Abstract

A theoretical model based on a novel experiment scheme of dual-channel optical chaotic communication has been presented, and is proved to be reasonable by comparing the numerical simulations with the experimental results. After deducing the transmission function of semiconductor laser by small-signal analysis, how to reasonably select the system parameters has been given in order to realize the effective transmission of signal. Moreover, the cross talk between two channels has been analyzed quantitatively. For a 250MHz modulation message, the numerical simulation shows that it can be hidden efficiently during the transmission and decoded easily in the receiver.

© 2005 Optical Society of America

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References

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    [CrossRef]
  2. S. Tang and J. M. Liu, �??Effects of message encoding and becoding on synchronized chaotic optical communications,�?? IEEE J. Quantum Electron. 39, 1468-1474 (2003).
    [CrossRef]
  3. J. Ohtsubo, �??Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,�?? IEEE J. Quantum Electron. 38, 1141-1153 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. S. Sivaprakasam, and K. A. Shore, �??Message encoding and decoding using chaotic external-cavity diode lasers,�?? IEEE J. Quantum Electron. 36, 35-39 (2000).
    [CrossRef]
  14. A. Uchida, Y. Liu, and P. Davis, �??Characteristics of chaotic masking in synchronized semiconductor lasers,�?? IEEE J. Quantum Electron. 39, 963-970 (2003).
    [CrossRef]
  15. S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, �??Regimes of chaotic synchronization in external-cavity laser diodes,�?? IEEE J. Quantum Electron. 38, 1155-1160 (2002).
    [CrossRef]
  16. S. Sivaprakasam, and K. A. Shore, �??Cascaded synchronization of external-cavity laser diodes,�?? Opt. Lett. 66, 253-255 (2001).
    [CrossRef]
  17. J. Paul, S. Sivaprakasam, P. S. Spencer, and K. A. Shore, �??Optically modulated chaotic communication scheme with external-cavity length as a key to security,�?? J. Opt. Soc. Am. B 20, 497-503 (2003).
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Electron. Lett. (1)

J. Paul, S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, �??GHz bandwidth message transmission using chaotic diode lasers,�?? Electron. Lett. 38, 28-29 (2002).
[CrossRef]

IEEE J. Quantum Electron. (6)

S. Tang and J. M. Liu, �??Effects of message encoding and becoding on synchronized chaotic optical communications,�?? IEEE J. Quantum Electron. 39, 1468-1474 (2003).
[CrossRef]

J. Ohtsubo, �??Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,�?? IEEE J. Quantum Electron. 38, 1141-1153 (2002).
[CrossRef]

J. M. Liu, H. F. Chen, and S. Tang, �??Synchronized chaotic optical communications at high bit rates,�?? IEEE J. Quantum Electron. 38, 1184-1196 (2002).
[CrossRef]

S. Sivaprakasam, and K. A. Shore, �??Message encoding and decoding using chaotic external-cavity diode lasers,�?? IEEE J. Quantum Electron. 36, 35-39 (2000).
[CrossRef]

A. Uchida, Y. Liu, and P. Davis, �??Characteristics of chaotic masking in synchronized semiconductor lasers,�?? IEEE J. Quantum Electron. 39, 963-970 (2003).
[CrossRef]

S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, �??Regimes of chaotic synchronization in external-cavity laser diodes,�?? IEEE J. Quantum Electron. 38, 1155-1160 (2002).
[CrossRef]

IEEE Trans. Circuits Syst. I (1)

S. Tang, H. F. Chen, S. K. Hwang, and J. M. Liu, �??Message encoding and decoding through chaos modulation in chaotic optical communications,�?? IEEE Trans. Circuits Syst. I 49, 163-169 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore, �??Dual and dual-cross synchronizations in chaotic systems,�?? Opt. Commun. 216, 179-183 (2003).
[CrossRef]

Opt. Lett. (1)

S. Sivaprakasam, and K. A. Shore, �??Cascaded synchronization of external-cavity laser diodes,�?? Opt. Lett. 66, 253-255 (2001).
[CrossRef]

Phys. Lett. A (1)

L. S. Tsimring, and M. M. Sushchik, �??Multiplexing chaotic signals using synchronization,�?? Phys. Lett. A 213, 155-166 (1996).
[CrossRef]

Phys. Rev. E (1)

Y. Liu, and P. Davis, �??Dual synchronization of chaos,�?? Phys. Rev. E 61, 2176-2179 (2000).
[CrossRef]

Science (1)

G. D. Van Wiggeren, and R. Roy, �??Communication with chaotic lasers,�?? Science 279, 1198-1200 (1998).
[CrossRef]

Other (1)

G. P. Agrawal, and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, 1993).

Cited By

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Figures (12)

Fig. 1.
Fig. 1.

Schematic diagram of the dual-channel optical chaotic communication system: TL1, transmitter laser 1; TL2, transmitter laser 2; RL, receiver laser; DEC, decoder laser; BS1-BS6, beam splitters; M1-M4, mirrors; OI, optical isolators; S1-S2, message.

Fig. 2.
Fig. 2.

(a). The chaotic temporal waveforms of TL1, RL, DEC.

Fig. 2.
Fig. 2.

(b). Chaotic attractors of TL1.

Fig. 2.
Fig. 2.

(c). Synchronization errors of TL1 to RL.

Fig. 2.
Fig. 2.

(d). Synchronization errors of TL1 to DEC.

Fig. 3.
Fig. 3.

(a). Transmission functions at different injection coefficient k.

Fig. 3.
Fig. 3.

(b). Transmission functions at different frequency detuning Δf R1.

Fig. 4.
Fig. 4.

The cross-correlation function for different values of kcro /kinj .

Fig. 5.
Fig. 5.

(a). Correlation plot of DEC and TL1.

Fig. 5.
Fig. 5.

(b). Correlation plot of DEC and TL2.

Fig. 6.
Fig. 6.

(a). RF spectra of TL1, RL, DEC and the roughly recovered message.

Fig. 6.
Fig. 6.

(b). Recovered message after passing through a fourth-order Butterworth low-pass filter.

Equations (28)

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d E T 1 , 2 , D ( t ) d t = 1 2 ( G T 1 , 2 , D γ P ) E T 1 , 2 , D ( t ) + k T 1 , 2 , D τ L E T 1 , 2 , R ( t τ T 1 , 2 , D ) cos [ θ T 1 , 2 , D ( t ) ]
+ 2 β N T 1 , 2 , D ( t ) ζ T 1 , 2 , D ( t )
d Φ T 1 , 2 , D ( t ) d t = α 2 ( G T 1 , 2 , D γ P ) k T 1 , 2 , D τ L E T 1 , 2 , R ( t τ T 1 , 2 , D ) E T 1 , 2 , D ( t ) sin [ θ T 1 , 2 , D ( t ) ]
d N T 1 , 2 , D ( t ) d t = J T 1 , 2 , D γ e N T 1 , 2 , D ( t ) G T 1 , 2 , D E T 1 , 2 , D ( t ) 2
θ T 1 , 2 ( t ) = ω T 1 , 2 τ T 1 , 2 + Φ T 1 , 2 ( t ) Φ T 1 , 2 ( t τ T 1 , 2 )
θ D ( t ) = ( ω D ω R ) t + ω R τ D + Φ D ( t ) Φ R ( t τ D )
d dt ( E R 1 ( t ) E R 2 ( t ) ) = 1 2 { ( G R 1 0 0 G R 2 ) γ P } ( E R 1 ( t ) E R 2 ( t ) ) + 1 τ L ( k 11 k 12 k 21 k 22 ) ( E 1 ( t τ inj ) cos [ θ R 1 ( t ) ] E 2 ( t τ inj ) cos [ θ R 2 ( t ) ] ) + ( 2 β N R 1 ( t ) ζ R 1 ( t ) 2 β N R 2 ( t ) ζ R 2 ( t ) )
d dt ( Φ R 1 ( t ) Φ R 2 ( t ) ) = α 2 [ ( G R 1 G R 2 ) γ p ] 1 τ L ( k 11 k 12 k 21 k 22 ) ( E 1 ( t τ inj ) E R 1 ( t ) sin [ θ R 1 ( t ) ] E 2 ( t τ inj ) E R 2 ( t ) sin [ θ R 2 ( t ) ] )
d dt ( N R 1 ( t ) N R 2 ( t ) ) = J γ e ( N R 1 ( t ) N R 2 ( t ) ) ( G R 1 0 0 G R 2 ) ( E R 1 ( t ) 2 E R 2 ( t ) 2 )
θ R 1 , R 2 ( t ) = ( Δ ω ) R 1 , R 2 t + ω 1 , 2 τ inj + Φ R 1 ( t ) Φ 1 , 2 ( t τ inj )
d E R 1 ( t ) d t = 1 2 ( G R 1 γ P ) E R 1 ( t ) + k inj τ L E 1 ( t τ inj ) cos [ θ R 1 ( t ) ] + k cro τ L E 2 ( t τ inj ) cos [ θ R 2 ( t ) ]
+ 2 β N R 1 ( t ) ζ R 1 ( t )
d Φ R 1 ( t ) d t = α 2 ( G R 1 γ P ) k inj τ L E 1 ( t τ inj ) E R 1 ( t ) sin [ θ R 1 ( t ) ] k cro τ L E 2 ( t τ inj ) E R 1 ( t ) sin [ θ R 2 ( t ) ]
d N R 1 ( t ) d t = J γ e N R 1 ( t ) ( G R 1 γ P ) E R 1 ( t ) 2
θ R 1 , R 2 ( t ) = ( Δ ω ) R 1 , R 2 t + ω 1 , 2 τ inj + Φ R 1 ( t ) Φ 1 , 2 ( t τ inj )
d δ E R 1 ( t ) d t = 1 2 [ g ( N R 1 ¯ N 0 ) γ P ] δ E R 1 ( t ) k inj τ L E 1 ¯ [ sin ( Φ R 1 ¯ ) + k cro k inj sin ( Φ R 2 ¯ + Δ ω R 2 t ) ] δ Φ R 1 ( t )
+ k inj τ L cos ( Φ R 1 ¯ ) δ E 1 ( t τ inj ) + 1 2 g E R 1 ¯ δ N R 1 ( t )
d δ Φ R 1 ( t ) d t = k inj τ L E 1 ¯ E R 1 ¯ 2 [ sin ( Φ R 1 ¯ ) + k cro k inj sin ( Φ R 2 ¯ + Δ ω R 2 t ) ] δ E R 1 ( t ) + α 2 g δ N R 1 ( t )
k inj τ L E 1 ¯ E R 1 ¯ [ cos ( Φ R 1 ¯ ) + k cro k inj cos ( Φ R 2 ¯ + Δ ω R 2 t ) ] δ Φ R 1 ( t ) k inj τ L 1 E R 1 ¯ sin ( Φ R 1 ¯ ) δ E 1 ( t τ inj )
d δ N R 1 ( t ) d t = γ e δ N R 1 ( t ) 2 g E R 1 ¯ ( N R 1 ¯ N 0 ) δ E R 1 ( t ) g E R 1 ¯ 2 δ N R 1 ( t )
T ( ω ) = δ E R 1 ( ω ) δ E 1 ( ω ) = q 1 2 + q 2 2 q 3 2 + q 4 2
q 1 = ( B 3 ω 2 + B 1 ) cos ( ω ω 0 ) B 2 ω sin ( ω ω 0 ) , q 2 = B 2 ω cos ( ω ω 0 ) + ( B 3 ω 2 + B 1 ) sin ( ω ω 0 )
q 3 = ω 3 + A 2 ω , q 4 = A 3 ω 2 + A 1
A 1 = η [ Γ c ( Ω c Γ b Ω s η ) + Λ ( α Ω s Ω c ) ] , A 2 = Γ b Γ c Ω s η 2 + Ω c η ( Γ b Γ c ) Λ
A 3 = Ω c η Γ b + Γ c , B 1 = k inj τ l η Γ c , B 2 = k inj τ l η Ω c Γ c , B 3 = Ω c ,
Λ = g 2 E R 2 ¯ 2 ( N R 1 ¯ N 0 ) , Γ b = 1 2 [ g ( N R 1 ¯ N 0 ) γ p ] , Γ c = g E R 1 ¯ 2 + γ e
Ω c = k inj τ L cos ( Φ R 1 ¯ ) , Ω s = [ k inj τ L sin ( Φ R 1 ¯ ) ] 2 , η = E 1 ¯ E R 1 ¯ , ω 0 = 1 τ inj .
C = ( ( E 1 ( t ) ) 2 ( E 1 ) 2 ) ( ( E D ( t ) ) 2 ( E D ) 2 ) ( ( E 1 ( t ) ) 2 ( E 1 ) 2 ) 2 ( ( E D ( t ) ) 2 ( E D ) 2 ) 2

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