Abstract

A methodology for treating the semiconductor laser as a current-controlled oscillator in an optical phase-lock loop is presented. The formalism is applied to phase demodulation of optical beams, reduction of phase noise by self-homodyning, and phase locking of a semiconductor laser array.

© 2005 Optical Society of America

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References

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  1. See, e.g., J. G. Proakis, Digital Communication, 4th ed. (McGraw-Hill, 2001), pp. 341–357.
  2. Y. Yamamoto, O. Nilsson, and S. Saito, IEEE J. Quantum Electron. QE-21, 1919 (1985).
    [CrossRef]
  3. M. Ohtsu and S. Kotajima, IEEE J. Quantum Electron. 21, 1905 (1985).
    [CrossRef]
  4. T. Koch and J. Bowers, Electron. Lett. 20, 1038 (1984).
    [CrossRef]
  5. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997), p. 594.
  6. Ref. 5, pp. 393–396.

1985 (2)

Y. Yamamoto, O. Nilsson, and S. Saito, IEEE J. Quantum Electron. QE-21, 1919 (1985).
[CrossRef]

M. Ohtsu and S. Kotajima, IEEE J. Quantum Electron. 21, 1905 (1985).
[CrossRef]

1984 (1)

T. Koch and J. Bowers, Electron. Lett. 20, 1038 (1984).
[CrossRef]

Bowers, J.

T. Koch and J. Bowers, Electron. Lett. 20, 1038 (1984).
[CrossRef]

Koch, T.

T. Koch and J. Bowers, Electron. Lett. 20, 1038 (1984).
[CrossRef]

Kotajima, S.

M. Ohtsu and S. Kotajima, IEEE J. Quantum Electron. 21, 1905 (1985).
[CrossRef]

Nilsson, O.

Y. Yamamoto, O. Nilsson, and S. Saito, IEEE J. Quantum Electron. QE-21, 1919 (1985).
[CrossRef]

Ohtsu, M.

M. Ohtsu and S. Kotajima, IEEE J. Quantum Electron. 21, 1905 (1985).
[CrossRef]

Proakis, J. G.

See, e.g., J. G. Proakis, Digital Communication, 4th ed. (McGraw-Hill, 2001), pp. 341–357.

Saito, S.

Y. Yamamoto, O. Nilsson, and S. Saito, IEEE J. Quantum Electron. QE-21, 1919 (1985).
[CrossRef]

Yamamoto, Y.

Y. Yamamoto, O. Nilsson, and S. Saito, IEEE J. Quantum Electron. QE-21, 1919 (1985).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997), p. 594.

Electron. Lett. (1)

T. Koch and J. Bowers, Electron. Lett. 20, 1038 (1984).
[CrossRef]

IEEE J. Quantum Electron. (2)

Y. Yamamoto, O. Nilsson, and S. Saito, IEEE J. Quantum Electron. QE-21, 1919 (1985).
[CrossRef]

M. Ohtsu and S. Kotajima, IEEE J. Quantum Electron. 21, 1905 (1985).
[CrossRef]

Other (3)

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997), p. 594.

Ref. 5, pp. 393–396.

See, e.g., J. G. Proakis, Digital Communication, 4th ed. (McGraw-Hill, 2001), pp. 341–357.

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Figures (2)

Fig. 1
Fig. 1

Model for the laser noise dynamics in an optical PLL. ϕ l ( t ) is a deterministic phase depending explicitly and deterministically on the input (injection) current G i ( t ) . The random phase fluctuations due to the spontaneous emission are represented by ϕ n ( t ) . The actual phase of the laser field is ϕ l ( t ) + ϕ n ( t ) .

Fig. 2
Fig. 2

Individual SCLs all lock to a reference wave at ω s , thus forming a coherent array.

Equations (23)

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Δ ω l ( t ) = α 2 [ 1 P 0 d ( Δ P ) d t + ϵ τ P Δ P ( t ) ] .
P ( t ) = g [ i l ( t ) i l , th ] ,
Δ ω l ( t ) = α 2 [ 1 ( i l 0 i l , th ) d ( Δ i l ) d t + ϵ g τ P Δ i l ] = a d d t Δ i l + b Δ i l ( t ) ,
ω l ( t ) = ω 0 + Δ ω l ( t ) , Δ i l ( t ) i l ( t ) i l , th ,
i ( t ) K [ ( ω s ω 0 ) t + ϕ s ( t ) ϕ l ( t ) ] , K η A s A l ,
d i d t = K [ ( ω s ω 0 ) + d ϕ s d t d ϕ l d t ] .
1 K d ( Δ i ) d t = ( ω s ω 0 ) + d ϕ s d t a G d d t Δ i b G Δ i .
b G ( Δ i ) S S = ω s ω 0 .
d i 1 ( t ) d t = K d ϕ s d t K a G d i 1 ( t ) d t K b G i 1 .
i ̃ 1 ( Ω ) = j Ω K K b G + j Ω ( 1 + K a G ) ϕ ̃ s ( Ω ) ,
i ̃ 1 ( Ω ) j Ω b G ϕ ̃ S ( Ω ) , i 1 ( t ) 1 b G d d t ϕ S ( t ) ,
i ̃ 1 ( Ω ) K 1 + K a G ϕ ̃ s ( Ω ) , i 1 ( t ) K 1 + K a G ϕ s ( t ) ,
α = 5 , i 0 i th = 5 × 10 2 , a = 50 , G = 100 ,
K η A l A s 3 × 10 3 , ϵ = 10 23 , Γ a = 0.1 ,
V = 3 × 10 16 ,
b 5 × 10 10 , K b G 1.5 × 10 10 , K a G 15 ,
a G 5 × 10 3 .
ϕ l ( t ) = 0 t Δ ω l ( t ) d t = G [ a i 1 ( t ) + b 0 t Δ i 1 ( t ) d t ] ,
ϕ ̃ l ( Ω ) = G a i ̃ 1 ( Ω ) + G b j Ω i ̃ 1 ( Ω ) ,
ϕ ̃ l ( Ω ) = j Ω + b a b a + j Ω ( 1 + 1 K a G ) ϕ ̃ s ( Ω ) .
i ( t ) = K [ ( ω s ω 0 ) t ϕ l ( t ) ϕ n ( t ) ] .
ϕ ̃ l ( Ω ) = j Ω + b a b a + j Ω ( 1 + 1 K a G ) ϕ ̃ n ( Ω ) .
ϕ ̃ laser ( Ω ) = X ( Ω 2 + Ω 2 X + j Ω b a ) Ω 2 ( 1 + X ) 2 + ( b a ) 2 ϕ ̃ n ( Ω ) ,

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