Abstract

In this paper we propose a novel silicon microcavity design based on the dispersion engineered photonic crystals (PhCs). With the unique self-collimation property of PhCs, we optimize the passive cavity by tuning the design parameters, such as coupling gap size and array size, to achieve higher Q factor and drop efficiency. Highest cavity mode below the band edge is of particular interest. The strong mode confinement in the low index active material offers an opportunity to realize a lasing mechanism. To investigate the lasing dynamics we introduce the rate equations of atomic system into the electromagnetic polarization to fully describe the nonlinearity of active medium. With these auxiliary differential equations we solve the time evolutions of the electromagnetic waves and atomic populations by using the FDTD method.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. B. Jalali, M. Paniccia, and G. Reed, "Silicon photonics," IEEE Microw. Mag. 7, 58-68 (2006).
    [CrossRef]
  2. L. Pavesi, "Will silicon bethe photonic material of the third millenium," J. Phys.: Condens. Matter 15, R1169-R1196 (2003).
    [CrossRef]
  3. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, "A continues-wave Raman silicon laser," Nature 433, 725-728 (2005).
    [CrossRef] [PubMed]
  4. O. Boyraz and B. Jalali, "Demonstartion of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
    [CrossRef] [PubMed]
  5. D. W. Prather, S. Shi, D. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. Schneider, and J. Murakowski, "Routing optical waves without waveguides," Opt. Lett. 29, 50-52 (2004).
    [CrossRef] [PubMed]
  6. M. R. Newton, K. A. Morey, Y. H. Zhang, R. J. Snow, M. Diwekar, J. Shi, and H. S. White, "Anisotropic diffusion in face-centered cubic opals," Nano. Lett. 4, 875-880 (2004).
    [CrossRef]
  7. K. K. Tsia and A. W. Poon, "Dispersion-guided resonances in two dimensional photonic-crystal embedded microcavities," Opt. Express 12, 5711-5722 (2004).
    [CrossRef] [PubMed]
  8. D. W. Prather, A. Sharkawy, and S. Shi, Handbook of Nanoscience, Engineering and Technology (CRC Press, 2002) 1, b.
  9. S. Chang and A. Taflove, "Finite-difference time-domain model of lasing action in a four-level two-electron atomic system," Opt. Express 12, 3827-3833 (2004).
    [CrossRef] [PubMed]
  10. A. Taflove, Computational Electromagnetics: The Finite-Difference Time Domain Method (Artech House, Boston 1995).
  11. A. Nagra and R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Trans. Antennas Propag. 46, 334-340 (1998).
    [CrossRef]
  12. X. Jiang and C. M. Soukoulis, "Time dependent theory for random lasers," Phys. Rev. Lett. 85, 70-73 (2000).
    [CrossRef] [PubMed]
  13. P. Sebbah and C. Vanneste, "Random laser in the localized regime," Phys. Rev. B 66,144202 (2002).
    [CrossRef]

2006

B. Jalali, M. Paniccia, and G. Reed, "Silicon photonics," IEEE Microw. Mag. 7, 58-68 (2006).
[CrossRef]

2005

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, "A continues-wave Raman silicon laser," Nature 433, 725-728 (2005).
[CrossRef] [PubMed]

2004

2003

L. Pavesi, "Will silicon bethe photonic material of the third millenium," J. Phys.: Condens. Matter 15, R1169-R1196 (2003).
[CrossRef]

2002

P. Sebbah and C. Vanneste, "Random laser in the localized regime," Phys. Rev. B 66,144202 (2002).
[CrossRef]

2000

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

1998

A. Nagra and R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Trans. Antennas Propag. 46, 334-340 (1998).
[CrossRef]

IEEE Microw. Mag.

B. Jalali, M. Paniccia, and G. Reed, "Silicon photonics," IEEE Microw. Mag. 7, 58-68 (2006).
[CrossRef]

IEEE Trans. Antennas Propag.

A. Nagra and R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Trans. Antennas Propag. 46, 334-340 (1998).
[CrossRef]

J. Phys.: Condens. Matter

L. Pavesi, "Will silicon bethe photonic material of the third millenium," J. Phys.: Condens. Matter 15, R1169-R1196 (2003).
[CrossRef]

Nano. Lett.

M. R. Newton, K. A. Morey, Y. H. Zhang, R. J. Snow, M. Diwekar, J. Shi, and H. S. White, "Anisotropic diffusion in face-centered cubic opals," Nano. Lett. 4, 875-880 (2004).
[CrossRef]

Nature

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, "A continues-wave Raman silicon laser," Nature 433, 725-728 (2005).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

P. Sebbah and C. Vanneste, "Random laser in the localized regime," Phys. Rev. B 66,144202 (2002).
[CrossRef]

Phys. Rev. Lett.

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

Other

D. W. Prather, A. Sharkawy, and S. Shi, Handbook of Nanoscience, Engineering and Technology (CRC Press, 2002) 1, b.

A. Taflove, Computational Electromagnetics: The Finite-Difference Time Domain Method (Artech House, Boston 1995).

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 (8)

Fig. 1.
Fig. 1.

(a) The dispersion surface of the first band for silicon PhC with circular holes filled with Er-doped glass. (b) Flat EFCs perpendicular to ΓM direction at frequency of 0.18c/a.

Fig. 2.
Fig. 2.

(a) Schematic of silicon laser based on dispersion engineered photonic crystals where the active material is introduced by backfilling the air holes of the PhC. (b) The highest cavity mode below the band edge.

Fig. 3.
Fig. 3.

Q factor and drop efficiency as a function of gap size between the waveguide and resonator.

Fig. 4.
Fig. 4.

Populations in the simplified four-level atomic system.

Fig. 5.
Fig. 5.

(a) Lasing dynamics by monitoring output in the straight dielectric waveguide, (b) steady output of single optical mode as shown within the time window in figure (a).

Fig. 6.
Fig. 6.

Snapshots of 2D field distribution at three instant time of 10, 30 and 50ps.

Fig. 7.
Fig. 7.

Normalized population inversion at pumping rate of 2×108/s.

Fig. 8.
Fig. 8.

Output intensity as the function of the pumping rate.

Equations (2)

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

{ dN 3 ( t ) dt = W p N 0 ( t ) N 3 ( t ) τ 32 dN 2 ( t ) dt = N 3 ( t ) τ 32 + 1 ω a E ( t ) · d P ( t ) dt N 2 ( t ) τ 21 dN 1 ( t ) dt = N 2 ( t ) τ 21 + 1 ω a E ( t ) · d P ( t ) dt N 1 ( t ) τ 10 dN 0 ( t ) dt = N 1 ( t ) τ 10 + W p N 0 ( t )
d 2 P ( t ) dt 2 + Δ ω a d P ( t ) dt + ω a 2 P ( t ) = κ e 2 m Δ N ( t ) E ( t )

Metrics