Abstract

This paper presents a Mueller-matrix approach to simulate the azimuth and ellipticity trajectory of a probe light in a tensile-strained bulk semiconductor optical amplifier (SOA) in a conventional pump–probe scheme. The physical mechanisms for the variations of polarization azimuth and ellipticity angle of the probe originate from the significant nonuniform distributions of carrier density across the active region in the presence of an intense pump light. Due to this carrier-density nonuniformity, the effective refractive indexes experienced by transverse-electric (TE) and transverse-magnetic (TM) modes of the probe are different. This results in a phase shift between TE and TM modes of the probe upon leaving the SOA. Simulations of the carrier distributions along the cavity length at different pump-light levels are demonstrated using multisection rate equations, which take into account the longitudinal nonuniform carrier density. The optical gain is considered via the parabolic band approximation. The influences of the spontaneous recombination and carrier-dependent material loss on the amplifier performance are included. The Mueller-matrix formalism is utilized to predict the variations of azimuth and ellipticity angle, which greatly reduces the complexity of the simulations in comparison with Jones-matrix formalism. The suggested approach is beneficial to experimental investigations due to the fact that during the optical-tuning process, Stokes parameters are virtually measurable on the Poincaré sphere, and the Stokes vector of the incoming probe can be adjusted by a polarization controller and monitored by a polarization analyzer. Based on these carrier-induced nonlinearities in SOAs, an optical and gate with extinction ratio larger than 14 dB and Q-factor larger than 25 is presented at a bit rate of 2.5 Gb/s.

© 2007 IEEE

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  2. D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, D. C. Rogers, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).
  3. J. Mork, A. Mecozzi, G. Eisenstein, "The modulation response of a semiconductor laser amplifier," IEEE J. Sel. Topics Quantum Electron. 5, 851-860 (1999).
  4. M. F. C. Stephens, M. Asghari, R. V. Penty, I. H. White, "Demonstration of ultrafast all-optical wavelength conversion utilizing birefringence in semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 9, 449-451 (1997).
  5. L. G. Guo, M. J. Connelly, "Signal-induced birefringence and dichroism in a tensile-strained bulk semiconductor optical amplifier and its application to wavelength conversion," J. Lightw. Technol. 23, 4037-4045 (2005).
  6. H. J. S. Dorren, D. Lenstra, Y. Liu, M. T. Hill, G.-D. Khoe, "Nonlinear polarization rotation in semiconductor optical amplifiers: Theory and application to all-optical flip-flop memories," IEEE J. Quantum Electron. 39, 141-148 (2003).
  7. J. P. Turkiewicz, G. D. Khoe, H. de Waardt, "All-optical 1310 to 1550 nm wavelength conversion by utilizing nonlinear polarization rotation in semiconductor optical amplifier," Electron. Lett. 41, 29-30 (2005).
  8. H. Soto, J. D. Topomondzob, D. Erasmeb, M. Castro, "All-optical nor gates with two and three input logic signals based on cross-polarization modulation in a semiconductor optical amplifier," Opt. Commun. 218, 243-247 (2003).
  9. E. Alvarez, H. Soto, J. Torres, "Investigation of the carrier density dependence on the confinement factor in a bulk semiconductor optical amplifier with a ridge waveguide," Opt. Commun. 222, 161-167 (2003).
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  13. L. Q. Guo, Broad-band antireflection coatings for improved grating-external-cavity diode laser performance Ph.D. dissertation Dept. Eng. Physics, McMaster Univ.HamiltonONCanada (2002).
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  16. M. J. Connelly, "Wideband semiconductor optical amplifier steady-state numerical model," IEEE J. Quantum Electron. 37, 439-447 (2001).
  17. M. Asada, A. R. Adams, K. E. Stubkjaer, Y. Suematsu, Y. Itaya, S. Arai, "The temperature dependence of the threshold current of GaInAsP/InP DH lasers," IEEE J. Quantum Electron. QE-17, 611-619 (1981).
  18. H. Kawaguchi, Bistabilities and Nonlinearities in Laser Diodes (Artech House, 1994).
  19. R. Olshansky, C. B. Su, J. Manning, W. Powazinik, "Measurement of radiative and nonradiative recombination rates in InGaAsP and AIGaAs light sources ," IEEE J. Quantum Electron. QE-20, 838-854 (1984).
  20. M. Kot, K. Zdansky, "Measurement of radiative and nonradiative recombination rate in InGaAsP-InP LED's," IEEE J. Quantum Electron. 28, 1746-1750 (1992).
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  23. E. Wintner, E. P. Ippen, "Nonlinear carrier dynamics in GaInAsP compounds," Appl. Phys. Lett. 44, 999-1001 (1984).
  24. D. T. Cassidy, "Spontaneous-emission factor of semiconductor diode lasers," J. Opt. Soc. Amer. B, Opt. Phys. 8, 747-752 (1991).
  25. K. L. Hall, E. R. Thoen, E. P. Ippen, Semiconductors and Semimetals (Academic, 1999) pp. 83.
  26. L. Q. Guo, M. J. Connelly, "Demonstration of birefringence in a bulk semiconductor optical amplifier and its application to all-optical wavelength conversion," Proc. Symp. Opt. Fiber Meas. (2004) pp. 167-170.
  27. D. Goldstein, Polarized Light (Marcel Dekker, 2003).
  28. G. Talli, M. J. Adams, "Amplified spontaneous emission in semiconductor optical amplifiers: Modeling and experiments ," Opt. Commun. 218, 161-166 (2003).
  29. T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, "Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and intermodulation distortion," J. Lightw. Technol. 10, 1056-1065 (1992).
  30. H. Soto, D. Erasme, "Modeling and experimental measurements of the switching behavior of semiconductor optical amplifiers," Opt. Quantum Electron. 28, 669-682 (1996).
  31. L. Q. Guo, M. J. Connelly, "All-optical and gate using nonlinear polarization rotation in a bulk semiconductor optical amplifier," Proc. Tech. Dig.: Opt. Amplif. and Their Appl. (2005) pp. 1-3.
  32. S. Y. Lu, R. A. Chipman, "Mueller matrices and the degree of polarization," Opt. Commun. 146, 11-14 (1998).
  33. J. M. Wiesenfeld, A. H. Gnauck, G. Raybon, U. Koren, "High-speed multiple-quantum-well optical power amplifier," IEEE Photon. Technol. Lett. 4, 708-711 (1992).
  34. J. Jacquet, P. Brosson, A. Olivier, A. Perales, A. Bodere, D. Leclerc, "Carrier-induced differential refractive index in GaInAsP-GaInAs separate confinement multiquantum well lasers," IEEE Photon. Technol. Lett. 2, 620-622 (1990).
  35. M. J. Hamp, Asymmetry multiple quantum well lasers Ph.D. dissertation Dept. Eng. Physics, McMaster Univ.HamiltonONCanada (2000).
  36. R. W. H. Engelmann, C.-L. Shieh, C. Shu, Quantum Well Lasers (Academic, 1993).
  37. L. M. Walpita, "Solutions for planar optical waveguide equations by selecting zero elements in a characteristic matrix," J. Opt. Soc. Amer. A, Opt. Image Sci. 2, 595-602 (1985).

2005 (2)

L. G. Guo, M. J. Connelly, "Signal-induced birefringence and dichroism in a tensile-strained bulk semiconductor optical amplifier and its application to wavelength conversion," J. Lightw. Technol. 23, 4037-4045 (2005).

J. P. Turkiewicz, G. D. Khoe, H. de Waardt, "All-optical 1310 to 1550 nm wavelength conversion by utilizing nonlinear polarization rotation in semiconductor optical amplifier," Electron. Lett. 41, 29-30 (2005).

2003 (4)

H. Soto, J. D. Topomondzob, D. Erasmeb, M. Castro, "All-optical nor gates with two and three input logic signals based on cross-polarization modulation in a semiconductor optical amplifier," Opt. Commun. 218, 243-247 (2003).

E. Alvarez, H. Soto, J. Torres, "Investigation of the carrier density dependence on the confinement factor in a bulk semiconductor optical amplifier with a ridge waveguide," Opt. Commun. 222, 161-167 (2003).

H. J. S. Dorren, D. Lenstra, Y. Liu, M. T. Hill, G.-D. Khoe, "Nonlinear polarization rotation in semiconductor optical amplifiers: Theory and application to all-optical flip-flop memories," IEEE J. Quantum Electron. 39, 141-148 (2003).

G. Talli, M. J. Adams, "Amplified spontaneous emission in semiconductor optical amplifiers: Modeling and experiments ," Opt. Commun. 218, 161-166 (2003).

2002 (1)

M. Zhao, J. D. Merlier, G. Morthier, R. Baets, "Dynamic birefringence of the linear optical amplifier and application in optical regeneration ," IEEE J. Sel. Topics Quantum Electron. 8, 1399-1404 (2002).

2001 (1)

M. J. Connelly, "Wideband semiconductor optical amplifier steady-state numerical model," IEEE J. Quantum Electron. 37, 439-447 (2001).

1999 (3)

H. Soto, D. Erasme, G. Guekos, "Cross-polarization modulation in semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 11, 970-972 (1999).

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, D. C. Rogers, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).

J. Mork, A. Mecozzi, G. Eisenstein, "The modulation response of a semiconductor laser amplifier," IEEE J. Sel. Topics Quantum Electron. 5, 851-860 (1999).

1998 (1)

S. Y. Lu, R. A. Chipman, "Mueller matrices and the degree of polarization," Opt. Commun. 146, 11-14 (1998).

1997 (1)

M. F. C. Stephens, M. Asghari, R. V. Penty, I. H. White, "Demonstration of ultrafast all-optical wavelength conversion utilizing birefringence in semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 9, 449-451 (1997).

1996 (1)

H. Soto, D. Erasme, "Modeling and experimental measurements of the switching behavior of semiconductor optical amplifiers," Opt. Quantum Electron. 28, 669-682 (1996).

1992 (3)

J. M. Wiesenfeld, A. H. Gnauck, G. Raybon, U. Koren, "High-speed multiple-quantum-well optical power amplifier," IEEE Photon. Technol. Lett. 4, 708-711 (1992).

M. Kot, K. Zdansky, "Measurement of radiative and nonradiative recombination rate in InGaAsP-InP LED's," IEEE J. Quantum Electron. 28, 1746-1750 (1992).

T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, "Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and intermodulation distortion," J. Lightw. Technol. 10, 1056-1065 (1992).

1991 (2)

D. T. Cassidy, "Spontaneous-emission factor of semiconductor diode lasers," J. Opt. Soc. Amer. B, Opt. Phys. 8, 747-752 (1991).

N. Pfeffer, F. Charra, J. M. Nunzi, "Phase and frequency resolution of picosecond optical Kerr nonlinearities," Opt. Lett. 16, 1987-1989 (1991).

1990 (1)

J. Jacquet, P. Brosson, A. Olivier, A. Perales, A. Bodere, D. Leclerc, "Carrier-induced differential refractive index in GaInAsP-GaInAs separate confinement multiquantum well lasers," IEEE Photon. Technol. Lett. 2, 620-622 (1990).

1987 (1)

J. Wang, H. Olesen, K. E. Stubkjaer, "Recombination, gain and bandwidth characteristics of 1.3-μm semiconductor laser amplifiers," J. Lightw. Technol. LT-5, 184-189 (1987).

1985 (1)

L. M. Walpita, "Solutions for planar optical waveguide equations by selecting zero elements in a characteristic matrix," J. Opt. Soc. Amer. A, Opt. Image Sci. 2, 595-602 (1985).

1984 (2)

R. Olshansky, C. B. Su, J. Manning, W. Powazinik, "Measurement of radiative and nonradiative recombination rates in InGaAsP and AIGaAs light sources ," IEEE J. Quantum Electron. QE-20, 838-854 (1984).

E. Wintner, E. P. Ippen, "Nonlinear carrier dynamics in GaInAsP compounds," Appl. Phys. Lett. 44, 999-1001 (1984).

1981 (1)

M. Asada, A. R. Adams, K. E. Stubkjaer, Y. Suematsu, Y. Itaya, S. Arai, "The temperature dependence of the threshold current of GaInAsP/InP DH lasers," IEEE J. Quantum Electron. QE-17, 611-619 (1981).

Appl. Phys. Lett. (1)

E. Wintner, E. P. Ippen, "Nonlinear carrier dynamics in GaInAsP compounds," Appl. Phys. Lett. 44, 999-1001 (1984).

Electron. Lett. (1)

J. P. Turkiewicz, G. D. Khoe, H. de Waardt, "All-optical 1310 to 1550 nm wavelength conversion by utilizing nonlinear polarization rotation in semiconductor optical amplifier," Electron. Lett. 41, 29-30 (2005).

IEEE J. Quantum Electron. (5)

H. J. S. Dorren, D. Lenstra, Y. Liu, M. T. Hill, G.-D. Khoe, "Nonlinear polarization rotation in semiconductor optical amplifiers: Theory and application to all-optical flip-flop memories," IEEE J. Quantum Electron. 39, 141-148 (2003).

M. J. Connelly, "Wideband semiconductor optical amplifier steady-state numerical model," IEEE J. Quantum Electron. 37, 439-447 (2001).

M. Asada, A. R. Adams, K. E. Stubkjaer, Y. Suematsu, Y. Itaya, S. Arai, "The temperature dependence of the threshold current of GaInAsP/InP DH lasers," IEEE J. Quantum Electron. QE-17, 611-619 (1981).

R. Olshansky, C. B. Su, J. Manning, W. Powazinik, "Measurement of radiative and nonradiative recombination rates in InGaAsP and AIGaAs light sources ," IEEE J. Quantum Electron. QE-20, 838-854 (1984).

M. Kot, K. Zdansky, "Measurement of radiative and nonradiative recombination rate in InGaAsP-InP LED's," IEEE J. Quantum Electron. 28, 1746-1750 (1992).

IEEE J. Sel. Topics Quantum Electron. (2)

M. Zhao, J. D. Merlier, G. Morthier, R. Baets, "Dynamic birefringence of the linear optical amplifier and application in optical regeneration ," IEEE J. Sel. Topics Quantum Electron. 8, 1399-1404 (2002).

J. Mork, A. Mecozzi, G. Eisenstein, "The modulation response of a semiconductor laser amplifier," IEEE J. Sel. Topics Quantum Electron. 5, 851-860 (1999).

IEEE Photon. Technol. Lett. (4)

M. F. C. Stephens, M. Asghari, R. V. Penty, I. H. White, "Demonstration of ultrafast all-optical wavelength conversion utilizing birefringence in semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 9, 449-451 (1997).

H. Soto, D. Erasme, G. Guekos, "Cross-polarization modulation in semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 11, 970-972 (1999).

J. M. Wiesenfeld, A. H. Gnauck, G. Raybon, U. Koren, "High-speed multiple-quantum-well optical power amplifier," IEEE Photon. Technol. Lett. 4, 708-711 (1992).

J. Jacquet, P. Brosson, A. Olivier, A. Perales, A. Bodere, D. Leclerc, "Carrier-induced differential refractive index in GaInAsP-GaInAs separate confinement multiquantum well lasers," IEEE Photon. Technol. Lett. 2, 620-622 (1990).

J. Lightw. Technol. (3)

L. G. Guo, M. J. Connelly, "Signal-induced birefringence and dichroism in a tensile-strained bulk semiconductor optical amplifier and its application to wavelength conversion," J. Lightw. Technol. 23, 4037-4045 (2005).

J. Wang, H. Olesen, K. E. Stubkjaer, "Recombination, gain and bandwidth characteristics of 1.3-μm semiconductor laser amplifiers," J. Lightw. Technol. LT-5, 184-189 (1987).

T. Durhuus, B. Mikkelsen, K. E. Stubkjaer, "Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and intermodulation distortion," J. Lightw. Technol. 10, 1056-1065 (1992).

J. Opt. Soc. Amer. A, Opt. Image Sci. (1)

L. M. Walpita, "Solutions for planar optical waveguide equations by selecting zero elements in a characteristic matrix," J. Opt. Soc. Amer. A, Opt. Image Sci. 2, 595-602 (1985).

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

D. T. Cassidy, "Spontaneous-emission factor of semiconductor diode lasers," J. Opt. Soc. Amer. B, Opt. Phys. 8, 747-752 (1991).

Opt. Commun. (4)

G. Talli, M. J. Adams, "Amplified spontaneous emission in semiconductor optical amplifiers: Modeling and experiments ," Opt. Commun. 218, 161-166 (2003).

S. Y. Lu, R. A. Chipman, "Mueller matrices and the degree of polarization," Opt. Commun. 146, 11-14 (1998).

H. Soto, J. D. Topomondzob, D. Erasmeb, M. Castro, "All-optical nor gates with two and three input logic signals based on cross-polarization modulation in a semiconductor optical amplifier," Opt. Commun. 218, 243-247 (2003).

E. Alvarez, H. Soto, J. Torres, "Investigation of the carrier density dependence on the confinement factor in a bulk semiconductor optical amplifier with a ridge waveguide," Opt. Commun. 222, 161-167 (2003).

Opt. Lett. (1)

Opt. Quantum Electron. (1)

H. Soto, D. Erasme, "Modeling and experimental measurements of the switching behavior of semiconductor optical amplifiers," Opt. Quantum Electron. 28, 669-682 (1996).

Science (1)

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, D. C. Rogers, "Nonlinear optics for high-speed digital information processing," Science 286, 1523-1528 (1999).

Other (12)

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

M. J. Hamp, Asymmetry multiple quantum well lasers Ph.D. dissertation Dept. Eng. Physics, McMaster Univ.HamiltonONCanada (2000).

R. W. H. Engelmann, C.-L. Shieh, C. Shu, Quantum Well Lasers (Academic, 1993).

L. Q. Guo, M. J. Connelly, "All-optical and gate using nonlinear polarization rotation in a bulk semiconductor optical amplifier," Proc. Tech. Dig.: Opt. Amplif. and Their Appl. (2005) pp. 1-3.

L. Q. Guo, Broad-band antireflection coatings for improved grating-external-cavity diode laser performance Ph.D. dissertation Dept. Eng. Physics, McMaster Univ.HamiltonONCanada (2002).

K. L. Hall, E. R. Thoen, E. P. Ippen, Semiconductors and Semimetals (Academic, 1999) pp. 83.

L. Q. Guo, M. J. Connelly, "Demonstration of birefringence in a bulk semiconductor optical amplifier and its application to all-optical wavelength conversion," Proc. Symp. Opt. Fiber Meas. (2004) pp. 167-170.

D. Goldstein, Polarized Light (Marcel Dekker, 2003).

G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, 1993).

H. Kawaguchi, Bistabilities and Nonlinearities in Laser Diodes (Artech House, 1994).

L. A. Coldren, S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

L. A. Coldren, S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

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