Abstract

An improved expression for the time-bandwidth product (ΔtΔf) of picosecond optical pulses from gain-switched semiconductor lasers was obtained by a series of numerical simulations based on rate equations without making any assumption for a particular pulse shape and chirp condition. The relation can be expressed by ΔtΔf=0.311+(1.64α)2 as a function of the linewidth-enhancement factor α. The influence of the spontaneous emission factor β on the relation is also examined.

© 1994 Optical Society of America

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  1. C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
    [CrossRef]
  2. M. Osinski, D. F. G. Gallagher, I. H. White, Electron. Lett. 21, 981 (1985).
    [CrossRef]
  3. P. Andersson, T. Andersson, J. Lightwave Technol. LT-4, 795 (1986).
    [CrossRef]
  4. M. Osinski, J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987).
    [CrossRef]
  5. H. F. Liu, Y. Ogawa, S. Oshiba, T. Nonaka, IEEE J. Quantum Electron. 27, 1655 (1991).
    [CrossRef]
  6. B. Tromborg, J. Mørk, IEEE J. Quantum Electron. 26, 642 (1990).
    [CrossRef]
  7. B. W. Hakki, J. Appl. Phys. 51, 68 (1980).
    [CrossRef]
  8. A. Takada, T. Sugie, M Saruwatari, J. Lightwave Technol. LT-5, 1525 (1987).
    [CrossRef]
  9. M. Osinski, M. J. Adams, Electron. Lett. 20, 525 (1984).
    [CrossRef]
  10. J. E. Carroll, I. H. White, D. F. G. Gallagher, Proc. Inst. Electr. Eng. 133, 279 (1986).
  11. R. Olshansky, P. Hill, V. Lanzisera, W. Powazinik, IEEE J. Quantum Electron. QE-231410 (1987).
    [CrossRef]
  12. Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
    [CrossRef]

1991 (1)

H. F. Liu, Y. Ogawa, S. Oshiba, T. Nonaka, IEEE J. Quantum Electron. 27, 1655 (1991).
[CrossRef]

1990 (1)

B. Tromborg, J. Mørk, IEEE J. Quantum Electron. 26, 642 (1990).
[CrossRef]

1987 (3)

A. Takada, T. Sugie, M Saruwatari, J. Lightwave Technol. LT-5, 1525 (1987).
[CrossRef]

M. Osinski, J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987).
[CrossRef]

R. Olshansky, P. Hill, V. Lanzisera, W. Powazinik, IEEE J. Quantum Electron. QE-231410 (1987).
[CrossRef]

1986 (2)

J. E. Carroll, I. H. White, D. F. G. Gallagher, Proc. Inst. Electr. Eng. 133, 279 (1986).

P. Andersson, T. Andersson, J. Lightwave Technol. LT-4, 795 (1986).
[CrossRef]

1985 (1)

M. Osinski, D. F. G. Gallagher, I. H. White, Electron. Lett. 21, 981 (1985).
[CrossRef]

1984 (1)

M. Osinski, M. J. Adams, Electron. Lett. 20, 525 (1984).
[CrossRef]

1983 (1)

C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
[CrossRef]

1980 (1)

B. W. Hakki, J. Appl. Phys. 51, 68 (1980).
[CrossRef]

1977 (1)

Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
[CrossRef]

Adams, M. J.

M. Osinski, M. J. Adams, Electron. Lett. 20, 525 (1984).
[CrossRef]

Akiba, S.

Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
[CrossRef]

Andersson, P.

P. Andersson, T. Andersson, J. Lightwave Technol. LT-4, 795 (1986).
[CrossRef]

Andersson, T.

P. Andersson, T. Andersson, J. Lightwave Technol. LT-4, 795 (1986).
[CrossRef]

Burrus, C. A.

C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
[CrossRef]

Buus, J.

M. Osinski, J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987).
[CrossRef]

Carroll, J. E.

J. E. Carroll, I. H. White, D. F. G. Gallagher, Proc. Inst. Electr. Eng. 133, 279 (1986).

Gallagher, D. F. G.

J. E. Carroll, I. H. White, D. F. G. Gallagher, Proc. Inst. Electr. Eng. 133, 279 (1986).

M. Osinski, D. F. G. Gallagher, I. H. White, Electron. Lett. 21, 981 (1985).
[CrossRef]

Hakki, B. W.

B. W. Hakki, J. Appl. Phys. 51, 68 (1980).
[CrossRef]

Hill, P.

R. Olshansky, P. Hill, V. Lanzisera, W. Powazinik, IEEE J. Quantum Electron. QE-231410 (1987).
[CrossRef]

Hong, T.

Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
[CrossRef]

Lanzisera, V.

R. Olshansky, P. Hill, V. Lanzisera, W. Powazinik, IEEE J. Quantum Electron. QE-231410 (1987).
[CrossRef]

Lee, T. P.

C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
[CrossRef]

Lin, C.

C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
[CrossRef]

Liu, H. F.

H. F. Liu, Y. Ogawa, S. Oshiba, T. Nonaka, IEEE J. Quantum Electron. 27, 1655 (1991).
[CrossRef]

Mørk, J.

B. Tromborg, J. Mørk, IEEE J. Quantum Electron. 26, 642 (1990).
[CrossRef]

Nonaka, T.

H. F. Liu, Y. Ogawa, S. Oshiba, T. Nonaka, IEEE J. Quantum Electron. 27, 1655 (1991).
[CrossRef]

Ogawa, Y.

H. F. Liu, Y. Ogawa, S. Oshiba, T. Nonaka, IEEE J. Quantum Electron. 27, 1655 (1991).
[CrossRef]

Olshansky, R.

R. Olshansky, P. Hill, V. Lanzisera, W. Powazinik, IEEE J. Quantum Electron. QE-231410 (1987).
[CrossRef]

Oshiba, S.

H. F. Liu, Y. Ogawa, S. Oshiba, T. Nonaka, IEEE J. Quantum Electron. 27, 1655 (1991).
[CrossRef]

Osinski, M.

M. Osinski, J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987).
[CrossRef]

M. Osinski, D. F. G. Gallagher, I. H. White, Electron. Lett. 21, 981 (1985).
[CrossRef]

M. Osinski, M. J. Adams, Electron. Lett. 20, 525 (1984).
[CrossRef]

Powazinik, W.

R. Olshansky, P. Hill, V. Lanzisera, W. Powazinik, IEEE J. Quantum Electron. QE-231410 (1987).
[CrossRef]

Saruwatari, M

A. Takada, T. Sugie, M Saruwatari, J. Lightwave Technol. LT-5, 1525 (1987).
[CrossRef]

Suematsu, Y.

Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
[CrossRef]

Sugie, T.

A. Takada, T. Sugie, M Saruwatari, J. Lightwave Technol. LT-5, 1525 (1987).
[CrossRef]

Takada, A.

A. Takada, T. Sugie, M Saruwatari, J. Lightwave Technol. LT-5, 1525 (1987).
[CrossRef]

Tromborg, B.

B. Tromborg, J. Mørk, IEEE J. Quantum Electron. 26, 642 (1990).
[CrossRef]

White, I. H.

J. E. Carroll, I. H. White, D. F. G. Gallagher, Proc. Inst. Electr. Eng. 133, 279 (1986).

M. Osinski, D. F. G. Gallagher, I. H. White, Electron. Lett. 21, 981 (1985).
[CrossRef]

Appl. Phys. Lett. (1)

C. Lin, T. P. Lee, C. A. Burrus, Appl. Phys. Lett. 42, 141 (1983).
[CrossRef]

Electron. Lett. (2)

M. Osinski, D. F. G. Gallagher, I. H. White, Electron. Lett. 21, 981 (1985).
[CrossRef]

M. Osinski, M. J. Adams, Electron. Lett. 20, 525 (1984).
[CrossRef]

IEEE J. Quantum Electron. (5)

M. Osinski, J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987).
[CrossRef]

H. F. Liu, Y. Ogawa, S. Oshiba, T. Nonaka, IEEE J. Quantum Electron. 27, 1655 (1991).
[CrossRef]

B. Tromborg, J. Mørk, IEEE J. Quantum Electron. 26, 642 (1990).
[CrossRef]

R. Olshansky, P. Hill, V. Lanzisera, W. Powazinik, IEEE J. Quantum Electron. QE-231410 (1987).
[CrossRef]

Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
[CrossRef]

J. Appl. Phys. (1)

B. W. Hakki, J. Appl. Phys. 51, 68 (1980).
[CrossRef]

J. Lightwave Technol. (2)

A. Takada, T. Sugie, M Saruwatari, J. Lightwave Technol. LT-5, 1525 (1987).
[CrossRef]

P. Andersson, T. Andersson, J. Lightwave Technol. LT-4, 795 (1986).
[CrossRef]

Proc. Inst. Electr. Eng. (1)

J. E. Carroll, I. H. White, D. F. G. Gallagher, Proc. Inst. Electr. Eng. 133, 279 (1986).

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Figures (5)

Fig. 1
Fig. 1

Simulated power spectra of the pulses (Δt = 29 ps for all cases) from gain-switched semiconductor lasers: (a) α = 0, (b) α = 3, (c) α = 6. Jdc = l.0Ith, Jrf = 2.0Ith, fm = 1 GHz; ΔF is the frequency deviation from the center oscillation frequency (ω0/2π).

Fig. 2
Fig. 2

Simulated pulse waveform and accompanying instantaneous frequency deviation Δfi. The parameter values are the same as in Fig. 1(c).

Fig. 3
Fig. 3

Time–bandwidth product versus the α parameter

Fig. 4
Fig. 4

Example of the power spectrum of a pulse (Δt = 17 ps) from a gain-switched semiconductor laser for a large modulation-amplitude case. The parameter values from Eqs. (1)(3) are α = 6, Jdc = 0, Jrf = 4.8Ith, and fm = 1 GHz. The spectrum is distorted asymmetrically. The width indicated by the arrows is the FWHM. It is understood that the FWHM is inadequate to use for evaluating the bandwidth Δf for the large modulation-amplitude case.

Fig. 5
Fig. 5

Time-bandwidth product versus the α parameter when the β value is changed from 10−6 to 10−2 by steps.

Equations (3)

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d E d t = 1 2 ( 1 + i α ) [ G ( N - N 0 ) - 1 τ p + β T 1 N S ] E ,
d N d t = J - 1 T 1 N - G ( N - N 0 ) S ,
J = J dc + J rf sin 2 π f m t ,

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