Abstract

The fundamental possibility of chaos generation in directly modulated semiconductor lasers is studied on the basis of the rate equation with the form of a driven nonlinear oscillator. The origin of chaos generation and the effect of the spontaneous emission factor, which affects the nonlinearity of the dumping force and the restoring force in the rate equation, have been clarified.

© 1988 Optical Society of America

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References

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  1. K. Otsuka and H. Iwamura, Phys. Rev. A 28, 3153 (1983).
    [CrossRef]
  2. H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
    [CrossRef]
  3. C. H. Lee, T. H. Yoon, and S.-Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
    [CrossRef]
  4. Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
    [CrossRef]
  5. H. G. Winful, Y. C. Chen, and J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
    [CrossRef]
  6. M. Tang and S. Wang, Appl. Phys. Lett. 48, 900 (1986).
    [CrossRef]
  7. G. P. Agrawal, Appl. Phys. Lett. 49, 1013 (1986).
    [CrossRef]
  8. J. Test, J. Perez, and C. Jeffris, Phys. Rev. Lett. 48, 714 (1982).
    [CrossRef]
  9. F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, Opt. Commun. 51, 308 (1984).
    [CrossRef]

1986 (3)

H. G. Winful, Y. C. Chen, and J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
[CrossRef]

M. Tang and S. Wang, Appl. Phys. Lett. 48, 900 (1986).
[CrossRef]

G. P. Agrawal, Appl. Phys. Lett. 49, 1013 (1986).
[CrossRef]

1985 (2)

C. H. Lee, T. H. Yoon, and S.-Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
[CrossRef]

Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

1984 (2)

H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
[CrossRef]

F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, Opt. Commun. 51, 308 (1984).
[CrossRef]

1983 (1)

K. Otsuka and H. Iwamura, Phys. Rev. A 28, 3153 (1983).
[CrossRef]

1982 (1)

J. Test, J. Perez, and C. Jeffris, Phys. Rev. Lett. 48, 714 (1982).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Appl. Phys. Lett. 49, 1013 (1986).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, Opt. Commun. 51, 308 (1984).
[CrossRef]

Chen, Y. C.

H. G. Winful, Y. C. Chen, and J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
[CrossRef]

Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

Iwamura, H.

K. Otsuka and H. Iwamura, Phys. Rev. A 28, 3153 (1983).
[CrossRef]

Jeffris, C.

J. Test, J. Perez, and C. Jeffris, Phys. Rev. Lett. 48, 714 (1982).
[CrossRef]

Kawaguchi, H.

H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
[CrossRef]

Lee, C. H.

C. H. Lee, T. H. Yoon, and S.-Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
[CrossRef]

Lippi, G. L.

F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, Opt. Commun. 51, 308 (1984).
[CrossRef]

Liu, J. M.

H. G. Winful, Y. C. Chen, and J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
[CrossRef]

Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

Otsuka, K.

K. Otsuka and H. Iwamura, Phys. Rev. A 28, 3153 (1983).
[CrossRef]

Perez, J.

J. Test, J. Perez, and C. Jeffris, Phys. Rev. Lett. 48, 714 (1982).
[CrossRef]

Puccioni, G. P.

F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, Opt. Commun. 51, 308 (1984).
[CrossRef]

Shin, S.-Y.

C. H. Lee, T. H. Yoon, and S.-Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
[CrossRef]

Tang, M.

M. Tang and S. Wang, Appl. Phys. Lett. 48, 900 (1986).
[CrossRef]

Test, J.

J. Test, J. Perez, and C. Jeffris, Phys. Rev. Lett. 48, 714 (1982).
[CrossRef]

Wang, S.

M. Tang and S. Wang, Appl. Phys. Lett. 48, 900 (1986).
[CrossRef]

Winful, H. G.

H. G. Winful, Y. C. Chen, and J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
[CrossRef]

Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

Yoon, T. H.

C. H. Lee, T. H. Yoon, and S.-Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
[CrossRef]

Appl. Phys. Lett. (6)

H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
[CrossRef]

C. H. Lee, T. H. Yoon, and S.-Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
[CrossRef]

Y. C. Chen, H. G. Winful, and J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

H. G. Winful, Y. C. Chen, and J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
[CrossRef]

M. Tang and S. Wang, Appl. Phys. Lett. 48, 900 (1986).
[CrossRef]

G. P. Agrawal, Appl. Phys. Lett. 49, 1013 (1986).
[CrossRef]

Opt. Commun. (1)

F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, Opt. Commun. 51, 308 (1984).
[CrossRef]

Phys. Rev. A (1)

K. Otsuka and H. Iwamura, Phys. Rev. A 28, 3153 (1983).
[CrossRef]

Phys. Rev. Lett. (1)

J. Test, J. Perez, and C. Jeffris, Phys. Rev. Lett. 48, 714 (1982).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

x dependence of F1(x) (friction coefficient) and F2(x) (restoring force) as a parameter of B (spontaneous emission factor): (a) 10−5, (b) 10−10, (c) 10−15, (d) 10−20, and (e) 0. Solid lines denote the restoring force, and dotted lines denote the friction coefficient.

Fig. 2
Fig. 2

Variation of photon densities with time for (a) m = 0.2, (b) 0.4, (c) 0.6, (d) 0.8, (e) 1.0, and (f) 1.4.

Fig. 3
Fig. 3

Fourier-transformed spectra of the photon-density variation of Fig. 2.

Fig. 4
Fig. 4

Variation of the frequency spectra of photon-density fluctuation for various values of B: (a) 10−5, (b) 10−12, (c) 10−20, and (d) 10−30.

Fig. 5
Fig. 5

(a) Photon-density variation and (b) frequency spectrum assuming linear restoring force in the second-order rate equation.

Fig. 6
Fig. 6

(a) Photon-density variation and (b) frequency spectrum when we assume that B = 10−5 in the restoring force and B = 0 in the friction coefficient.

Fig. 7
Fig. 7

Variation of (a) photon density, (b) F1(x), (c) F2(x), and (d) frequency spectrum when we assume that B = 0 in both the friction coefficient and the restoring force.

Fig. 8
Fig. 8

Variation of (a) photon density, (b) F1(x), (c) F2(x), and (d) frequency spectrum when we assume that B = 10−10 in the friction coefficient and B = 0 in the restoring force.

Fig. 9
Fig. 9

Variation of (a) photon density, (b) F1(x), (c) F2(x), and (d) frequency spectrum when we assume that B = 10−5 in the friction coefficient and B = 0 in the restoring force.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

d N / d t = I / e V N / T n A ( N N 0 ) S ,
d S / d t = A ( N N 0 ) S S / T p + B N / T n ,
I = I b + I m sin ( 2 π f m t ) .
N = N 0 + 1 / A T p + [ d ( In S ) / d t ] / A ,
S = S 0 exp x ,
+ F 1 ( x ) + F 2 ( x ) = A C ( t ) .
F 1 ( x ) = ( 1 B ) / T n + A S 0 exp ( x ) + ( R / S 0 ) exp ( x ) ,
F 2 ( x ) = ( A S 0 / T n ) [ exp ( x ) 1 ] [ ( 1 B ) / T n ] ( R / S 0 ) [ exp ( x ) 1 ] ,
C ( t ) = I ( t ) / e V ( N 0 + 1 / A T p ) / T n + B / A T n T p + R S 0 / T p + ( R / A T n ) ( 1 B ) / S 0 ,
R = B ( N 0 + 1 / A T p ) / T n .
F 2 ( x ) = A S 0 x / T p .

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