Abstract

An exact analytical expression for the time–bandwidth product ΔtΔf of chirped sech2 pulses is derived. The relation can be expressed by ΔtΔf = 0.1786 arcosh(cosh πα + 2) as a function of the laser’s phase–amplitude coupling factor α. An experimental measurement of the α factor that relies on this formula is discussed.

© 1995 Optical Society of America

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Errata

P. Lazaridis, G. Debarge, and P. Gallion, "Time-bandwidth product of chirped sech2 pulses: application to phase–amplitude-coupling factor measurement: addendum," Opt. Lett. 21, 164-164 (1996)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-21-2-164

References

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    [CrossRef]
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1994

1992

1991

H. F. Liu, Y. Ogawa, S. Oshiba, Appl. Phys. Lett. 59, 1284 (1991).
[CrossRef]

1987

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

1985

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

1984

T. L. Koch, J. E. Bowers, Electron. Lett. 20, 1038 (1984).
[CrossRef]

Bowers, J. E.

T. L. Koch, J. E. Bowers, Electron. Lett. 20, 1038 (1984).
[CrossRef]

Buus, J.

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

Cho, Y.

Gallagher, D. F. G.

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

Gradshteyn, I. S.

I. S. Gradshteyn, I. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), Eq. (3.985.1), p. 506.

Kawai, Y.

Koch, T. L.

T. L. Koch, J. E. Bowers, Electron. Lett. 20, 1038 (1984).
[CrossRef]

Liu, H. F.

H. F. Liu, S. Oshiba, Y. Ogawa, Y. Kawai, Opt. Lett. 17, 64 (1992).
[CrossRef] [PubMed]

H. F. Liu, Y. Ogawa, S. Oshiba, Appl. Phys. Lett. 59, 1284 (1991).
[CrossRef]

Ogawa, Y.

H. F. Liu, S. Oshiba, Y. Ogawa, Y. Kawai, Opt. Lett. 17, 64 (1992).
[CrossRef] [PubMed]

H. F. Liu, Y. Ogawa, S. Oshiba, Appl. Phys. Lett. 59, 1284 (1991).
[CrossRef]

Oshiba, S.

H. F. Liu, S. Oshiba, Y. Ogawa, Y. Kawai, Opt. Lett. 17, 64 (1992).
[CrossRef] [PubMed]

H. F. Liu, Y. Ogawa, S. Oshiba, Appl. Phys. Lett. 59, 1284 (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]

Ryzhik, I.

I. S. Gradshteyn, I. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), Eq. (3.985.1), p. 506.

Wada, K.

White, I. H.

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

Appl. Phys. Lett.

H. F. Liu, Y. Ogawa, S. Oshiba, Appl. Phys. Lett. 59, 1284 (1991).
[CrossRef]

Electron. Lett.

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

T. L. Koch, J. E. Bowers, Electron. Lett. 20, 1038 (1984).
[CrossRef]

IEEE J. Quantum Electron.

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

Opt. Lett.

Other

I. S. Gradshteyn, I. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), Eq. (3.985.1), p. 506.

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Figures (4)

Fig. 1
Fig. 1

Normalized intensity of (1) a sech2 and (2) a Gaussian pulse having the same FWHM time duration. Time is normalized relative to the FWHM.

Fig. 2
Fig. 2

Instantaneous frequency deviation for the chirped (1) sech2 and (2) Gaussian pulses versus normalized time.

Fig. 3
Fig. 3

Normalized power spectrum of the chirped (1) sech2 and (2) Gaussian pulses as a function of normalized frequency.

Fig. 4
Fig. 4

Time–bandwidth product of the chirped (1) sech2 and (2) Gaussian pulses as a function of the laser’s phase–amplitude-coupling factor.

Tables (1)

Tables Icon

Table 1 Comparison of Phase–Amplitude-Coupling Factor a Values Estimated by the Gaussian and the Soliton sech2 Approximations from ΔtΔf Measurement Data

Equations (7)

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d φ ( t ) d t = α 2 1 P d P d t ,
P ( t ) = E ( t ) 2 = sech 2 ( t / τ ) ,
Δ t = 2 arcosh ( 2 ) τ = 1.763 τ ,
E ˜ ( ω ) = FT [ sech p ( t / τ ) ] = 2 p - 1 τ Γ ( p ) Γ ( p + j ω τ 2 ) Γ ( p - j ω τ 2 ) .
E ˜ ( ω ) 2 E ˜ ( 0 ) 2 = sech [ π 2 ( ω τ + α ) ] sech [ π 2 ( ω τ - α ) ] sech 2 ( π α / 2 ) .
E ˜ ( ω ) 2 E ˜ ( 0 ) 2 = exp ( - ω 2 τ 1 2 1 + α 2 ) ,
Δ t Δ f = [ 2 arcosh ( 2 ) π 2 ] arcosh ( cosh π α + 2 ) ,

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