Abstract

Nearly degenerate four-wave mixing in above-threshold laser diodes with low or asymmetric facet reflectivities is investigated theoretically. It is shown that the conjugate reflectivity and the four-wave mixing bandwidth are enhanced in lasers with low-reflectivity facets. It is shown, in particular, that the maximum conjugate reflectivity can be obtained in lasers with highly asymmetric facet reflectivities. Longitudinal variations of both the nonlinear interaction and the gain distribution in the laser cavity are taken into account in the model. Such variations are shown to be essential in describing four-wave mixing in laser diodes with low or strongly asymmetric facet reflectivities.

© 1994 Optical Society of America

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  1. H. Nakajima and R. Frey, “Collinear nearly degenerate four-wave mixing in intracavity amplifying media,” IEEE J. Quantum Electron. QE-22, 1349–1354 (1986).
    [CrossRef]
  2. R. Nietzke, P. Panknin, W. Elsässer, and E. O. Göbel, “Four-wave mixing in GaAs/AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 25, 1399–1406 (1989).
    [CrossRef]
  3. F. Favre and D. L. Guen, “Four-wave mixing in traveling wave semiconductor laser amplifiers,” IEEE J. Quantum Electron. 26, 858–864 (1990).
    [CrossRef]
  4. T. Mukai and T. Saitoh, “Detuning characteristics and conversion efficiency of nearly degenerate four-wave mixing in a 1.5 μ m traveling-wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 26, 865–874 (1990).
    [CrossRef]
  5. S. Jiang and M. Dagenais, “Observation of nearly degenerate and cavity-enhanced highly nondegenerate four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 62, 2757–2759 (1993).
    [CrossRef]
  6. S. Jiang and M. Dagenais, “Nearly degenerate four-wave mixing in Fabry–Perot semiconductor lasers,” Opt. Lett. 18, 1337–1339 (1993).
    [CrossRef]
  7. L. F. Tiemeijer, P. I. Kuindersma, P. J. A. Thijs, and G. L. J. Rikken, “Passive FM locking in InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 25, 1385–1391 (1989).
    [CrossRef]
  8. K. A. Shore and W. M. Yee, “Theory of self-locking FM operation in semiconductor lasers,” Proc. Inst. Electr. Eng. Part J 138, 91–96 (1991).
  9. W. M. Yee and K. A. Shore, “Multimode analysis of self-locked FM operation in laser diodes,” Proc. Inst. Electr. Eng. Part J 140, 21–25 (1993).
  10. L. F. Tiemeijer, “Effects of nonlinear gain on four-wave mixing and asymmetric gain saturation in a semiconductor laser amplifier,” Appl. Phys. Lett. 59, 499–501 (1991).
    [CrossRef]
  11. S. R. Chinn, “Measurement of nonlinear gain suppression and four-wave mixing in quantum well lasers,” Appl. Phys. Lett. 59, 1673–1675 (1991).
    [CrossRef]
  12. K. Kikuchi, M. Kakui, C. E. Zah, and T. P. Lee, “Observation of highly nondegenerate four-wave mixing in 1.5 μ m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient,” IEEE J. Quantum Electron. 28, 151–156 (1992).
    [CrossRef]
  13. J. Zhou, N. Park, J. W. Dawson, and K. J. Vahala, “Highly nondegenerate four-wave mixing and gain nonlinearity in a strained multiple-quantum-well optical amplifier,” Appl. Phys. Lett. 62, 2301–2303 (1993).
    [CrossRef]
  14. J. M. Liu and T. B. Simpson, “Characterization of fundamental parameters of a semiconductor laser with an injected optical probe,” IEEE Photon. Technol. Lett. 4, 380–382 (1993).
    [CrossRef]
  15. N. Schunk, “All-optical frequency conversion in a traveling wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 27, 1271–1279 (1991).
    [CrossRef]
  16. G. P. Agrawal and I. M. I. Habbab, “Effects of four-wave mixing on multichannel amplification in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 26, 501–505 (1990).
    [CrossRef]
  17. G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147–159 (1988).
    [CrossRef]
  18. A. Mecozzi, A. D’Ottavi, and R. Hui, “Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers operating above threshold,” IEEE J. Quantum Electron. 29, 1477–1487 (1993).
    [CrossRef]
  19. R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60, 2454–2456 (1992).
    [CrossRef]
  20. T. B. Simpson and J. M. Liu, “Phase and amplitude characteristics of nearly degenerate four-wave mixing in Fabry–Perot semiconductor lasers,” J. Appl. Phys. 73, 2587–2589 (1993).
    [CrossRef]
  21. I. Middlemast, J. Sarma, K. A. Shore, A. I. Kucharska, E. D. Fletcher, and P. Blood, “Absorptive bistability in inhomogeneously pumped quantum well laser diodes,” Proc. Inst. Electr. Eng. Part J 138, 301–308 (1991).
  22. A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in semiconductor laser,” IEEE J. Quantum Electron. QE-11, 510–515 (1975).
    [CrossRef]
  23. M. Yamada, “Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers,” J. Appl. Phys. 66, 81–89 (1989).
    [CrossRef]

1993 (7)

W. M. Yee and K. A. Shore, “Multimode analysis of self-locked FM operation in laser diodes,” Proc. Inst. Electr. Eng. Part J 140, 21–25 (1993).

J. Zhou, N. Park, J. W. Dawson, and K. J. Vahala, “Highly nondegenerate four-wave mixing and gain nonlinearity in a strained multiple-quantum-well optical amplifier,” Appl. Phys. Lett. 62, 2301–2303 (1993).
[CrossRef]

J. M. Liu and T. B. Simpson, “Characterization of fundamental parameters of a semiconductor laser with an injected optical probe,” IEEE Photon. Technol. Lett. 4, 380–382 (1993).
[CrossRef]

S. Jiang and M. Dagenais, “Observation of nearly degenerate and cavity-enhanced highly nondegenerate four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 62, 2757–2759 (1993).
[CrossRef]

A. Mecozzi, A. D’Ottavi, and R. Hui, “Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers operating above threshold,” IEEE J. Quantum Electron. 29, 1477–1487 (1993).
[CrossRef]

T. B. Simpson and J. M. Liu, “Phase and amplitude characteristics of nearly degenerate four-wave mixing in Fabry–Perot semiconductor lasers,” J. Appl. Phys. 73, 2587–2589 (1993).
[CrossRef]

S. Jiang and M. Dagenais, “Nearly degenerate four-wave mixing in Fabry–Perot semiconductor lasers,” Opt. Lett. 18, 1337–1339 (1993).
[CrossRef]

1992 (2)

R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60, 2454–2456 (1992).
[CrossRef]

K. Kikuchi, M. Kakui, C. E. Zah, and T. P. Lee, “Observation of highly nondegenerate four-wave mixing in 1.5 μ m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient,” IEEE J. Quantum Electron. 28, 151–156 (1992).
[CrossRef]

1991 (5)

I. Middlemast, J. Sarma, K. A. Shore, A. I. Kucharska, E. D. Fletcher, and P. Blood, “Absorptive bistability in inhomogeneously pumped quantum well laser diodes,” Proc. Inst. Electr. Eng. Part J 138, 301–308 (1991).

N. Schunk, “All-optical frequency conversion in a traveling wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 27, 1271–1279 (1991).
[CrossRef]

L. F. Tiemeijer, “Effects of nonlinear gain on four-wave mixing and asymmetric gain saturation in a semiconductor laser amplifier,” Appl. Phys. Lett. 59, 499–501 (1991).
[CrossRef]

S. R. Chinn, “Measurement of nonlinear gain suppression and four-wave mixing in quantum well lasers,” Appl. Phys. Lett. 59, 1673–1675 (1991).
[CrossRef]

K. A. Shore and W. M. Yee, “Theory of self-locking FM operation in semiconductor lasers,” Proc. Inst. Electr. Eng. Part J 138, 91–96 (1991).

1990 (3)

G. P. Agrawal and I. M. I. Habbab, “Effects of four-wave mixing on multichannel amplification in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 26, 501–505 (1990).
[CrossRef]

F. Favre and D. L. Guen, “Four-wave mixing in traveling wave semiconductor laser amplifiers,” IEEE J. Quantum Electron. 26, 858–864 (1990).
[CrossRef]

T. Mukai and T. Saitoh, “Detuning characteristics and conversion efficiency of nearly degenerate four-wave mixing in a 1.5 μ m traveling-wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 26, 865–874 (1990).
[CrossRef]

1989 (3)

R. Nietzke, P. Panknin, W. Elsässer, and E. O. Göbel, “Four-wave mixing in GaAs/AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 25, 1399–1406 (1989).
[CrossRef]

L. F. Tiemeijer, P. I. Kuindersma, P. J. A. Thijs, and G. L. J. Rikken, “Passive FM locking in InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 25, 1385–1391 (1989).
[CrossRef]

M. Yamada, “Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers,” J. Appl. Phys. 66, 81–89 (1989).
[CrossRef]

1988 (1)

1986 (1)

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

1975 (1)

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in semiconductor laser,” IEEE J. Quantum Electron. QE-11, 510–515 (1975).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal and I. M. I. Habbab, “Effects of four-wave mixing on multichannel amplification in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 26, 501–505 (1990).
[CrossRef]

G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147–159 (1988).
[CrossRef]

Blood, P.

I. Middlemast, J. Sarma, K. A. Shore, A. I. Kucharska, E. D. Fletcher, and P. Blood, “Absorptive bistability in inhomogeneously pumped quantum well laser diodes,” Proc. Inst. Electr. Eng. Part J 138, 301–308 (1991).

Bogatov, A. P.

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in semiconductor laser,” IEEE J. Quantum Electron. QE-11, 510–515 (1975).
[CrossRef]

Chinn, S. R.

S. R. Chinn, “Measurement of nonlinear gain suppression and four-wave mixing in quantum well lasers,” Appl. Phys. Lett. 59, 1673–1675 (1991).
[CrossRef]

D’Ottavi, A.

A. Mecozzi, A. D’Ottavi, and R. Hui, “Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers operating above threshold,” IEEE J. Quantum Electron. 29, 1477–1487 (1993).
[CrossRef]

Dagenais, M.

S. Jiang and M. Dagenais, “Observation of nearly degenerate and cavity-enhanced highly nondegenerate four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 62, 2757–2759 (1993).
[CrossRef]

S. Jiang and M. Dagenais, “Nearly degenerate four-wave mixing in Fabry–Perot semiconductor lasers,” Opt. Lett. 18, 1337–1339 (1993).
[CrossRef]

Dawson, J. W.

J. Zhou, N. Park, J. W. Dawson, and K. J. Vahala, “Highly nondegenerate four-wave mixing and gain nonlinearity in a strained multiple-quantum-well optical amplifier,” Appl. Phys. Lett. 62, 2301–2303 (1993).
[CrossRef]

Eliseev, P. G.

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in semiconductor laser,” IEEE J. Quantum Electron. QE-11, 510–515 (1975).
[CrossRef]

Elsässer, W.

R. Nietzke, P. Panknin, W. Elsässer, and E. O. Göbel, “Four-wave mixing in GaAs/AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 25, 1399–1406 (1989).
[CrossRef]

Favre, F.

F. Favre and D. L. Guen, “Four-wave mixing in traveling wave semiconductor laser amplifiers,” IEEE J. Quantum Electron. 26, 858–864 (1990).
[CrossRef]

Fletcher, E. D.

I. Middlemast, J. Sarma, K. A. Shore, A. I. Kucharska, E. D. Fletcher, and P. Blood, “Absorptive bistability in inhomogeneously pumped quantum well laser diodes,” Proc. Inst. Electr. Eng. Part J 138, 301–308 (1991).

Frey, R.

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

Göbel, E. O.

R. Nietzke, P. Panknin, W. Elsässer, and E. O. Göbel, “Four-wave mixing in GaAs/AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 25, 1399–1406 (1989).
[CrossRef]

Guen, D. L.

F. Favre and D. L. Guen, “Four-wave mixing in traveling wave semiconductor laser amplifiers,” IEEE J. Quantum Electron. 26, 858–864 (1990).
[CrossRef]

Habbab, I. M. I.

G. P. Agrawal and I. M. I. Habbab, “Effects of four-wave mixing on multichannel amplification in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 26, 501–505 (1990).
[CrossRef]

Hui, R.

A. Mecozzi, A. D’Ottavi, and R. Hui, “Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers operating above threshold,” IEEE J. Quantum Electron. 29, 1477–1487 (1993).
[CrossRef]

R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60, 2454–2456 (1992).
[CrossRef]

Jiang, S.

S. Jiang and M. Dagenais, “Nearly degenerate four-wave mixing in Fabry–Perot semiconductor lasers,” Opt. Lett. 18, 1337–1339 (1993).
[CrossRef]

S. Jiang and M. Dagenais, “Observation of nearly degenerate and cavity-enhanced highly nondegenerate four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 62, 2757–2759 (1993).
[CrossRef]

Kakui, M.

K. Kikuchi, M. Kakui, C. E. Zah, and T. P. Lee, “Observation of highly nondegenerate four-wave mixing in 1.5 μ m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient,” IEEE J. Quantum Electron. 28, 151–156 (1992).
[CrossRef]

Kikuchi, K.

K. Kikuchi, M. Kakui, C. E. Zah, and T. P. Lee, “Observation of highly nondegenerate four-wave mixing in 1.5 μ m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient,” IEEE J. Quantum Electron. 28, 151–156 (1992).
[CrossRef]

Kucharska, A. I.

I. Middlemast, J. Sarma, K. A. Shore, A. I. Kucharska, E. D. Fletcher, and P. Blood, “Absorptive bistability in inhomogeneously pumped quantum well laser diodes,” Proc. Inst. Electr. Eng. Part J 138, 301–308 (1991).

Kuindersma, P. I.

L. F. Tiemeijer, P. I. Kuindersma, P. J. A. Thijs, and G. L. J. Rikken, “Passive FM locking in InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 25, 1385–1391 (1989).
[CrossRef]

Lee, T. P.

K. Kikuchi, M. Kakui, C. E. Zah, and T. P. Lee, “Observation of highly nondegenerate four-wave mixing in 1.5 μ m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient,” IEEE J. Quantum Electron. 28, 151–156 (1992).
[CrossRef]

Liu, J. M.

T. B. Simpson and J. M. Liu, “Phase and amplitude characteristics of nearly degenerate four-wave mixing in Fabry–Perot semiconductor lasers,” J. Appl. Phys. 73, 2587–2589 (1993).
[CrossRef]

J. M. Liu and T. B. Simpson, “Characterization of fundamental parameters of a semiconductor laser with an injected optical probe,” IEEE Photon. Technol. Lett. 4, 380–382 (1993).
[CrossRef]

Mecozzi, A.

A. Mecozzi, A. D’Ottavi, and R. Hui, “Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers operating above threshold,” IEEE J. Quantum Electron. 29, 1477–1487 (1993).
[CrossRef]

R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60, 2454–2456 (1992).
[CrossRef]

Middlemast, I.

I. Middlemast, J. Sarma, K. A. Shore, A. I. Kucharska, E. D. Fletcher, and P. Blood, “Absorptive bistability in inhomogeneously pumped quantum well laser diodes,” Proc. Inst. Electr. Eng. Part J 138, 301–308 (1991).

Mukai, T.

T. Mukai and T. Saitoh, “Detuning characteristics and conversion efficiency of nearly degenerate four-wave mixing in a 1.5 μ m traveling-wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 26, 865–874 (1990).
[CrossRef]

Nakajima, H.

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

Nietzke, R.

R. Nietzke, P. Panknin, W. Elsässer, and E. O. Göbel, “Four-wave mixing in GaAs/AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 25, 1399–1406 (1989).
[CrossRef]

Panknin, P.

R. Nietzke, P. Panknin, W. Elsässer, and E. O. Göbel, “Four-wave mixing in GaAs/AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 25, 1399–1406 (1989).
[CrossRef]

Park, N.

J. Zhou, N. Park, J. W. Dawson, and K. J. Vahala, “Highly nondegenerate four-wave mixing and gain nonlinearity in a strained multiple-quantum-well optical amplifier,” Appl. Phys. Lett. 62, 2301–2303 (1993).
[CrossRef]

Rikken, G. L. J.

L. F. Tiemeijer, P. I. Kuindersma, P. J. A. Thijs, and G. L. J. Rikken, “Passive FM locking in InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 25, 1385–1391 (1989).
[CrossRef]

Saitoh, T.

T. Mukai and T. Saitoh, “Detuning characteristics and conversion efficiency of nearly degenerate four-wave mixing in a 1.5 μ m traveling-wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 26, 865–874 (1990).
[CrossRef]

Sarma, J.

I. Middlemast, J. Sarma, K. A. Shore, A. I. Kucharska, E. D. Fletcher, and P. Blood, “Absorptive bistability in inhomogeneously pumped quantum well laser diodes,” Proc. Inst. Electr. Eng. Part J 138, 301–308 (1991).

Schunk, N.

N. Schunk, “All-optical frequency conversion in a traveling wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 27, 1271–1279 (1991).
[CrossRef]

Shore, K. A.

W. M. Yee and K. A. Shore, “Multimode analysis of self-locked FM operation in laser diodes,” Proc. Inst. Electr. Eng. Part J 140, 21–25 (1993).

K. A. Shore and W. M. Yee, “Theory of self-locking FM operation in semiconductor lasers,” Proc. Inst. Electr. Eng. Part J 138, 91–96 (1991).

I. Middlemast, J. Sarma, K. A. Shore, A. I. Kucharska, E. D. Fletcher, and P. Blood, “Absorptive bistability in inhomogeneously pumped quantum well laser diodes,” Proc. Inst. Electr. Eng. Part J 138, 301–308 (1991).

Simpson, T. B.

J. M. Liu and T. B. Simpson, “Characterization of fundamental parameters of a semiconductor laser with an injected optical probe,” IEEE Photon. Technol. Lett. 4, 380–382 (1993).
[CrossRef]

T. B. Simpson and J. M. Liu, “Phase and amplitude characteristics of nearly degenerate four-wave mixing in Fabry–Perot semiconductor lasers,” J. Appl. Phys. 73, 2587–2589 (1993).
[CrossRef]

Sverdlov, B. N.

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in semiconductor laser,” IEEE J. Quantum Electron. QE-11, 510–515 (1975).
[CrossRef]

Thijs, P. J. A.

L. F. Tiemeijer, P. I. Kuindersma, P. J. A. Thijs, and G. L. J. Rikken, “Passive FM locking in InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 25, 1385–1391 (1989).
[CrossRef]

Tiemeijer, L. F.

L. F. Tiemeijer, “Effects of nonlinear gain on four-wave mixing and asymmetric gain saturation in a semiconductor laser amplifier,” Appl. Phys. Lett. 59, 499–501 (1991).
[CrossRef]

L. F. Tiemeijer, P. I. Kuindersma, P. J. A. Thijs, and G. L. J. Rikken, “Passive FM locking in InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 25, 1385–1391 (1989).
[CrossRef]

Vahala, K. J.

J. Zhou, N. Park, J. W. Dawson, and K. J. Vahala, “Highly nondegenerate four-wave mixing and gain nonlinearity in a strained multiple-quantum-well optical amplifier,” Appl. Phys. Lett. 62, 2301–2303 (1993).
[CrossRef]

Yamada, M.

M. Yamada, “Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers,” J. Appl. Phys. 66, 81–89 (1989).
[CrossRef]

Yee, W. M.

W. M. Yee and K. A. Shore, “Multimode analysis of self-locked FM operation in laser diodes,” Proc. Inst. Electr. Eng. Part J 140, 21–25 (1993).

K. A. Shore and W. M. Yee, “Theory of self-locking FM operation in semiconductor lasers,” Proc. Inst. Electr. Eng. Part J 138, 91–96 (1991).

Zah, C. E.

K. Kikuchi, M. Kakui, C. E. Zah, and T. P. Lee, “Observation of highly nondegenerate four-wave mixing in 1.5 μ m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient,” IEEE J. Quantum Electron. 28, 151–156 (1992).
[CrossRef]

Zhou, J.

J. Zhou, N. Park, J. W. Dawson, and K. J. Vahala, “Highly nondegenerate four-wave mixing and gain nonlinearity in a strained multiple-quantum-well optical amplifier,” Appl. Phys. Lett. 62, 2301–2303 (1993).
[CrossRef]

Appl. Phys. Lett. (5)

S. Jiang and M. Dagenais, “Observation of nearly degenerate and cavity-enhanced highly nondegenerate four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 62, 2757–2759 (1993).
[CrossRef]

L. F. Tiemeijer, “Effects of nonlinear gain on four-wave mixing and asymmetric gain saturation in a semiconductor laser amplifier,” Appl. Phys. Lett. 59, 499–501 (1991).
[CrossRef]

S. R. Chinn, “Measurement of nonlinear gain suppression and four-wave mixing in quantum well lasers,” Appl. Phys. Lett. 59, 1673–1675 (1991).
[CrossRef]

J. Zhou, N. Park, J. W. Dawson, and K. J. Vahala, “Highly nondegenerate four-wave mixing and gain nonlinearity in a strained multiple-quantum-well optical amplifier,” Appl. Phys. Lett. 62, 2301–2303 (1993).
[CrossRef]

R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60, 2454–2456 (1992).
[CrossRef]

IEEE J. Quantum Electron. (10)

N. Schunk, “All-optical frequency conversion in a traveling wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 27, 1271–1279 (1991).
[CrossRef]

G. P. Agrawal and I. M. I. Habbab, “Effects of four-wave mixing on multichannel amplification in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 26, 501–505 (1990).
[CrossRef]

K. Kikuchi, M. Kakui, C. E. Zah, and T. P. Lee, “Observation of highly nondegenerate four-wave mixing in 1.5 μ m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient,” IEEE J. Quantum Electron. 28, 151–156 (1992).
[CrossRef]

L. F. Tiemeijer, P. I. Kuindersma, P. J. A. Thijs, and G. L. J. Rikken, “Passive FM locking in InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 25, 1385–1391 (1989).
[CrossRef]

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

R. Nietzke, P. Panknin, W. Elsässer, and E. O. Göbel, “Four-wave mixing in GaAs/AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 25, 1399–1406 (1989).
[CrossRef]

F. Favre and D. L. Guen, “Four-wave mixing in traveling wave semiconductor laser amplifiers,” IEEE J. Quantum Electron. 26, 858–864 (1990).
[CrossRef]

T. Mukai and T. Saitoh, “Detuning characteristics and conversion efficiency of nearly degenerate four-wave mixing in a 1.5 μ m traveling-wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 26, 865–874 (1990).
[CrossRef]

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in semiconductor laser,” IEEE J. Quantum Electron. QE-11, 510–515 (1975).
[CrossRef]

A. Mecozzi, A. D’Ottavi, and R. Hui, “Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers operating above threshold,” IEEE J. Quantum Electron. 29, 1477–1487 (1993).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. M. Liu and T. B. Simpson, “Characterization of fundamental parameters of a semiconductor laser with an injected optical probe,” IEEE Photon. Technol. Lett. 4, 380–382 (1993).
[CrossRef]

J. Appl. Phys. (2)

T. B. Simpson and J. M. Liu, “Phase and amplitude characteristics of nearly degenerate four-wave mixing in Fabry–Perot semiconductor lasers,” J. Appl. Phys. 73, 2587–2589 (1993).
[CrossRef]

M. Yamada, “Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers,” J. Appl. Phys. 66, 81–89 (1989).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Proc. Inst. Electr. Eng. Part J (3)

K. A. Shore and W. M. Yee, “Theory of self-locking FM operation in semiconductor lasers,” Proc. Inst. Electr. Eng. Part J 138, 91–96 (1991).

W. M. Yee and K. A. Shore, “Multimode analysis of self-locked FM operation in laser diodes,” Proc. Inst. Electr. Eng. Part J 140, 21–25 (1993).

I. Middlemast, J. Sarma, K. A. Shore, A. I. Kucharska, E. D. Fletcher, and P. Blood, “Absorptive bistability in inhomogeneously pumped quantum well laser diodes,” Proc. Inst. Electr. Eng. Part J 138, 301–308 (1991).

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Figures (7)

Fig. 1
Fig. 1

Amplitudes of normalized carrier density deviation|ΔnΩ| along the longitudinal direction of the laser cavity.

Fig. 2
Fig. 2

Evolution of normalized conjugate intensity along the longitudinal direction of the laser cavity. Significant differences are observed between results obtained with the PCIP model (solid curves) and the uniform-gain model (dashed curves).

Fig. 3
Fig. 3

(a) Probe and (b) conjugate output power versus frequency detuning Ω = ω1ω0 for β = 3 (solid curve) and β = 4 (dashed curve). R = R1 = R2 = 0.3.

Fig. 4
Fig. 4

(a) Probe and (b) conjugate transmittivity as a function of frequency detuning for different τs. R1 = R2 = 0.3 and β = 3.0.

Fig. 5
Fig. 5

Conjugate transmittivity Tc, at different output powers P0 against frequency detuning. β = 3 and R = 0.3. Similar curves are observed for probe transmittivity.

Fig. 6
Fig. 6

Effects of varying the facet reflectivity R = R1 = R2 on conjugate transmittivity. β = 3. Similar curves are obtained for probe transmittivity.

Fig. 7
Fig. 7

(a) Conjugate reflectivity Rc and (b) conjugate transmittivity Tc against front-facet reflectivity for lasers with different threshold gain values.

Equations (36)

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2 E - n 2 c 2 2 E t 2 = 1 0 c 2 2 P t 2 ,
E ( x , y , z ) = U ( x , y ) j E j ( z ) exp ( - i ω j t ) ,
P ( x , y , z ) = U ( x , y ) j P j ( z ) exp ( - i ω j t ) ,
ω 1 - ω 0 = ω 0 - ω 2 = Ω .
d 2 E j d z 2 + k j 2 E j = - Γ ω j 2 0 c 2 P j ,
g ( N ) = a ( N - N 0 ) ,
P = 0 χ E ,
P 0 ( z ) = 0 A g ( N ¯ ) E 0 ( z ) ,
P 1 ( z ) = 0 A g ( N ¯ ) [ E 1 ( z ) - Δ n Ω E 0 ] ,
P 2 ( z ) = 0 A g ( N ¯ ) [ E 2 ( z ) - Δ n Ω * E 0 ] ,
A = - ( n c / ω 0 ) ( β + i ) ,
Δ n Ω = - Δ N Ω ( N ¯ - N 0 ) = ( E 0 * E 1 + E 0 E 2 * ) / P s ( 1 + E 0 2 / P s - i Ω τ s ) ,
g ( N ¯ ) = a ( N ¯ - N 0 ) = ( a τ s / e d ) J - a N 0 1 + E 0 2 / P s ,
E j ( z ) = P s [ A j + ( z ) exp ( i k 0 z ) + A j - ( z ) exp ( - i k 0 z ) ] ,
P j ( z ) = P j + ( z ) exp ( i k 0 z ) + P j - ( z ) exp ( - i k 0 z ) .
d A 0 ± d z ± α int 2 A 0 ± = ± i ω 0 Γ 2 n c 0 P s P 0 ± ,
d A 1 ± d z i n ¯ Ω c A 1 ± ± α int 2 A 1 ± = ± i ω 1 Γ 2 n c 0 P s P 1 ± ,
d A 2 ± d z ± i n ¯ Ω c A 2 ± ± α int 2 A 2 ± = ± i ω 2 Γ 2 n c 0 P s P 2 ± ,
d A 0 ± d z = ± α 0 A 0 ± α int 2 A 0 ± ,
d A 1 ± d z = ± i n ¯ Ω c A 1 ± ± α 0 ( A 1 ± - Δ n Ω A 0 ± ) α int 2 A 1 ± ,
d A 2 ± d z = i n ¯ Ω c A 2 ± ± α 0 ( A 2 ± - Δ n Ω * A 0 ± ) α int 2 A 2 ± ,
Δ n Ω ( z ) = A 0 + ( A 2 + ) * + ( A 0 + ) * A 1 + + A 0 - ( A 2 - ) * + ( A 0 - ) * A 1 - ( 1 + P T - i Ω τ s ) ,
α 0 ( z ) = g 0 ( 1 - i β ) 2 [ 1 + P T ( z ) ] ,
P T ( z ) = A 0 + ( z ) 2 + A 0 - ( z ) 2 ,
A j + ( z = 0 ) = 1 - R 1 E in + R 1 A j - ( z = 0 ) ,
E R , j = 1 - R 1 A j - ( z = 0 ) + R 1 E in ,
A j - ( z = L ) exp ( - i κ L ) = R 2 A j + ( z = L ) exp ( i κ L ) ,
E T , j = 1 - R 2 A j + ( z = L ) exp ( i κ L ) ,
R p = | E R , 1 E in | 2 ,             T p = | E T , 1 E in | 2 ,
R c = | E R , 2 E in | 2 ,             T c = | E T , 2 E in | 2 .
R 1 R 2 exp [ ( 1 M n = 1 M g n - α int ) L ] exp ( i φ ) = 1 ,
φ = 2 κ L - β L M n = 1 M g n
2 κ L = 2 m π + β L M n = 1 M g n ,
P ¯ T = 1 L 0 L A 0 + ( z ) 2 + A 0 - ( z ) 2 d z = g 0 g th - 1 ,
g th = α int + 1 2 L ln ( 1 R 1 R 2 ) ,
Ω R = ( g th v g P ¯ T τ s ) 1 / 2 ,

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