Abstract

We propose a scheme for encoding digital data within a spiky chaotic carrier from a loss-modulated solid-state laser. Decoding is performed in real time with a synchronized chaotic laser system.

© 1994 Optical Society of America

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References

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  1. L. M. Pecora, T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990); Phys. Rev. A 44, 2374 (1991).
    [CrossRef] [PubMed]
  2. K. M. Cuomo, A. V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993); K. M. Cuomo, A. V. Oppenheim, S. H. Strogatz, IEEE Trans. Circuits Syst. 40, 626 (1993).
    [CrossRef] [PubMed]
  3. H. G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990); R. Roy, K. S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994); T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu, Phys. Rev. Lett. 72, 3502 (1994).
    [CrossRef] [PubMed]
  4. L. Fabiny, P. Colet, R. Roy, D. Lenstra, Phys. Rev. A 47, 4287 (1993).
    [CrossRef] [PubMed]
  5. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 963.
  6. S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, Mass., 1994), pp. 340-341; K. M. Cuomo, A. V. Oppenheim, S. H. Strogatz, Int. J. Bifurc. Chaos 3, 1629 (1993).
    [CrossRef]
  7. L. Glass, M. C. Mackey, From Clocks to Chaos, The Rhythms of Life (Princeton U. Press, Princeton, N.J., 1988); A. Longtin, A. Bulsara, F. Moss, Phys. Rev. Lett. 67, 656 (1991).
    [CrossRef] [PubMed]

1993 (2)

K. M. Cuomo, A. V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993); K. M. Cuomo, A. V. Oppenheim, S. H. Strogatz, IEEE Trans. Circuits Syst. 40, 626 (1993).
[CrossRef] [PubMed]

L. Fabiny, P. Colet, R. Roy, D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

1990 (2)

L. M. Pecora, T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990); Phys. Rev. A 44, 2374 (1991).
[CrossRef] [PubMed]

H. G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990); R. Roy, K. S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994); T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu, Phys. Rev. Lett. 72, 3502 (1994).
[CrossRef] [PubMed]

Carroll, T. L.

L. M. Pecora, T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990); Phys. Rev. A 44, 2374 (1991).
[CrossRef] [PubMed]

Colet, P.

L. Fabiny, P. Colet, R. Roy, D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Cuomo, K. M.

K. M. Cuomo, A. V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993); K. M. Cuomo, A. V. Oppenheim, S. H. Strogatz, IEEE Trans. Circuits Syst. 40, 626 (1993).
[CrossRef] [PubMed]

Fabiny, L.

L. Fabiny, P. Colet, R. Roy, D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Glass, L.

L. Glass, M. C. Mackey, From Clocks to Chaos, The Rhythms of Life (Princeton U. Press, Princeton, N.J., 1988); A. Longtin, A. Bulsara, F. Moss, Phys. Rev. Lett. 67, 656 (1991).
[CrossRef] [PubMed]

Lenstra, D.

L. Fabiny, P. Colet, R. Roy, D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Mackey, M. C.

L. Glass, M. C. Mackey, From Clocks to Chaos, The Rhythms of Life (Princeton U. Press, Princeton, N.J., 1988); A. Longtin, A. Bulsara, F. Moss, Phys. Rev. Lett. 67, 656 (1991).
[CrossRef] [PubMed]

Oppenheim, A. V.

K. M. Cuomo, A. V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993); K. M. Cuomo, A. V. Oppenheim, S. H. Strogatz, IEEE Trans. Circuits Syst. 40, 626 (1993).
[CrossRef] [PubMed]

Pecora, L. M.

L. M. Pecora, T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990); Phys. Rev. A 44, 2374 (1991).
[CrossRef] [PubMed]

Rahman, L.

H. G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990); R. Roy, K. S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994); T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu, Phys. Rev. Lett. 72, 3502 (1994).
[CrossRef] [PubMed]

Roy, R.

L. Fabiny, P. Colet, R. Roy, D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 963.

Strogatz, S. H.

S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, Mass., 1994), pp. 340-341; K. M. Cuomo, A. V. Oppenheim, S. H. Strogatz, Int. J. Bifurc. Chaos 3, 1629 (1993).
[CrossRef]

Winful, H. G.

H. G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990); R. Roy, K. S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994); T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu, Phys. Rev. Lett. 72, 3502 (1994).
[CrossRef] [PubMed]

Phys. Rev. A (1)

L. Fabiny, P. Colet, R. Roy, D. Lenstra, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

L. M. Pecora, T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990); Phys. Rev. A 44, 2374 (1991).
[CrossRef] [PubMed]

K. M. Cuomo, A. V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993); K. M. Cuomo, A. V. Oppenheim, S. H. Strogatz, IEEE Trans. Circuits Syst. 40, 626 (1993).
[CrossRef] [PubMed]

H. G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990); R. Roy, K. S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994); T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu, Phys. Rev. Lett. 72, 3502 (1994).
[CrossRef] [PubMed]

Other (3)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 963.

S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, Mass., 1994), pp. 340-341; K. M. Cuomo, A. V. Oppenheim, S. H. Strogatz, Int. J. Bifurc. Chaos 3, 1629 (1993).
[CrossRef]

L. Glass, M. C. Mackey, From Clocks to Chaos, The Rhythms of Life (Princeton U. Press, Princeton, N.J., 1988); A. Longtin, A. Bulsara, F. Moss, Phys. Rev. Lett. 67, 656 (1991).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Typical time traces for the intensities of (a) the transmitter and (b) the receiver lasers when they are synchronized, with α0T = α0R = 0.01, α1T = α1R = 0.0002, ΩT = ΩR = 541.6 ms−1, γT = γR = 0.03, ɛT = ɛR = 8.33 × 10−9 s−1, ωT = 0, ωR = 50,000 rad/s, and κ = 10−4.

Fig. 2
Fig. 2

Maximum (solid curves) and mean (dashed curves) values of S for different receiver detunings. The values of S were calculated for 10 ms by use of Eq. (5) after an initial period of 2 ms to allow transients to disappear. ωR = 0 (circles), ωR = 50,000 rad/s (asterisks), and ωR = 500,000 rad/s (squares). The parameters are the same as those in Fig. 1, except that α0T = α0T + κ.

Fig. 3
Fig. 3

Illustration of encoding and decoding for 11001 bit sequence: (a) |AbET|2 (solid curve) and |ET′|2 (dashed curve) displaced from the original pulses by 2 μs for clarity, (b) receiver output |AbER|2, (c) detected difference (|ET′|2 − |AbER|2), (d) value of the integral M. Encoding and decoding were performed with Ab = 0.9, A1 = 1.05Ab, A0 = 0.95Ab, κ = 1.11 × 10−4, Ith = 10, ΔT1 = 21 μs, ΔT2 = 42 μs, IDET = 5, ΔTDET = 36 μs, and α0R = α0T + kAb. The other parameters are the same as those in Fig. 1.

Fig. 4
Fig. 4

Values of M obtained for the pulses when a bit one (shaded histogram), a bit zero (unshaded histogram), or no bit (black histogram) is encoded. The parameters are the same as those in Fig. 3.

Equations (6)

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E ˙ T = ( 1 / τ c ) [ G T α T ( t ) ] E T + i ω T E T + ε T η T ,
G ˙ T = ( 1 / τ f ) [ γ T G T ( 1 + | E T | 2 ) ] ,
E ˙ R = ( 1 / τ c ) { [ G R α R ( t ) ] E R + κ E T } + i ω R E R + ε R η R ,
G ˙ R = ( 1 / τ f ) [ γ R G R ( 1 + | E R | 2 ) ] ,
S = | pu 1 se ( | E R | 2 | E T | 2 ) d t | | pu 1 se ( | E R | 2 + | E T | 2 ) d t | .
M = T s T s + Δ T DET ( | E T | 2 | A b E R | 2 ) d t ,

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