Abstract

Nonlinearity effects, arising within a semiconductor optical amplifier (SOA), have been deeply investigated with particular interest for exploiting them in wavelength conversion. This application shrinks the research area to a precise scenario: a strong pump signal travels through the active medium simultaneously with a modulated signal to be converted. In this case, it is possible to neglect the spectral distribution of the optical power and phase relationship between propagating signals. SOAs have been also studied as line amplifiers for wavelength-division multiplexing (WDM) phase-modulated signals. Aim of this paper is to extend the propagation model in an SOA, in order to simulate nonlinearities occurring in the amplification of a WDM comb signal evaluating-wave mixing on constant envelope modulation schemes (differential phase-shift keying). This can be carried out due to an enhanced analytical model based on the optical field and medium interaction, overcoming the wide-used rate equation approach, which is based on the overall photons density.

© 2009 IEEE

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  1. A. Reale, S. D. Carlo, P. Lugli, D. Campi, C. Cacciatore, A. Stano, G. Fornuto, "Study of gain compression mechanisms in multiple-quantum-well In$_{1-x}$Ga$_x$As semiconductor optical amplifiers," IEEE J. Quantum Electron. 35, 1697-1703 (1999).
  2. G. Contestabile, N. Calabretta, M. Presi, E. Ciaramella, "Single and multicast wavelength conversion at 40 gb/s by means of fast nonlinear polarization switching in an SOA," IEEE Photon. Technol. Lett. 17, 2652-2654 (2005).
  3. H. Simos, A. Bogris, D. Syvridis, "Investigation of a 2R all-optical regenerator based on four-wave mixing in a semiconductor optical amplifier," J. Lightw. Technol. 22, 595-604 (2004).
  4. G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, L. Potì, "Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate," IEEE Photon. Technol. Lett. 18, 917-919 (2006).
  5. C. Schubert, S. Diez, J. Berger, R. Ludwig, U. Feiste, H. G. Weber, G. Toptchiyski, K. Petermann, V. Krajinovic, "160-gb/s all-optical demultiplexing using a gain-transparent ultrafast-nonlinear interferometer (GT-UNI)," IEEE Photon. Technol. Lett. 13, 475-477 (2001).
  6. E. Ciaramella, A. D'Errico, V. Donzella, "Using semiconductor optical-amplifiers with constant envelope WDM signals," IEEE J. Quantum Electron. 44, 403-409 (2008).
  7. I. Fatadin, D. Ives, M. Wicks, "Numerical simulation of intensity and phase noise from extracted parameters for cw dfb lasers," IEEE J. Quantum Electron. 42, 934-941 (2006).
  8. S. Balle, "Simple analytical approximations for the gain and refractive index spectra in quantum-well lasers," Phys. Rev. A 57, 1304-1312 (1998).
  9. J. Revuelta, L. Pesquera, S. Balle, "Wavelength-dependent output properties of quantum well optical amplifiers," Proc. Conf. Laser Electro-Opt. (2000) pp. 420-421.
  10. G. Bosco, P. Poggiolini, "On the $Q$-factor inaccuracy in the performance analysis of optical direct-detection dpsk systems," IEEE Photon. Technol. Lett. 16, 665-667 (2004).
  11. G. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  12. R. Kazarinov, C. Henry, R. Logan, "Longitudinal mode self-stabilization in semiconductor lasers," J. Appl. Phys. 53, 4631-4644 (1982).
  13. A. Yariv, Quantum Electronics (Wiley, 1989).
  14. B. Thedrez, A. Jones, R. Frey, "Two-level description of gain and mixing susceptibility in amplifying semiconductor materials," IEEE J. Quantum Electron. 24, 1499-1506 (1988).
  15. D. Hjelme, A. Mickelson, "Gain nonlinearities due to carrier density dependent dispersion in semiconductor lasers," IEEE J. Quantum Electron. 25, 1625-1631 (1989).
  16. G. Agrawal, "Gain nonlinearities in semiconductor lasers: Theory and application to distributed feedback lasers," IEEE J. Quantum Electron. QE-23, 860-868 (1987).
  17. M. Asada, A. Kameyama, Y. Suematsu, "Gain and intervalence band absorption in quantum-well lasers," IEEE J. Quantum Electron. QE-20, 745-753 (1984).
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  19. M. Connelly, Semiconductor Optical Amplifiers (Kluwer, 2002).
  20. A. Matsumoto, K. Nishimura, K. Utaka, M. Usami, "Operational design on high-speed semiconductor optical amplifier with assist light for application to wavelength converters using cross-phase modulation," IEEE J. Quantum Electron. 42, 313-323 (2006).
  21. N. Nilsson, "Empirical approximation for the fermi energy of a semiconductor with parabolic bands," Appl. Phys. Lett. 33, 653-654 (1978).
  22. N. Storkfelt, B. Mikkelsen, D. Olesen, M. Yamaguchi, K. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5 $\mu$m ridge waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).
  23. C. Ning, R. Indik, J. Moloney, "Effective bloch equations for semiconductor lasers and amplifiers," IEEE J. Quantum Electron. 33, 1543-1550 (1997).
  24. A. Reale, S. D. Carlo, P. Lugli, "Gain dynamics in traveling-wave optical amplifiers," IEEE J. Sel. Topics Quantum Electron. 7, 293-299 (2001).
  25. K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer Science+Business Media, Inc., 2005).
  26. F. Matera, M. Settembre, "Comparison of the performance of optically amplified transmission systems," IEEE J. Lightw. Technol. 14, 1-12 (1996).
  27. A. Mecozzi, "Limits to long-haul coherent transmission set by the kerr nonlinearity and noise of the in-line amplifiers," IEEE J. Lightw. Technol. 12, 1993-2000 (1994).
  28. N. S. Bergano, F. Kerfoot, C. Davidson, "Margin measurements in optical amplifier systems," IEEE Photon. Technol. Lett. 5, 304-306 (1993).

2008 (1)

E. Ciaramella, A. D'Errico, V. Donzella, "Using semiconductor optical-amplifiers with constant envelope WDM signals," IEEE J. Quantum Electron. 44, 403-409 (2008).

2006 (3)

I. Fatadin, D. Ives, M. Wicks, "Numerical simulation of intensity and phase noise from extracted parameters for cw dfb lasers," IEEE J. Quantum Electron. 42, 934-941 (2006).

G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, L. Potì, "Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate," IEEE Photon. Technol. Lett. 18, 917-919 (2006).

A. Matsumoto, K. Nishimura, K. Utaka, M. Usami, "Operational design on high-speed semiconductor optical amplifier with assist light for application to wavelength converters using cross-phase modulation," IEEE J. Quantum Electron. 42, 313-323 (2006).

2005 (1)

G. Contestabile, N. Calabretta, M. Presi, E. Ciaramella, "Single and multicast wavelength conversion at 40 gb/s by means of fast nonlinear polarization switching in an SOA," IEEE Photon. Technol. Lett. 17, 2652-2654 (2005).

2004 (2)

H. Simos, A. Bogris, D. Syvridis, "Investigation of a 2R all-optical regenerator based on four-wave mixing in a semiconductor optical amplifier," J. Lightw. Technol. 22, 595-604 (2004).

G. Bosco, P. Poggiolini, "On the $Q$-factor inaccuracy in the performance analysis of optical direct-detection dpsk systems," IEEE Photon. Technol. Lett. 16, 665-667 (2004).

2001 (2)

C. Schubert, S. Diez, J. Berger, R. Ludwig, U. Feiste, H. G. Weber, G. Toptchiyski, K. Petermann, V. Krajinovic, "160-gb/s all-optical demultiplexing using a gain-transparent ultrafast-nonlinear interferometer (GT-UNI)," IEEE Photon. Technol. Lett. 13, 475-477 (2001).

A. Reale, S. D. Carlo, P. Lugli, "Gain dynamics in traveling-wave optical amplifiers," IEEE J. Sel. Topics Quantum Electron. 7, 293-299 (2001).

1999 (1)

A. Reale, S. D. Carlo, P. Lugli, D. Campi, C. Cacciatore, A. Stano, G. Fornuto, "Study of gain compression mechanisms in multiple-quantum-well In$_{1-x}$Ga$_x$As semiconductor optical amplifiers," IEEE J. Quantum Electron. 35, 1697-1703 (1999).

1998 (1)

S. Balle, "Simple analytical approximations for the gain and refractive index spectra in quantum-well lasers," Phys. Rev. A 57, 1304-1312 (1998).

1997 (1)

C. Ning, R. Indik, J. Moloney, "Effective bloch equations for semiconductor lasers and amplifiers," IEEE J. Quantum Electron. 33, 1543-1550 (1997).

1996 (1)

F. Matera, M. Settembre, "Comparison of the performance of optically amplified transmission systems," IEEE J. Lightw. Technol. 14, 1-12 (1996).

1994 (2)

A. Mecozzi, "Limits to long-haul coherent transmission set by the kerr nonlinearity and noise of the in-line amplifiers," IEEE J. Lightw. Technol. 12, 1993-2000 (1994).

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

1993 (1)

N. S. Bergano, F. Kerfoot, C. Davidson, "Margin measurements in optical amplifier systems," IEEE Photon. Technol. Lett. 5, 304-306 (1993).

1991 (1)

N. Storkfelt, B. Mikkelsen, D. Olesen, M. Yamaguchi, K. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5 $\mu$m ridge waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).

1989 (1)

D. Hjelme, A. Mickelson, "Gain nonlinearities due to carrier density dependent dispersion in semiconductor lasers," IEEE J. Quantum Electron. 25, 1625-1631 (1989).

1988 (1)

B. Thedrez, A. Jones, R. Frey, "Two-level description of gain and mixing susceptibility in amplifying semiconductor materials," IEEE J. Quantum Electron. 24, 1499-1506 (1988).

1987 (1)

G. Agrawal, "Gain nonlinearities in semiconductor lasers: Theory and application to distributed feedback lasers," IEEE J. Quantum Electron. QE-23, 860-868 (1987).

1984 (1)

M. Asada, A. Kameyama, Y. Suematsu, "Gain and intervalence band absorption in quantum-well lasers," IEEE J. Quantum Electron. QE-20, 745-753 (1984).

1982 (1)

R. Kazarinov, C. Henry, R. Logan, "Longitudinal mode self-stabilization in semiconductor lasers," J. Appl. Phys. 53, 4631-4644 (1982).

1978 (1)

N. Nilsson, "Empirical approximation for the fermi energy of a semiconductor with parabolic bands," Appl. Phys. Lett. 33, 653-654 (1978).

Appl. Phys. Lett. (1)

N. Nilsson, "Empirical approximation for the fermi energy of a semiconductor with parabolic bands," Appl. Phys. Lett. 33, 653-654 (1978).

IEEE J. Lightw. Technol. (2)

F. Matera, M. Settembre, "Comparison of the performance of optically amplified transmission systems," IEEE J. Lightw. Technol. 14, 1-12 (1996).

A. Mecozzi, "Limits to long-haul coherent transmission set by the kerr nonlinearity and noise of the in-line amplifiers," IEEE J. Lightw. Technol. 12, 1993-2000 (1994).

IEEE J. Quantum Electron. (10)

A. Matsumoto, K. Nishimura, K. Utaka, M. Usami, "Operational design on high-speed semiconductor optical amplifier with assist light for application to wavelength converters using cross-phase modulation," IEEE J. Quantum Electron. 42, 313-323 (2006).

C. Ning, R. Indik, J. Moloney, "Effective bloch equations for semiconductor lasers and amplifiers," IEEE J. Quantum Electron. 33, 1543-1550 (1997).

A. Reale, S. D. Carlo, P. Lugli, D. Campi, C. Cacciatore, A. Stano, G. Fornuto, "Study of gain compression mechanisms in multiple-quantum-well In$_{1-x}$Ga$_x$As semiconductor optical amplifiers," IEEE J. Quantum Electron. 35, 1697-1703 (1999).

E. Ciaramella, A. D'Errico, V. Donzella, "Using semiconductor optical-amplifiers with constant envelope WDM signals," IEEE J. Quantum Electron. 44, 403-409 (2008).

I. Fatadin, D. Ives, M. Wicks, "Numerical simulation of intensity and phase noise from extracted parameters for cw dfb lasers," IEEE J. Quantum Electron. 42, 934-941 (2006).

B. Thedrez, A. Jones, R. Frey, "Two-level description of gain and mixing susceptibility in amplifying semiconductor materials," IEEE J. Quantum Electron. 24, 1499-1506 (1988).

D. Hjelme, A. Mickelson, "Gain nonlinearities due to carrier density dependent dispersion in semiconductor lasers," IEEE J. Quantum Electron. 25, 1625-1631 (1989).

G. Agrawal, "Gain nonlinearities in semiconductor lasers: Theory and application to distributed feedback lasers," IEEE J. Quantum Electron. QE-23, 860-868 (1987).

M. Asada, A. Kameyama, Y. Suematsu, "Gain and intervalence band absorption in quantum-well lasers," IEEE J. Quantum Electron. QE-20, 745-753 (1984).

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

IEEE J. Sel. Topics Quantum Electron. (1)

A. Reale, S. D. Carlo, P. Lugli, "Gain dynamics in traveling-wave optical amplifiers," IEEE J. Sel. Topics Quantum Electron. 7, 293-299 (2001).

IEEE Photon. Technol. Lett. (6)

N. Storkfelt, B. Mikkelsen, D. Olesen, M. Yamaguchi, K. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5 $\mu$m ridge waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).

N. S. Bergano, F. Kerfoot, C. Davidson, "Margin measurements in optical amplifier systems," IEEE Photon. Technol. Lett. 5, 304-306 (1993).

G. Bosco, P. Poggiolini, "On the $Q$-factor inaccuracy in the performance analysis of optical direct-detection dpsk systems," IEEE Photon. Technol. Lett. 16, 665-667 (2004).

G. Contestabile, N. Calabretta, M. Presi, E. Ciaramella, "Single and multicast wavelength conversion at 40 gb/s by means of fast nonlinear polarization switching in an SOA," IEEE Photon. Technol. Lett. 17, 2652-2654 (2005).

G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, L. Potì, "Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate," IEEE Photon. Technol. Lett. 18, 917-919 (2006).

C. Schubert, S. Diez, J. Berger, R. Ludwig, U. Feiste, H. G. Weber, G. Toptchiyski, K. Petermann, V. Krajinovic, "160-gb/s all-optical demultiplexing using a gain-transparent ultrafast-nonlinear interferometer (GT-UNI)," IEEE Photon. Technol. Lett. 13, 475-477 (2001).

J. Appl. Phys. (1)

R. Kazarinov, C. Henry, R. Logan, "Longitudinal mode self-stabilization in semiconductor lasers," J. Appl. Phys. 53, 4631-4644 (1982).

J. Lightw. Technol. (1)

H. Simos, A. Bogris, D. Syvridis, "Investigation of a 2R all-optical regenerator based on four-wave mixing in a semiconductor optical amplifier," J. Lightw. Technol. 22, 595-604 (2004).

Phys. Rev. A (1)

S. Balle, "Simple analytical approximations for the gain and refractive index spectra in quantum-well lasers," Phys. Rev. A 57, 1304-1312 (1998).

Other (5)

J. Revuelta, L. Pesquera, S. Balle, "Wavelength-dependent output properties of quantum well optical amplifiers," Proc. Conf. Laser Electro-Opt. (2000) pp. 420-421.

A. Yariv, Quantum Electronics (Wiley, 1989).

G. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

M. Connelly, Semiconductor Optical Amplifiers (Kluwer, 2002).

K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer Science+Business Media, Inc., 2005).

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