Abstract

Interference fringes of a laser diode Michelson interferometer are distorted by the external reflection of light to the laser diode. We demonstrate by a numerical model that one can stabilize the interference fringes by controlling chaos with a sinusoidal modulation of the injection current. We optimized the modulation frequency by referring to an AM power spectrum of the intrinsic fluctuation of a compound-cavity laser diode output and optimized the modulation depth by referring to a bifurcation diagram plotted against modulation depth. The controlled system with optimally tuned sinusoidal modulation is stable with changes in external power reflection. A small perturbation of dc bias of less than 2% can improve the stability of the interference fringes.

© 1996 Optical Society of America

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References

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  1. Y. Braiman, I. Goldhirsh, Phys. Rev. Lett. 66, 2545 (1991).
    [CrossRef] [PubMed]
  2. Y. Liu, N. Kikuchi, J. Ohotsubo, Phys. Rev. E 51, 2697 (1995).
    [CrossRef]
  3. N. Watanabe, K. Karaki, Opt. Lett. 20, 1032 (1995).
    [CrossRef] [PubMed]
  4. R. Lang, K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
    [CrossRef]
  5. J. Mørk, B. Tromborg, J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
    [CrossRef]
  6. G. B. Mindlin, R. Gilmore, Physica D 58, 229 (1992).
    [CrossRef]

1995 (2)

Y. Liu, N. Kikuchi, J. Ohotsubo, Phys. Rev. E 51, 2697 (1995).
[CrossRef]

N. Watanabe, K. Karaki, Opt. Lett. 20, 1032 (1995).
[CrossRef] [PubMed]

1992 (2)

J. Mørk, B. Tromborg, J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

G. B. Mindlin, R. Gilmore, Physica D 58, 229 (1992).
[CrossRef]

1991 (1)

Y. Braiman, I. Goldhirsh, Phys. Rev. Lett. 66, 2545 (1991).
[CrossRef] [PubMed]

1980 (1)

R. Lang, K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Braiman, Y.

Y. Braiman, I. Goldhirsh, Phys. Rev. Lett. 66, 2545 (1991).
[CrossRef] [PubMed]

Gilmore, R.

G. B. Mindlin, R. Gilmore, Physica D 58, 229 (1992).
[CrossRef]

Goldhirsh, I.

Y. Braiman, I. Goldhirsh, Phys. Rev. Lett. 66, 2545 (1991).
[CrossRef] [PubMed]

Karaki, K.

Kikuchi, N.

Y. Liu, N. Kikuchi, J. Ohotsubo, Phys. Rev. E 51, 2697 (1995).
[CrossRef]

Kobayashi, K.

R. Lang, K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Lang, R.

R. Lang, K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Liu, Y.

Y. Liu, N. Kikuchi, J. Ohotsubo, Phys. Rev. E 51, 2697 (1995).
[CrossRef]

Mark, J.

J. Mørk, B. Tromborg, J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Mindlin, G. B.

G. B. Mindlin, R. Gilmore, Physica D 58, 229 (1992).
[CrossRef]

Mørk, J.

J. Mørk, B. Tromborg, J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Ohotsubo, J.

Y. Liu, N. Kikuchi, J. Ohotsubo, Phys. Rev. E 51, 2697 (1995).
[CrossRef]

Tromborg, B.

J. Mørk, B. Tromborg, J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Watanabe, N.

IEEE J. Quantum Electron. (2)

R. Lang, K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

J. Mørk, B. Tromborg, J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

Y. Liu, N. Kikuchi, J. Ohotsubo, Phys. Rev. E 51, 2697 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

Y. Braiman, I. Goldhirsh, Phys. Rev. Lett. 66, 2545 (1991).
[CrossRef] [PubMed]

Physica D (1)

G. B. Mindlin, R. Gilmore, Physica D 58, 229 (1992).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the LD Michelson interferometer. The reflectable optics is set 20 mm from the laser facet.

Fig. 2
Fig. 2

(a) Bifurcation diagram of fluctuation of I/Isol. (b) Power spectrum of the fluctuation obtained with 0.087% power reflection. C1 and C2 are fixed. The horizontal axis is external power reflection. The intensity I is normalized by the intensity of the solitary LD. Conditions for calculations are α = 2.0, L = 10 mm, injection current I = 1.3Ith, τp = 2 ps, τs = 0.5 ns, τin = 8 ps, Gn = 1.1 × 10−12 m3 s−1.

Fig. 3
Fig. 3

Bifurcation diagram of the fluctuation of I as a function of (a) modulation frequency and (b) depth. Conditions are the same as for Fig. 2 except that power reflection is 0.087%. The modulation depth is 2.1% for (a). The frequency is 2.16 GHz for (b). The arrows indicate the windows of periodicity.

Fig. 4
Fig. 4

Effect of the sinusoidally modulated injection on optical-path-dependent interference fringes. The speed of C1 is 600 mm/s. The fringes shown are with (a) no external reflection, (b) power reflection of 0.087%, (c) power reflection of 0.087% and application of modulation frequency of 2.16 GHz and modulation depth of 0.8%, and (d) power reflection of 0.087% and application of modulation frequency of 2.16 GHz and modulation depth of 2.1%.

Fig. 5
Fig. 5

Bifurcation diagram of the fluctuation of light intensity as a function of the power reflection. C1 and C2 are fixed. Applied sinusoidal modulation frequency is 2.16 GHz, and depth is 2.1%. The calculation conditions are the same as for Fig. 2.

Equations (5)

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d E 0 ( t ) d t = 1 2 [ G ( N , E 0 ) 1 τ p ] E 0 ( t ) + κ τ in E 0 ( t τ ) × cos [ ω 0 τ + ϕ ( t ) ϕ ( t τ ) ] + R 2 V E 0 ( t ) ,
d ϕ ( t ) d t = 1 2 α [ G n ( N N th ) ] κ τ in E 0 ( t τ ) E 0 ( t ) × sin [ ω 0 τ + ϕ ( t ) ϕ ( t τ ) ] ,
d N ( t ) d t = J 0 [ ( 1 + m ) sin ( ω i t ) ] N ( t ) τ s G ( N , E 0 ) | E 0 ( t ) | 2 .
G ( N , E 0 ) = G n ( N N 0 ) [ 1 ε | E 0 ( t ) | 2 ] .
u 1 = E 0 ( t τ 1 ) exp { j [ ω 0 ( t τ 1 ) + ϕ ( t τ 1 ) ] } , u 2 = E 0 ( t τ 2 ) exp { j [ ω 0 ( t τ 2 ) + ϕ ( t τ 2 ) ] } .

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