Abstract

The two-wave mixing in the broad-area semiconductor amplifier was investigated, both theoretically and experimentally. In detail we investigated how the optical gain is affected by the presence of the two-wave mixing interference grating. In the experimental setup we are able to turn on and off the interference pattern in the semiconductor amplifier. This arrangement allows us to determine the two-wave mixing gain. The coupled-wave equations of two-wave mixing were derived based on the Maxwell’s wave equation and rate equation of the carrier density. The analytical solutions of the coupled-wave equations were obtained in the condition of small signal and the total intensity is far below the saturation intensity of the amplifier. The results show that when the amplifier is operated below transparency we obtain an increase in the optical gain, and when the amplifier is operated above transparency we obtain a decrease in the optical gain. The experimental results obtained in an 810 nm, 200 µm wide GaAlAs amplifier show good agreement with the theory. A diffusion length of 2.0 µm is determined from the experiment.

© 2006 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]
  8. A. Brignon and J.-P. Huignard, "Two-wave mixing in Nd:YAG by gain saturation," Opt. Lett. 18, 1639-1641 (1993).
    [CrossRef] [PubMed]
  9. G. P. Agrawal, "Four-wave mixing and phase conjugation in semiconductor laser media," Opt. Lett. 12, 260-262 (1987).
    [CrossRef] [PubMed]
  10. M. Chi, O. B. Jensen, J. Holm, C. Pedersen, P. E. Andersen, G. Erbert, B. Bumpf, and P. M. Petersen, "Tunable high-power narrow-linewidth semiconductor laser based on an external-cavity tapered amplifier," Opt. Express 13, 10589-10596 (2005).
    [CrossRef] [PubMed]
  11. L. Goldberg, D. Mehuys, M. R. Surette, and D. C. Hall, "High-power, near-diffraction-limited large-area traveling-wave semiconductor amplifiers," J. Quantum Electron. 29, 2028-2042 (1993).
    [CrossRef]
  12. J. R. Marciante and G. P. Agrawal, "Nonlinear mechanisms of filamentation in broad-area semiconductor lasers," J. Quantum Electron. 32, 590-596 (1996).
    [CrossRef]

2005 (2)

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]

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 (2)

A. Brignon and J.-P. Huignard, "Two-wave mixing in Nd:YAG by gain saturation," Opt. Lett. 18, 1639-1641 (1993).
[CrossRef] [PubMed]

L. Goldberg, D. Mehuys, M. R. Surette, and D. C. Hall, "High-power, near-diffraction-limited large-area traveling-wave semiconductor amplifiers," J. Quantum Electron. 29, 2028-2042 (1993).
[CrossRef]

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]

Agrawal, G. P.

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

G. P. Agrawal, "Four-wave mixing and phase conjugation in semiconductor laser media," Opt. Lett. 12, 260-262 (1987).
[CrossRef] [PubMed]

Andersen, P. E.

Brignon, A.

Bumpf, B.

Burger, J.

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]

Carter, G. M.

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]

Chi, M.

Dapkus, P. D.

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]

Dubovitsky, S.

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]

Erbert, G.

Frey, R.

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

Fujimoto, J. G.

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]

Goldberg, L.

L. Goldberg, D. Mehuys, M. R. Surette, and D. C. Hall, "High-power, near-diffraction-limited large-area traveling-wave semiconductor amplifiers," J. Quantum Electron. 29, 2028-2042 (1993).
[CrossRef]

Hall, D. C.

L. Goldberg, D. Mehuys, M. R. Surette, and D. C. Hall, "High-power, near-diffraction-limited large-area traveling-wave semiconductor amplifiers," J. Quantum Electron. 29, 2028-2042 (1993).
[CrossRef]

Holm, J.

Huignard, J.-P.

Jensen, O. B.

Jensen, S. B.

Kürz, P.

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]

Lucente, M.

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]

Marciante, J. R.

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

Mehuys, D.

L. Goldberg, D. Mehuys, M. R. Surette, and D. C. Hall, "High-power, near-diffraction-limited large-area traveling-wave semiconductor amplifiers," J. Quantum Electron. 29, 2028-2042 (1993).
[CrossRef]

Mukai, T.

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]

Nagar, R.

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]

Nakajima, H.

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

Pedersen, C.

Petersen, P. M.

Samsøe, E.

Steier, W. H.

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]

Surette, M. R.

L. Goldberg, D. Mehuys, M. R. Surette, and D. C. Hall, "High-power, near-diffraction-limited large-area traveling-wave semiconductor amplifiers," J. Quantum Electron. 29, 2028-2042 (1993).
[CrossRef]

Tishinin, D.

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]

Uppal, K.

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]

Zhu, D. X.

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]

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. (2)

L. Goldberg, D. Mehuys, M. R. Surette, and D. C. Hall, "High-power, near-diffraction-limited large-area traveling-wave semiconductor amplifiers," J. Quantum Electron. 29, 2028-2042 (1993).
[CrossRef]

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 (4)

Fig. 1.
Fig. 1.

Experimental set-up for the TWM in broad-area amplifier. M: mirror, BSs: beam splitter, HWP: half-wave plate, BAA: broad-area amplifier (the units are in mm).

Fig. 2.
Fig. 2.

The relative position of the interference pattern, the carrier density grating, the index and the gain grating formed in the BAA.

Fig. 3.
Fig. 3.

The g TWM versus the output power of the pump. The squares are measured data; the line is the fitted result with Eq. (13).

Fig. 4.
Fig. 4.

The g TWM versus the grating vector in the BAA. The squares are measured data: the curve is the fitted result with Eq. (13).

Equations (13)

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

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 t ) + A 2 e i ( K 2 · r ω t ) ,
P = ε 0 χ ( N ) E ,
χ ( N ) = n c ω ( β + i ) g ( N ) ,
dN dt = I qV N τ + D 2 N g ( N ) E 2 ћ ω ,
N = N B + Δ N exp ( i K x ) + Δ N * exp ( i K x ) ,
N B = I τ q V + N 0 E 2 P s 1 + E 2 P s
Δ N = ( N B N 0 ) A 1 A 2 * P s 1 + D τ K 2 + E 2 P s
A 1 z i [ α ( β + i ) 1 + E 2 P s ] ( 1 A 2 2 P s 1 + D τ K 2 + E 2 P s ) A 1 = 0 ,
A 2 z i [ α ( β + i ) 1 + E 2 P s ] ( 1 A 1 2 P s 1 + D τ K 2 + E 2 P s ) A 2 = 0 ,
A 1 = A 10 exp [ ( 1 i β ) α z ] ,
A 2 = A 20 exp [ ( 1 i β ) ( α z γ ( e 2 α z 1 ) 2 ) ] ,
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 ( 1 + D τ K 2 ) P s ,

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