Abstract

In this paper we propose an electromagnetic analysis of active silicon nano-crystal (Si-nc) waveguide devices. To account for the nonlinearity in the active medium we introduce a four level rate equation model whose parameters are based on experimentally reported material properties. The electromagnetic polarization serves to couple the quantum mechanical and electromagnetic behavior within the ADE-FDTD scheme. The developed modeling tool is used to simulate waveguide amplifiers, enhanced spontaneous emission microcavities, and the temporal lasing dynamics of active Si-nc based devices.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Pavesi, "Will silicon be the photonic material of the third millenium?," J. Phys. Condens Matter 15, R1169-R1196 (2003).
    [CrossRef]
  2. B. Jalali and S. Fathpour, "Silicon photonics," J. Lightwave Technol.,  24, 4600-4615 (2006).
    [CrossRef]
  3. L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
    [CrossRef] [PubMed]
  4. J. Ruan, P. M. Fauchet, L. Dal Negro, M. Cazzanelli, and L. Pavesi, "Stimulated emission in nanocrystalline silicon superlattices," Appl. Phys. Lett. 83, 5479-5481 (2003).
    [CrossRef]
  5. A. Fojtik, J. Valenta, I. Pelant, M. Kalal, and P. Fiala, "On the road to silicon-nanoparticle laser," J. Mater. Process Technol. 181, 88-92 (2007).
    [CrossRef]
  6. D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
    [CrossRef] [PubMed]
  7. V. Ovchinnikov, A. Malinin, V. Sokolov, O. Kilpela, and J. Sinkkonen, "Photo and electroluminescence from PECVD grown a-Si : H/SiO2 multilayers," Opt. Mater. 17, 103-106 (2001).
    [CrossRef]
  8. T. Creazzo, B. Redding, T. Hodson, D. W. Prather, "Fabrication and characterization of silicon/silicon dioxide super lattices for silicon based light emitting devices," Proc. SPIE 6645 (2007).
    [CrossRef]
  9. A. S. Nagra and R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Transactions on Antennas and Propagation,  46, 334-340 (1998).
  10. S. Shi and D. W. Prather, "Lasing dynamics of a silicon photonic crystal microcavity," Opt. Express 15, 10294-10302 (2007).
    [CrossRef] [PubMed]
  11. S. Y. Shi, G. Jin, and D. W. Prather, "Electromagnetic simulation of quantum well structures," Opt. Express 14, 2459-2472 (2006).
    [CrossRef] [PubMed]
  12. S. H. 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]
  13. S. Shi, T. Creazzo, B. Redding, D. W. Prather, Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19711 are preparing a manuscript to be called "Simulation of Light Amplification and Enhanced Spontaneous Emission in Silicon Nanocrystals."
  14. L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
    [CrossRef]
  15. A. H. Taflove, S. C., Computational Electrodynamics: the finite-difference time-domain method (Artech House Publishers; 3rd edition, 2005).
  16. L. G. Pavesi, S. Dal Negro, L., Towards the First Silicon Laser (Kluwer Academic Publishers, 2002).
  17. D. Kovalev, H. Heckler, G. Polisski, and F. Koch, "Optical Properties of si nanocrystals," Phys. Status Solidi B 215, 871 (1999).
    [CrossRef]
  18. A. Belarouci and F. Gourbilleau, "Microcavity enhanced spontaneous emission from silicon nanocrystals," J. Appl. Phys. 101, 73108 (2007).
    [CrossRef]

2007 (3)

A. Fojtik, J. Valenta, I. Pelant, M. Kalal, and P. Fiala, "On the road to silicon-nanoparticle laser," J. Mater. Process Technol. 181, 88-92 (2007).
[CrossRef]

A. Belarouci and F. Gourbilleau, "Microcavity enhanced spontaneous emission from silicon nanocrystals," J. Appl. Phys. 101, 73108 (2007).
[CrossRef]

S. Shi and D. W. Prather, "Lasing dynamics of a silicon photonic crystal microcavity," Opt. Express 15, 10294-10302 (2007).
[CrossRef] [PubMed]

2006 (2)

2004 (1)

2003 (3)

J. Ruan, P. M. Fauchet, L. Dal Negro, M. Cazzanelli, and L. Pavesi, "Stimulated emission in nanocrystalline silicon superlattices," Appl. Phys. Lett. 83, 5479-5481 (2003).
[CrossRef]

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

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

2001 (1)

V. Ovchinnikov, A. Malinin, V. Sokolov, O. Kilpela, and J. Sinkkonen, "Photo and electroluminescence from PECVD grown a-Si : H/SiO2 multilayers," Opt. Mater. 17, 103-106 (2001).
[CrossRef]

2000 (1)

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
[CrossRef] [PubMed]

1999 (1)

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, "Optical Properties of si nanocrystals," Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

1998 (1)

A. S. Nagra and R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Transactions on Antennas and Propagation,  46, 334-340 (1998).

1996 (1)

D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
[CrossRef] [PubMed]

Baribeau, J. M.

D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
[CrossRef] [PubMed]

Belarouci, A.

A. Belarouci and F. Gourbilleau, "Microcavity enhanced spontaneous emission from silicon nanocrystals," J. Appl. Phys. 101, 73108 (2007).
[CrossRef]

Cazzanelli, M.

J. Ruan, P. M. Fauchet, L. Dal Negro, M. Cazzanelli, and L. Pavesi, "Stimulated emission in nanocrystalline silicon superlattices," Appl. Phys. Lett. 83, 5479-5481 (2003).
[CrossRef]

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

Chang, S. H.

Dal Negro, L.

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

J. Ruan, P. M. Fauchet, L. Dal Negro, M. Cazzanelli, and L. Pavesi, "Stimulated emission in nanocrystalline silicon superlattices," Appl. Phys. Lett. 83, 5479-5481 (2003).
[CrossRef]

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
[CrossRef] [PubMed]

Daldosso, N.

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

Fathpour, S.

Fauchet, P. M.

J. Ruan, P. M. Fauchet, L. Dal Negro, M. Cazzanelli, and L. Pavesi, "Stimulated emission in nanocrystalline silicon superlattices," Appl. Phys. Lett. 83, 5479-5481 (2003).
[CrossRef]

Fiala, P.

A. Fojtik, J. Valenta, I. Pelant, M. Kalal, and P. Fiala, "On the road to silicon-nanoparticle laser," J. Mater. Process Technol. 181, 88-92 (2007).
[CrossRef]

Fojtik, A.

A. Fojtik, J. Valenta, I. Pelant, M. Kalal, and P. Fiala, "On the road to silicon-nanoparticle laser," J. Mater. Process Technol. 181, 88-92 (2007).
[CrossRef]

Franzo, G.

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
[CrossRef] [PubMed]

Gaburro, Z.

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

Gourbilleau, F.

A. Belarouci and F. Gourbilleau, "Microcavity enhanced spontaneous emission from silicon nanocrystals," J. Appl. Phys. 101, 73108 (2007).
[CrossRef]

Heckler, H.

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, "Optical Properties of si nanocrystals," Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

Iacona, F.

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

Jalali, B.

Jin, G.

Kalal, M.

A. Fojtik, J. Valenta, I. Pelant, M. Kalal, and P. Fiala, "On the road to silicon-nanoparticle laser," J. Mater. Process Technol. 181, 88-92 (2007).
[CrossRef]

Kilpela, O.

V. Ovchinnikov, A. Malinin, V. Sokolov, O. Kilpela, and J. Sinkkonen, "Photo and electroluminescence from PECVD grown a-Si : H/SiO2 multilayers," Opt. Mater. 17, 103-106 (2001).
[CrossRef]

Koch, F.

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, "Optical Properties of si nanocrystals," Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

Kovalev, D.

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, "Optical Properties of si nanocrystals," Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

Lockwood, D. J.

D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
[CrossRef] [PubMed]

Lu, Z. H.

D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
[CrossRef] [PubMed]

Malinin, A.

V. Ovchinnikov, A. Malinin, V. Sokolov, O. Kilpela, and J. Sinkkonen, "Photo and electroluminescence from PECVD grown a-Si : H/SiO2 multilayers," Opt. Mater. 17, 103-106 (2001).
[CrossRef]

Mazzoleni, C.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
[CrossRef] [PubMed]

Nagra, A. S.

A. S. Nagra and R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Transactions on Antennas and Propagation,  46, 334-340 (1998).

Ovchinnikov, V.

V. Ovchinnikov, A. Malinin, V. Sokolov, O. Kilpela, and J. Sinkkonen, "Photo and electroluminescence from PECVD grown a-Si : H/SiO2 multilayers," Opt. Mater. 17, 103-106 (2001).
[CrossRef]

Pacifici, D.

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

Pavesi, L.

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

J. Ruan, P. M. Fauchet, L. Dal Negro, M. Cazzanelli, and L. Pavesi, "Stimulated emission in nanocrystalline silicon superlattices," Appl. Phys. Lett. 83, 5479-5481 (2003).
[CrossRef]

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

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
[CrossRef] [PubMed]

Pelant, I.

A. Fojtik, J. Valenta, I. Pelant, M. Kalal, and P. Fiala, "On the road to silicon-nanoparticle laser," J. Mater. Process Technol. 181, 88-92 (2007).
[CrossRef]

Polisski, G.

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, "Optical Properties of si nanocrystals," Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

Prather, D. W.

Priolo, F.

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
[CrossRef] [PubMed]

Ruan, J.

J. Ruan, P. M. Fauchet, L. Dal Negro, M. Cazzanelli, and L. Pavesi, "Stimulated emission in nanocrystalline silicon superlattices," Appl. Phys. Lett. 83, 5479-5481 (2003).
[CrossRef]

Shi, S.

Shi, S. Y.

Sinkkonen, J.

V. Ovchinnikov, A. Malinin, V. Sokolov, O. Kilpela, and J. Sinkkonen, "Photo and electroluminescence from PECVD grown a-Si : H/SiO2 multilayers," Opt. Mater. 17, 103-106 (2001).
[CrossRef]

Sokolov, V.

V. Ovchinnikov, A. Malinin, V. Sokolov, O. Kilpela, and J. Sinkkonen, "Photo and electroluminescence from PECVD grown a-Si : H/SiO2 multilayers," Opt. Mater. 17, 103-106 (2001).
[CrossRef]

Taflove, A.

Valenta, J.

A. Fojtik, J. Valenta, I. Pelant, M. Kalal, and P. Fiala, "On the road to silicon-nanoparticle laser," J. Mater. Process Technol. 181, 88-92 (2007).
[CrossRef]

York, R. A.

A. S. Nagra and R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Transactions on Antennas and Propagation,  46, 334-340 (1998).

Appl. Phys. Lett. (1)

J. Ruan, P. M. Fauchet, L. Dal Negro, M. Cazzanelli, and L. Pavesi, "Stimulated emission in nanocrystalline silicon superlattices," Appl. Phys. Lett. 83, 5479-5481 (2003).
[CrossRef]

IEEE Transactions on Antennas and Propagation (1)

A. S. Nagra and R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Transactions on Antennas and Propagation,  46, 334-340 (1998).

J. Appl. Phys. (1)

A. Belarouci and F. Gourbilleau, "Microcavity enhanced spontaneous emission from silicon nanocrystals," J. Appl. Phys. 101, 73108 (2007).
[CrossRef]

J. Lightwave Technol. (1)

J. Mater. Process Technol. (1)

A. Fojtik, J. Valenta, I. Pelant, M. Kalal, and P. Fiala, "On the road to silicon-nanoparticle laser," J. Mater. Process Technol. 181, 88-92 (2007).
[CrossRef]

J. Phys. Condens Matter (1)

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

Nature (1)

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Mater. (1)

V. Ovchinnikov, A. Malinin, V. Sokolov, O. Kilpela, and J. Sinkkonen, "Photo and electroluminescence from PECVD grown a-Si : H/SiO2 multilayers," Opt. Mater. 17, 103-106 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
[CrossRef] [PubMed]

Phys. Status Solidi B (1)

D. Kovalev, H. Heckler, G. Polisski, and F. Koch, "Optical Properties of si nanocrystals," Phys. Status Solidi B 215, 871 (1999).
[CrossRef]

Physica E-Low-Dimensional Systems & Nanostructures (1)

L. Dal Negro, M. Cazzanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, "Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals," Physica E-Low-Dimensional Systems & Nanostructures 16, 297-308 (2003).
[CrossRef]

Other (4)

A. H. Taflove, S. C., Computational Electrodynamics: the finite-difference time-domain method (Artech House Publishers; 3rd edition, 2005).

L. G. Pavesi, S. Dal Negro, L., Towards the First Silicon Laser (Kluwer Academic Publishers, 2002).

S. Shi, T. Creazzo, B. Redding, D. W. Prather, Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19711 are preparing a manuscript to be called "Simulation of Light Amplification and Enhanced Spontaneous Emission in Silicon Nanocrystals."

T. Creazzo, B. Redding, T. Hodson, D. W. Prather, "Fabrication and characterization of silicon/silicon dioxide super lattices for silicon based light emitting devices," Proc. SPIE 6645 (2007).
[CrossRef]

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.

Si-nc active material can be represented by a four-level rate equation model where stimulated and spontaneous emission occur for transitions between E2 and E1.

Fig. 2.
Fig. 2.

(a) Configuration for waveguide amplification study. A Gaussian pulse in air is incident on a pumped Si-nc waveguide. A detector in air at the end of the waveguide measures the amplification by normalizing to the output without pumping. (b) Configuration for amplified spontaneous emission study. Optional DBRs create a microcavity to enhance spontaneous emission of pumped Si-ncs.

Fig. 3.
Fig. 3.

(a) Amplification spectra through a pumped Si-nc waveguide for TE and TM cases. Detected signal under pumping is normalized to detected signal without pumping to eliminate loss due to reflection at waveguide interfaces. (b) The 2D plot of amplitude of the steady state field at the peak wavelength of 750nm.

Fig. 4.
Fig. 4.

DBRs enhance PL signal of Si-ncs by ~4X in the TE case and ~8X in the TM case. (a) The spectral response for TE and TM with and without 3 periods of DBRs is shown, normalized to the peak PL emission for the no-DBR case. (b) The steady state amplitude of the Ez component is shown, the TM case corresponds to its peak wavelength of 770nm while the TE case corresponds to its peak wavelength of 677nm.

Fig. 5.
Fig. 5.

Lasing dynamics for optimized microcavity subject to Wp=5×1011. (a) The amplitude of the Ez field and the population inversion are shown as functions of time. The population inversion has been normalized to the total population. (b) The lasing structure’s steady state emission.

Fig. 6.
Fig. 6.

Peak optical output intensity as a function of pumping rate. The lasing threshold condition, when the output goes to zero, corresponds to a pumping rate of 4.3×1011 s-1.

Equations (4)

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

{ dN 3 ( t ) dt = N 3 ( t ) τ 32 + W p N 0 dN 2 ( t ) dt = N 3 ( t ) τ 32 N 2 ( t ) τ 21 + 1 ħ ω s E ( t ) · d P ( t ) dt dN 1 ( t ) dt = N 2 ( t ) τ 21 N 1 ( t ) τ 10 - 1 ħ ω s E ( t ) · d P ( t ) dt dN 0 ( t ) dt = N 1 ( t ) τ 10 W p N 0
d 2 P ( t ) dt 2 + Δ ω s d P ( t ) dt + ω s 2 P ( t ) = κ Δ N 12 ( t ) E ( t ) ,
κ = c ε 0 ε r σ s Δ ω s .
× E = μ 0 H t , × H = ε 0 ε r E t + P t + J .

Metrics