Abstract

The two-wave mixing in a broad-area semiconductor amplifier with moving gratings is investigated theoretically, where a pump beam and a signal beam with different frequencies are considered, thus both a moving phase grating and a moving gain grating are induced in the amplifier. The coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave equation and rate equation of the carrier density. The analytical solutions of the coupled-wave equations are obtained in the condition of small signal when the total intensity is far below the saturation intensity of the amplifier. The results show that the optical gain of the amplifier is affected by both the moving phase grating and the moving gain grating, and there is energy exchange between the pump and signal beams. Depending on the moving direction of the gratings and the anti-guiding parameter, the optical gain may increase or decrease due to the two-wave mixing.

© 2008 Optical Society of America

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References

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  1. H. Nakajima and R. Frey, "Collinear nearly degenerate four-wave mixing in intracavity amplifying media," IEEE J. Quantum Electron. 22, 1349-1354 (1986).
    [CrossRef]
  2. P. Kürz, R. Nagar, and T. Mukai, "Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode," Appl. Phys. Lett. 68, 1180-1182 (1996).
    [CrossRef]
  3. M. Lucente, G. M. Carter, and J. G. Fujimoto, "Nonlinear mixing and phase conjugation in broad-area diode lasers," Appl. Phys. Lett. 53, 467-469 (1988).
    [CrossRef]
  4. M. Lucente, J. G. Fujimoto, and G. M. Carter, "Spatial and frequency dependence of four-wave mixing in broad-area diode lasers," Appl. Phys. Lett. 53, 1897-1899 (1988).
    [CrossRef]
  5. D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, "Noncollinear four-wave mixing in a broad area semiconductor optical amplifier," Appl. Phys. Lett. 70, 2082-2084 (1997).
    [CrossRef]
  6. P. M. Petersen, E. Samsøe, S. B. Jensen, and P. E. Andersen, "Guiding of laser modes based on self-pumped four-wave mixing in a semiconductor amplifier," Opt. Express 13, 3340-3347 (2005).
    [CrossRef] [PubMed]
  7. P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I and II, (Springer-Verlag, Berlin, 1988, 1989).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. Q1. J. R. Marciante and G. P. Agrawal, "Nonlinear mechanisms of filamentation in broad-area semiconductor lasers," J. Quantum Electron. 32, 590-596 (1996).
    [CrossRef]

2006 (1)

2005 (1)

1997 (1)

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, "Noncollinear four-wave mixing in a broad area semiconductor optical amplifier," Appl. Phys. Lett. 70, 2082-2084 (1997).
[CrossRef]

1996 (2)

P. Kürz, R. Nagar, and T. Mukai, "Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode," Appl. Phys. Lett. 68, 1180-1182 (1996).
[CrossRef]

Q1. J. R. Marciante and G. P. Agrawal, "Nonlinear mechanisms of filamentation in broad-area semiconductor lasers," J. Quantum Electron. 32, 590-596 (1996).
[CrossRef]

1993 (1)

1988 (2)

M. Lucente, G. M. Carter, and J. G. Fujimoto, "Nonlinear mixing and phase conjugation in broad-area diode lasers," Appl. Phys. Lett. 53, 467-469 (1988).
[CrossRef]

M. Lucente, J. G. Fujimoto, and G. M. Carter, "Spatial and frequency dependence of four-wave mixing in broad-area diode lasers," Appl. Phys. Lett. 53, 1897-1899 (1988).
[CrossRef]

1987 (1)

1986 (1)

H. Nakajima and R. Frey, "Collinear nearly degenerate four-wave mixing in intracavity amplifying media," IEEE J. Quantum Electron. 22, 1349-1354 (1986).
[CrossRef]

Appl. Phys. Lett. (4)

P. Kürz, R. Nagar, and T. Mukai, "Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode," Appl. Phys. Lett. 68, 1180-1182 (1996).
[CrossRef]

M. Lucente, G. M. Carter, and J. G. Fujimoto, "Nonlinear mixing and phase conjugation in broad-area diode lasers," Appl. Phys. Lett. 53, 467-469 (1988).
[CrossRef]

M. Lucente, J. G. Fujimoto, and G. M. Carter, "Spatial and frequency dependence of four-wave mixing in broad-area diode lasers," Appl. Phys. Lett. 53, 1897-1899 (1988).
[CrossRef]

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, "Noncollinear four-wave mixing in a broad area semiconductor optical amplifier," Appl. Phys. Lett. 70, 2082-2084 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. Nakajima and R. Frey, "Collinear nearly degenerate four-wave mixing in intracavity amplifying media," IEEE J. Quantum Electron. 22, 1349-1354 (1986).
[CrossRef]

J. Quantum Electron. (1)

Q1. J. R. Marciante and G. P. Agrawal, "Nonlinear mechanisms of filamentation in broad-area semiconductor lasers," J. Quantum Electron. 32, 590-596 (1996).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Other (1)

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I and II, (Springer-Verlag, Berlin, 1988, 1989).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Configuration of the two-wave mixing in a broad-area semiconductor amplifier with moving gratings, K shows the direction of the grating vector.

Fig. 2.
Fig. 2.

The two-wave mixing gain g TWM versus δ with different anti-guiding parameter β according to Eq. (14).

Fig. 3.
Fig. 3.

The relative position of the interference pattern, the carrier density grating, the index grating and the gain grating formed in the BAA, assuming 1+DτK 2+|E 0|2/Ps =δτ, i.e., θ=π/4.

Equations (20)

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2 E n 2 c 2 2 E t 2 = 1 ε 0 c 2 2 P t 2 ,
E = A 1 e i ( K 1 · r ω 1 t ) + A 2 e i ( K 2 · r ω 2 t ) ,
P = ε 0 χ ( N ) E ,
χ ( N ) = nc ω ( β + i ) g ( N ) ,
dN dt = I qV N τ + D 2 N g ( N ) E 2 ħ ω ,
N = N B + Δ N exp [ i ( Kx + t ) ] + Δ N * exp [ i ( K x δ t ) ] ,
N B = I τ qV + N 0 E 0 2 P s 1 + E 0 2 P s ,
Δ N = ( N B N 0 ) A 1 A 2 * P s 1 + D τ K 2 + E 0 2 P s + i δ τ ,
cos θ 1 A 1 z i [ α ( β + i ) 1 + E 0 2 P s ] ( 1 A 2 2 P s 1 + D τ K 2 + E 0 2 P s + i δ τ ) A 1 = 0 ,
cos θ 2 A 2 z i [ α ( β + i ) 1 + E 0 2 P s ] ( 1 A 1 2 P s 1 + D τ K 2 + E 0 2 P s i δ τ ) A 2 = 0 ,
A 1 = A 10 exp [ ( 1 i β ) α z ] ,
A 2 = A 20 exp ( 1 i β ) ( α z γ 1 ( e 2 α z 1 ) 2 ) ,
γ 1 = A 10 2 P s ( 1 + 1 ( 1 + D τ K 2 i δ τ ) ) .
g TWM = ln [ A 2 ( z 0 ) coherent pump 2 A 2 ( z 0 ) noncoherent pump 2 ] = A 1 ( z 0 ) 2 A 10 2 P s 1 + D τ K 2 + β δ τ ( 1 + D τ K 2 ) 2 + ( δ τ ) 2 ,
N m = A 1 A 2 * ( N B N 0 ) P s ( 1 + D τ K 2 + E 0 2 P s ) 2 + ( δ τ ) 2 exp [ i ( K x + δ t + π θ ) ] + c . c . ,
θ = arctg δ τ 1 + D τ K 2 + E 0 2 P s ( π 2 < θ < π 2 ) .
Δ g = Γ a ( N B N 0 ) 2 P s A 1 A 2 * ( 1 + D τ K 2 + E 0 2 P s ) 2 + ( δ τ ) 2 exp [ i ( K x + δ t + π θ ) ] + c . c . .
Δ n = Γ a λ ( N B N 0 ) 4 π P s β A 1 A 2 * ( 1 + D τ K 2 + E 0 2 P s ) 2 + ( δ τ ) 2 exp [ i ( K x + δ t θ ) ] + c . c . ,
g gain cos ( π θ ) ( 1 + D τ K 2 + E 0 P s 2 ) 2 + ( δ τ ) 2 .
g phase β sin ( θ ) ( 1 + D τ K 2 + E 0 P s 2 ) 2 + ( δ τ ) 2 .

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