Abstract

We propose and analyze a new technique for optical pulse shaping that uses fiber Bragg gratings, which overcomes the depletion effects associated with long uniform gratings operating in the weak-grating limit (Born approximation). Our approach requires a simple linear reflection of the original input pulse to be shaped from a suitable apodized linearly chirped fiber Bragg grating and is based on the fact that, under certain conditions, the spectral and temporal reflection impulse responses of the grating are scaled versions of its corresponding apodization profile. Temporal waveforms in the picosecond/nanosecond regime can be accurately synthesized with this approach.

© 2002 Optical Society of America

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  3. F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, and P. Tournois, “Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping,” Opt. Lett. 25, 575–577 (2000).
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    [CrossRef]
  6. S. Longhi, M. Marano, P. Laporta, and V. Pruneri, “Multiplication and reshaping of high-repetition-rate optical pulse trains using highly dispersive fiber Bragg gratings,” IEEE Photon. Technol. Lett. 12, 1498–1500 (2000).
    [CrossRef]
  7. M. Marano, S. Longhi, P. Laporta, M. Belmonte, and B. Agogliati, “All-optical square-pulse generation and multiplication at 1.5 μm by use of a novel class of fiber Bragg gratings,” Opt. Lett. 26, 1615–1617 (2001).
    [CrossRef]
  8. 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]
  9. G. Curatu, S. LaRochelle, C. Pare, and P.-A. Belanger, “Antisymmetric pulse generation using phase-shifted fibre Bragg grating,” Electron Lett. 38, 307–309 (2002).
    [CrossRef]
  10. J. Desbois, F. Gires, and P. Tournois, “A new approach to picosecond laser pulse analysis, shaping and coding,” IEEE J. Quantum Electron. QE-9, 213–218 (1973).
    [CrossRef]
  11. J. Agostinelli, G. Harvey, T. Stone, and C. Gabel, “Optical pulse shaping with a grating pair,” Appl. Opt. 18, 2500–2504 (1979).
    [CrossRef] [PubMed]
  12. X. Ribeyre, C. Rouyer, F. Raoult, D. Husson, C. Sauteret, and A. Migus, “All-optical programmable shaping of narrow-band nanosecond pulses with picosecond accuracy by use of adapted chirps and quadratic nonlinearities,” Opt. Lett. 26, 1173–1175 (2001).
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  14. R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of non uniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
    [CrossRef]
  15. L. Poladian, “Simple grating synthesis algorithm,” Opt. Lett. 25, 787–789 (2000).
    [CrossRef]
  16. J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36, 517–527 (2000).
    [CrossRef]
  17. J. Azaña, L. R. Chen, M. A. Muriel, and P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fiber Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
    [CrossRef]
  18. P. C. Chou, H. A. Haus, and J. F. Brennan III, “Reconfigurable time-domain spectral shaping of an optical pulse stretched by a fiber Bragg grating,” Opt. Lett. 25, 524–526 (2000).
    [CrossRef]
  19. H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
    [CrossRef]
  20. L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, “Ultrashort pulse reflection from fiber gratings: a numerical investigation,” J. Lightwave Technol. 15, 1503–1512 (1997).
    [CrossRef]
  21. L. R. Chen, J. E. Sipe, S. D. Benjamin, H. Jung, and P. W. E. Smith, “Dynamics of ultrashort pulse propagation in fiber gratings,” Opt. Express 1, 242–249 (1997).
    [CrossRef] [PubMed]
  22. 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 gratings,” IEEE Photon. Technol. Lett. 14, 203–205 (2002).
    [CrossRef]
  23. R. Kashyap, “Design of step-chirped fibre Bragg gratings,” Opt. Commun. 136, 461–469 (1997).
    [CrossRef]
  24. F. Oullette, J.-F. Cliché, and S. Gagnon, “All-fiber devices for chromatic dispersion compensation on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
    [CrossRef]
  25. L. R. Chen, P. W. E. Smith, and C. Martijn de Sterke, “Wavelength-encoding/time-spreading optical code division multiple access system with in-fiber chirped Moiré gratings,” Appl. Opt. 38, 4500–4508 (1999).
    [CrossRef]
  26. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
    [CrossRef]
  27. B. Malo, S. Theriault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodised infibre Bragg grating reflectors photoimprimed using a phase-mask,” Electron. Lett. 31, 223–225 (1995).
    [CrossRef]
  28. M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with a uniform phase mask,” Electron. Lett. 31, 92–94 (1995).
    [CrossRef]
  29. K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778 (1998).
    [CrossRef]
  30. K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, and M. Durkin, “Effects of nonideal group delay and reflection characteristics of fiber grating dispersion compensators,” in 23rd European Conference on Optical Communications, IEE Conf. Publ. (London) 448(2), 45–48 (1997).
  31. L. Cohen, “Time-frequency distributions—A review,” IEEE Trans. Acoust., Speech, Signal Process. 77, 941 (1989).

2002 (2)

G. Curatu, S. LaRochelle, C. Pare, and P.-A. Belanger, “Antisymmetric pulse generation using phase-shifted fibre Bragg grating,” Electron Lett. 38, 307–309 (2002).
[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 gratings,” IEEE Photon. Technol. Lett. 14, 203–205 (2002).
[CrossRef]

2001 (3)

2000 (5)

P. C. Chou, H. A. Haus, and J. F. Brennan III, “Reconfigurable time-domain spectral shaping of an optical pulse stretched by a fiber Bragg grating,” Opt. Lett. 25, 524–526 (2000).
[CrossRef]

F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, and P. Tournois, “Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping,” Opt. Lett. 25, 575–577 (2000).
[CrossRef]

L. Poladian, “Simple grating synthesis algorithm,” Opt. Lett. 25, 787–789 (2000).
[CrossRef]

S. Longhi, M. Marano, P. Laporta, and V. Pruneri, “Multiplication and reshaping of high-repetition-rate optical pulse trains using highly dispersive fiber Bragg gratings,” IEEE Photon. Technol. Lett. 12, 1498–1500 (2000).
[CrossRef]

J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36, 517–527 (2000).
[CrossRef]

1999 (3)

J. Azaña, L. R. Chen, M. A. Muriel, and P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fiber Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[CrossRef]

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of non uniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

L. R. Chen, P. W. E. Smith, and C. Martijn de Sterke, “Wavelength-encoding/time-spreading optical code division multiple access system with in-fiber chirped Moiré gratings,” Appl. Opt. 38, 4500–4508 (1999).
[CrossRef]

1998 (1)

K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778 (1998).
[CrossRef]

1997 (6)

K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, and M. Durkin, “Effects of nonideal group delay and reflection characteristics of fiber grating dispersion compensators,” in 23rd European Conference on Optical Communications, IEE Conf. Publ. (London) 448(2), 45–48 (1997).

R. Kashyap, “Design of step-chirped fibre Bragg gratings,” Opt. Commun. 136, 461–469 (1997).
[CrossRef]

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

Ph. Emplit, M. Haeltermann, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997).
[CrossRef]

L. R. Chen, J. E. Sipe, S. D. Benjamin, H. Jung, and P. W. E. Smith, “Dynamics of ultrashort pulse propagation in fiber gratings,” Opt. Express 1, 242–249 (1997).
[CrossRef] [PubMed]

L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, “Ultrashort pulse reflection from fiber gratings: a numerical investigation,” J. Lightwave Technol. 15, 1503–1512 (1997).
[CrossRef]

1995 (2)

B. Malo, S. Theriault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodised infibre Bragg grating reflectors photoimprimed using a phase-mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with a uniform phase mask,” Electron. Lett. 31, 92–94 (1995).
[CrossRef]

1994 (2)

F. Oullette, J.-F. Cliché, and S. Gagnon, “All-fiber devices for chromatic dispersion compensation on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

1989 (1)

L. Cohen, “Time-frequency distributions—A review,” IEEE Trans. Acoust., Speech, Signal Process. 77, 941 (1989).

1988 (1)

1979 (1)

1976 (1)

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
[CrossRef]

1973 (1)

J. Desbois, F. Gires, and P. Tournois, “A new approach to picosecond laser pulse analysis, shaping and coding,” IEEE J. Quantum Electron. QE-9, 213–218 (1973).
[CrossRef]

Agogliati, B.

Agostinelli, J.

Albert, J.

B. Malo, S. Theriault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodised infibre Bragg grating reflectors photoimprimed using a phase-mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

Azaña, J.

J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36, 517–527 (2000).
[CrossRef]

J. Azaña, L. R. Chen, M. A. Muriel, and P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fiber Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[CrossRef]

Barcelos, S.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with a uniform phase mask,” Electron. Lett. 31, 92–94 (1995).
[CrossRef]

Belanger, P.-A.

G. Curatu, S. LaRochelle, C. Pare, and P.-A. Belanger, “Antisymmetric pulse generation using phase-shifted fibre Bragg grating,” Electron Lett. 38, 307–309 (2002).
[CrossRef]

Belmonte, M.

Benjamin, S. D.

L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, “Ultrashort pulse reflection from fiber gratings: a numerical investigation,” J. Lightwave Technol. 15, 1503–1512 (1997).
[CrossRef]

L. R. Chen, J. E. Sipe, S. D. Benjamin, H. Jung, and P. W. E. Smith, “Dynamics of ultrashort pulse propagation in fiber gratings,” Opt. Express 1, 242–249 (1997).
[CrossRef] [PubMed]

Bilodeau, F.

B. Malo, S. Theriault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodised infibre Bragg grating reflectors photoimprimed using a phase-mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

Brennan III, J. F.

Chen, L. R.

L. R. Chen, P. W. E. Smith, and C. Martijn de Sterke, “Wavelength-encoding/time-spreading optical code division multiple access system with in-fiber chirped Moiré gratings,” Appl. Opt. 38, 4500–4508 (1999).
[CrossRef]

J. Azaña, L. R. Chen, M. A. Muriel, and P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fiber Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[CrossRef]

L. R. Chen, J. E. Sipe, S. D. Benjamin, H. Jung, and P. W. E. Smith, “Dynamics of ultrashort pulse propagation in fiber gratings,” Opt. Express 1, 242–249 (1997).
[CrossRef] [PubMed]

L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, “Ultrashort pulse reflection from fiber gratings: a numerical investigation,” J. Lightwave Technol. 15, 1503–1512 (1997).
[CrossRef]

Cheng, Z.

Chou, P. C.

Cliché, J.-F.

F. Oullette, J.-F. Cliché, and S. Gagnon, “All-fiber devices for chromatic dispersion compensation on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

Cohen, L.

L. Cohen, “Time-frequency distributions—A review,” IEEE Trans. Acoust., Speech, Signal Process. 77, 941 (1989).

Cole, M. J.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with a uniform phase mask,” Electron. Lett. 31, 92–94 (1995).
[CrossRef]

Curatu, G.

G. Curatu, S. LaRochelle, C. Pare, and P.-A. Belanger, “Antisymmetric pulse generation using phase-shifted fibre Bragg grating,” Electron Lett. 38, 307–309 (2002).
[CrossRef]

De Lathouwer, M.

Ph. Emplit, M. Haeltermann, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997).
[CrossRef]

de Sterke, C. Martijn

Desbois, J.

J. Desbois, F. Gires, and P. Tournois, “A new approach to picosecond laser pulse analysis, shaping and coding,” IEEE J. Quantum Electron. QE-9, 213–218 (1973).
[CrossRef]

Durkin, M.

K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, and M. Durkin, “Effects of nonideal group delay and reflection characteristics of fiber grating dispersion compensators,” in 23rd European Conference on Optical Communications, IEE Conf. Publ. (London) 448(2), 45–48 (1997).

Ellis, A. D.

Emplit, Ph.

Ph. Emplit, M. Haeltermann, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997).
[CrossRef]

Ennser, K.

K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778 (1998).
[CrossRef]

K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, and M. Durkin, “Effects of nonideal group delay and reflection characteristics of fiber grating dispersion compensators,” in 23rd European Conference on Optical Communications, IEE Conf. Publ. (London) 448(2), 45–48 (1997).

Feced, R.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of non uniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

Gabel, C.

Gagnon, S.

F. Oullette, J.-F. Cliché, and S. Gagnon, “All-fiber devices for chromatic dispersion compensation on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

Gires, F.

J. Desbois, F. Gires, and P. Tournois, “A new approach to picosecond laser pulse analysis, shaping and coding,” IEEE J. Quantum Electron. QE-9, 213–218 (1973).
[CrossRef]

Haeltermann, M.

Ph. Emplit, M. Haeltermann, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997).
[CrossRef]

Harvey, G.

Haus, H. A.

Heritage, J. P.

Hill, K. O.

B. Malo, S. Theriault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodised infibre Bragg grating reflectors photoimprimed using a phase-mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

Husson, D.

Ibsen, M.

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 gratings,” IEEE Photon. Technol. Lett. 14, 203–205 (2002).
[CrossRef]

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]

K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, and M. Durkin, “Effects of nonideal group delay and reflection characteristics of fiber grating dispersion compensators,” in 23rd European Conference on Optical Communications, IEE Conf. Publ. (London) 448(2), 45–48 (1997).

Inoue, Y.

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

Johnson, D. C.

B. Malo, S. Theriault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodised infibre Bragg grating reflectors photoimprimed using a phase-mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

Jung, H.

Kashyap, R.

R. Kashyap, “Design of step-chirped fibre Bragg gratings,” Opt. Commun. 136, 461–469 (1997).
[CrossRef]

Ph. Emplit, M. Haeltermann, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997).
[CrossRef]

Kirschner, E. M.

Kogelnik, H.

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
[CrossRef]

Kolner, B. H.

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

Kurokawa, T.

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

Laming, R. I.

K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34, 770–778 (1998).
[CrossRef]

K. Ennser, R. I. Laming, M. N. Zervas, M. Ibsen, and M. Durkin, “Effects of nonideal group delay and reflection characteristics of fiber grating dispersion compensators,” in 23rd European Conference on Optical Communications, IEE Conf. Publ. (London) 448(2), 45–48 (1997).

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with a uniform phase mask,” Electron. Lett. 31, 92–94 (1995).
[CrossRef]

Laporta, P.

M. Marano, S. Longhi, P. Laporta, M. Belmonte, and B. Agogliati, “All-optical square-pulse generation and multiplication at 1.5 μm by use of a novel class of fiber Bragg gratings,” Opt. Lett. 26, 1615–1617 (2001).
[CrossRef]

S. Longhi, M. Marano, P. Laporta, and V. Pruneri, “Multiplication and reshaping of high-repetition-rate optical pulse trains using highly dispersive fiber Bragg gratings,” IEEE Photon. Technol. Lett. 12, 1498–1500 (2000).
[CrossRef]

LaRochelle, S.

G. Curatu, S. LaRochelle, C. Pare, and P.-A. Belanger, “Antisymmetric pulse generation using phase-shifted fibre Bragg grating,” Electron Lett. 38, 307–309 (2002).
[CrossRef]

Laude, V.

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 gratings,” IEEE Photon. Technol. Lett. 14, 203–205 (2002).
[CrossRef]

Loh, W. H.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with a uniform phase mask,” Electron. Lett. 31, 92–94 (1995).
[CrossRef]

Longhi, S.

M. Marano, S. Longhi, P. Laporta, M. Belmonte, and B. Agogliati, “All-optical square-pulse generation and multiplication at 1.5 μm by use of a novel class of fiber Bragg gratings,” Opt. Lett. 26, 1615–1617 (2001).
[CrossRef]

S. Longhi, M. Marano, P. Laporta, and V. Pruneri, “Multiplication and reshaping of high-repetition-rate optical pulse trains using highly dispersive fiber Bragg gratings,” IEEE Photon. Technol. Lett. 12, 1498–1500 (2000).
[CrossRef]

Malo, B.

B. Malo, S. Theriault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodised infibre Bragg grating reflectors photoimprimed using a phase-mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

Marano, M.

M. Marano, S. Longhi, P. Laporta, M. Belmonte, and B. Agogliati, “All-optical square-pulse generation and multiplication at 1.5 μm by use of a novel class of fiber Bragg gratings,” Opt. Lett. 26, 1615–1617 (2001).
[CrossRef]

S. Longhi, M. Marano, P. Laporta, and V. Pruneri, “Multiplication and reshaping of high-repetition-rate optical pulse trains using highly dispersive fiber Bragg gratings,” IEEE Photon. Technol. Lett. 12, 1498–1500 (2000).
[CrossRef]

Migus, A.

Muriel, M. A.

J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36, 517–527 (2000).
[CrossRef]

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of non uniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

J. Azaña, L. R. Chen, M. A. Muriel, and P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fiber Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[CrossRef]

Naganuma, K.

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

Okamoto, K.

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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 gratings,” IEEE Photon. Technol. Lett. 14, 203–205 (2002).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Computed temporal and spectral responses of the weak uniform FBG designed to synthesize a sequence of four different square optical pulses (by operating in the weak-grating limit): (a) Amplitude envelope of the temporal reflection impulse response (solid curve) and target waveform (apodization profile scaled in time, dashed curve). Closer inspections of the third and fourth pulses of the sequence are shown at the right. The inset shows the apodization profile of the FBG. (b) Top plot: reflectivity. Bottom plot: reflection group-delay response.

Fig. 2
Fig. 2

Computed temporal and spectral responses of the two weak uniform FBGs designed to synthesize a sequence of two symmetric-triangular pulses (by operating in the weak-grating limit): (a) Amplitude envelope of the respective temporal reflection impulse response (dashed curve for the weaker grating and dotted curve for the stronger grating) and target waveform (apodization profile scaled in time, solid curve). The inset shows the apodization profile of the FBG. (b) Top plot: reflectivity. Bottom plot: reflection group-delay response.

Fig. 3
Fig. 3

Computed spectral and temporal responses of the two apodized linearly chirped FBGs designed to synthesize a sequence of two symmetric-triangular pulses (by space-to-frequency-to-time mapping): (a) Top plot, reflectivity; bottom plot, reflection group-delay response; the inset shows the corresponding apodization profiles (dotted curve for the direct-law apodization and dashed curve for the arctanh law apodization). (b) Amplitude envelope of the respective temporal reflection impulse responses (dotted and dashed curves for the direct law and arctanh law, respectively) and target waveform (solid curve). The inset shows a closer look of the temporal waveforms, centered in the part of the pulses where deviations between synthesized waveforms and target one are larger.

Fig. 4
Fig. 4

Computed input and output signals from the arctanh law apodized linearly chirped FBG for an input Gaussian pulse with a duration of 5-ps FWHM. (a) Incident signal upon the grating: the plot at the bottom shows the signal in the temporal domain; the plot at the left shows the signal in the frequency domain; the larger image shows the joint time–frequency representation of the signal. (b) Reflected signal from the grating, with the same definitions as for (a). Dashed curve in the bottom plot represents the target temporal waveform.

Fig. 5
Fig. 5

Computed reflected signal from the weak uniform FBG in Fig. 2 (designed to synthesize a triangular pulse sequence by operation in the weak-grating limit) for an input Gaussian pulse with a duration of 5-ps FWHM: same definitions as for Fig. 4(a). The dashed curve in the bottom plot represents the target temporal waveform.

Equations (18)

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n(z)=nav(z)+Δnmax A(z)cos2πΛ0z+φ(z),0zL,
A(z)exp[jφ(z)]h̑rt=2c 0znav(z)dz,
h̑r(t){A(z)exp[jφ(z)]}z=c/(2nav)t
ν(z)=2navcΦ¨νz+ν0,
|Hr(ν)|Az=cΦ¨ν2nav ν,
h̑r(t)=h¯r(t) * ϕr(t)=-+dth¯r(t)ϕr(t-t).
ϕr(t)=J-1{exp[jΦr(ν)]}expj(π/Φ¨ν)t2.
h̑r(t)Δt1dth¯r(t)expj πΦ¨ν(t-t)2=expj πΦ¨νt2Δt1dth¯r(t)×expj πΦ¨νt2exp-j 2πΦ¨νtt,
|Φ¨ν|Δt124,
h̑r(t)expj πΦ¨νt2Δt1dth¯r(t)exp-j 2πΦ¨νtt=expj πΦ¨νt2Hrν=tΦ¨ν,
h̑r(t)expj πΦ¨νt2Az=c2navt,
|Hr(ν=ν0)|peak=tanh(κL),
|Hr(ν)|tanhmAz=cΦ¨ν2nav ν,
h̑r(t)expj πΦ¨νt2tanhmAz=c2navt.
A(z)arctanhh̑rt=2navcz,
|Φ¨ν|K24Δνr2,
ΔνrK24Δtout.
ΔtminK24Δνinput.

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