Abstract

Short-pulse propagation in semiconductor optical amplifiers (SOAs) has been widely studied for applications in optical signal processing and optical communications areas. Even though it is possible to integrate differential equations numerically, such implementations may not provide adequate insight into the device operation. We propose a systematic way to construct analytical solutions for the gain-recovery dynamics of SOAs and show excellent agreement with numerically integrated results. Our approach makes use of the multiple-scale technique. The main contribution of this work is to put earlier heuristic approaches into a firm theoretical base so that approximate analytical solutions for carrier-recovery dynamics can be systematically constructed for different variants of SOA models. We derive analytical solutions for the signal gain and pulse-energy gain at an arbitrary point with the SOA waveguide. Surpassing previous work in this area, we also show that it is possible to obtain analytical solutions when waveguide attenuation is not negligible.

© 2008 IEEE

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  1. P. G. Eliseev, V. V. Luc, "Semiconductor optical amplifiers: Multifunctional possibilities, photoresponse and phase shift properties," Pure Appl. Opt. 4, 295-313 (1995).
  2. M. Premaratne, A. J. Lowery, "Modulation resonance enhancement in SCH quantum-well lasers with an external Bragg reflector," IEEE J. Quantum Electron. 34, 716-728 (1998).
  3. B. Dagens, A. Labrousse, R. Brenot, B. Lavigne, M. Renaud, "SOA-based devices for all-optical signal processing," Proc. Opt. Fiber Commun. Conf. Exhibition (OFC 2003) (2003) pp. 582-583.
  4. G. P. Agrawal, N. A. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297-2306 (1989).
  5. A. Mecozzi, J. Mork, "Saturation induced by picosecond pulses in semiconductor optical amplifiers," J. Opt. Soc. Amer. B, Opt. Phys. 14, 761-770 (1997).
  6. J. P. Sokoloff, P. R. Prucnal, I. Glesk, M. Kane, "A terahertz optical asymmetric demultiplexer (TOAD)," IEEE Photon. Technol. Lett. 5, 787-790 (1993).
  7. M. Eiselt, W. Pieper, H. G. Weber, "SLALOM: Semiconductor laser amplifier in a loop mirror," J. Lightw. Technol. 13, 2099-2112 (1995).
  8. T. Wang, Z. Li, C. Lou, Y. Wu, Y. Gao, "Comb-like filter preprocessing to reduce the pattern effect in the clock recovery based on SOA," IEEE Photon Technol. Lett. 14, 855-857 (2002).
  9. M. Weiming, L. Yuhua, A.-M. Mohammed, L. Guifang, "All-optical clock recovery for both RZ and NRZ data," IEEE Photon. Technol. Lett. 14, 873-875 (2002).
  10. E. S. Awad, C. J. K. Richardson, P. S. Cho, N. Moulton, J. Goldhar, "Optical clock recovery using SOA for relative timing extraction between counterpropagating short picosecond pulses," IEEE Photon. Technol. Lett. 14, 396-398 (2002).
  11. M. Premaratne, A. J. Lowery, "Analytical characterization of SOA-based optical pulse delay discriminator," J. Lightw. Technol. 23, 2778-2787 (2005).
  12. M. Premaratne, A. J. Lowery, "Semiclassical analysis of the impact of noise in SOA-based optical pulse delay discriminator optical pulse delay discriminator," IEEE J. Sel. Topics Quantum Electron. 12, 708-716 (2006).
  13. K. L. Hall, K. A. Rauschenbach, "Fiber optics and optical communications–100-Gb/s bitwise logic," Opt. Lett. 23, 1271-1273 (1998).
  14. A. Hamie, A. Sharaiha, M. Guegan, B. Pucel, "All-optical logic NOR gate using two-cascaded semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 14, 1439-1441 (2002).
  15. P. G. Kryukov, V. S. Letokhov, "Propagation of a light pulse in a resonantly amplifying (absorbing) medium," Sov. Phys. Uspekhi 12, 641-672 (1970).
  16. A. E. Siegman, Lasers (Univ. Sci., 1986).
  17. L. M. Frantz, J. S. Nodvik, "Theory of pulse propagation in a laser amplifier," J. Appl. Phys. 34, 2346-2349 (1963).
  18. A. E. Siegman, "Design considerations for laser pulse amplifiers," J. Appl. Phys. 35, 460-461 (1964).
  19. B. S. Gopalakrishna Pillai, M. Premaratne, D. Abramson, K. L. Lee, A. Nirmalathas, C. Lim, S. Shinada, N. Wada, T. Miyazaki, "Analytical characterization of optical pulse propagation in polarization-sensitive semiconductor optical amplifiers," IEEE J. Quantum Electron. 42, 1062-1077 (2006).
  20. A. W. Bush, Perturbation Methods For Engineers and Scientists (CRC Press, 1992).
  21. A. H. Nayfeh, Perturbation Methods (Wiley-Interscience, 2000).
  22. P. V. Kokotovic, H. Khalil, J. O'Reilly, Singular Perturbations in Control Analysis and Design (Academic, 1984).
  23. A. J. Jerri, Introduction to Integral Equations with Applications (Wiley, 1999).

2006 (2)

M. Premaratne, A. J. Lowery, "Semiclassical analysis of the impact of noise in SOA-based optical pulse delay discriminator optical pulse delay discriminator," IEEE J. Sel. Topics Quantum Electron. 12, 708-716 (2006).

B. S. Gopalakrishna Pillai, M. Premaratne, D. Abramson, K. L. Lee, A. Nirmalathas, C. Lim, S. Shinada, N. Wada, T. Miyazaki, "Analytical characterization of optical pulse propagation in polarization-sensitive semiconductor optical amplifiers," IEEE J. Quantum Electron. 42, 1062-1077 (2006).

2005 (1)

M. Premaratne, A. J. Lowery, "Analytical characterization of SOA-based optical pulse delay discriminator," J. Lightw. Technol. 23, 2778-2787 (2005).

2002 (4)

A. Hamie, A. Sharaiha, M. Guegan, B. Pucel, "All-optical logic NOR gate using two-cascaded semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 14, 1439-1441 (2002).

T. Wang, Z. Li, C. Lou, Y. Wu, Y. Gao, "Comb-like filter preprocessing to reduce the pattern effect in the clock recovery based on SOA," IEEE Photon Technol. Lett. 14, 855-857 (2002).

M. Weiming, L. Yuhua, A.-M. Mohammed, L. Guifang, "All-optical clock recovery for both RZ and NRZ data," IEEE Photon. Technol. Lett. 14, 873-875 (2002).

E. S. Awad, C. J. K. Richardson, P. S. Cho, N. Moulton, J. Goldhar, "Optical clock recovery using SOA for relative timing extraction between counterpropagating short picosecond pulses," IEEE Photon. Technol. Lett. 14, 396-398 (2002).

1998 (2)

M. Premaratne, A. J. Lowery, "Modulation resonance enhancement in SCH quantum-well lasers with an external Bragg reflector," IEEE J. Quantum Electron. 34, 716-728 (1998).

K. L. Hall, K. A. Rauschenbach, "Fiber optics and optical communications–100-Gb/s bitwise logic," Opt. Lett. 23, 1271-1273 (1998).

1997 (1)

A. Mecozzi, J. Mork, "Saturation induced by picosecond pulses in semiconductor optical amplifiers," J. Opt. Soc. Amer. B, Opt. Phys. 14, 761-770 (1997).

1995 (2)

P. G. Eliseev, V. V. Luc, "Semiconductor optical amplifiers: Multifunctional possibilities, photoresponse and phase shift properties," Pure Appl. Opt. 4, 295-313 (1995).

M. Eiselt, W. Pieper, H. G. Weber, "SLALOM: Semiconductor laser amplifier in a loop mirror," J. Lightw. Technol. 13, 2099-2112 (1995).

1993 (1)

J. P. Sokoloff, P. R. Prucnal, I. Glesk, M. Kane, "A terahertz optical asymmetric demultiplexer (TOAD)," IEEE Photon. Technol. Lett. 5, 787-790 (1993).

1989 (1)

G. P. Agrawal, N. A. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297-2306 (1989).

1970 (1)

P. G. Kryukov, V. S. Letokhov, "Propagation of a light pulse in a resonantly amplifying (absorbing) medium," Sov. Phys. Uspekhi 12, 641-672 (1970).

1964 (1)

A. E. Siegman, "Design considerations for laser pulse amplifiers," J. Appl. Phys. 35, 460-461 (1964).

1963 (1)

L. M. Frantz, J. S. Nodvik, "Theory of pulse propagation in a laser amplifier," J. Appl. Phys. 34, 2346-2349 (1963).

IEEE J. Quantum Electron. (1)

G. P. Agrawal, N. A. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297-2306 (1989).

IEEE Photon. Technol. Lett. (1)

E. S. Awad, C. J. K. Richardson, P. S. Cho, N. Moulton, J. Goldhar, "Optical clock recovery using SOA for relative timing extraction between counterpropagating short picosecond pulses," IEEE Photon. Technol. Lett. 14, 396-398 (2002).

IEEE J. Quantum Electron. (2)

M. Premaratne, A. J. Lowery, "Modulation resonance enhancement in SCH quantum-well lasers with an external Bragg reflector," IEEE J. Quantum Electron. 34, 716-728 (1998).

B. S. Gopalakrishna Pillai, M. Premaratne, D. Abramson, K. L. Lee, A. Nirmalathas, C. Lim, S. Shinada, N. Wada, T. Miyazaki, "Analytical characterization of optical pulse propagation in polarization-sensitive semiconductor optical amplifiers," IEEE J. Quantum Electron. 42, 1062-1077 (2006).

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

M. Premaratne, A. J. Lowery, "Semiclassical analysis of the impact of noise in SOA-based optical pulse delay discriminator optical pulse delay discriminator," IEEE J. Sel. Topics Quantum Electron. 12, 708-716 (2006).

IEEE Photon Technol. Lett. (1)

T. Wang, Z. Li, C. Lou, Y. Wu, Y. Gao, "Comb-like filter preprocessing to reduce the pattern effect in the clock recovery based on SOA," IEEE Photon Technol. Lett. 14, 855-857 (2002).

IEEE Photon. Technol. Lett. (1)

A. Hamie, A. Sharaiha, M. Guegan, B. Pucel, "All-optical logic NOR gate using two-cascaded semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 14, 1439-1441 (2002).

IEEE Photon. Technol. Lett. (2)

M. Weiming, L. Yuhua, A.-M. Mohammed, L. Guifang, "All-optical clock recovery for both RZ and NRZ data," IEEE Photon. Technol. Lett. 14, 873-875 (2002).

J. P. Sokoloff, P. R. Prucnal, I. Glesk, M. Kane, "A terahertz optical asymmetric demultiplexer (TOAD)," IEEE Photon. Technol. Lett. 5, 787-790 (1993).

J. Lightw. Technol. (1)

M. Premaratne, A. J. Lowery, "Analytical characterization of SOA-based optical pulse delay discriminator," J. Lightw. Technol. 23, 2778-2787 (2005).

J. Appl. Phys. (2)

L. M. Frantz, J. S. Nodvik, "Theory of pulse propagation in a laser amplifier," J. Appl. Phys. 34, 2346-2349 (1963).

A. E. Siegman, "Design considerations for laser pulse amplifiers," J. Appl. Phys. 35, 460-461 (1964).

J. Lightw. Technol. (1)

M. Eiselt, W. Pieper, H. G. Weber, "SLALOM: Semiconductor laser amplifier in a loop mirror," J. Lightw. Technol. 13, 2099-2112 (1995).

J. Opt. Soc. Amer. B, Opt. Phys. (1)

A. Mecozzi, J. Mork, "Saturation induced by picosecond pulses in semiconductor optical amplifiers," J. Opt. Soc. Amer. B, Opt. Phys. 14, 761-770 (1997).

Opt. Lett. (1)

Pure Appl. Opt. (1)

P. G. Eliseev, V. V. Luc, "Semiconductor optical amplifiers: Multifunctional possibilities, photoresponse and phase shift properties," Pure Appl. Opt. 4, 295-313 (1995).

Sov. Phys. Uspekhi (1)

P. G. Kryukov, V. S. Letokhov, "Propagation of a light pulse in a resonantly amplifying (absorbing) medium," Sov. Phys. Uspekhi 12, 641-672 (1970).

Other (6)

A. E. Siegman, Lasers (Univ. Sci., 1986).

B. Dagens, A. Labrousse, R. Brenot, B. Lavigne, M. Renaud, "SOA-based devices for all-optical signal processing," Proc. Opt. Fiber Commun. Conf. Exhibition (OFC 2003) (2003) pp. 582-583.

A. W. Bush, Perturbation Methods For Engineers and Scientists (CRC Press, 1992).

A. H. Nayfeh, Perturbation Methods (Wiley-Interscience, 2000).

P. V. Kokotovic, H. Khalil, J. O'Reilly, Singular Perturbations in Control Analysis and Design (Academic, 1984).

A. J. Jerri, Introduction to Integral Equations with Applications (Wiley, 1999).

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