Abstract

The three-dimensional finite-difference time-domain method that can handle dispersive and dynamic nonlinear-gain media is proposed and realized. The effect of carrier diffusion is included through the laser rate equations. Through this three-dimensional nonlinear gain FDTD method, rich laser-dynamics behaviors, such as the lasing threshold, the relaxation oscillation, and the spatial hole burning, are directly observed from a hexapole mode.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819 (1999).
    [CrossRef] [PubMed]
  2. H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, Y. H. Lee, and J. S. Kim, “Nondegenerate monopole-mode two-dimensional photonic band gap laser,” Appl. Phys. Lett. 79, 3032 (2001).
    [CrossRef]
  3. H. Y. Ryu, S. H. Kim, H. G. Park, J. K. Hwang, Y. H. Lee, and J. S. Kim, “Square-lattice photonic bandgap single-cell laser operating in the lowest-order whispering gallery mode,” Appl. Phys. Lett. 80, 3883 (2002).
    [CrossRef]
  4. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, chap. 5, 8, 11 (Artech House, Boston, Mass, 1995).
  5. H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444 (2004).
    [CrossRef] [PubMed]
  6. K. Nozaki and T. Baba, “Carrier and photon analyses of photonic microlasers by two-dimensional rate equations,” J. Sel. Area. Commun. 23, 1411 (2005).
    [CrossRef]
  7. R. J. Luebbers and F. Hunsburger, “FDTD for n-th-order dispersive media,” IEEE Trans. Antennas Propagat. 40, 1297–1301 (1992)
    [CrossRef]
  8. J. Schuster and R. Luebbers, “An accurate FDTD algorithm for dispersive media using a piecewise constant recursive convolution technique,” IEEE Antennas and propagation Soc. Internat. Symp. Digest, 4, 2018 (1998).
  9. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits, chap. 2 (A Wiley-Interscience Publication, 1995).
  10. W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics (Springer-Verlag, Berlin, Germany 1994), Sec. 10-4.
    [CrossRef]
  11. G. H. Song, S. Kim, and K. Hwang, “FDTD Simulation of Photonic-Crystal Lasers and Their Relaxation Oscillation,” J. Opt. Soc. Kor. 6, 87 (2002).
    [CrossRef]
  12. M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” J. Sel. Top. Quantum Electron. 5, 673 (1999).
    [CrossRef]

Appl. Phys. Lett. (2)

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, Y. H. Lee, and J. S. Kim, “Nondegenerate monopole-mode two-dimensional photonic band gap laser,” Appl. Phys. Lett. 79, 3032 (2001).
[CrossRef]

H. Y. Ryu, S. H. Kim, H. G. Park, J. K. Hwang, Y. H. Lee, and J. S. Kim, “Square-lattice photonic bandgap single-cell laser operating in the lowest-order whispering gallery mode,” Appl. Phys. Lett. 80, 3883 (2002).
[CrossRef]

IEEE Antennas and propagation Soc. Inter (1)

J. Schuster and R. Luebbers, “An accurate FDTD algorithm for dispersive media using a piecewise constant recursive convolution technique,” IEEE Antennas and propagation Soc. Internat. Symp. Digest, 4, 2018 (1998).

IEEE Trans. Antennas Propagat. (1)

R. J. Luebbers and F. Hunsburger, “FDTD for n-th-order dispersive media,” IEEE Trans. Antennas Propagat. 40, 1297–1301 (1992)
[CrossRef]

J. Opt. Soc. Kor. (1)

G. H. Song, S. Kim, and K. Hwang, “FDTD Simulation of Photonic-Crystal Lasers and Their Relaxation Oscillation,” J. Opt. Soc. Kor. 6, 87 (2002).
[CrossRef]

J. Sel. Area. Commun. (1)

K. Nozaki and T. Baba, “Carrier and photon analyses of photonic microlasers by two-dimensional rate equations,” J. Sel. Area. Commun. 23, 1411 (2005).
[CrossRef]

J. Sel. Top. Quantum Electron. (1)

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” J. Sel. Top. Quantum Electron. 5, 673 (1999).
[CrossRef]

Science (2)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819 (1999).
[CrossRef] [PubMed]

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444 (2004).
[CrossRef] [PubMed]

Other (3)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, chap. 5, 8, 11 (Artech House, Boston, Mass, 1995).

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits, chap. 2 (A Wiley-Interscience Publication, 1995).

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics (Springer-Verlag, Berlin, Germany 1994), Sec. 10-4.
[CrossRef]

Supplementary Material (1)

» Media 1: GIF (134 KB)     

Cited By

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

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

The scheme of the gain FDTD method.

Fig. 2.
Fig. 2.

The PhC cavity structure in the simulation. The gray area in (a) and (b) is the nonlinear gain region in the PhC slab. The black area in (c) and (d) is the spatially uniform current pumping area with the radius of 2.5a.

Fig. 3.
Fig. 3.

Hz -field profile of the hexapole mode. The hexapole mode shows up from spontaneous emission. See also animation. (gif, 141kb)

Fig. 4.
Fig. 4.

(a) The Lorentz dispersion of the imaginary part of ε and the locations of the resonant modes of PhC single cell cavity. (b) The Hz profiles of the resonant modes.

Fig. 5.
Fig. 5.

Dynamics of the hexapole photonic-crystal laser mode. (a) The solid and dashed curves represent the changing number of the participating photons and the temporal variation of the modal gain, respectively. Lasing action begins at A. (b) Temporal behavior of the Hz field.

Fig. 6.
Fig. 6.

Carrier density snapshots at successive time intervals, revealing the hole-burning effect. The inset in (d) is the inverted plot for the electric field intensity.

Tables (1)

Tables Icon

Table 1. Parameters of gain medium used in simulation

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ε ( r , ω ) ε [ 1 + Γ ( r ) ω 0 ω i γ 0 + Γ ( r ) ω 0 + ω + i γ 0 ] ,
Γ ( r , t ) 2 γ 0 c n ( r ) ω 0 G ( N ( r , t ) ; r ) ,
D ( r , t ) P ( r , t ) + ε 0 E ( r , t ) = t ε ˇ ( r , t t ) E ( r , t ) d t ,
d N ( r , t ) d t = J ( r , t ) q e N ( r , t ) τ + E ( r , t ) ω 0 P ( r , t ) t + D 2 N ( r , t ) ,
N ( r , t ) τ AN ( r , t ) + B N 2 ( r , t ) + C N 3 ( r , t )
B N 2 + E ω 0 P t = E ω 0 [ × H + ε E t ]
G ( N ; r , t ) = G 0 ln ( N ( r , t ) N tr ) ,
G mod = G mat ( r ) ε ( r ) E ( r ) 2 d 3 r ε ( r ) E ( r ) 2 d 3 r ,

Metrics