Abstract

The effects of self-mixing interference on gain-coupled (GC) distributed-feedback (DFB) lasers are analyzed. From coupled-wave theory, the oscillation frequency and threshold gain variations are theoretically deduced. The influences on self-mixing from the coupling length coefficient, the linewidth enhancement factor of the GC DFB laser, and the reflection coefficient of the external reflector are discussed along with numerical analysis and are compared with the effects of self-mixing interference of λ/4 phase-shifted DFB lasers and Fabry-Perot (F-P) lasers. Our results show that high-accuracy self-mixing sensors can be obtained with GC DFB lasers.

© 2005 Optical Society of America

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References

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  1. G. Mourat, N. Servagent, and T. Bosch, �??Distance measurement by using the self-mixing effect in a three-electrode distributed Bragg reflector laser diode,�?? Opt. Eng. 39, 738-743 (2000).
    [CrossRef]
  2. P. A. Porta, D. P. Curtin, and J. G. McInerney, �??Laser doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers,�?? IEEE Photon Technol. Lett. 14, 1719-1721 (2002).
    [CrossRef]
  3. H. Huan and M.Wang, �??Self-mixing interference effect of DFB semiconductor lasers,�?? Appl. Phys. B 79, 325-330 (2004).
    [CrossRef]
  4. M. F. Alam, M. A. Karim, and S. Lslam, �??Dependence of external optical feedback sensitivity on structural parameters of DFB semiconductor lasers,�?? in Proceedings of the IEEE 1996 National Aerospace and Electronics Conference (NAECON 1996) (IEEE, 1996), Vol. 2, pp. 670-677.
  5. F. Favre, �??Theoretical analysis of external optical feedback on DFB,�?? IEEE J. Quantum Electron. 23, 81-88 (1987).
    [CrossRef]
  6. F. Favre, �??Sensitivity to external feedback for gain-coupled DFB semiconductor lasers,�?? Electron. Lett. 27, 433-435 (1991).
    [CrossRef]

Appl. Phys. B (1)

H. Huan and M.Wang, �??Self-mixing interference effect of DFB semiconductor lasers,�?? Appl. Phys. B 79, 325-330 (2004).
[CrossRef]

Electron. Lett. (1)

F. Favre, �??Sensitivity to external feedback for gain-coupled DFB semiconductor lasers,�?? Electron. Lett. 27, 433-435 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

F. Favre, �??Theoretical analysis of external optical feedback on DFB,�?? IEEE J. Quantum Electron. 23, 81-88 (1987).
[CrossRef]

IEEE NAECON 1996 (1)

M. F. Alam, M. A. Karim, and S. Lslam, �??Dependence of external optical feedback sensitivity on structural parameters of DFB semiconductor lasers,�?? in Proceedings of the IEEE 1996 National Aerospace and Electronics Conference (NAECON 1996) (IEEE, 1996), Vol. 2, pp. 670-677.

IEEE Photon Technol. Lett. (1)

P. A. Porta, D. P. Curtin, and J. G. McInerney, �??Laser doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers,�?? IEEE Photon Technol. Lett. 14, 1719-1721 (2002).
[CrossRef]

Opt. Eng. (1)

G. Mourat, N. Servagent, and T. Bosch, �??Distance measurement by using the self-mixing effect in a three-electrode distributed Bragg reflector laser diode,�?? Opt. Eng. 39, 738-743 (2000).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Curves showing |Cr| versus |κL|. (a) Gain-coupled DFB laser for different values of rl. (b) Gain-coupled DFB laser compared with λ/4 phase-shifted DFB laser and F-P laser.

Fig. 2.
Fig. 2.

Self-mixing interference at different |κL| values. (a) Numerical solution of the frequency. (b) Numerical solution of the output signal. (c) Output signal accompanying cosine variation of the external cavity length.

Fig. 3.
Fig. 3.

Self-mixing interference at different α m values. (a) Numerical solution of the output signal. (b) Output signal accompanying cosine variation of the external cavity length.

Fig. 4.
Fig. 4.

Self-mixing interference at different r values. (a) Numerical solution of the output signal. (b) Output signal accompany cosine variation of the external cavity length.

Fig. 5.
Fig. 5.

Self-mixing interference of gain-coupled, λ/4 phase-shifted DFB and F-P laser. (a) |κL|=0.85. (b) |κL|=0.99.

Equations (18)

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d E + d z = ( j δ + g th 2 ) E + j ( κ i + j κ g ) E - ,
d E - d z = ( j δ g th 2 ) E - + j ( κ i + j κ g ) E + ,
E + = a 1 exp ( γ z ) + a 2 exp ( γ z ) ,
E - = b 1 exp ( γ z ) + b 2 exp ( γ z ) ,
γ 2 = ( g th 2 j δ ) 2 + ( κ i + j κ g ) ( κ i + j κ g ) .
E + ( 0 ) = r 1 E ( 0 ) ,
E + ( L ) exp ( j β B L ) = r r E + ( L ) exp ( j β B L ) ,
( 1 r 1 r r ) γ L cos h ( γ L ) ( g th 2 L j δ L ) [ 1 + r 1 r r exp ( j β B L ) ] sin h ( γ L )
+ j ( κ i L + j κ g L ) [ r + r 1 r r exp ( j β B L ) ] sin h ( γ L ) = 0 .
r r = r r + ( 1 r r 2 ) r exp ( j ω τ ) .
C r = ( Δ g th 2 L j Δ δ L ) [ r · exp ( −j ω τ ) ] .
Δ δ = n c Δ ω + ω c Δ n .
Δ ω τ = τ { c n L [ j C r r · exp ( −j ω τ ) j Δ g th 2 L ] ω nL Δ n L } .
Δ ω τ = 2 n ( 1 + α m 2 ) 1 2 C r × r L ext L sin [ ω τ arg ( C r ) arg ( r ) a tan ( α m ) ] ,
Δ G = 4 n τ C r × r L ext L cos [ ω τ arg ( C r ) arg ( r ) ] ,
X = 2 n ( 1 + α m 2 ) 1 2 C r × r L ext L .
γ L coth ( γ L ) ( g th 2 L j δ L ) L + j ( κ i L + j κ g L ) r 1 = 0 .
C r = [ q L 2 + ( κ L ) 2 ] [ 2 r r q L ( κ L ) j ( 1 + r r 2 ) ] q L [ κ L ( 1 + r r 2 ) j r r ] + j 2 r r q L 2 κ L ,

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