Abstract

Boundary condition for the finite-difference-time-domain (FDTD) photonic simulation truncated with a gain medium is studied. Reflection occurs when applying the perfectly matched layer (PML) due to the impedance mismatch. The implementation of PML for the simulation truncated with gain medium is presented including both the un-split and split-field formulation, respectively. Numerical validation through simulating the light propagating in an active semiconductor waveguide containing gain medium indicates that the boundary formulation derived can effectively absorb the out-going light under different carrier densities.

© 2011 IEEE

PDF Article

References

  • View by:
  • |
  • |

  1. M. Bahl, N. C. Panoiu, R. M. Osgood, Jr."Modeling ultrashort field dynamics in surface emitting lasers by using finite-difference time-domain method," IEEE J. Quantum Electron. 41, 1244-1252 (2005).
  2. W. H. P. Pernice, F. P. Payne, D. F. G. Gallagher, "A finite-difference time-domain method for the simulation of gain materials with carrier diffusion in photonic crystals," J. Lightw. Technol. 25, 2306-2314 (2007).
  3. Y. Huang, S. T. Ho, "Computational model of solid-state, molecular, or atomic media for FDTD simulation based on a multi-level multielectron system governed by Pauli exclusion and Fermi-Dirac thermalization with application to semiconductor photonics," Opt. Exp. 14, 3569-3587 (2006).
  4. 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).
  5. X. Jiang, C. M. Soukoulis, "Time dependent theory for random lasers," Phys. Rev. Lett. 85, 70-73 (2000).
  6. S. Chang, A. Taflove, "Finite-difference time-domain model of lasing action in a four-level two-electron atomic system," Opt. Exp. 12, 3827-3833 (2004).
  7. Y. Huang, S. T. Ho, "Dynamical semiconductor medium FDTD simulation of current-injection nanophotonic devices," Opt. Quantum Electron. 40, 337-341 (2008).
  8. M. K. Seo, G. H. Song, I. K. Hwang, Y. H. Lee, "Nonlinear dispersive three-dimensional finite-difference time-domain analysis for photonic-crystal lasers," Opt. Exp. 13, 9645-9651 (2005).
  9. P. Bermel, E. Lidorikis, Y. Fink, J. D. Joannopoulos, "Active materials embedded in photonic crystals and coupled to electromagnetic radiation," Phys. Rev. B 73, 1651251-1651258 (2006).
  10. Fang, Th. Koschny, M. Wegener, C. M. Soukoulis, "Self-consistent calculation of metamaterials with gain," Phys. Rev. B 79 79, 2411041-2411044 (2009).
  11. S. Shi, G. Jin, D. W. Prather, "Electromagnetic simulation of quantum well structures," Opt. Exp. 14, 2459-2472 (2006).
  12. Y. Huang, S. T. Ho, "High-speed low-power photonic transistor devices based on optically-controlled gain or absorption to affect optical interference," Opt. Exp. 16, 16806-16824 (2008).
  13. J. P. Berenger, "Perfectly matched layer for the FDTD solution of wave-structure interaction problems," IEEE Trans. Antenna Propag. 44, 110-117 (1996).
  14. S. D. Gedney, "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antenna Propag. 44, 1630-1639 (1996).
  15. O. Ramadan, "Unconditionally stable nearly PML algorithm for linear dispersive media," IEEE Microw. Wireless Components Lett. 15, 490-492 (2005).
  16. O. Ramadan, "Uncondictionally stable crank-nicolson nearly PML algorithm for truncating linear lorentz dispersive FDTD domains," IEEE Trans. Microw. Theory Tech. 54, 2807-2812 (2006).
  17. Z. Y. Huang, G. W. Pan, "Universally applicable uni-axial perfect matched layer formulation for explicit and implicit finite difference time domain algorithms," IET Microwaves, Antennas Propag. 2, 668-676 (2008).
  18. K. Kawano, T. Kitoh, Introduction to Optical Waveguide Analysis Solving Maxwell's Equations and the Schrödinger Equation (Wiley, 2001).
  19. C. H. Henry, R. A. Logan, K. A. Bertness, "Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers," J. Appl. Phys. 52, 4457-4461.
  20. J. Berenger, "Numerical reflection from FDTD-PMLs: A comparison of the split PML with the unsplit and CFS PMLs," IEEE Trans. Antenna Propag. 50, 258-265 (2002).
  21. P. Kosmas, C. Rappaport, "A simple absorbing boundary condition for FDTD modeling of lossy, dispersive media based on the one-way wave equation," IEEE Trans. Antenna Propag. 52, 2476-2479 (2004).

2009 (1)

Fang, Th. Koschny, M. Wegener, C. M. Soukoulis, "Self-consistent calculation of metamaterials with gain," Phys. Rev. B 79 79, 2411041-2411044 (2009).

2008 (3)

Y. Huang, S. T. Ho, "High-speed low-power photonic transistor devices based on optically-controlled gain or absorption to affect optical interference," Opt. Exp. 16, 16806-16824 (2008).

Z. Y. Huang, G. W. Pan, "Universally applicable uni-axial perfect matched layer formulation for explicit and implicit finite difference time domain algorithms," IET Microwaves, Antennas Propag. 2, 668-676 (2008).

Y. Huang, S. T. Ho, "Dynamical semiconductor medium FDTD simulation of current-injection nanophotonic devices," Opt. Quantum Electron. 40, 337-341 (2008).

2007 (1)

W. H. P. Pernice, F. P. Payne, D. F. G. Gallagher, "A finite-difference time-domain method for the simulation of gain materials with carrier diffusion in photonic crystals," J. Lightw. Technol. 25, 2306-2314 (2007).

2006 (4)

Y. Huang, S. T. Ho, "Computational model of solid-state, molecular, or atomic media for FDTD simulation based on a multi-level multielectron system governed by Pauli exclusion and Fermi-Dirac thermalization with application to semiconductor photonics," Opt. Exp. 14, 3569-3587 (2006).

P. Bermel, E. Lidorikis, Y. Fink, J. D. Joannopoulos, "Active materials embedded in photonic crystals and coupled to electromagnetic radiation," Phys. Rev. B 73, 1651251-1651258 (2006).

S. Shi, G. Jin, D. W. Prather, "Electromagnetic simulation of quantum well structures," Opt. Exp. 14, 2459-2472 (2006).

O. Ramadan, "Uncondictionally stable crank-nicolson nearly PML algorithm for truncating linear lorentz dispersive FDTD domains," IEEE Trans. Microw. Theory Tech. 54, 2807-2812 (2006).

2005 (3)

O. Ramadan, "Unconditionally stable nearly PML algorithm for linear dispersive media," IEEE Microw. Wireless Components Lett. 15, 490-492 (2005).

M. K. Seo, G. H. Song, I. K. Hwang, Y. H. Lee, "Nonlinear dispersive three-dimensional finite-difference time-domain analysis for photonic-crystal lasers," Opt. Exp. 13, 9645-9651 (2005).

M. Bahl, N. C. Panoiu, R. M. Osgood, Jr."Modeling ultrashort field dynamics in surface emitting lasers by using finite-difference time-domain method," IEEE J. Quantum Electron. 41, 1244-1252 (2005).

2004 (3)

S. Chang, A. Taflove, "Finite-difference time-domain model of lasing action in a four-level two-electron atomic system," Opt. Exp. 12, 3827-3833 (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).

P. Kosmas, C. Rappaport, "A simple absorbing boundary condition for FDTD modeling of lossy, dispersive media based on the one-way wave equation," IEEE Trans. Antenna Propag. 52, 2476-2479 (2004).

2002 (1)

J. Berenger, "Numerical reflection from FDTD-PMLs: A comparison of the split PML with the unsplit and CFS PMLs," IEEE Trans. Antenna Propag. 50, 258-265 (2002).

2000 (1)

X. Jiang, C. M. Soukoulis, "Time dependent theory for random lasers," Phys. Rev. Lett. 85, 70-73 (2000).

1996 (2)

J. P. Berenger, "Perfectly matched layer for the FDTD solution of wave-structure interaction problems," IEEE Trans. Antenna Propag. 44, 110-117 (1996).

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

IEEE Microw. Wireless Components Lett. (1)

O. Ramadan, "Unconditionally stable nearly PML algorithm for linear dispersive media," IEEE Microw. Wireless Components Lett. 15, 490-492 (2005).

IEEE J. Quantum Electron. (1)

M. Bahl, N. C. Panoiu, R. M. Osgood, Jr."Modeling ultrashort field dynamics in surface emitting lasers by using finite-difference time-domain method," IEEE J. Quantum Electron. 41, 1244-1252 (2005).

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).

IEEE Trans. Antenna Propag. (4)

J. P. Berenger, "Perfectly matched layer for the FDTD solution of wave-structure interaction problems," IEEE Trans. Antenna Propag. 44, 110-117 (1996).

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

J. Berenger, "Numerical reflection from FDTD-PMLs: A comparison of the split PML with the unsplit and CFS PMLs," IEEE Trans. Antenna Propag. 50, 258-265 (2002).

P. Kosmas, C. Rappaport, "A simple absorbing boundary condition for FDTD modeling of lossy, dispersive media based on the one-way wave equation," IEEE Trans. Antenna Propag. 52, 2476-2479 (2004).

IEEE Trans. Microw. Theory Tech. (1)

O. Ramadan, "Uncondictionally stable crank-nicolson nearly PML algorithm for truncating linear lorentz dispersive FDTD domains," IEEE Trans. Microw. Theory Tech. 54, 2807-2812 (2006).

IET Microwaves, Antennas Propag. (1)

Z. Y. Huang, G. W. Pan, "Universally applicable uni-axial perfect matched layer formulation for explicit and implicit finite difference time domain algorithms," IET Microwaves, Antennas Propag. 2, 668-676 (2008).

J. Appl. Phys. (1)

C. H. Henry, R. A. Logan, K. A. Bertness, "Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers," J. Appl. Phys. 52, 4457-4461.

J. Lightw. Technol. (1)

W. H. P. Pernice, F. P. Payne, D. F. G. Gallagher, "A finite-difference time-domain method for the simulation of gain materials with carrier diffusion in photonic crystals," J. Lightw. Technol. 25, 2306-2314 (2007).

Opt. Quantum Electron. (1)

Y. Huang, S. T. Ho, "Dynamical semiconductor medium FDTD simulation of current-injection nanophotonic devices," Opt. Quantum Electron. 40, 337-341 (2008).

Opt. Exp. (5)

M. K. Seo, G. H. Song, I. K. Hwang, Y. H. Lee, "Nonlinear dispersive three-dimensional finite-difference time-domain analysis for photonic-crystal lasers," Opt. Exp. 13, 9645-9651 (2005).

Y. Huang, S. T. Ho, "Computational model of solid-state, molecular, or atomic media for FDTD simulation based on a multi-level multielectron system governed by Pauli exclusion and Fermi-Dirac thermalization with application to semiconductor photonics," Opt. Exp. 14, 3569-3587 (2006).

S. Shi, G. Jin, D. W. Prather, "Electromagnetic simulation of quantum well structures," Opt. Exp. 14, 2459-2472 (2006).

Y. Huang, S. T. Ho, "High-speed low-power photonic transistor devices based on optically-controlled gain or absorption to affect optical interference," Opt. Exp. 16, 16806-16824 (2008).

S. Chang, A. Taflove, "Finite-difference time-domain model of lasing action in a four-level two-electron atomic system," Opt. Exp. 12, 3827-3833 (2004).

Phys. Rev. B (1)

P. Bermel, E. Lidorikis, Y. Fink, J. D. Joannopoulos, "Active materials embedded in photonic crystals and coupled to electromagnetic radiation," Phys. Rev. B 73, 1651251-1651258 (2006).

Phys. Rev. B 79 (1)

Fang, Th. Koschny, M. Wegener, C. M. Soukoulis, "Self-consistent calculation of metamaterials with gain," Phys. Rev. B 79 79, 2411041-2411044 (2009).

Phys. Rev. Lett. (1)

X. Jiang, C. M. Soukoulis, "Time dependent theory for random lasers," Phys. Rev. Lett. 85, 70-73 (2000).

Other (1)

K. Kawano, T. Kitoh, Introduction to Optical Waveguide Analysis Solving Maxwell's Equations and the Schrödinger Equation (Wiley, 2001).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.