Abstract

A new algorithm based on auxiliary differential equation and finite difference time domain method (ADE-FDTD method) is presented to model a waveguide whose active layer is constituted of a silica matrix doped with rare-earth and silicon nanograins. The typical lifetime of rare-earth can be as large as some ms, whereas the electromagnetic field in a visible range and near-infrared is characterized by a period of the order of fs. Due to the large difference between these two characteristic times, the conventional ADE-FDTD method is not suited to treat such systems. A new algorithm is presented so that the steady state of rare earth and silicon nanograins electronic levels populations along with the electromagnetic field can be fully described. This algorithm is stable and applicable to a wide range of optical gain materials in which large differences of characteristic lifetimes are present.

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    [CrossRef]
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    [CrossRef]

2012 (2)

M. Govoni, Marri, and S. Ossicini, “Carrier multiplication between interacting nanocrystals for fostering silicon-based photovoltaics,” Nat. Photonics6, 672–679 (2012).
[CrossRef]

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, and F. Gourbilleau, “Study of optical losses of Nd3+doped silicon rich silicon oxide for laser cavity,” Thin Solid Films520, 4026–4030 (2012).
[CrossRef]

2011 (2)

O. Debieu, J. Cardin, X. Portier, and F. Gourbilleau, “Effect of the Nd content on the structural and photoluminescence properties of silicon-rich silicon dioxide thin films,” Nanoscale Res. Lett.6, 1–8 (2011).
[CrossRef]

C. Dufour, J. Cardin, O. Debieu, A. Fafin, and F. Gourbilleau, “Electromagnetic modeling of waveguide amplifier based on Nd3+ Si-rich SiO2 layers by means of the ADE-FDTD method,” Nanoscale Res. Lett.6, 1–5 (2011).
[CrossRef]

2008 (2)

V. Toccafondo, S. Faralli, and F. Di Pasquale, “Evanescent Multimode Longitudinal Pumping Scheme for Si-Nanocluster Sensitized Er3+Doped Waveguide Amplifiers,” J. Lightwave Techno.26, 3584–3591 (2008).
[CrossRef]

A. Fallahkhair, K. Li, and T. Murphy, “Vector finite difference modesolver for anisotropic dielectric waveguides,” J. Lightwave Techno.26, 1423–1431 (2008).
[CrossRef]

2006 (2)

D. Biallo, A. D’Orazio, and V. Petruzzelli, “Enhanced light extraction in Er3+doped SiO2-TiO2 microcavity embedded in one-dimensional photonic crystal,” J. Non-Cryst. Solids352, 3823–3828 (2006).
[CrossRef]

P. R. Amestoy, A. Guermouche, J.-Y. L’Excellent, and S. Pralet, “Hybrid scheduling for the parallel solution of linear systems,” Parallel Computing32, 136–156 (2006).
[CrossRef]

2005 (1)

2004 (3)

2003 (1)

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, and L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B67, 245301(2003).
[CrossRef]

2001 (2)

P. R. Amestoy, I. S. Duff, J. Koster, and J.-Y. L’Excellent, “A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling,” SIAM. J. Matrix Anal. & Appl.23, 15–41 (2001).
[CrossRef]

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, and A. Irrera, “Role of the energy transfer in the optical properties of undoped and Er-doped interacting Si nanocrystals,” J. Appl. Phys.89, 264–272 (2001).
[CrossRef]

1998 (2)

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

P. Kik and A. Polman, “Erbium-doped optical-waveguide amplifiers on silicon,” Mater. Res. Bull.23, 48–54 (1998).

1997 (1)

M. Fujii, M. Yoshida, Y. Kanzawa, S. Hayashi, and K. Yamamoto, “1.54 m photoluminescence of Er3+ doped into SiO2 films containing Si nanocrystals: Evidence for energy transfer from Si nanocrystals to Er3+,” Appl. Phys. Lett.71, 1198–1200 (1997).
[CrossRef]

1996 (1)

S. C. Hagness, R. M. Joseph, and A. Taflove, “Subpicosecond electrodynamics of distributed Bragg reflector microlasers: Results from finite difference time domain simulations,” Radio Sci.31, 931–941 (1996).
[CrossRef]

1994 (3)

J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. comput. phys.114, 185–200 (1994).
[CrossRef]

A. J. Kenyon, P. F. Trwoga, M. Federighi, and C. W. Pitt, “Optical properties of PECVD erbium-doped silicon-rich silica: evidence for energy transfer between silicon microclusters and erbium ions,” J. Phys.: Condens. Matter6, 319–324 (1994).
[CrossRef]

P.G. Petropoulos, “Stability and phase error analysis of FD-TD in dispersive dielectrics,” IEEE Trans. Antennas Propag.42, 62–69 (1994).
[CrossRef]

1991 (1)

W. Miniscalco, “Erbium-doped glasses for fiber amplifiers at 1500 nm,” J. Lightwave Techno.9, 234–250 (1991).
[CrossRef]

1975 (1)

A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech.23, 623–630 (1975).
[CrossRef]

1966 (1)

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

Amestoy, P. R.

P. R. Amestoy, A. Guermouche, J.-Y. L’Excellent, and S. Pralet, “Hybrid scheduling for the parallel solution of linear systems,” Parallel Computing32, 136–156 (2006).
[CrossRef]

P. R. Amestoy, I. S. Duff, J. Koster, and J.-Y. L’Excellent, “A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling,” SIAM. J. Matrix Anal. & Appl.23, 15–41 (2001).
[CrossRef]

Berenger, J.

J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. comput. phys.114, 185–200 (1994).
[CrossRef]

Biallo, D.

D. Biallo, A. D’Orazio, and V. Petruzzelli, “Enhanced light extraction in Er3+doped SiO2-TiO2 microcavity embedded in one-dimensional photonic crystal,” J. Non-Cryst. Solids352, 3823–3828 (2006).
[CrossRef]

Boucher, Y. G.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, and F. Gourbilleau, “Study of optical losses of Nd3+doped silicon rich silicon oxide for laser cavity,” Thin Solid Films520, 4026–4030 (2012).
[CrossRef]

Brodwin, M. E.

A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech.23, 623–630 (1975).
[CrossRef]

Cardin, J.

C. Dufour, J. Cardin, O. Debieu, A. Fafin, and F. Gourbilleau, “Electromagnetic modeling of waveguide amplifier based on Nd3+ Si-rich SiO2 layers by means of the ADE-FDTD method,” Nanoscale Res. Lett.6, 1–5 (2011).
[CrossRef]

O. Debieu, J. Cardin, X. Portier, and F. Gourbilleau, “Effect of the Nd content on the structural and photoluminescence properties of silicon-rich silicon dioxide thin films,” Nanoscale Res. Lett.6, 1–8 (2011).
[CrossRef]

Chang, S.-H.

Charrier, J.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, and F. Gourbilleau, “Study of optical losses of Nd3+doped silicon rich silicon oxide for laser cavity,” Thin Solid Films520, 4026–4030 (2012).
[CrossRef]

D’Orazio, A.

D. Biallo, A. D’Orazio, and V. Petruzzelli, “Enhanced light extraction in Er3+doped SiO2-TiO2 microcavity embedded in one-dimensional photonic crystal,” J. Non-Cryst. Solids352, 3823–3828 (2006).
[CrossRef]

Dal Negro, L.

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, and L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B67, 245301(2003).
[CrossRef]

Debieu, O.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, and F. Gourbilleau, “Study of optical losses of Nd3+doped silicon rich silicon oxide for laser cavity,” Thin Solid Films520, 4026–4030 (2012).
[CrossRef]

C. Dufour, J. Cardin, O. Debieu, A. Fafin, and F. Gourbilleau, “Electromagnetic modeling of waveguide amplifier based on Nd3+ Si-rich SiO2 layers by means of the ADE-FDTD method,” Nanoscale Res. Lett.6, 1–5 (2011).
[CrossRef]

O. Debieu, J. Cardin, X. Portier, and F. Gourbilleau, “Effect of the Nd content on the structural and photoluminescence properties of silicon-rich silicon dioxide thin films,” Nanoscale Res. Lett.6, 1–8 (2011).
[CrossRef]

Di Pasquale, F.

V. Toccafondo, S. Faralli, and F. Di Pasquale, “Evanescent Multimode Longitudinal Pumping Scheme for Si-Nanocluster Sensitized Er3+Doped Waveguide Amplifiers,” J. Lightwave Techno.26, 3584–3591 (2008).
[CrossRef]

Duff, I. S.

P. R. Amestoy, I. S. Duff, J. Koster, and J.-Y. L’Excellent, “A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling,” SIAM. J. Matrix Anal. & Appl.23, 15–41 (2001).
[CrossRef]

Dufour, C.

C. Dufour, J. Cardin, O. Debieu, A. Fafin, and F. Gourbilleau, “Electromagnetic modeling of waveguide amplifier based on Nd3+ Si-rich SiO2 layers by means of the ADE-FDTD method,” Nanoscale Res. Lett.6, 1–5 (2011).
[CrossRef]

Dumeige, Y.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, and F. Gourbilleau, “Study of optical losses of Nd3+doped silicon rich silicon oxide for laser cavity,” Thin Solid Films520, 4026–4030 (2012).
[CrossRef]

Fafin, A.

C. Dufour, J. Cardin, O. Debieu, A. Fafin, and F. Gourbilleau, “Electromagnetic modeling of waveguide amplifier based on Nd3+ Si-rich SiO2 layers by means of the ADE-FDTD method,” Nanoscale Res. Lett.6, 1–5 (2011).
[CrossRef]

Fallahkhair, A.

A. Fallahkhair, K. Li, and T. Murphy, “Vector finite difference modesolver for anisotropic dielectric waveguides,” J. Lightwave Techno.26, 1423–1431 (2008).
[CrossRef]

Faralli, S.

V. Toccafondo, S. Faralli, and F. Di Pasquale, “Evanescent Multimode Longitudinal Pumping Scheme for Si-Nanocluster Sensitized Er3+Doped Waveguide Amplifiers,” J. Lightwave Techno.26, 3584–3591 (2008).
[CrossRef]

Federighi, M.

A. J. Kenyon, P. F. Trwoga, M. Federighi, and C. W. Pitt, “Optical properties of PECVD erbium-doped silicon-rich silica: evidence for energy transfer between silicon microclusters and erbium ions,” J. Phys.: Condens. Matter6, 319–324 (1994).
[CrossRef]

Franzo, G.

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, and L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B67, 245301(2003).
[CrossRef]

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, and A. Irrera, “Role of the energy transfer in the optical properties of undoped and Er-doped interacting Si nanocrystals,” J. Appl. Phys.89, 264–272 (2001).
[CrossRef]

Fujii, M.

M. Fujii, M. Yoshida, Y. Kanzawa, S. Hayashi, and K. Yamamoto, “1.54 m photoluminescence of Er3+ doped into SiO2 films containing Si nanocrystals: Evidence for energy transfer from Si nanocrystals to Er3+,” Appl. Phys. Lett.71, 1198–1200 (1997).
[CrossRef]

Gourbilleau, F.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, and F. Gourbilleau, “Study of optical losses of Nd3+doped silicon rich silicon oxide for laser cavity,” Thin Solid Films520, 4026–4030 (2012).
[CrossRef]

O. Debieu, J. Cardin, X. Portier, and F. Gourbilleau, “Effect of the Nd content on the structural and photoluminescence properties of silicon-rich silicon dioxide thin films,” Nanoscale Res. Lett.6, 1–8 (2011).
[CrossRef]

C. Dufour, J. Cardin, O. Debieu, A. Fafin, and F. Gourbilleau, “Electromagnetic modeling of waveguide amplifier based on Nd3+ Si-rich SiO2 layers by means of the ADE-FDTD method,” Nanoscale Res. Lett.6, 1–5 (2011).
[CrossRef]

Govoni, M.

M. Govoni, Marri, and S. Ossicini, “Carrier multiplication between interacting nanocrystals for fostering silicon-based photovoltaics,” Nat. Photonics6, 672–679 (2012).
[CrossRef]

Guermouche, A.

P. R. Amestoy, A. Guermouche, J.-Y. L’Excellent, and S. Pralet, “Hybrid scheduling for the parallel solution of linear systems,” Parallel Computing32, 136–156 (2006).
[CrossRef]

Hagness, S. C.

S. C. Hagness, R. M. Joseph, and A. Taflove, “Subpicosecond electrodynamics of distributed Bragg reflector microlasers: Results from finite difference time domain simulations,” Radio Sci.31, 931–941 (1996).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 1995).

Hayashi, S.

M. Fujii, M. Yoshida, Y. Kanzawa, S. Hayashi, and K. Yamamoto, “1.54 m photoluminescence of Er3+ doped into SiO2 films containing Si nanocrystals: Evidence for energy transfer from Si nanocrystals to Er3+,” Appl. Phys. Lett.71, 1198–1200 (1997).
[CrossRef]

Iacona, F.

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, and L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B67, 245301(2003).
[CrossRef]

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, and A. Irrera, “Role of the energy transfer in the optical properties of undoped and Er-doped interacting Si nanocrystals,” J. Appl. Phys.89, 264–272 (2001).
[CrossRef]

Irrera, A.

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, and A. Irrera, “Role of the energy transfer in the optical properties of undoped and Er-doped interacting Si nanocrystals,” J. Appl. Phys.89, 264–272 (2001).
[CrossRef]

Joseph, R. M.

S. C. Hagness, R. M. Joseph, and A. Taflove, “Subpicosecond electrodynamics of distributed Bragg reflector microlasers: Results from finite difference time domain simulations,” Radio Sci.31, 931–941 (1996).
[CrossRef]

Kanzawa, Y.

M. Fujii, M. Yoshida, Y. Kanzawa, S. Hayashi, and K. Yamamoto, “1.54 m photoluminescence of Er3+ doped into SiO2 films containing Si nanocrystals: Evidence for energy transfer from Si nanocrystals to Er3+,” Appl. Phys. Lett.71, 1198–1200 (1997).
[CrossRef]

Kenyon, A. J.

A. J. Kenyon, P. F. Trwoga, M. Federighi, and C. W. Pitt, “Optical properties of PECVD erbium-doped silicon-rich silica: evidence for energy transfer between silicon microclusters and erbium ions,” J. Phys.: Condens. Matter6, 319–324 (1994).
[CrossRef]

Kik, P.

P. Kik and A. Polman, “Erbium-doped optical-waveguide amplifiers on silicon,” Mater. Res. Bull.23, 48–54 (1998).

Koster, J.

P. R. Amestoy, I. S. Duff, J. Koster, and J.-Y. L’Excellent, “A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling,” SIAM. J. Matrix Anal. & Appl.23, 15–41 (2001).
[CrossRef]

L’Excellent, J.-Y.

P. R. Amestoy, A. Guermouche, J.-Y. L’Excellent, and S. Pralet, “Hybrid scheduling for the parallel solution of linear systems,” Parallel Computing32, 136–156 (2006).
[CrossRef]

P. R. Amestoy, I. S. Duff, J. Koster, and J.-Y. L’Excellent, “A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling,” SIAM. J. Matrix Anal. & Appl.23, 15–41 (2001).
[CrossRef]

Lee, H.

Li, K.

A. Fallahkhair, K. Li, and T. Murphy, “Vector finite difference modesolver for anisotropic dielectric waveguides,” J. Lightwave Techno.26, 1423–1431 (2008).
[CrossRef]

Marri,

M. Govoni, Marri, and S. Ossicini, “Carrier multiplication between interacting nanocrystals for fostering silicon-based photovoltaics,” Nat. Photonics6, 672–679 (2012).
[CrossRef]

Miniscalco, W.

W. Miniscalco, “Erbium-doped glasses for fiber amplifiers at 1500 nm,” J. Lightwave Techno.9, 234–250 (1991).
[CrossRef]

Murphy, T.

A. Fallahkhair, K. Li, and T. Murphy, “Vector finite difference modesolver for anisotropic dielectric waveguides,” J. Lightwave Techno.26, 1423–1431 (2008).
[CrossRef]

Nagra, A.

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

Nordlander, P.

C. Oubre and P. Nordlander, “Optical properties of metallodielectric nanostructures calculated using the finite difference time domain method,” J. Phys. Chem. B108, 17740–17747 (2004).
[CrossRef]

Ossicini, S.

M. Govoni, Marri, and S. Ossicini, “Carrier multiplication between interacting nanocrystals for fostering silicon-based photovoltaics,” Nat. Photonics6, 672–679 (2012).
[CrossRef]

Oubre, C.

C. Oubre and P. Nordlander, “Optical properties of metallodielectric nanostructures calculated using the finite difference time domain method,” J. Phys. Chem. B108, 17740–17747 (2004).
[CrossRef]

Pacifici, D.

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, and L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B67, 245301(2003).
[CrossRef]

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, and A. Irrera, “Role of the energy transfer in the optical properties of undoped and Er-doped interacting Si nanocrystals,” J. Appl. Phys.89, 264–272 (2001).
[CrossRef]

Park, N.

Petropoulos, P.G.

P.G. Petropoulos, “Stability and phase error analysis of FD-TD in dispersive dielectrics,” IEEE Trans. Antennas Propag.42, 62–69 (1994).
[CrossRef]

Petruzzelli, V.

D. Biallo, A. D’Orazio, and V. Petruzzelli, “Enhanced light extraction in Er3+doped SiO2-TiO2 microcavity embedded in one-dimensional photonic crystal,” J. Non-Cryst. Solids352, 3823–3828 (2006).
[CrossRef]

Pirasteh, P.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, and F. Gourbilleau, “Study of optical losses of Nd3+doped silicon rich silicon oxide for laser cavity,” Thin Solid Films520, 4026–4030 (2012).
[CrossRef]

Pitt, C. W.

A. J. Kenyon, P. F. Trwoga, M. Federighi, and C. W. Pitt, “Optical properties of PECVD erbium-doped silicon-rich silica: evidence for energy transfer between silicon microclusters and erbium ions,” J. Phys.: Condens. Matter6, 319–324 (1994).
[CrossRef]

Polman, A.

A. Polman and F. C. J. M. van Veggel, “Broadband sensitizers for erbium-doped planar optical amplifiers: review,” J. Opt. Soc. Am. B21, 871–892 (2004).
[CrossRef]

P. Kik and A. Polman, “Erbium-doped optical-waveguide amplifiers on silicon,” Mater. Res. Bull.23, 48–54 (1998).

Portier, X.

O. Debieu, J. Cardin, X. Portier, and F. Gourbilleau, “Effect of the Nd content on the structural and photoluminescence properties of silicon-rich silicon dioxide thin films,” Nanoscale Res. Lett.6, 1–8 (2011).
[CrossRef]

Pralet, S.

P. R. Amestoy, A. Guermouche, J.-Y. L’Excellent, and S. Pralet, “Hybrid scheduling for the parallel solution of linear systems,” Parallel Computing32, 136–156 (2006).
[CrossRef]

Priolo, F.

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, and L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B67, 245301(2003).
[CrossRef]

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, and A. Irrera, “Role of the energy transfer in the optical properties of undoped and Er-doped interacting Si nanocrystals,” J. Appl. Phys.89, 264–272 (2001).
[CrossRef]

Shin, J.

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[CrossRef]

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[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 1995).

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V. Toccafondo, S. Faralli, and F. Di Pasquale, “Evanescent Multimode Longitudinal Pumping Scheme for Si-Nanocluster Sensitized Er3+Doped Waveguide Amplifiers,” J. Lightwave Techno.26, 3584–3591 (2008).
[CrossRef]

Trwoga, P. F.

A. J. Kenyon, P. F. Trwoga, M. Federighi, and C. W. Pitt, “Optical properties of PECVD erbium-doped silicon-rich silica: evidence for energy transfer between silicon microclusters and erbium ions,” J. Phys.: Condens. Matter6, 319–324 (1994).
[CrossRef]

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[CrossRef]

Yamamoto, K.

M. Fujii, M. Yoshida, Y. Kanzawa, S. Hayashi, and K. Yamamoto, “1.54 m photoluminescence of Er3+ doped into SiO2 films containing Si nanocrystals: Evidence for energy transfer from Si nanocrystals to Er3+,” Appl. Phys. Lett.71, 1198–1200 (1997).
[CrossRef]

Yee, K.

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

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

Yoshida, M.

M. Fujii, M. Yoshida, Y. Kanzawa, S. Hayashi, and K. Yamamoto, “1.54 m photoluminescence of Er3+ doped into SiO2 films containing Si nanocrystals: Evidence for energy transfer from Si nanocrystals to Er3+,” Appl. Phys. Lett.71, 1198–1200 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

M. Fujii, M. Yoshida, Y. Kanzawa, S. Hayashi, and K. Yamamoto, “1.54 m photoluminescence of Er3+ doped into SiO2 films containing Si nanocrystals: Evidence for energy transfer from Si nanocrystals to Er3+,” Appl. Phys. Lett.71, 1198–1200 (1997).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

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

P.G. Petropoulos, “Stability and phase error analysis of FD-TD in dispersive dielectrics,” IEEE Trans. Antennas Propag.42, 62–69 (1994).
[CrossRef]

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

IEEE Trans. Microwave Theory Tech. (1)

A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech.23, 623–630 (1975).
[CrossRef]

J. Appl. Phys. (1)

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, and A. Irrera, “Role of the energy transfer in the optical properties of undoped and Er-doped interacting Si nanocrystals,” J. Appl. Phys.89, 264–272 (2001).
[CrossRef]

J. comput. phys. (1)

J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. comput. phys.114, 185–200 (1994).
[CrossRef]

J. Lightwave Techno. (3)

V. Toccafondo, S. Faralli, and F. Di Pasquale, “Evanescent Multimode Longitudinal Pumping Scheme for Si-Nanocluster Sensitized Er3+Doped Waveguide Amplifiers,” J. Lightwave Techno.26, 3584–3591 (2008).
[CrossRef]

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D. Biallo, A. D’Orazio, and V. Petruzzelli, “Enhanced light extraction in Er3+doped SiO2-TiO2 microcavity embedded in one-dimensional photonic crystal,” J. Non-Cryst. Solids352, 3823–3828 (2006).
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C. Oubre and P. Nordlander, “Optical properties of metallodielectric nanostructures calculated using the finite difference time domain method,” J. Phys. Chem. B108, 17740–17747 (2004).
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J. Phys.: Condens. Matter (1)

A. J. Kenyon, P. F. Trwoga, M. Federighi, and C. W. Pitt, “Optical properties of PECVD erbium-doped silicon-rich silica: evidence for energy transfer between silicon microclusters and erbium ions,” J. Phys.: Condens. Matter6, 319–324 (1994).
[CrossRef]

Mater. Res. Bull. (1)

P. Kik and A. Polman, “Erbium-doped optical-waveguide amplifiers on silicon,” Mater. Res. Bull.23, 48–54 (1998).

Nanoscale Res. Lett. (2)

C. Dufour, J. Cardin, O. Debieu, A. Fafin, and F. Gourbilleau, “Electromagnetic modeling of waveguide amplifier based on Nd3+ Si-rich SiO2 layers by means of the ADE-FDTD method,” Nanoscale Res. Lett.6, 1–5 (2011).
[CrossRef]

O. Debieu, J. Cardin, X. Portier, and F. Gourbilleau, “Effect of the Nd content on the structural and photoluminescence properties of silicon-rich silicon dioxide thin films,” Nanoscale Res. Lett.6, 1–8 (2011).
[CrossRef]

Nat. Photonics (1)

M. Govoni, Marri, and S. Ossicini, “Carrier multiplication between interacting nanocrystals for fostering silicon-based photovoltaics,” Nat. Photonics6, 672–679 (2012).
[CrossRef]

Opt. Express (2)

Parallel Computing (1)

P. R. Amestoy, A. Guermouche, J.-Y. L’Excellent, and S. Pralet, “Hybrid scheduling for the parallel solution of linear systems,” Parallel Computing32, 136–156 (2006).
[CrossRef]

Phys. Rev. B (1)

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, and L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B67, 245301(2003).
[CrossRef]

Radio Sci. (1)

S. C. Hagness, R. M. Joseph, and A. Taflove, “Subpicosecond electrodynamics of distributed Bragg reflector microlasers: Results from finite difference time domain simulations,” Radio Sci.31, 931–941 (1996).
[CrossRef]

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P. R. Amestoy, I. S. Duff, J. Koster, and J.-Y. L’Excellent, “A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling,” SIAM. J. Matrix Anal. & Appl.23, 15–41 (2001).
[CrossRef]

Thin Solid Films (1)

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, and F. Gourbilleau, “Study of optical losses of Nd3+doped silicon rich silicon oxide for laser cavity,” Thin Solid Films520, 4026–4030 (2012).
[CrossRef]

Other (2)

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 1995).

A. E. Siegman, Lasers (University Science Books, 1986).

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Figures (10)

Fig. 1
Fig. 1

The new algorithm flowchart showing the alternation of the short time loop calculating electromagnetic field and polarizations and the long time loop including calculation of levels populations.

Fig. 2
Fig. 2

The typical evolution of <Iij> (t) when the populations do not vary and ΔNij > 0

Fig. 3
Fig. 3

Evolution of the level Ni according to the number of long time iteration R

Fig. 4
Fig. 4

Cross section as a function of the pulsation with a transition at 3.8 × 1015 rad.s−1

Fig. 5
Fig. 5

General view of the waveguide constituted by a bottom and strip cladding layers of silica surrounding the active layer constituted by silicon rich silicon oxide (SRSO) matrix doped with silicon nanograins (Si-ng) and Nd3+ ions.

Fig. 6
Fig. 6

Excitation mechanism of rare earth

Fig. 7
Fig. 7

Longitudinal section view of Z-component of the Poynting vector of the pump (on the left) and of the signal (on the right). The pump (λs = 488 nm) and the signal (λp = 1064 nm) power injected are respectively 1 W.mm−2 and 1 mW.mm−2

Fig. 8
Fig. 8

Transverse section view of Z-component of the Poynting vector of the pump (on the left) and of the signal (on the right) in the middle of the waveguide. The pump (λs = 488 nm) and the signal (λp = 1064 nm) power injected are respectively 1 W.mm−2 and 1 mW.mm−2

Fig. 9
Fig. 9

Longitudinal section view of N Si * / N Si tot (on the left) and N3/Ntot (on the right)

Fig. 10
Fig. 10

Local gross gain per unit length at the center of the active layer as a function of the pumping power, (horizontal dashed line) Losses of 0.8 dB.cm−1 found by Pirastesh et al [27].

Tables (3)

Tables Icon

Table 1 FDTD algorithm parameters

Tables Icon

Table 2 Pulsation, linewidth and number of polarizations chosen of radiative transitions

Tables Icon

Table 3 Lifetimes of different transitions for Si-ng and Nd3+

Equations (19)

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

{ E = μ H t ρ H H = ε 0 ε r E t + P tot t + σ E
d 2 P i j ( t ) d t 2 + Δ ω i j d P i j ( t ) d t + ω i j 2 P i j ( t ) = κ i j Δ N i j ( t ) E ( t )
κ i j = 6 π ε 0 c 3 ω i j 2 τ i j n
Δ t 2 π 100 ω i j
d N 1 ( t ) d t = 1 ω 12 E ( t ) d P 21 ( t ) d t + N 2 ( t ) τ 21 | n r r
< I i j > ( t n + 1 ) < I i j > ( t n 1 ) < I i j > ( t n ) < η
< I i j > ( t ) = 1 t 0 t I i j ( t ) d t
σ ( ω ) = κ i j ω i j ε 0 c ( ω Δ ω i j ( ω i j 2 ω 2 ) 2 + ω 2 Δ ω i j 2 )
σ ( ω i j ) = κ i j ε 0 c 1 Δ ω i j
σ = κ i j ε 0 c 1 N p Δ ω i j
d N Si 1 ( t ) d t = + 1 ω Si 10 E ( t ) d P Si 10 ( t ) d t N Si 1 ( t ) τ Si 10 | n r r K N Si 1 ( t ) N 0 ( t )
d N Si 0 ( t ) d t = 1 ω Si 10 E ( t ) d P Si 10 ( t ) d t + N Si 1 ( t ) τ Si 10 | n r r + K N Si 1 ( t ) N 0 ( t )
d N 4 ( t ) d t = N 4 ( t ) τ 43 | n r + K N Si 1 ( t ) N 0 ( t )
d N 3 ( t ) d t = + 1 ω 30 E ( t ) d P 30 ( t ) d t + 1 ω 31 E ( t ) d P 31 ( t ) d t + 1 ω 32 E ( t ) d P 32 ( t ) d t + N 4 ( t ) τ 43 | n r N 3 ( t ) τ 30 | n r r N 3 ( t ) τ 31 | n r r N 3 ( t ) τ 32 | n r r
d N 2 ( t ) d t = 1 ω 32 E ( t ) d P 32 ( t ) d t + N 3 ( t ) τ 32 | n r r N 2 ( t ) τ 21 | n r
d N 1 ( t ) d t = 1 ω 31 E ( t ) d P 31 ( t ) d t + N 3 ( t ) τ 31 | n r r N 1 ( t ) τ 10 | n r + N 2 ( t ) τ 21 | n r
d N 0 ( t ) d t = 1 ω 30 E ( t ) d P 30 ( t ) d t + N 3 ( t ) τ 30 | n r r + N 1 ( t ) τ 10 | n r K N Si 1 ( t ) N 0 ( t )
g dB . cm 1 ( x , y , z ) = 10 ln 10 ( σ e m N 3 ( x , y , z ) σ abs N 1 ( x , y , z ) ) )
g dB . cm 1 ( x , y , z ) 10 ln 10 ( σ e m N 3 ( x , y , z ) )

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