Abstract

A theoretical investigation of the role of interband effects in wave mixing in semiconductor optical amplifiers (SOA) is reported. Carrier density modulation (CDM) caused by optical wave beating in SOAs is examined along with its dependence on different operating parameters. Unlike most wave mixing theories, in which the existence and form of carrier pulsations are assumed a priori, we model the carrier dynamics and optical propagation in the time domain directly without invoking such an assumption. The dependence of CDM on the bias current, input power, and detuning between the pump and probe waves is investigated. Selected simulation results are verified experimentally. Good qualitative agreement is obtained between simulations and experiments for nearly degenerate wave mixing (restricted to 3GHz by experimental limitations).

© 2010 Optical Society of America

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2007 (1)

T. Baba, “Photonic crystals remember the light,” Nat. Photonics 1, 11-12 (2007).
[CrossRef]

2006 (2)

J. H. Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik (Stuttgart) 117, 199-209 (2006).
[CrossRef]

C. Politi, D. Klonidis, and M. J. O'Mahony, “Dynamic behaviour of wavelength converters based on FWM in SOAs,” IEEE J. Quantum Electron. 42, 108-125 (2006).
[CrossRef]

2005 (1)

2004 (1)

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

2003 (1)

X. Li and J. Park, “Time-domain modeling and simulation of the broadband behavior of semiconductor optical amplifiers,” Proc. SPIE 5248, 227-239 (2003).
[CrossRef]

2001 (2)

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37, 439-447 (2001).
[CrossRef]

I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for III-V compound semiconductors and their alloys,” Appl. Sci. Res., Sect. B 89, 5815-5875 (2001).

2000 (5)

E. M. Pratt. and J. E. Carroll, “Gain modelling and particle balance in semiconductor lasers,” IEE Proc.: Optoelectron. 147, 77-82 (2000).
[CrossRef]

N. K. Das, Y. Yamayoshi, and H. Kawagushi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184-1192 (2000).
[CrossRef]

E. Suhir, “Microelectronics and photonics--the future,” Microelectron. J. 31, 839-851 (2000).
[CrossRef]

K. E. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. 6, 1428-1435 (2000).
[CrossRef]

V. I. Tolstikhin, “Carrier charge imbalance and optical properties of separate confinement heterostructure quantum well lasers,” J. Appl. Phys. 87, 7342-7348 (2000).
[CrossRef]

1999 (4)

1998 (2)

J. K. White, J. V. Moloney, A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus, “Multilongitudinal-mode dynamics in a semiconductor laser subject to optical injection,” IEEE J. Quantum Electron. 34, 1469-1473 (1998).
[CrossRef]

D. Nesset, T. Kelly, and D. Marcenac, “All-optical wavelength conversion using SOA nonlinearities,” IEEE Commun. Mag. 36, 56-61 (1998).
[CrossRef]

1997 (6)

D. F. Geraghty, R. B. Lee, K. J. Vahala, M. Verdiell, M. Ziari, and A. Mathur, “Wavelength conversion up to 18 nm at 10 Gb/s by four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 9, 452-454 (1997).
[CrossRef]

R. Paiella, G. Hunziker, U. Koren, and K. J. Vahala, “Polarization-dependent optical nonlinearities of multiquantum-well laser amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3, 529-540 (1997).
[CrossRef]

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, “Numerical simulation of broad-area high-power semiconductor laser amplifiers,” IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[CrossRef]

J. Wang and H. Schweizer, “A quantitative comparison of the classical rate-equation model with the carrier heating model on dynamics of the quantum-well laser: the role of carrier energy relaxation, electron-hole interaction, and Auger effect,” IEEE J. Quantum Electron. 33, 1350-1359 (1997).
[CrossRef]

J. M. Tang and K. A. Shore, “Carrier diffusion and depletion effects on multiwave mixing in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 1280-1286 (1997).
[CrossRef]

S. Diez, C. Schmidt, R. Ludwig, H. G. Weber, K. Obermann, S. Kindt, I. Koltchanov, and K. Petermann, “Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching,” IEEE J. Sel. Top. Quantum Electron. 3, 1131-1145 (1997).
[CrossRef]

1996 (3)

I. Koltchanov, S. Kindt, K. Petermann, S. Diez, R. Ludwig, R. Schnabel, and H. G. Weber, “Analytical theory of terahertz four-wave mixing in semiconductor-laser amplifiers,” Appl. Phys. Lett. 68, 2787-2789 (1996).
[CrossRef]

K. J. Vahala, J. Zhou, D. Geraghty, R. Lee, M. Newkirk, and B. Miller, “Four-wave mixing in semiconductor travelling-wave amplifiers for wavelength conversion in all-optical networks,” Int. J. High Speed Electron. Syst. 7, 153-177 (1996).
[CrossRef]

A. E. Kelly, I. F. Lealman, L. J. Rivers, S. D. Perrin, and M. Silver, “Polarisation insensitive, 25 dB gain semiconductor laser amplifier without antireflection coatings,” Electron. Lett. 32, 1835-1836 (1996).
[CrossRef]

1995 (3)

D. J. Jones, L. M. Zhang, J. E. Carroll, and D. D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
[CrossRef]

M. Kovačević and A. Acampora, “Benefits of wavelength translation in all-optical clear-channel networks,” IEEE J. Sel. Areas Commun. 14, 868-880 (1995).

P. G. Eliseev and V. V. Luc, “Semiconductor optical amplifiers: multifunctional possibilities, photoresponse and phase shift properties,” Pure Appl. Opt. 4, 295-313 (1995).
[CrossRef]

1994 (2)

A. Uskov, J. Mork, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769-1781 (1994).
[CrossRef]

W. M. Yee and K. A. Shore, “Nearly degenerate four-wave mixing in laser diodes with nonuniform longitudinal gain distribution,” J. Opt. Soc. Am. B 11, 1221-1228 (1994).
[CrossRef]

1992 (1)

D. C. Hutchings, M. Sheik-bahae, D. J. Hagan, and E. W. V. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1-30 (1992).
[CrossRef]

1990 (1)

T. Mukai and T. Saitoh, “Detuning characterisitcs and conversion efficiency of nearly degenerate four-wave mixing in a 1.5-μm travelling-wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 26, 865-875 (1990).
[CrossRef]

1989 (1)

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

1988 (1)

1987 (3)

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

Y. L. Wong and J. E. Carroll, “A travelling-wave rate equation analysis for semiconductor lasers,” Solid-State Electron. 30, 13-19 (1987).
[CrossRef]

K. Inoue, T. Mukai, and T. Saitoh, “Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier,” Appl. Phys. Lett. 51, 1051-1053 (1987).
[CrossRef]

1986 (1)

Y. R. Shen, “Basic considerations of four-wave mixing and dynamic gratings,” IEEE J. Quantum Electron. QE-22, 1196-1203 (1986).
[CrossRef]

1985 (1)

T. Mukai, Y. Yamamoto, and T. Kimura, “Optical amplification by semiconductor lasers,” Semicond. Semimetals 22, 265-317 (1985).
[CrossRef]

Acampora, A.

M. Kovačević and A. Acampora, “Benefits of wavelength translation in all-optical clear-channel networks,” IEEE J. Sel. Areas Commun. 14, 868-880 (1995).

Agrawal, G. P.

Baba, T.

T. Baba, “Photonic crystals remember the light,” Nat. Photonics 1, 11-12 (2007).
[CrossRef]

Bischoff, S.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Bream, P. J.

P. J. Bream, S. Sujecki, and E. C. Larkins, “Nonequilibrium gain and nonlinear optical response of QWs for functional photonic devices,” presented at the 6th International Conference on Numerical Simulation of Optoelectronic Devices, Nanyang Technological University, Singapore, 11-14 September 2006.

Bründermann, E.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Buxens, A.

Carroll, J. E.

E. M. Pratt. and J. E. Carroll, “Gain modelling and particle balance in semiconductor lasers,” IEE Proc.: Optoelectron. 147, 77-82 (2000).
[CrossRef]

D. J. Jones, L. M. Zhang, J. E. Carroll, and D. D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
[CrossRef]

Y. L. Wong and J. E. Carroll, “A travelling-wave rate equation analysis for semiconductor lasers,” Solid-State Electron. 30, 13-19 (1987).
[CrossRef]

Caulfield, J. H.

J. H. Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik (Stuttgart) 117, 199-209 (2006).
[CrossRef]

Chow, W. W.

W. W. Chow and S. W. Koch, Semiconductor-LaserFundamentals: Physics of Gain Materials (Springer-Verlag, 1999).

Clausen, A. T.

Connelly, M. J.

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37, 439-447 (2001).
[CrossRef]

Dai, Z.

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, “Numerical simulation of broad-area high-power semiconductor laser amplifiers,” IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[CrossRef]

Das, N. K.

N. K. Das, Y. Yamayoshi, and H. Kawagushi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184-1192 (2000).
[CrossRef]

Diez, S.

G. Toptchiyski, S. Kindt, K. Petermann, E. Hillinger, S. Diez, and H. G. Weber, “Time-domain modeling of semiconductor optical amplifiers for OTDM applications,” J. Lightwave Technol. 17, 2577-2583 (1999).
[CrossRef]

S. Diez, C. Schmidt, R. Ludwig, H. G. Weber, K. Obermann, S. Kindt, I. Koltchanov, and K. Petermann, “Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching,” IEEE J. Sel. Top. Quantum Electron. 3, 1131-1145 (1997).
[CrossRef]

I. Koltchanov, S. Kindt, K. Petermann, S. Diez, R. Ludwig, R. Schnabel, and H. G. Weber, “Analytical theory of terahertz four-wave mixing in semiconductor-laser amplifiers,” Appl. Phys. Lett. 68, 2787-2789 (1996).
[CrossRef]

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, 1986).

Ebeling, K. J.

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, “Numerical simulation of broad-area high-power semiconductor laser amplifiers,” IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[CrossRef]

Eliseev, P. G.

P. G. Eliseev and V. V. Luc, “Semiconductor optical amplifiers: multifunctional possibilities, photoresponse and phase shift properties,” Pure Appl. Opt. 4, 295-313 (1995).
[CrossRef]

Elsasser, W.

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

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge Univ. Press, 2002).

Gavrielides, A.

J. K. White, J. V. Moloney, A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus, “Multilongitudinal-mode dynamics in a semiconductor laser subject to optical injection,” IEEE J. Quantum Electron. 34, 1469-1473 (1998).
[CrossRef]

Geraghty, D.

K. J. Vahala, J. Zhou, D. Geraghty, R. Lee, M. Newkirk, and B. Miller, “Four-wave mixing in semiconductor travelling-wave amplifiers for wavelength conversion in all-optical networks,” Int. J. High Speed Electron. Syst. 7, 153-177 (1996).
[CrossRef]

Geraghty, D. F.

D. F. Geraghty, R. B. Lee, K. J. Vahala, M. Verdiell, M. Ziari, and A. Mathur, “Wavelength conversion up to 18 nm at 10 Gb/s by four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 9, 452-454 (1997).
[CrossRef]

Gobel, E. O.

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

Hagan, D. J.

D. C. Hutchings, M. Sheik-bahae, D. J. Hagan, and E. W. V. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1-30 (1992).
[CrossRef]

Hasselbeck, M. P.

M. Sheik-Bahae and M. P. Hasselbeck, “Third-order optical nonlinearities,” in OSA Handbook of Optics. IV, M.Bass, ed. (Mc-GrawHill, 2001), pp. 17.1-17.34.

Havenith, M.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Hillinger, E.

Hoffmann, S.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Hofmann, M.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Hohl, A.

J. K. White, J. V. Moloney, A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus, “Multilongitudinal-mode dynamics in a semiconductor laser subject to optical injection,” IEEE J. Quantum Electron. 34, 1469-1473 (1998).
[CrossRef]

Hunziker, G.

R. Paiella, G. Hunziker, U. Koren, and K. J. Vahala, “Polarization-dependent optical nonlinearities of multiquantum-well laser amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3, 529-540 (1997).
[CrossRef]

Hur, S.

Hutchings, D. C.

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D. J. Jones, L. M. Zhang, J. E. Carroll, and D. D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
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J. K. White, J. V. Moloney, A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus, “Multilongitudinal-mode dynamics in a semiconductor laser subject to optical injection,” IEEE J. Quantum Electron. 34, 1469-1473 (1998).
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N. K. Das, Y. Yamayoshi, and H. Kawagushi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184-1192 (2000).
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A. E. Kelly, I. F. Lealman, L. J. Rivers, S. D. Perrin, and M. Silver, “Polarisation insensitive, 25 dB gain semiconductor laser amplifier without antireflection coatings,” Electron. Lett. 32, 1835-1836 (1996).
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D. Nesset, T. Kelly, and D. Marcenac, “All-optical wavelength conversion using SOA nonlinearities,” IEEE Commun. Mag. 36, 56-61 (1998).
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Kimura, T.

T. Mukai, Y. Yamamoto, and T. Kimura, “Optical amplification by semiconductor lasers,” Semicond. Semimetals 22, 265-317 (1985).
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G. Toptchiyski, S. Kindt, K. Petermann, E. Hillinger, S. Diez, and H. G. Weber, “Time-domain modeling of semiconductor optical amplifiers for OTDM applications,” J. Lightwave Technol. 17, 2577-2583 (1999).
[CrossRef]

S. Diez, C. Schmidt, R. Ludwig, H. G. Weber, K. Obermann, S. Kindt, I. Koltchanov, and K. Petermann, “Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching,” IEEE J. Sel. Top. Quantum Electron. 3, 1131-1145 (1997).
[CrossRef]

I. Koltchanov, S. Kindt, K. Petermann, S. Diez, R. Ludwig, R. Schnabel, and H. G. Weber, “Analytical theory of terahertz four-wave mixing in semiconductor-laser amplifiers,” Appl. Phys. Lett. 68, 2787-2789 (1996).
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S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
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S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
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I. Koltchanov, S. Kindt, K. Petermann, S. Diez, R. Ludwig, R. Schnabel, and H. G. Weber, “Analytical theory of terahertz four-wave mixing in semiconductor-laser amplifiers,” Appl. Phys. Lett. 68, 2787-2789 (1996).
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Larkins, E. C.

P. J. Bream, S. Sujecki, and E. C. Larkins, “Nonequilibrium gain and nonlinear optical response of QWs for functional photonic devices,” presented at the 6th International Conference on Numerical Simulation of Optoelectronic Devices, Nanyang Technological University, Singapore, 11-14 September 2006.

Lealman, I. F.

A. E. Kelly, I. F. Lealman, L. J. Rivers, S. D. Perrin, and M. Silver, “Polarisation insensitive, 25 dB gain semiconductor laser amplifier without antireflection coatings,” Electron. Lett. 32, 1835-1836 (1996).
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K. J. Vahala, J. Zhou, D. Geraghty, R. Lee, M. Newkirk, and B. Miller, “Four-wave mixing in semiconductor travelling-wave amplifiers for wavelength conversion in all-optical networks,” Int. J. High Speed Electron. Syst. 7, 153-177 (1996).
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D. F. Geraghty, R. B. Lee, K. J. Vahala, M. Verdiell, M. Ziari, and A. Mathur, “Wavelength conversion up to 18 nm at 10 Gb/s by four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 9, 452-454 (1997).
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[CrossRef]

I. Koltchanov, S. Kindt, K. Petermann, S. Diez, R. Ludwig, R. Schnabel, and H. G. Weber, “Analytical theory of terahertz four-wave mixing in semiconductor-laser amplifiers,” Appl. Phys. Lett. 68, 2787-2789 (1996).
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D. Nesset, T. Kelly, and D. Marcenac, “All-optical wavelength conversion using SOA nonlinearities,” IEEE Commun. Mag. 36, 56-61 (1998).
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D. J. Jones, L. M. Zhang, J. E. Carroll, and D. D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
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A. Uskov, J. Mork, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769-1781 (1994).
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D. F. Geraghty, R. B. Lee, K. J. Vahala, M. Verdiell, M. Ziari, and A. Mathur, “Wavelength conversion up to 18 nm at 10 Gb/s by four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 9, 452-454 (1997).
[CrossRef]

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S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
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I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for III-V compound semiconductors and their alloys,” Appl. Sci. Res., Sect. B 89, 5815-5875 (2001).

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K. J. Vahala, J. Zhou, D. Geraghty, R. Lee, M. Newkirk, and B. Miller, “Four-wave mixing in semiconductor travelling-wave amplifiers for wavelength conversion in all-optical networks,” Int. J. High Speed Electron. Syst. 7, 153-177 (1996).
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[CrossRef]

J. K. White, J. V. Moloney, A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus, “Multilongitudinal-mode dynamics in a semiconductor laser subject to optical injection,” IEEE J. Quantum Electron. 34, 1469-1473 (1998).
[CrossRef]

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A. Uskov, J. Mork, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769-1781 (1994).
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Mørk, J.

Moskalenko, A. S.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
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T. Mukai and T. Saitoh, “Detuning characterisitcs and conversion efficiency of nearly degenerate four-wave mixing in a 1.5-μm travelling-wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 26, 865-875 (1990).
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K. Inoue, T. Mukai, and T. Saitoh, “Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier,” Appl. Phys. Lett. 51, 1051-1053 (1987).
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T. Mukai, Y. Yamamoto, and T. Kimura, “Optical amplification by semiconductor lasers,” Semicond. Semimetals 22, 265-317 (1985).
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D. Nesset, T. Kelly, and D. Marcenac, “All-optical wavelength conversion using SOA nonlinearities,” IEEE Commun. Mag. 36, 56-61 (1998).
[CrossRef]

Newkirk, M.

K. J. Vahala, J. Zhou, D. Geraghty, R. Lee, M. Newkirk, and B. Miller, “Four-wave mixing in semiconductor travelling-wave amplifiers for wavelength conversion in all-optical networks,” Int. J. High Speed Electron. Syst. 7, 153-177 (1996).
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S. Diez, C. Schmidt, R. Ludwig, H. G. Weber, K. Obermann, S. Kindt, I. Koltchanov, and K. Petermann, “Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching,” IEEE J. Sel. Top. Quantum Electron. 3, 1131-1145 (1997).
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O'Mahony, M. J.

C. Politi, D. Klonidis, and M. J. O'Mahony, “Dynamic behaviour of wavelength converters based on FWM in SOAs,” IEEE J. Quantum Electron. 42, 108-125 (2006).
[CrossRef]

Paiella, R.

R. Paiella, G. Hunziker, U. Koren, and K. J. Vahala, “Polarization-dependent optical nonlinearities of multiquantum-well laser amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3, 529-540 (1997).
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R. Nietzke, P. Panknin, W. Elsasser, and E. O. Gobel, “Four-wave mixing in GaAs/AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 25, 1399-1406 (1989).
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X. Li and J. Park, “Time-domain modeling and simulation of the broadband behavior of semiconductor optical amplifiers,” Proc. SPIE 5248, 227-239 (2003).
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A. E. Kelly, I. F. Lealman, L. J. Rivers, S. D. Perrin, and M. Silver, “Polarisation insensitive, 25 dB gain semiconductor laser amplifier without antireflection coatings,” Electron. Lett. 32, 1835-1836 (1996).
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G. Toptchiyski, S. Kindt, K. Petermann, E. Hillinger, S. Diez, and H. G. Weber, “Time-domain modeling of semiconductor optical amplifiers for OTDM applications,” J. Lightwave Technol. 17, 2577-2583 (1999).
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S. Diez, C. Schmidt, R. Ludwig, H. G. Weber, K. Obermann, S. Kindt, I. Koltchanov, and K. Petermann, “Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching,” IEEE J. Sel. Top. Quantum Electron. 3, 1131-1145 (1997).
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I. Koltchanov, S. Kindt, K. Petermann, S. Diez, R. Ludwig, R. Schnabel, and H. G. Weber, “Analytical theory of terahertz four-wave mixing in semiconductor-laser amplifiers,” Appl. Phys. Lett. 68, 2787-2789 (1996).
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C. Politi, D. Klonidis, and M. J. O'Mahony, “Dynamic behaviour of wavelength converters based on FWM in SOAs,” IEEE J. Quantum Electron. 42, 108-125 (2006).
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I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for III-V compound semiconductors and their alloys,” Appl. Sci. Res., Sect. B 89, 5815-5875 (2001).

Rivers, L. J.

A. E. Kelly, I. F. Lealman, L. J. Rivers, S. D. Perrin, and M. Silver, “Polarisation insensitive, 25 dB gain semiconductor laser amplifier without antireflection coatings,” Electron. Lett. 32, 1835-1836 (1996).
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Saito, S.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
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T. Mukai and T. Saitoh, “Detuning characterisitcs and conversion efficiency of nearly degenerate four-wave mixing in a 1.5-μm travelling-wave semiconductor laser amplifier,” IEEE J. Quantum Electron. 26, 865-875 (1990).
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K. Inoue, T. Mukai, and T. Saitoh, “Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier,” Appl. Phys. Lett. 51, 1051-1053 (1987).
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Sakai, K.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. V. Moloney, A. S. Moskalenko, M. Kira, S. W. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
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S. Diez, C. Schmidt, R. Ludwig, H. G. Weber, K. Obermann, S. Kindt, I. Koltchanov, and K. Petermann, “Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching,” IEEE J. Sel. Top. Quantum Electron. 3, 1131-1145 (1997).
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I. Koltchanov, S. Kindt, K. Petermann, S. Diez, R. Ludwig, R. Schnabel, and H. G. Weber, “Analytical theory of terahertz four-wave mixing in semiconductor-laser amplifiers,” Appl. Phys. Lett. 68, 2787-2789 (1996).
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J. Wang and H. Schweizer, “A quantitative comparison of the classical rate-equation model with the carrier heating model on dynamics of the quantum-well laser: the role of carrier energy relaxation, electron-hole interaction, and Auger effect,” IEEE J. Quantum Electron. 33, 1350-1359 (1997).
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D. C. Hutchings, M. Sheik-bahae, D. J. Hagan, and E. W. V. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1-30 (1992).
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A. E. Kelly, I. F. Lealman, L. J. Rivers, S. D. Perrin, and M. Silver, “Polarisation insensitive, 25 dB gain semiconductor laser amplifier without antireflection coatings,” Electron. Lett. 32, 1835-1836 (1996).
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D. C. Hutchings, M. Sheik-bahae, D. J. Hagan, and E. W. V. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24, 1-30 (1992).
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P. J. Bream, S. Sujecki, and E. C. Larkins, “Nonequilibrium gain and nonlinear optical response of QWs for functional photonic devices,” presented at the 6th International Conference on Numerical Simulation of Optoelectronic Devices, Nanyang Technological University, Singapore, 11-14 September 2006.

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Summerfield, M. A.

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J. M. Tang and K. A. Shore, “Carrier diffusion and depletion effects on multiwave mixing in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 1280-1286 (1997).
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge Univ. Press, 2002).

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Tucker, R. S.

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Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, “Numerical simulation of broad-area high-power semiconductor laser amplifiers,” IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[CrossRef]

Uskov, A.

A. Uskov, J. Mork, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769-1781 (1994).
[CrossRef]

Vahala, K. J.

R. Paiella, G. Hunziker, U. Koren, and K. J. Vahala, “Polarization-dependent optical nonlinearities of multiquantum-well laser amplifiers,” IEEE J. Sel. Top. Quantum Electron. 3, 529-540 (1997).
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D. F. Geraghty, R. B. Lee, K. J. Vahala, M. Verdiell, M. Ziari, and A. Mathur, “Wavelength conversion up to 18 nm at 10 Gb/s by four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 9, 452-454 (1997).
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K. J. Vahala, J. Zhou, D. Geraghty, R. Lee, M. Newkirk, and B. Miller, “Four-wave mixing in semiconductor travelling-wave amplifiers for wavelength conversion in all-optical networks,” Int. J. High Speed Electron. Syst. 7, 153-177 (1996).
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Verdiell, M.

D. F. Geraghty, R. B. Lee, K. J. Vahala, M. Verdiell, M. Ziari, and A. Mathur, “Wavelength conversion up to 18 nm at 10 Gb/s by four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 9, 452-454 (1997).
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge Univ. Press, 2002).

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J. H. Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik (Stuttgart) 117, 199-209 (2006).
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I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for III-V compound semiconductors and their alloys,” Appl. Sci. Res., Sect. B 89, 5815-5875 (2001).

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J. Wang and H. Schweizer, “A quantitative comparison of the classical rate-equation model with the carrier heating model on dynamics of the quantum-well laser: the role of carrier energy relaxation, electron-hole interaction, and Auger effect,” IEEE J. Quantum Electron. 33, 1350-1359 (1997).
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G. Toptchiyski, S. Kindt, K. Petermann, E. Hillinger, S. Diez, and H. G. Weber, “Time-domain modeling of semiconductor optical amplifiers for OTDM applications,” J. Lightwave Technol. 17, 2577-2583 (1999).
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S. Diez, C. Schmidt, R. Ludwig, H. G. Weber, K. Obermann, S. Kindt, I. Koltchanov, and K. Petermann, “Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching,” IEEE J. Sel. Top. Quantum Electron. 3, 1131-1145 (1997).
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J. K. White, J. V. Moloney, A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus, “Multilongitudinal-mode dynamics in a semiconductor laser subject to optical injection,” IEEE J. Quantum Electron. 34, 1469-1473 (1998).
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N. K. Das, Y. Yamayoshi, and H. Kawagushi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184-1192 (2000).
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Yee, W. M.

Zavalin, A.

J. H. Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik (Stuttgart) 117, 199-209 (2006).
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D. J. Jones, L. M. Zhang, J. E. Carroll, and D. D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
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K. J. Vahala, J. Zhou, D. Geraghty, R. Lee, M. Newkirk, and B. Miller, “Four-wave mixing in semiconductor travelling-wave amplifiers for wavelength conversion in all-optical networks,” Int. J. High Speed Electron. Syst. 7, 153-177 (1996).
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D. F. Geraghty, R. B. Lee, K. J. Vahala, M. Verdiell, M. Ziari, and A. Mathur, “Wavelength conversion up to 18 nm at 10 Gb/s by four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 9, 452-454 (1997).
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Figures (6)

Fig. 1
Fig. 1

Representation of longitudinal grid showing positions where fields and carrier densities are estimated.

Fig. 2
Fig. 2

Assessing recursive filters designed for (a) gain spectrum, (b) refractive index change. The number of poles was set to 8. The fits were obtained by inputting a delta function to the designed filter.

Fig. 3
Fig. 3

Simulated spectra (a) input optical field; (b) output optical field; (c) carrier density: detuning 2 GHz , pump power 0.7 dBm , probe power 0.8 dBm , I bias = 150 mA ; (d) same as in (c) except higher pump power ( + 4.7 dBm ) . Logarithmic scale used for clarity.

Fig. 4
Fig. 4

Normalized carrier density modulation as a function of the detuning frequency; pump power = 0.7 dBm , probe power. 0.8 dBm , I bias = 150 mA .

Fig. 5
Fig. 5

(a) CDM amplitude as a function of bias current: detuning = 1.23 GHz ; pump power = 0.7 dBm ; probe power = 0.8 dBm ; TSA1, truncated series assumption, truncated at the first harmonic. (b) Measured small signal gain dependence on bias current for input power of 28 dBm .

Fig. 6
Fig. 6

Dependence of CDM amplitude on input pump power for different probe powers: detuning = 1.230 GHz , I bias = 150 mA . (a) Probe power = 0.8 dBm . (b) Probe power = + 4.7 dBm .

Tables (1)

Tables Icon

Table 1 SOA Simulation Parameters

Equations (22)

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× × E + n 2 c 2 2 E t 2 = 1 ϵ 0 c 2 2 P t 2 ,
E ( x , y , z , t ) = 1 2 U ( x , y ) { ψ + ( z , t ) exp [ i ( ω t k z ) ] + ψ ( z , t ) exp [ i ( ω t + k z ) ] + c.c } ,
P ( x , y , z , t ) = 1 2 U ( x , y ) { P + ( z , t ) exp [ i ( ω t k z ) ] + P ( z , t ) exp [ i ( ω t + k z ) ] + c.c. } ,
n c ψ ± t ± ψ ± z = i Γ x y k 2 ϵ 0 n 2 P ± ,
ψ + ( 0 , t ) = R 1 ψ ( 0 , t ) + 1 R 1 ψ in 1 ( 0 , t ) ,
ψ ( L , t ) = R 2 ψ + ( L , t ) + 1 R 2 ψ in 2 ( L , t ) ,
N ( z , t ) t = η J ( z , t ) e d γ nr ( N ) N i Γ x y 4 { ( ψ + ) ( P + ) * + ( ψ ) ( P ) * c.c. } ,
J ext ( z , t ) = V bias V jcn ( z , t ) r s ,
V jcn ( z , t ) = E F n ( z , t ) E F p ( z , t ) e .
E F n , p = k T [ ln ( N N c , v ) + 1 2 ( N N c , v ) + 1 24 ( N N c , v ) 2 0.0000347 ( N N c , v ) 3 ] .
P ̃ ± ( ω , N , E ̃ ) = ϵ 0 χ eff ( ω , N , E ̃ ) E ̃ ± .
χ eff = n χ ( n + 1 ) E ̃ n : n = 0 , 1 , 2 .
χ eff ( ω , N , E ̃ ) = 1 k { i [ g net ( ω , N , E ̃ ) ( 1 Γ x y Γ x y ) α conf ] + k Δ n ( ω , N , E ̃ ) } ,
g ( ω ) = 1 ω n ¯ g π e 2 n 2 c ϵ 0 m 0 2 i c = i v | M T | 2 ρ red m D ( f n f p ) ,
R s p ( ω ) = 1 ω π e 2 n 2 ϵ 0 m 0 2 i c = i v | M avg | 2 ρ red m D f n ( 1 f p ) ,
| M avg | 2 = 1 3 all 3 polarizations | M T | 2 .
L ( E e h ω ) = τ in π sech ( E e h ω τ in ) ,
g ( ω ) = g ( N , T ) 1 + ϵ shb S ( ω ) ,
Δ n ( ω ; ξ ) = c 2 π ω Δ g ( ω ; ξ ) ω ω d ω ,
y [ n ] = a 0 x [ n ] + a 1 x [ n 1 ] + a 2 x [ n 2 ] + + b 1 y [ n 1 ] + b 2 y [ n 2 ] + ,
| ψ ± | j n + 1 = γ j + 1 n | ψ ± | j + 1 n + γ j 1 n | ψ ± | j 1 n + γ j ( g , ind ) n × { r = 0 N p 1 [ | i a r ( g ) | j 1 2 n + 1 2 + | k a r ( ind ) | j 1 2 n + 1 2 ] | ψ in ± | j n r + r = 1 N p 1 [ | i b r ( g ) | j 1 2 n + 1 2 + | k b r ( ind ) | j 1 2 n + 1 2 ] | ψ out ± | j n r } .
Δ N ( t ) = N ( t ) N S S ,

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