Abstract

The noise spectra and frequency chirping of semiconductor lasers in the presence of arbitrary amounts of optical feedback are analyzed. Short external cavities with strong optical feedback are found to reduce the noise dramatically in semiconductor lasers, especially in the high-frequency regime. Frequency chirping is shown to be closely related to the nonlinear gain effect.

© 1989 Optical Society of America

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References

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  1. P. Spano, S. Piazzolla, M. Tamburrini, IEEE J. Quantum Electron. QE-20, 350 (1984).
    [CrossRef]
  2. A. R. Chraplyvy et al., Electron. Lett. 22, 88 (1986).
    [CrossRef]
  3. R. Hui, S. Tao, in Proceedings of IEEE International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper K-5.
  4. R. W. Tkach, A. R. Chraplyvy, IEEE J. Lightwave Technol. LT-4, 1655 (1986).
    [CrossRef]
  5. D. A. Hjelme, A. Mickelson, IEEE J. Quantum Electron. QE-23, 1000 (1987).
    [CrossRef]
  6. C. H. Henry, R. F. Kazarinov, IEEE J. Quantum Electron. QE-22, 294 (1986).
    [CrossRef]
  7. R. Hui, S. Tao, “Improved rate equations for external cavity semiconductor lasers,” IEEE J. Quantum Electron. (to be published).

1987 (1)

D. A. Hjelme, A. Mickelson, IEEE J. Quantum Electron. QE-23, 1000 (1987).
[CrossRef]

1986 (3)

C. H. Henry, R. F. Kazarinov, IEEE J. Quantum Electron. QE-22, 294 (1986).
[CrossRef]

A. R. Chraplyvy et al., Electron. Lett. 22, 88 (1986).
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, IEEE J. Lightwave Technol. LT-4, 1655 (1986).
[CrossRef]

1984 (1)

P. Spano, S. Piazzolla, M. Tamburrini, IEEE J. Quantum Electron. QE-20, 350 (1984).
[CrossRef]

Chraplyvy, A. R.

A. R. Chraplyvy et al., Electron. Lett. 22, 88 (1986).
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, IEEE J. Lightwave Technol. LT-4, 1655 (1986).
[CrossRef]

Henry, C. H.

C. H. Henry, R. F. Kazarinov, IEEE J. Quantum Electron. QE-22, 294 (1986).
[CrossRef]

Hjelme, D. A.

D. A. Hjelme, A. Mickelson, IEEE J. Quantum Electron. QE-23, 1000 (1987).
[CrossRef]

Hui, R.

R. Hui, S. Tao, in Proceedings of IEEE International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper K-5.

R. Hui, S. Tao, “Improved rate equations for external cavity semiconductor lasers,” IEEE J. Quantum Electron. (to be published).

Kazarinov, R. F.

C. H. Henry, R. F. Kazarinov, IEEE J. Quantum Electron. QE-22, 294 (1986).
[CrossRef]

Mickelson, A.

D. A. Hjelme, A. Mickelson, IEEE J. Quantum Electron. QE-23, 1000 (1987).
[CrossRef]

Piazzolla, S.

P. Spano, S. Piazzolla, M. Tamburrini, IEEE J. Quantum Electron. QE-20, 350 (1984).
[CrossRef]

Spano, P.

P. Spano, S. Piazzolla, M. Tamburrini, IEEE J. Quantum Electron. QE-20, 350 (1984).
[CrossRef]

Tamburrini, M.

P. Spano, S. Piazzolla, M. Tamburrini, IEEE J. Quantum Electron. QE-20, 350 (1984).
[CrossRef]

Tao, S.

R. Hui, S. Tao, in Proceedings of IEEE International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper K-5.

R. Hui, S. Tao, “Improved rate equations for external cavity semiconductor lasers,” IEEE J. Quantum Electron. (to be published).

Tkach, R. W.

R. W. Tkach, A. R. Chraplyvy, IEEE J. Lightwave Technol. LT-4, 1655 (1986).
[CrossRef]

Electron. Lett. (1)

A. R. Chraplyvy et al., Electron. Lett. 22, 88 (1986).
[CrossRef]

IEEE J. Lightwave Technol. (1)

R. W. Tkach, A. R. Chraplyvy, IEEE J. Lightwave Technol. LT-4, 1655 (1986).
[CrossRef]

IEEE J. Quantum Electron. (3)

D. A. Hjelme, A. Mickelson, IEEE J. Quantum Electron. QE-23, 1000 (1987).
[CrossRef]

C. H. Henry, R. F. Kazarinov, IEEE J. Quantum Electron. QE-22, 294 (1986).
[CrossRef]

P. Spano, S. Piazzolla, M. Tamburrini, IEEE J. Quantum Electron. QE-20, 350 (1984).
[CrossRef]

Other (2)

R. Hui, S. Tao, in Proceedings of IEEE International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, New York, 1988), paper K-5.

R. Hui, S. Tao, “Improved rate equations for external cavity semiconductor lasers,” IEEE J. Quantum Electron. (to be published).

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Figures (3)

Fig. 1
Fig. 1

Three-mirror-cavity model for external-cavity semiconductor lasers.

Fig. 2
Fig. 2

Noise power spectrum of the external-cavity semiconductor laser for various feedback levels, with nl = 0.9 mm, n0L = 9 mm, and ϕ = 240°. (a) Phase-noise spectrum, (b) intensity-noise spectrum. Curves 1, no feedback; curves 2, weak feedback with R3 = 0.01 and r2 = 0.565; curves 3, strong feedback with R3 = 0.4 and r2 = 0.2.

Fig. 3
Fig. 3

CPR versus the feedback phase for various feedback levels, (a) nl = 0.9 mm and n0L = 9 mm; curve 1, R3 = 0.1 and r2 = 0.565; curve 2, R3 = 0.3 and r2 = 0.565; curve 3, strong feedback with R3 = 0.5 and r2 = 0.1. (b) nl = 0.9 mm and n0L = 10 cm; curve 1, R3 = 0.01 and r2 = 0.565; curve 2, R3 = 0.3 and r2 = 0.565; curve 3, strong feedback with R3 = 0.5 and r2 = 0.1.

Equations (12)

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( 1 + τ τ i H 2 ) I ˙ ( t ) = I ( t ) [ Δ G + 2 τ i H 1 2 τ τ i P 2 ϕ ˙ n ( t ) ] + R s + F I ( t ) ,
( 1 + τ τ i H 2 ) ϕ ˙ n ( t ) = ( Ω ω 0 ) + α 2 Δ G 1 τ i P 1 + τ 2 τ i I ˙ ( t ) I ( t ) P 2 + F ϕ ( t ) ,
N ˙ ( t ) = G I ( t ) N ( t ) τ e + M ( t ) e + F N ( t ) ,
H 1 = 1 2 ln [ 1 + 2 ( R 3 / r 2 ) cos ϕ + ( R 3 / r 2 ) 2 1 + 2 r 2 R 3 cos ϕ + ( r 2 R 3 ) 2 ] , P 1 = tan 1 [ R 3 ( 1 r 2 2 ) sin ϕ r 2 ( 1 + R 3 2 ) + R 3 ( 1 + r 2 2 ) cos ϕ ] , H 2 = 1 τ d P 1 d ω 0 , P 2 = 1 τ d H 1 d ω 0 , ϕ ω 0 τ .
I ( t ) = I 0 + δ I ( t ) , N ( t ) = N 0 + δ N ( t ) , M ( t ) = M 0 + m ( t ) .
G = Γ A ( N N e ) ( 1 a I ) ,
[ A 11 A 12 A 13 A 21 A 22 A 23 A 31 A 32 A 33 ] [ δ I ( i w ) ϕ n ( i w ) δ N ( i w ) ] = [ F I ( i w ) F ϕ ( i w ) F N ( i w ) + m ( i w ) / e ] ,
S I ( i w ) = R s | Y | 2 { ( 2 I 0 + 1 ) | A 22 A 33 | 2 + | A 12 A 33 | 2 / 2 I 0 + | A 12 A 33 A 13 A 22 | 2 2 Re [ A 22 A 33 ( A 12 A 23 A 13 A 22 ) * ] } ,
S ϕ ( i w ) = R s ω 2 | Y | 2 { ( 2 I 0 + 1 ) | A 23 A 31 A 21 A 33 | 2 + | A 11 A 33 A 13 A 31 | 2 / 2 I 0 + | A 13 A 21 A 11 A 23 | 2 Re [ ( A 23 A 31 A 21 A 33 ) ( A 13 A 21 A 11 A 23 ) * ] } ,
S ϕ ( 0 ) = R s 4 I 0 α 2 [ 2 I 0 + 1 + ( Γ A ) 2 + 2 I 0 ( γ + 1 ) 2 ] { ∊γ ( 1 + τ τ i H 2 ) + [ 1 + τ τ i ( H 2 α P 2 ) ] } 2 ,
CPR = δf ( iw ) / δI ( iw ) ,
CPR = i w [ α ( 1 + τ τ i H 2 ) + τ τ i P 2 ] + α ( a G 0 I 0 + R s / I 0 ) 4 π I 0 [ 1 + τ τ i ( H 2 α P 2 ) ] .

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