Abstract

A numerical model based on the finite-difference time-domain method is developed to simulate fluctuations which accompany the dephasing of atomic polarization and the decay of excited state's population. This model is based on the Maxwell–Bloch equations with $c$-number stochastic noise terms. We successfully apply our method to a numerical simulation of the atomic superfluorescence process. This method opens the door to further studies of the effects of stochastic noise on light-matter interaction and transient processes in complex systems without prior knowledge of modes.

© 2009 IEEE

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  1. A. Taflove, S. Hagness, Computational Electrodynamics (Artech House, 2005).
  2. A. S. Nagra, R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Trans. Antennas Propag. 46, 334-340 (1999).
  3. R. W. Ziolkowski, J. M. Arnold, D. M. Georgy, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3094 (1995).
  4. K. Böhringer, O. Hess, "A full-time-domain approach to spatio–temporal dynamics of semiconductor lasers. I. Theoretical formulation," Prog. Quantum Electron. 32, 159-246 (2008).
  5. K. Böhringer, O. Hess, "A full-time-domain approach to spatio–temporal dynamics of semiconductor lasers. II. Spatio–temporal dynamics," Prog. Quantum Electron. 32, 247-307 (2008).
  6. D. Marcuse, "Computer simulation of laser photon fluctuations: Theory of a single-cavity laser," IEEE J. Quantum Electron. 20, 1139-1148 (1984).
  7. D. Marcuse, "Computer simulation of laser photon fluctuations: Single-cavity laser results," IEEE J. Quantum Electron. QE-20, 1148-1155 (1984).
  8. G. Gray, R. Roy, "Noise in nearly-single-mode semiconductor lasers," Phys. Rev. A 40, 2452-2462 (1989).
  9. M. Kira, F. Jackie, W. Hoyer, S. W. Koch, "Quantum theory of spontaneous emission and coherent effects in semiconductor microstructures," Prog. Quantum Electron. 23, 189-279 (1999).
  10. H. F. Hofmann, O. Hess, "Quantum Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers," Phys. Rev. A 59, 2342-2358 (1999).
  11. G. M. Slavcheva, J. M. Arnold, R. W. Ziolkowski, "FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities," IEEE J. Sel. Topics Quantum Electron. 10, 1052-1062 (2004).
  12. J. Andreasen, H. Cao, A. Taflove, P. Kumar, C. qi Cao, "Finite-different time-domain simulation of thermal noise in open cavities," Phys. Rev. A 77, (2008) 023810.
  13. P. D. Drummond, M. G. Raymer, "Quantum theory of propagation of nonclassical radiation in a near-resonant medium," Phys. Rev. A 44, 2072-2085 (1991).
  14. H. Haken, Laser Theory (Springer-Verlag, 1983).
  15. B. Bidégaray, "Time discretizations for Maxwell–Bloch equations," Numer. Meth. Part. D. E. 19, 284-300 (2003).
  16. M. Brysbaert, "Algorithms for randomness in the behavioral sciences: A tutorial," Behav. Res. Meth. Ins. C. 23, 45-60 (1991).
  17. M. S. Malcuit, J. J. Maki, D. J. Simpkin, R. W. Boyd, "Transition from superfluorescence to amplified spontaneous emission," Phys. Rev. Lett. 59, 1189-1192 (1987).
  18. J. J. Maki, M. S. Malcuit, M. G. Raymer, R. W. Boyd, P. D. Drummond, "Influence of collisional dephasing processes on superfluorescence," Phys. Rev. A 40, 5135-5142 (1989).
  19. F. Haake, H. King, G. Schröoder, J. Haus, R. Glauber, "Fluctuations in superfluorescence," Phys. Rev. A. 20, 2047-2063 (1979).
  20. B. Bidégaray, A. Bourgeade, D. Reignier, "Introducing physical relaxation terms in Bloch equations," J. Comput. Phys. 170, 603-613 (2001).
  21. C. Besse, B. Bidégaray-Fesquet, A. Bourgeade, P. Degond, O. Saut, "A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: An application to KDP," M2AN Math. Model. Numer. Anal. 38, 321-344 (2004).
  22. A. Bourgeade, O. Saut, "Numerical methods for the bidimensional Maxwell–Bloch equations in nonlinear crystals," J. Comput. Phys. 213, 823-843 (2006).

2008 (3)

K. Böhringer, O. Hess, "A full-time-domain approach to spatio–temporal dynamics of semiconductor lasers. I. Theoretical formulation," Prog. Quantum Electron. 32, 159-246 (2008).

K. Böhringer, O. Hess, "A full-time-domain approach to spatio–temporal dynamics of semiconductor lasers. II. Spatio–temporal dynamics," Prog. Quantum Electron. 32, 247-307 (2008).

J. Andreasen, H. Cao, A. Taflove, P. Kumar, C. qi Cao, "Finite-different time-domain simulation of thermal noise in open cavities," Phys. Rev. A 77, (2008) 023810.

2006 (1)

A. Bourgeade, O. Saut, "Numerical methods for the bidimensional Maxwell–Bloch equations in nonlinear crystals," J. Comput. Phys. 213, 823-843 (2006).

2004 (2)

C. Besse, B. Bidégaray-Fesquet, A. Bourgeade, P. Degond, O. Saut, "A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: An application to KDP," M2AN Math. Model. Numer. Anal. 38, 321-344 (2004).

G. M. Slavcheva, J. M. Arnold, R. W. Ziolkowski, "FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities," IEEE J. Sel. Topics Quantum Electron. 10, 1052-1062 (2004).

2003 (1)

B. Bidégaray, "Time discretizations for Maxwell–Bloch equations," Numer. Meth. Part. D. E. 19, 284-300 (2003).

2001 (1)

B. Bidégaray, A. Bourgeade, D. Reignier, "Introducing physical relaxation terms in Bloch equations," J. Comput. Phys. 170, 603-613 (2001).

1999 (3)

A. S. Nagra, R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Trans. Antennas Propag. 46, 334-340 (1999).

M. Kira, F. Jackie, W. Hoyer, S. W. Koch, "Quantum theory of spontaneous emission and coherent effects in semiconductor microstructures," Prog. Quantum Electron. 23, 189-279 (1999).

H. F. Hofmann, O. Hess, "Quantum Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers," Phys. Rev. A 59, 2342-2358 (1999).

1995 (1)

R. W. Ziolkowski, J. M. Arnold, D. M. Georgy, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3094 (1995).

1991 (2)

M. Brysbaert, "Algorithms for randomness in the behavioral sciences: A tutorial," Behav. Res. Meth. Ins. C. 23, 45-60 (1991).

P. D. Drummond, M. G. Raymer, "Quantum theory of propagation of nonclassical radiation in a near-resonant medium," Phys. Rev. A 44, 2072-2085 (1991).

1989 (2)

G. Gray, R. Roy, "Noise in nearly-single-mode semiconductor lasers," Phys. Rev. A 40, 2452-2462 (1989).

J. J. Maki, M. S. Malcuit, M. G. Raymer, R. W. Boyd, P. D. Drummond, "Influence of collisional dephasing processes on superfluorescence," Phys. Rev. A 40, 5135-5142 (1989).

1987 (1)

M. S. Malcuit, J. J. Maki, D. J. Simpkin, R. W. Boyd, "Transition from superfluorescence to amplified spontaneous emission," Phys. Rev. Lett. 59, 1189-1192 (1987).

1984 (2)

D. Marcuse, "Computer simulation of laser photon fluctuations: Theory of a single-cavity laser," IEEE J. Quantum Electron. 20, 1139-1148 (1984).

D. Marcuse, "Computer simulation of laser photon fluctuations: Single-cavity laser results," IEEE J. Quantum Electron. QE-20, 1148-1155 (1984).

1979 (1)

F. Haake, H. King, G. Schröoder, J. Haus, R. Glauber, "Fluctuations in superfluorescence," Phys. Rev. A. 20, 2047-2063 (1979).

Behav. Res. Meth. Ins. C. (1)

M. Brysbaert, "Algorithms for randomness in the behavioral sciences: A tutorial," Behav. Res. Meth. Ins. C. 23, 45-60 (1991).

IEEE J. Quantum Electron. (2)

D. Marcuse, "Computer simulation of laser photon fluctuations: Theory of a single-cavity laser," IEEE J. Quantum Electron. 20, 1139-1148 (1984).

D. Marcuse, "Computer simulation of laser photon fluctuations: Single-cavity laser results," IEEE J. Quantum Electron. QE-20, 1148-1155 (1984).

IEEE Trans. Antennas Propag. (1)

A. S. Nagra, R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Trans. Antennas Propag. 46, 334-340 (1999).

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

G. M. Slavcheva, J. M. Arnold, R. W. Ziolkowski, "FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities," IEEE J. Sel. Topics Quantum Electron. 10, 1052-1062 (2004).

J. Comput. Phys. (1)

A. Bourgeade, O. Saut, "Numerical methods for the bidimensional Maxwell–Bloch equations in nonlinear crystals," J. Comput. Phys. 213, 823-843 (2006).

J. Comput. Phys. (1)

B. Bidégaray, A. Bourgeade, D. Reignier, "Introducing physical relaxation terms in Bloch equations," J. Comput. Phys. 170, 603-613 (2001).

M2AN Math. Model. Numer. Anal. (1)

C. Besse, B. Bidégaray-Fesquet, A. Bourgeade, P. Degond, O. Saut, "A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: An application to KDP," M2AN Math. Model. Numer. Anal. 38, 321-344 (2004).

Numer. Meth. Part. D. E. (1)

B. Bidégaray, "Time discretizations for Maxwell–Bloch equations," Numer. Meth. Part. D. E. 19, 284-300 (2003).

Phys. Rev. A (2)

H. F. Hofmann, O. Hess, "Quantum Maxwell–Bloch equations for spatially inhomogeneous semiconductor lasers," Phys. Rev. A 59, 2342-2358 (1999).

P. D. Drummond, M. G. Raymer, "Quantum theory of propagation of nonclassical radiation in a near-resonant medium," Phys. Rev. A 44, 2072-2085 (1991).

Phys. Rev. A. (1)

F. Haake, H. King, G. Schröoder, J. Haus, R. Glauber, "Fluctuations in superfluorescence," Phys. Rev. A. 20, 2047-2063 (1979).

Phys. Rev. A (1)

J. J. Maki, M. S. Malcuit, M. G. Raymer, R. W. Boyd, P. D. Drummond, "Influence of collisional dephasing processes on superfluorescence," Phys. Rev. A 40, 5135-5142 (1989).

Phys. Rev. Lett. (1)

M. S. Malcuit, J. J. Maki, D. J. Simpkin, R. W. Boyd, "Transition from superfluorescence to amplified spontaneous emission," Phys. Rev. Lett. 59, 1189-1192 (1987).

Phys. Rev. A (3)

J. Andreasen, H. Cao, A. Taflove, P. Kumar, C. qi Cao, "Finite-different time-domain simulation of thermal noise in open cavities," Phys. Rev. A 77, (2008) 023810.

R. W. Ziolkowski, J. M. Arnold, D. M. Georgy, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3094 (1995).

G. Gray, R. Roy, "Noise in nearly-single-mode semiconductor lasers," Phys. Rev. A 40, 2452-2462 (1989).

Prog. Quantum Electron. (2)

M. Kira, F. Jackie, W. Hoyer, S. W. Koch, "Quantum theory of spontaneous emission and coherent effects in semiconductor microstructures," Prog. Quantum Electron. 23, 189-279 (1999).

K. Böhringer, O. Hess, "A full-time-domain approach to spatio–temporal dynamics of semiconductor lasers. I. Theoretical formulation," Prog. Quantum Electron. 32, 159-246 (2008).

Prog. Quantum Electron. (1)

K. Böhringer, O. Hess, "A full-time-domain approach to spatio–temporal dynamics of semiconductor lasers. II. Spatio–temporal dynamics," Prog. Quantum Electron. 32, 247-307 (2008).

Other (2)

A. Taflove, S. Hagness, Computational Electrodynamics (Artech House, 2005).

H. Haken, Laser Theory (Springer-Verlag, 1983).

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