Abstract

A theoretical analysis has been performed that explains a fringe-locking phenomenon observed in a two-beam interferometer in which a laser diode was subjected to optical feedback and modulation of its injection current. The dependence of wavelength change on the injection-current variation is calculated by use of a model of coupled resonators consisting of the laser cavity and the interferometer. The fringe phase change caused by modulation of the injection current is derived from this model and has proved to be suppressed within much less than 2π in excess of an integer multiple of 2π if the path difference of the interferometer is longer than 10  mm. The calculated phase fluctuation agrees well with those observed in experiments.

© 1999 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1998 (4)

J. Liu, I. Yamaguchi, T. Nakajima, and J. Kato, Opt. Rev. 4, 216 (1998).
[CrossRef]

J. Liu and I. Yamaguchi, Jpn. J. Appl. Phys. 37, 2610 (1998).
[CrossRef]

J. Liu and I. Yamaguchi, Jpn. J. Appl. Phys. 37, L930 (1998).
[CrossRef]

T. Yoshino and H. Yamaguchi, Opt. Lett. 23, 1576 (1998).
[CrossRef]

1997 (1)

1996 (1)

I. Yamaguchi, J. Liu, and J. Kato, Opt. Eng. 35, 2930 (1996).
[CrossRef]

1990 (1)

O. Sasaki, K. Takahashi, and T. Suzuki, Opt. Eng. 29, 1511 (1990).
[CrossRef]

1987 (1)

Frejlich, J.

Freschi, A. A.

Kato, J.

J. Liu, I. Yamaguchi, T. Nakajima, and J. Kato, Opt. Rev. 4, 216 (1998).
[CrossRef]

I. Yamaguchi, J. Liu, and J. Kato, Opt. Eng. 35, 2930 (1996).
[CrossRef]

Lee, B. S.

Liu, J.

J. Liu and I. Yamaguchi, Jpn. J. Appl. Phys. 37, 2610 (1998).
[CrossRef]

J. Liu and I. Yamaguchi, Jpn. J. Appl. Phys. 37, L930 (1998).
[CrossRef]

J. Liu, I. Yamaguchi, T. Nakajima, and J. Kato, Opt. Rev. 4, 216 (1998).
[CrossRef]

I. Yamaguchi, J. Liu, and J. Kato, Opt. Eng. 35, 2930 (1996).
[CrossRef]

Mnatzakanian, S.

Nakajima, T.

J. Liu, I. Yamaguchi, T. Nakajima, and J. Kato, Opt. Rev. 4, 216 (1998).
[CrossRef]

Nara, M.

Sasaki, O.

O. Sasaki, K. Takahashi, and T. Suzuki, Opt. Eng. 29, 1511 (1990).
[CrossRef]

Strand, T.

Suzuki, T.

O. Sasaki, K. Takahashi, and T. Suzuki, Opt. Eng. 29, 1511 (1990).
[CrossRef]

Takahashi, K.

O. Sasaki, K. Takahashi, and T. Suzuki, Opt. Eng. 29, 1511 (1990).
[CrossRef]

Yamaguchi, H.

Yamaguchi, I.

J. Liu and I. Yamaguchi, Jpn. J. Appl. Phys. 37, 2610 (1998).
[CrossRef]

J. Liu, I. Yamaguchi, T. Nakajima, and J. Kato, Opt. Rev. 4, 216 (1998).
[CrossRef]

J. Liu and I. Yamaguchi, Jpn. J. Appl. Phys. 37, L930 (1998).
[CrossRef]

I. Yamaguchi, J. Liu, and J. Kato, Opt. Eng. 35, 2930 (1996).
[CrossRef]

Yoshino, T.

Appl. Opt. (1)

Jpn. J. Appl. Phys. (2)

J. Liu and I. Yamaguchi, Jpn. J. Appl. Phys. 37, 2610 (1998).
[CrossRef]

J. Liu and I. Yamaguchi, Jpn. J. Appl. Phys. 37, L930 (1998).
[CrossRef]

Opt. Eng. (2)

I. Yamaguchi, J. Liu, and J. Kato, Opt. Eng. 35, 2930 (1996).
[CrossRef]

O. Sasaki, K. Takahashi, and T. Suzuki, Opt. Eng. 29, 1511 (1990).
[CrossRef]

Opt. Lett. (2)

Opt. Rev. (1)

J. Liu, I. Yamaguchi, T. Nakajima, and J. Kato, Opt. Rev. 4, 216 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Interference fringe patterns taken by a CCD camera during injection-current modulation of LD (a) without and (b) with optical feedback.

Fig. 2
Fig. 2

Representation of the whole system by an equivalent cavity.

Fig. 3
Fig. 3

Numerical results: (a) Dependence of wavelength on injection current and (b) enlarged view. (c) Phase in modulo 2π of injection-current calculated from (a).

Fig. 4
Fig. 4

Dependence of rms phase on OPD: (a) OPD close to 0, and (b) OPD of 300  mm.

Equations (12)

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ρegexpi2knLZk,L1,L2=1,
Zk,L1,L2=ρ0+τ0τ0ρ2ρ1exp2ikL1+τ0τ0ττρ2exp2ikL21-ρ0ρ2ρ1exp2ikL1-ρ0ττρ2exp2ikL2,
ρeZk,L1,L2cos2knL+ϕk,L1,L2>0,
Zk,L1,L2sin2knL+ϕk,L1,L2=0.
Z2=ρ02+a2+b2+2abcos2kL2-L11-2c2-2d2-2cdcos2kL2-L1,
2kL2-L1=2mπ,
2kL2-L1=2mπ+ΔΦ,
Δλ=χΔi,
λ=2nL/N,
Δλ=Δn2L/N+ΔL2n/N.
Δn=χN/2LΔi,
n=n0+χN/2LΔi,

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