Abstract

We developed a general numerical method to calculate the spontaneous emission lifetime in an arbitrary microcavity, using a finite-difference time-domain algorithm. For structures with rotational symmetry we also developed a more efficient but less general algorithm. To simulate an open radiation problem, we use absorbing boundaries to truncate the computational domain. The accuracy of this method is limited only by numerical error and finite reflection at the absorbing boundaries. We compare our result with cases that can be solved analytically and find excellent agreement. Finally, we apply the method to calculate the spontaneous emission lifetime in a slab waveguide and in a dielectric microdisk, respectively.

© 1999 Optical Society of America

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  1. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  2. T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Topics Quantum Electron. 3, 808–830 (1997).
  3. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
  4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University, Princeton, N.J., 1995).
  5. E. A. Hinds, “Perturbative cavity quantum electrodynamics,” in Cavity Quantum Electrodynamics, P. R. Berman, ed. (Academic, New York, 1994).
  6. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
  7. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
  8. Y. Chen, R. Mittra, and P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).
  9. C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
  10. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  11. R. J. Glauber and M. L. Lewenstein, “Quantum optics of dielectric media,” Phys. Rev. A 43, 467–491 (1991).
  12. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
  13. J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
  14. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
  15. M. Fusco, “FDTD algorithm in curvilinear coordinates,” IEEE Trans. Antennas Propag. 38, 76–89 (1990).
  16. M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75, 3302–3307 (1994).
  17. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

1997 (1)

T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Topics Quantum Electron. 3, 808–830 (1997).

1996 (4)

Y. Chen, R. Mittra, and P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).

1994 (2)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).

M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75, 3302–3307 (1994).

1991 (1)

R. J. Glauber and M. L. Lewenstein, “Quantum optics of dielectric media,” Phys. Rev. A 43, 467–491 (1991).

1990 (1)

M. Fusco, “FDTD algorithm in curvilinear coordinates,” IEEE Trans. Antennas Propag. 38, 76–89 (1990).

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).

1981 (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Baba, T.

T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Topics Quantum Electron. 3, 808–830 (1997).

Berenger, J. P.

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).

Chen, Y.

Y. Chen, R. Mittra, and P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).

Chin, M. K.

M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75, 3302–3307 (1994).

Chu, D. Y.

M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75, 3302–3307 (1994).

Fusco, M.

M. Fusco, “FDTD algorithm in curvilinear coordinates,” IEEE Trans. Antennas Propag. 38, 76–89 (1990).

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).

Glauber, R. J.

R. J. Glauber and M. L. Lewenstein, “Quantum optics of dielectric media,” Phys. Rev. A 43, 467–491 (1991).

Harms, P.

Y. Chen, R. Mittra, and P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).

Henry, C. H.

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).

Ho, S. T.

M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75, 3302–3307 (1994).

Kazarinov, R. F.

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).

Lewenstein, M. L.

R. J. Glauber and M. L. Lewenstein, “Quantum optics of dielectric media,” Phys. Rev. A 43, 467–491 (1991).

Mittra, R.

Y. Chen, R. Mittra, and P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).

Mur, G.

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).

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

T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Topics Quantum Electron. 3, 808–830 (1997).

IEEE Trans. Antennas Propag. (3)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).

M. Fusco, “FDTD algorithm in curvilinear coordinates,” IEEE Trans. Antennas Propag. 38, 76–89 (1990).

IEEE Trans. Electromagn. Compat. (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).

IEEE Trans. Microwave Theory Tech. (1)

Y. Chen, R. Mittra, and P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).

J. Appl. Phys. (1)

M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75, 3302–3307 (1994).

J. Comput. Phys. (2)

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Phys. Rev. A (1)

R. J. Glauber and M. L. Lewenstein, “Quantum optics of dielectric media,” Phys. Rev. A 43, 467–491 (1991).

Phys. Rev. Lett. (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).

Rev. Mod. Phys. (1)

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).

Other (4)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University, Princeton, N.J., 1995).

E. A. Hinds, “Perturbative cavity quantum electrodynamics,” in Cavity Quantum Electrodynamics, P. R. Berman, ed. (Academic, New York, 1994).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

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