Abstract

We give a simple stability analysis within the scope of steady-state solution for the grating-tuned strong-external-feedback semiconductor lasers. In our model, a fluctuation in the refractive index of an active medium through the coupling of carrier density will cause another fluctuation in the refractive index. If the latter is always smaller than the former, the fluctuation will be damped, and therefore the corresponding operating point of the laser is stable. Our analysis indicates that there are various stable and unstable operating-frequency ranges for various reflectivities of the internal facet of the laser diode. In addition, it agrees well with the experimental results and explains the bistability of threshold gain versus operating frequency.

© 1992 Optical Society of America

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References

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  1. R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
    [CrossRef]
  2. Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
    [CrossRef]
  3. R. Wyatt, K. H. Cameron, M. R. Matthews, “Tunable narrow line external cavity lasers for coherent optical systems,” Br. Telecom. Technol. J. 3, 5–11 (1985).
  4. P. Glas, R. Mueller, “Bistable operating of a GaAs–AlGaAs diode laser coupled to an external resonator of narrow spectral bandwidth,” Opt. Quantum Electron. 14, 375–380 (1982).
    [CrossRef]
  5. P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 1855–1860 (1987).
    [CrossRef]
  6. H. Sun, R. Ries, “Frequency tunable external cavity semiconductor laser,” Technischer Bericht 465 TB 24 (Deutschen Bundespost, Forschungsinstitut beim FTZ, 1990).
  7. B. Tromborg, H. Olesen, X. Pan, S. Saito, “Transmission line description of optical feedback and injection locking for Fabry–Perot and DFB lasers stability,” IEEE J. Quantum Electron. QE-23, 1875–1889 (1987).
    [CrossRef]

1987 (2)

P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 1855–1860 (1987).
[CrossRef]

B. Tromborg, H. Olesen, X. Pan, S. Saito, “Transmission line description of optical feedback and injection locking for Fabry–Perot and DFB lasers stability,” IEEE J. Quantum Electron. QE-23, 1875–1889 (1987).
[CrossRef]

1985 (1)

R. Wyatt, K. H. Cameron, M. R. Matthews, “Tunable narrow line external cavity lasers for coherent optical systems,” Br. Telecom. Technol. J. 3, 5–11 (1985).

1982 (1)

P. Glas, R. Mueller, “Bistable operating of a GaAs–AlGaAs diode laser coupled to an external resonator of narrow spectral bandwidth,” Opt. Quantum Electron. 14, 375–380 (1982).
[CrossRef]

1981 (1)

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

1980 (1)

R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
[CrossRef]

Cameron, K. H.

R. Wyatt, K. H. Cameron, M. R. Matthews, “Tunable narrow line external cavity lasers for coherent optical systems,” Br. Telecom. Technol. J. 3, 5–11 (1985).

Cutler, L. S.

P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 1855–1860 (1987).
[CrossRef]

Glas, P.

P. Glas, R. Mueller, “Bistable operating of a GaAs–AlGaAs diode laser coupled to an external resonator of narrow spectral bandwidth,” Opt. Quantum Electron. 14, 375–380 (1982).
[CrossRef]

Kimura, T.

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

Kobayashi, K.

R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
[CrossRef]

Lang, R.

R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
[CrossRef]

Matthews, M. R.

R. Wyatt, K. H. Cameron, M. R. Matthews, “Tunable narrow line external cavity lasers for coherent optical systems,” Br. Telecom. Technol. J. 3, 5–11 (1985).

Mueller, R.

P. Glas, R. Mueller, “Bistable operating of a GaAs–AlGaAs diode laser coupled to an external resonator of narrow spectral bandwidth,” Opt. Quantum Electron. 14, 375–380 (1982).
[CrossRef]

Olesen, H.

B. Tromborg, H. Olesen, X. Pan, S. Saito, “Transmission line description of optical feedback and injection locking for Fabry–Perot and DFB lasers stability,” IEEE J. Quantum Electron. QE-23, 1875–1889 (1987).
[CrossRef]

Pan, X.

B. Tromborg, H. Olesen, X. Pan, S. Saito, “Transmission line description of optical feedback and injection locking for Fabry–Perot and DFB lasers stability,” IEEE J. Quantum Electron. QE-23, 1875–1889 (1987).
[CrossRef]

Ries, R.

H. Sun, R. Ries, “Frequency tunable external cavity semiconductor laser,” Technischer Bericht 465 TB 24 (Deutschen Bundespost, Forschungsinstitut beim FTZ, 1990).

Saito, S.

B. Tromborg, H. Olesen, X. Pan, S. Saito, “Transmission line description of optical feedback and injection locking for Fabry–Perot and DFB lasers stability,” IEEE J. Quantum Electron. QE-23, 1875–1889 (1987).
[CrossRef]

Sun, H.

H. Sun, R. Ries, “Frequency tunable external cavity semiconductor laser,” Technischer Bericht 465 TB 24 (Deutschen Bundespost, Forschungsinstitut beim FTZ, 1990).

Tromborg, B.

B. Tromborg, H. Olesen, X. Pan, S. Saito, “Transmission line description of optical feedback and injection locking for Fabry–Perot and DFB lasers stability,” IEEE J. Quantum Electron. QE-23, 1875–1889 (1987).
[CrossRef]

Trutna, W. R.

P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 1855–1860 (1987).
[CrossRef]

Wyatt, R.

R. Wyatt, K. H. Cameron, M. R. Matthews, “Tunable narrow line external cavity lasers for coherent optical systems,” Br. Telecom. Technol. J. 3, 5–11 (1985).

Yamamoto, Y.

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

Zorabedian, P.

P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 1855–1860 (1987).
[CrossRef]

Br. Telecom. Technol. J. (1)

R. Wyatt, K. H. Cameron, M. R. Matthews, “Tunable narrow line external cavity lasers for coherent optical systems,” Br. Telecom. Technol. J. 3, 5–11 (1985).

IEEE J. Quantum Electron. (4)

R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
[CrossRef]

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. QE-23, 1855–1860 (1987).
[CrossRef]

B. Tromborg, H. Olesen, X. Pan, S. Saito, “Transmission line description of optical feedback and injection locking for Fabry–Perot and DFB lasers stability,” IEEE J. Quantum Electron. QE-23, 1875–1889 (1987).
[CrossRef]

Opt. Quantum Electron. (1)

P. Glas, R. Mueller, “Bistable operating of a GaAs–AlGaAs diode laser coupled to an external resonator of narrow spectral bandwidth,” Opt. Quantum Electron. 14, 375–380 (1982).
[CrossRef]

Other (1)

H. Sun, R. Ries, “Frequency tunable external cavity semiconductor laser,” Technischer Bericht 465 TB 24 (Deutschen Bundespost, Forschungsinstitut beim FTZ, 1990).

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Figures (3)

Fig. 1
Fig. 1

Compound-cavity semiconductor laser scheme.

Fig. 2
Fig. 2

Threshold-gain variation as a function of operating frequency with various values of r2 and fixed values of a = −7, r1 = 0.5, and r3 = 0.5; A, 0.2; B, 0.1; C, 0.05; D, 0.03. Ranges between marks u are unstable and between marks u and s are stable.

Fig. 3
Fig. 3

Detail-solving process for threshold gain as a function of operating frequency. The intersection points of curves are solution points.

Equations (7)

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r e ( ω ) = [ r 2 + r 3 exp ( i ω t e ) ] / [ 1 + r 2 r 3 exp ( i ω t e ) ] = r e ( ω t e ) exp [ i Arg ( γ e ) ] ,
g th = - ( 1 / l d ) ln ( r 1 r e ) ,
ω - ω d = - ( 1 / t d ) Arg ( r e ) ,
n - n 0 = ( α c / 2 ω ) ( g th - g th 0 ) ,
g th = ( 1 / α l d ) [ ( ω 0 - ω ) t 0 - Arg ( r e ) ] - ( 1 / l d ) ln ( r 1 r 2 ) ,
n ( 2 ) = ( α c / 2 ω ) δ g ( 1 ) + n 0 ( 1 ) .
Δ n ( 2 ) = n ( 2 ) - n ( 0 ) = ( α c / 2 ω ) δ g ( 1 ) + n 0 ( 1 ) - n ( 0 ) = ( α c / 2 ω ) δ g ( 1 ) + n 0 ( 0 ) + Δ n ( 1 ) - n ( 0 ) = ( α c / 2 ω ) [ δ g ( 1 ) - δ g ( 0 ) ] + Δ n ( 1 ) = ( α c / 2 ω ) [ g th ( 1 ) - g th ( 0 ) ] + Δ n ( 1 ) .

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