av ( ω 0 + p Δ ω ) 2 π ϕ ̈ ln ( 1 R p , max )
d p = { j ( p π ) p odd 1 2 p = 0
d p = j p π ( cos ( p π 4 ) cos ( p 3 π 4 ) ) p odd

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