Abstract

We investigated the power-frequency bistability of a grating external cavity laser diode (ECLD), which operates in the strong feedback regime, by studying the threshold carrier density and related refractive index. The frequency width of the hysteresis loop has been expressed in an explicit analytical form in terms of the linewidth enhancement factor, and the reflectivities of the external grating reflector as well as the diode facet that faces it.

© 1999 Optical Society of America

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References

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  1. P. Zorabedian, W. R. Trutna, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum. Electron. 23, 1855–1860 (1987).
    [CrossRef]
  2. J. Binder, G. D. Cormack, A. Somani, “Intermodal tuning characteristics of an InGaAsP laser with feedback from an external-grating reflector,” IEEE. J. Quantum Electron. 26, 1191–1199 (1990).
    [CrossRef]
  3. C. Yan, X. Wang, J. G. McInerey, “Multistability in grating-tuned external-cavity semiconductor lasers,” IEEE. J. Quantum Electron. 32, 813–821 (1996).
    [CrossRef]
  4. 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. 23, 1875–1889 (1997).
    [CrossRef]
  5. H. Sun, R. Ries, D. D. Liu, “Stability analysis for a grating-tuned strong-external-feedback semiconductor lasers,” Appl. Opt. 31, 4161–4164 (1992).
    [CrossRef] [PubMed]
  6. P. Zorabedian, “Axial-mode instability in tunable external-cavity semiconductor lasers,” IEEE. J. Quantum Electron. 30, 1542–1552 (1994).
    [CrossRef]
  7. X. Zhou, J. Chen, Y. Lu, “Analytical characterization of grating-tuned external-cavity semiconductor lasers,” Appl. Opt. 36, 4138–4141 (1997).
    [CrossRef] [PubMed]

1997 (2)

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. 23, 1875–1889 (1997).
[CrossRef]

X. Zhou, J. Chen, Y. Lu, “Analytical characterization of grating-tuned external-cavity semiconductor lasers,” Appl. Opt. 36, 4138–4141 (1997).
[CrossRef] [PubMed]

1996 (1)

C. Yan, X. Wang, J. G. McInerey, “Multistability in grating-tuned external-cavity semiconductor lasers,” IEEE. J. Quantum Electron. 32, 813–821 (1996).
[CrossRef]

1994 (1)

P. Zorabedian, “Axial-mode instability in tunable external-cavity semiconductor lasers,” IEEE. J. Quantum Electron. 30, 1542–1552 (1994).
[CrossRef]

1992 (1)

1990 (1)

J. Binder, G. D. Cormack, A. Somani, “Intermodal tuning characteristics of an InGaAsP laser with feedback from an external-grating reflector,” IEEE. J. Quantum Electron. 26, 1191–1199 (1990).
[CrossRef]

1987 (1)

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

Binder, J.

J. Binder, G. D. Cormack, A. Somani, “Intermodal tuning characteristics of an InGaAsP laser with feedback from an external-grating reflector,” IEEE. J. Quantum Electron. 26, 1191–1199 (1990).
[CrossRef]

Chen, J.

Cormack, G. D.

J. Binder, G. D. Cormack, A. Somani, “Intermodal tuning characteristics of an InGaAsP laser with feedback from an external-grating reflector,” IEEE. J. Quantum Electron. 26, 1191–1199 (1990).
[CrossRef]

Cutler, L. S.

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

Liu, D. D.

Lu, Y.

McInerey, J. G.

C. Yan, X. Wang, J. G. McInerey, “Multistability in grating-tuned external-cavity semiconductor lasers,” IEEE. J. Quantum Electron. 32, 813–821 (1996).
[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. 23, 1875–1889 (1997).
[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. 23, 1875–1889 (1997).
[CrossRef]

Ries, R.

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. 23, 1875–1889 (1997).
[CrossRef]

Somani, A.

J. Binder, G. D. Cormack, A. Somani, “Intermodal tuning characteristics of an InGaAsP laser with feedback from an external-grating reflector,” IEEE. J. Quantum Electron. 26, 1191–1199 (1990).
[CrossRef]

Sun, H.

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. 23, 1875–1889 (1997).
[CrossRef]

Trutna, W. R.

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

Wang, X.

C. Yan, X. Wang, J. G. McInerey, “Multistability in grating-tuned external-cavity semiconductor lasers,” IEEE. J. Quantum Electron. 32, 813–821 (1996).
[CrossRef]

Yan, C.

C. Yan, X. Wang, J. G. McInerey, “Multistability in grating-tuned external-cavity semiconductor lasers,” IEEE. J. Quantum Electron. 32, 813–821 (1996).
[CrossRef]

Zhou, X.

Zorabedian, P.

P. Zorabedian, “Axial-mode instability in tunable external-cavity semiconductor lasers,” IEEE. J. Quantum Electron. 30, 1542–1552 (1994).
[CrossRef]

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

Appl. Opt. (2)

IEEE J. Quantum. Electron. (1)

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

IEEE. J. Quantum Electron. (4)

J. Binder, G. D. Cormack, A. Somani, “Intermodal tuning characteristics of an InGaAsP laser with feedback from an external-grating reflector,” IEEE. J. Quantum Electron. 26, 1191–1199 (1990).
[CrossRef]

C. Yan, X. Wang, J. G. McInerey, “Multistability in grating-tuned external-cavity semiconductor lasers,” IEEE. J. Quantum Electron. 32, 813–821 (1996).
[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. 23, 1875–1889 (1997).
[CrossRef]

P. Zorabedian, “Axial-mode instability in tunable external-cavity semiconductor lasers,” IEEE. J. Quantum Electron. 30, 1542–1552 (1994).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

N - ν (carrier density-frequency) hysteresis loop of an ECLD calculated for (a) H = 1 and (b) H = 1.1.

Fig. 2
Fig. 2

Dependence of normalized loop width of the bistable ECLD on parameter H for α = 4, 5, 6, and 7.

Equations (33)

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1-rr1 exp-iρ-rr2F exp-iη+ r1r2F exp-iρ + η=0,
ρ=4πL1/cν, η=4πnNL2/cν,
Fν=expgνL2,
gν=aΓN/Hν-N0-γ,
Hν=1+ν-ν02/Q2.
Nν=HνN0+γ+lnFν/L2/aΓ,
Fν=R1-R12 cos2 η+R1-R1-RR11/2- r1-R1cos η/r2R1-R.
Iν=eVANν+BN2ν+CN3ν,
Nmin=N0+ln1+rr1/r2/r1+r/L2+γ/aΓ,
Nmax=N0+ln1-rr1/r2/r1-r/L2+γ/aΓ.
rr2 expaΓNt-N0-γL2=1.
nN=n1-hN-Nf,
Nf=HνNmax+Nmin/2.
m=2nL2νm/c.
η=δm-2mπhN-Nf-π/2,
δm=2πν-νm+Δν/4/Δν.
K sinδm-b1N-Nf=sin hb2N-Nf,
K=r1-R1/1-RR1R1-R1/2,
b1=2mπh, b2=aΓL2/H.
ν=νm+j+1/4Δν+ΔνΦ+b1N-Nf/2π
ν=νm+j+3/4Δν-ΔνΦ-b1N-Nf/2π,
Φ=arcsinsinhb2N-Nf/K.
-Kb1 cosδm-b1NA,C-Nf=b2 coshb2NA,C-Nf.
NA,C=lnS±S2-11/2/2b2+Nf,
νA,C=νm+3Δν/4±lnK2+11/2+K2-q21/2/1+q21/2Δν/2πq arcsinK2-q21/2/K1+q21/2Δν/2π,
S=2K2+1/1+q2-1,
q=b2/b1=1/αH.
d2ν/dN2=-Δνb1b12+b22/2πb2 × tanhb2NA,C-Nf.
δν1=lnK2+11/2+K2-q21/2/1+q21/2/πq-arcsinK2-q21/2/K1+q21/2/π.
αH1-RR1R1-R1/2/r1-R1.
2πνa-vm+Δν/4/Δν=π-arcsinsinhb2Nt-Nf/K+b1Nt-Nf.
δν2=b1Nt-NC/2π-arcsinsinhb2Nt-Nf/K/2π+arcsinsinhb2NC-Nf/K2π.
νm=νm+b1Nt-NfΔν/2π.

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