Abstract

We present a comparative study of the gain achievement in a waveguide whose active layer is constituted by a silica matrix containing silicon nanograins acting as sensitizer of either neodymium ions (Nd3+) or erbium ions (Er3+). By means of an auxiliary differential equation and finite difference time domain (ADE-FDTD) approach that we developed, we investigate the steady states regime of both rare earths ions and silicon nanograins levels populations as well as the electromagnetic field for different pumping powers ranging from 1 to 104 mW/mm2. Moreover, the achievable gain has been estimated in this pumping range. The Nd3+ doped waveguide shows a higher gross gain per unit length at 1064 nm (up to 30 dB/cm) than the one with Er3+ doped active layer at 1532 nm (up to 2 dB/cm). Taking into account the experimental background losses we demonstrate that a significant positive net gain can only be achieved with the Nd3+ doped waveguide.

© 2014 Optical Society of America

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2013 (1)

2012 (2)

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, F. Gourbilleau, “Study of optical losses of Nd3+ doped silicon rich silicon oxide for laser cavity,” Thin Solid Films 520, 4026–4030 (2012).
[CrossRef]

M. Govoni, I. Marri, S. Ossicini, “Carrier multiplication between interacting nanocrystals for fostering silicon-based photovoltaics,” Nat. Photonics 6, 672–679 (2012).
[CrossRef]

2011 (2)

C. Dufour, J. Cardin, O. Debieu, A. Fafin, 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]

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

2010 (2)

A. Podhorodecki, J. Misiewicz, F. Gourbilleau, J. Cardin, C. Dufour, “High energy excitation transfer from silicon nanocrystals to neodymium ions in silicon-rich oxide film,” Electrochem. Solid-State Lett. 13, K26–K28 (2010).
[CrossRef]

J. Yang, K. van Dalfsen, F. Ay, M. Pollnau, “High-gain Al2O3: Nd3+ channel waveguide amplifiers at 880 nm, 1060 nm, and 1330 nm,” Appl. Phys. B 101, 119–127 (2010).
[CrossRef]

2009 (1)

N. Daldosso, L. Pavesi, “Nanosilicon photonics,” Laser Photonics Rev. 3, 508–534 (2009).
[CrossRef]

2008 (2)

S. L. Oliveira, D. F. de Sousa, A. A. Andrade, L. A. O. Nunes, T. Catunda, “Upconversion in Nd3+-doped glasses: Microscopic theory and spectroscopic measurements,” J. Appl. Phys. 103, 023103 (2008).
[CrossRef]

V. Toccafondo, S. Faralli, F. Di Pasquale, “Evanescent multimode longitudinal pumping scheme for sinanocluster sensitized Er3 + doped waveguide amplifiers,” J. Lightwave Technol. 26, 3584–3591 (2008).
[CrossRef]

2006 (3)

A. N. MacDonald, A. Hryciw, Quan Li, A. Meldrum, “Luminescence of Nd-enriched silicon nanoparticle glasses,” Opt. Mater. 28, 820–824 (2006).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

E. O. Serqueira, N. O. Dantas, A. F. G. Monte, M. J. V. Bell, “Judd ofelt calculation of quantum efficiencies and branching ratios of Nd3+ doped glasses,” J. Non-Cryst. Solids 352, 3628–3632 (2006).
[CrossRef]

2005 (1)

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

2004 (2)

2003 (1)

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B 67, 245301 (2003).
[CrossRef]

2002 (2)

H.-S. Han, S.-Y. Seo, J. H. Shin, N. Park, “Coefficient determination related to optical gain in erbium-doped silicon-rich silicon oxide waveguide amplifier,” Appl. Phys. Lett. 81, 3720–3722 (2002).
[CrossRef]

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma, C. J. Humphreys, “Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms,” J. Appl. Phys. 91, 367–374 (2002).
[CrossRef]

2001 (1)

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, 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 (1)

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

1995 (1)

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare earth-doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

1991 (1)

W. L. Barnes, R. Laming, E. J. Tarbox, P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum. Electron. 27, 1004–1010 (1991).
[CrossRef]

1989 (1)

B. J. Ainslie, S. P. Craig, R. Wyatt, K. Moulding, “Optical and structural analysis of neodymium-doped silica-based optical fibre,” Matter. Lett. 8, 204–208 (1989).
[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]

Agrawal, G. P.

G. P. Agrawal, Fiber-optic communication systems (John Wiley & Sons, 2010).
[CrossRef]

Ainslie, B. J.

B. J. Ainslie, S. P. Craig, R. Wyatt, K. Moulding, “Optical and structural analysis of neodymium-doped silica-based optical fibre,” Matter. Lett. 8, 204–208 (1989).
[CrossRef]

Andrade, A. A.

S. L. Oliveira, D. F. de Sousa, A. A. Andrade, L. A. O. Nunes, T. Catunda, “Upconversion in Nd3+-doped glasses: Microscopic theory and spectroscopic measurements,” J. Appl. Phys. 103, 023103 (2008).
[CrossRef]

Ay, F.

J. Yang, K. van Dalfsen, F. Ay, M. Pollnau, “High-gain Al2O3: Nd3+ channel waveguide amplifiers at 880 nm, 1060 nm, and 1330 nm,” Appl. Phys. B 101, 119–127 (2010).
[CrossRef]

Barnes, W. L.

W. L. Barnes, R. Laming, E. J. Tarbox, P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum. Electron. 27, 1004–1010 (1991).
[CrossRef]

Battaglin, G.

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

Bell, M. J. V.

E. O. Serqueira, N. O. Dantas, A. F. G. Monte, M. J. V. Bell, “Judd ofelt calculation of quantum efficiencies and branching ratios of Nd3+ doped glasses,” J. Non-Cryst. Solids 352, 3628–3632 (2006).
[CrossRef]

Berencen, Y.

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

Bjarklev, A.

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare earth-doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

Boucher, Y. G.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, F. Gourbilleau, “Study of optical losses of Nd3+ doped silicon rich silicon oxide for laser cavity,” Thin Solid Films 520, 4026–4030 (2012).
[CrossRef]

Cardin, J.

A. Fafin, J. Cardin, C. Dufour, F. Gourbilleau, “Modeling of the electromagnetic field and level populations in a waveguide amplifier: a multi-scale time problem,” Opt. Express 21, 24171–24184 (2013).
[CrossRef] [PubMed]

C. Dufour, J. Cardin, O. Debieu, A. Fafin, 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]

A. Podhorodecki, J. Misiewicz, F. Gourbilleau, J. Cardin, C. Dufour, “High energy excitation transfer from silicon nanocrystals to neodymium ions in silicon-rich oxide film,” Electrochem. Solid-State Lett. 13, K26–K28 (2010).
[CrossRef]

Carrada, M.

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Catunda, T.

S. L. Oliveira, D. F. de Sousa, A. A. Andrade, L. A. O. Nunes, T. Catunda, “Upconversion in Nd3+-doped glasses: Microscopic theory and spectroscopic measurements,” J. Appl. Phys. 103, 023103 (2008).
[CrossRef]

Charrier, J.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, F. Gourbilleau, “Study of optical losses of Nd3+ doped silicon rich silicon oxide for laser cavity,” Thin Solid Films 520, 4026–4030 (2012).
[CrossRef]

Chryssou, C. E.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma, C. J. Humphreys, “Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms,” J. Appl. Phys. 91, 367–374 (2002).
[CrossRef]

Cognolato, L.

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Craig, S. P.

B. J. Ainslie, S. P. Craig, R. Wyatt, K. Moulding, “Optical and structural analysis of neodymium-doped silica-based optical fibre,” Matter. Lett. 8, 204–208 (1989).
[CrossRef]

Dal Negro, L.

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B 67, 245301 (2003).
[CrossRef]

Daldosso, N.

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

N. Daldosso, L. Pavesi, “Nanosilicon photonics,” Laser Photonics Rev. 3, 508–534 (2009).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Dantas, N. O.

E. O. Serqueira, N. O. Dantas, A. F. G. Monte, M. J. V. Bell, “Judd ofelt calculation of quantum efficiencies and branching ratios of Nd3+ doped glasses,” J. Non-Cryst. Solids 352, 3628–3632 (2006).
[CrossRef]

de Sousa, D. F.

S. L. Oliveira, D. F. de Sousa, A. A. Andrade, L. A. O. Nunes, T. Catunda, “Upconversion in Nd3+-doped glasses: Microscopic theory and spectroscopic measurements,” J. Appl. Phys. 103, 023103 (2008).
[CrossRef]

Debieu, O.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, F. Gourbilleau, “Study of optical losses of Nd3+ doped silicon rich silicon oxide for laser cavity,” Thin Solid Films 520, 4026–4030 (2012).
[CrossRef]

C. Dufour, J. Cardin, O. Debieu, A. Fafin, 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]

Di Pasquale, F.

Dufour, C.

A. Fafin, J. Cardin, C. Dufour, F. Gourbilleau, “Modeling of the electromagnetic field and level populations in a waveguide amplifier: a multi-scale time problem,” Opt. Express 21, 24171–24184 (2013).
[CrossRef] [PubMed]

C. Dufour, J. Cardin, O. Debieu, A. Fafin, 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]

A. Podhorodecki, J. Misiewicz, F. Gourbilleau, J. Cardin, C. Dufour, “High energy excitation transfer from silicon nanocrystals to neodymium ions in silicon-rich oxide film,” Electrochem. Solid-State Lett. 13, K26–K28 (2010).
[CrossRef]

Dumeige, Y.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, F. Gourbilleau, “Study of optical losses of Nd3+ doped silicon rich silicon oxide for laser cavity,” Thin Solid Films 520, 4026–4030 (2012).
[CrossRef]

Fafin, A.

A. Fafin, J. Cardin, C. Dufour, F. Gourbilleau, “Modeling of the electromagnetic field and level populations in a waveguide amplifier: a multi-scale time problem,” Opt. Express 21, 24171–24184 (2013).
[CrossRef] [PubMed]

C. Dufour, J. Cardin, O. Debieu, A. Fafin, 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]

Faralli, S.

Ferrarese Lupi, F.

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

Franzo, G.

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B 67, 245301 (2003).
[CrossRef]

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, 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]

Garcia, C.

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Garrido, B.

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Gourbilleau, F.

A. Fafin, J. Cardin, C. Dufour, F. Gourbilleau, “Modeling of the electromagnetic field and level populations in a waveguide amplifier: a multi-scale time problem,” Opt. Express 21, 24171–24184 (2013).
[CrossRef] [PubMed]

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, F. Gourbilleau, “Study of optical losses of Nd3+ doped silicon rich silicon oxide for laser cavity,” Thin Solid Films 520, 4026–4030 (2012).
[CrossRef]

C. Dufour, J. Cardin, O. Debieu, A. Fafin, 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]

A. Podhorodecki, J. Misiewicz, F. Gourbilleau, J. Cardin, C. Dufour, “High energy excitation transfer from silicon nanocrystals to neodymium ions in silicon-rich oxide film,” Electrochem. Solid-State Lett. 13, K26–K28 (2010).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Govoni, M.

M. Govoni, I. Marri, S. Ossicini, “Carrier multiplication between interacting nanocrystals for fostering silicon-based photovoltaics,” Nat. Photonics 6, 672–679 (2012).
[CrossRef]

Han, H.-S.

H.-S. Han, S.-Y. Seo, J. H. Shin, N. Park, “Coefficient determination related to optical gain in erbium-doped silicon-rich silicon oxide waveguide amplifier,” Appl. Phys. Lett. 81, 3720–3722 (2002).
[CrossRef]

Hole, D. E.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma, C. J. Humphreys, “Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms,” J. Appl. Phys. 91, 367–374 (2002).
[CrossRef]

Hryciw, A.

A. N. MacDonald, A. Hryciw, Quan Li, A. Meldrum, “Luminescence of Nd-enriched silicon nanoparticle glasses,” Opt. Mater. 28, 820–824 (2006).
[CrossRef]

Humphreys, C. J.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma, C. J. Humphreys, “Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms,” J. Appl. Phys. 91, 367–374 (2002).
[CrossRef]

Iacona, F.

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B 67, 245301 (2003).
[CrossRef]

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, 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, 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]

Jambois, O.

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

Kenyon, A. J.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma, C. J. Humphreys, “Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms,” J. Appl. Phys. 91, 367–374 (2002).
[CrossRef]

Laming, R.

W. L. Barnes, R. Laming, E. J. Tarbox, P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum. Electron. 27, 1004–1010 (1991).
[CrossRef]

Lester, C.

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare earth-doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

Li, Quan

A. N. MacDonald, A. Hryciw, Quan Li, A. Meldrum, “Luminescence of Nd-enriched silicon nanoparticle glasses,” Opt. Mater. 28, 820–824 (2006).
[CrossRef]

Lumholt, O.

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare earth-doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

MacDonald, A. N.

A. N. MacDonald, A. Hryciw, Quan Li, A. Meldrum, “Luminescence of Nd-enriched silicon nanoparticle glasses,” Opt. Mater. 28, 820–824 (2006).
[CrossRef]

Marri, I.

M. Govoni, I. Marri, S. Ossicini, “Carrier multiplication between interacting nanocrystals for fostering silicon-based photovoltaics,” Nat. Photonics 6, 672–679 (2012).
[CrossRef]

Melchiorri, M.

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Meldrum, A.

A. N. MacDonald, A. Hryciw, Quan Li, A. Meldrum, “Luminescence of Nd-enriched silicon nanoparticle glasses,” Opt. Mater. 28, 820–824 (2006).
[CrossRef]

Misiewicz, J.

A. Podhorodecki, J. Misiewicz, F. Gourbilleau, J. Cardin, C. Dufour, “High energy excitation transfer from silicon nanocrystals to neodymium ions in silicon-rich oxide film,” Electrochem. Solid-State Lett. 13, K26–K28 (2010).
[CrossRef]

Monte, A. F. G.

E. O. Serqueira, N. O. Dantas, A. F. G. Monte, M. J. V. Bell, “Judd ofelt calculation of quantum efficiencies and branching ratios of Nd3+ doped glasses,” J. Non-Cryst. Solids 352, 3628–3632 (2006).
[CrossRef]

Morkel, P. R.

W. L. Barnes, R. Laming, E. J. Tarbox, P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum. Electron. 27, 1004–1010 (1991).
[CrossRef]

Moulding, K.

B. J. Ainslie, S. P. Craig, R. Wyatt, K. Moulding, “Optical and structural analysis of neodymium-doped silica-based optical fibre,” Matter. Lett. 8, 204–208 (1989).
[CrossRef]

Nagra, A. S.

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

Navarro-Urrios, D.

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Nunes, L. A. O.

S. L. Oliveira, D. F. de Sousa, A. A. Andrade, L. A. O. Nunes, T. Catunda, “Upconversion in Nd3+-doped glasses: Microscopic theory and spectroscopic measurements,” J. Appl. Phys. 103, 023103 (2008).
[CrossRef]

Oliveira, S. L.

S. L. Oliveira, D. F. de Sousa, A. A. Andrade, L. A. O. Nunes, T. Catunda, “Upconversion in Nd3+-doped glasses: Microscopic theory and spectroscopic measurements,” J. Appl. Phys. 103, 023103 (2008).
[CrossRef]

Ossicini, S.

M. Govoni, I. Marri, S. Ossicini, “Carrier multiplication between interacting nanocrystals for fostering silicon-based photovoltaics,” Nat. Photonics 6, 672–679 (2012).
[CrossRef]

Pacifici, D.

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B 67, 245301 (2003).
[CrossRef]

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, 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.

H.-S. Han, S.-Y. Seo, J. H. Shin, N. Park, “Coefficient determination related to optical gain in erbium-doped silicon-rich silicon oxide waveguide amplifier,” Appl. Phys. Lett. 81, 3720–3722 (2002).
[CrossRef]

Pavesi, L.

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

N. Daldosso, L. Pavesi, “Nanosilicon photonics,” Laser Photonics Rev. 3, 508–534 (2009).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Pellegrino, P.

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Pirasteh, P.

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, F. Gourbilleau, “Study of optical losses of Nd3+ doped silicon rich silicon oxide for laser cavity,” Thin Solid Films 520, 4026–4030 (2012).
[CrossRef]

Pitanti, A.

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

Pitt, C. W.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma, C. J. Humphreys, “Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms,” J. Appl. Phys. 91, 367–374 (2002).
[CrossRef]

Podhorodecki, A.

A. Podhorodecki, J. Misiewicz, F. Gourbilleau, J. Cardin, C. Dufour, “High energy excitation transfer from silicon nanocrystals to neodymium ions in silicon-rich oxide film,” Electrochem. Solid-State Lett. 13, K26–K28 (2010).
[CrossRef]

Pollnau, M.

J. Yang, K. van Dalfsen, F. Ay, M. Pollnau, “High-gain Al2O3: Nd3+ channel waveguide amplifiers at 880 nm, 1060 nm, and 1330 nm,” Appl. Phys. B 101, 119–127 (2010).
[CrossRef]

Polman, A.

Priolo, F.

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B 67, 245301 (2003).
[CrossRef]

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, 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]

Prtljaga, N.

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

Ramirez, J. M.

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

Rasmussen, T.

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare earth-doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

Rizk, R.

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

Sada, C.

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

Seo, S.-Y.

H.-S. Han, S.-Y. Seo, J. H. Shin, N. Park, “Coefficient determination related to optical gain in erbium-doped silicon-rich silicon oxide waveguide amplifier,” Appl. Phys. Lett. 81, 3720–3722 (2002).
[CrossRef]

Serqueira, E. O.

E. O. Serqueira, N. O. Dantas, A. F. G. Monte, M. J. V. Bell, “Judd ofelt calculation of quantum efficiencies and branching ratios of Nd3+ doped glasses,” J. Non-Cryst. Solids 352, 3628–3632 (2006).
[CrossRef]

Sharma, N.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma, C. J. Humphreys, “Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms,” J. Appl. Phys. 91, 367–374 (2002).
[CrossRef]

Shimizu-Iwayama, T.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma, C. J. Humphreys, “Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms,” J. Appl. Phys. 91, 367–374 (2002).
[CrossRef]

Shin, J. H.

H.-S. Han, S.-Y. Seo, J. H. Shin, N. Park, “Coefficient determination related to optical gain in erbium-doped silicon-rich silicon oxide waveguide amplifier,” Appl. Phys. Lett. 81, 3720–3722 (2002).
[CrossRef]

Siegman., A. E.

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

Spiekman, L. H.

Taflove, A.

A. Taflove, Computational electrodynamics: The finite-difference time-domain method. (Artech House, Boston, 1995).

Tarbox, E. J.

W. L. Barnes, R. Laming, E. J. Tarbox, P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum. Electron. 27, 1004–1010 (1991).
[CrossRef]

Toccafondo, V.

van Dalfsen, K.

J. Yang, K. van Dalfsen, F. Ay, M. Pollnau, “High-gain Al2O3: Nd3+ channel waveguide amplifiers at 880 nm, 1060 nm, and 1330 nm,” Appl. Phys. B 101, 119–127 (2010).
[CrossRef]

van Veggel, F. C. J. M.

Vinciguerra, V.

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, 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]

Wyatt, R.

B. J. Ainslie, S. P. Craig, R. Wyatt, K. Moulding, “Optical and structural analysis of neodymium-doped silica-based optical fibre,” Matter. Lett. 8, 204–208 (1989).
[CrossRef]

Yang, J.

J. Yang, K. van Dalfsen, F. Ay, M. Pollnau, “High-gain Al2O3: Nd3+ channel waveguide amplifiers at 880 nm, 1060 nm, and 1330 nm,” Appl. Phys. B 101, 119–127 (2010).
[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]

York, R. A.

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

Zimmerman, D. R.

Appl. Phys. B (1)

J. Yang, K. van Dalfsen, F. Ay, M. Pollnau, “High-gain Al2O3: Nd3+ channel waveguide amplifiers at 880 nm, 1060 nm, and 1330 nm,” Appl. Phys. B 101, 119–127 (2010).
[CrossRef]

Appl. Phys. Lett. (3)

H.-S. Han, S.-Y. Seo, J. H. Shin, N. Park, “Coefficient determination related to optical gain in erbium-doped silicon-rich silicon oxide waveguide amplifier,” Appl. Phys. Lett. 81, 3720–3722 (2002).
[CrossRef]

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, L. Pavesi, F. Gourbilleau, M. Carrada, R. Rizk, C. Garcia, P. Pellegrino, B. Garrido, L. Cognolato, “Absorption cross section and signal enhancement in er-doped si nanocluster rib-loaded waveguides,” Appl. Phys. Lett. 86, 261103 (2005).
[CrossRef]

D. Navarro-Urrios, F. Ferrarese Lupi, N. Prtljaga, A. Pitanti, O. Jambois, J. M. Ramirez, Y. Berencen, N. Daldosso, B. Garrido, L. Pavesi, “Copropagating pump and probe experiments on Si-nc in SiO2 rib waveguides doped with er: The optical role of non-emitting ions,” Appl. Phys. Lett. 99, 231114 (2011).
[CrossRef]

Electrochem. Solid-State Lett. (1)

A. Podhorodecki, J. Misiewicz, F. Gourbilleau, J. Cardin, C. Dufour, “High energy excitation transfer from silicon nanocrystals to neodymium ions in silicon-rich oxide film,” Electrochem. Solid-State Lett. 13, K26–K28 (2010).
[CrossRef]

IEEE J. Quantum. Electron. (1)

W. L. Barnes, R. Laming, E. J. Tarbox, P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum. Electron. 27, 1004–1010 (1991).
[CrossRef]

IEEE J. Sel. Topics Quantum Electron. (1)

N. Daldosso, D. Navarro-Urrios, M. Melchiorri, C. Garcia, P. Pellegrino, B. Garrido, C. Sada, G. Battaglin, F. Gourbilleau, R. Rizk, L. Pavesi, “Er-Coupled Si Nanocluster Waveguide,” IEEE J. Sel. Topics Quantum Electron. 12, 1607–1617 (2006).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

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]

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

J. Appl. Phys. (3)

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma, C. J. Humphreys, “Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms,” J. Appl. Phys. 91, 367–374 (2002).
[CrossRef]

S. L. Oliveira, D. F. de Sousa, A. A. Andrade, L. A. O. Nunes, T. Catunda, “Upconversion in Nd3+-doped glasses: Microscopic theory and spectroscopic measurements,” J. Appl. Phys. 103, 023103 (2008).
[CrossRef]

F. Priolo, G. Franzo, D. Pacifici, V. Vinciguerra, F. Iacona, 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. Lightwave Technol. (3)

J. Non-Cryst. Solids (1)

E. O. Serqueira, N. O. Dantas, A. F. G. Monte, M. J. V. Bell, “Judd ofelt calculation of quantum efficiencies and branching ratios of Nd3+ doped glasses,” J. Non-Cryst. Solids 352, 3628–3632 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

N. Daldosso, L. Pavesi, “Nanosilicon photonics,” Laser Photonics Rev. 3, 508–534 (2009).
[CrossRef]

Matter. Lett. (1)

B. J. Ainslie, S. P. Craig, R. Wyatt, K. Moulding, “Optical and structural analysis of neodymium-doped silica-based optical fibre,” Matter. Lett. 8, 204–208 (1989).
[CrossRef]

Nanoscale Res. Lett. (1)

C. Dufour, J. Cardin, O. Debieu, A. Fafin, 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]

Nat. Photonics (1)

M. Govoni, I. Marri, S. Ossicini, “Carrier multiplication between interacting nanocrystals for fostering silicon-based photovoltaics,” Nat. Photonics 6, 672–679 (2012).
[CrossRef]

Opt. Express (1)

Opt. Mater. (1)

A. N. MacDonald, A. Hryciw, Quan Li, A. Meldrum, “Luminescence of Nd-enriched silicon nanoparticle glasses,” Opt. Mater. 28, 820–824 (2006).
[CrossRef]

Phys. Rev. B (1)

D. Pacifici, G. Franzo, F. Priolo, F. Iacona, L. Dal Negro, “Modeling and perspectives of the Si nanocrystals-Er interaction for optical amplification,” Phys. Rev. B 67, 245301 (2003).
[CrossRef]

Thin Solid Films (1)

P. Pirasteh, J. Charrier, Y. Dumeige, Y. G. Boucher, O. Debieu, F. Gourbilleau, “Study of optical losses of Nd3+ doped silicon rich silicon oxide for laser cavity,” Thin Solid Films 520, 4026–4030 (2012).
[CrossRef]

Other (3)

A. Taflove, Computational electrodynamics: The finite-difference time-domain method. (Artech House, Boston, 1995).

G. P. Agrawal, Fiber-optic communication systems (John Wiley & Sons, 2010).
[CrossRef]

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

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Figures (7)

Fig. 1
Fig. 1

Transverse section view of the waveguide constituted by bottom and strip cladding layers of silica surrouding the active layer constituted by silicon rich silicon oxide (SRSO) matrix doped with silicon nanograins (Si-ng) and Nd3+ or Er3+ ions.

Fig. 2
Fig. 2

Excitation mechanism of (a) erbium ions and (b) neodymium ions

Fig. 3
Fig. 3

Population inversion along the direction of propagation for the erbium ions (on the left) and the neodymium ions (on the right) for a pump power equal to 1000 mW/mm2

Fig. 4
Fig. 4

Population inversion of Si-ng along the direction of propagation in the case of erbium ions (on the left) and neodymium ions (on the right) for a pump power equal to 1000 mW/mm2

Fig. 5
Fig. 5

Population inversion of Si-ng along the direction of propagation in the case of erbium and neodymium recorded at x = 4.5 μm and y = 8.55 μm (center of the XY section of the active layer) for a pump power equal to 1000 mW/mm2

Fig. 6
Fig. 6

Population inversion for neodymium, erbium ions and silicon nanograins divided by the rare earth ions concentration (1020 at/cm3) recorded at x = 4.5 μm and y = 8.55 μm (center of the XY section of the active layer) and z=0 (beginning of the waveguide)

Fig. 7
Fig. 7

Local gross gain per unit length at the center of the active layer and in the beginning of the waveguide as a function of the pumping power for a waveguide doped with Nd3+ (open circle) and a waveguide doped with Er3+ (open square) recorded at x = 4.5 μm and y = 8.55 μm (center of the XY section of the active layer) and z = 0 (beginning of the waveguide). Losses found by Pirasteh et al [8] are represented (dashed line).

Tables (3)

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Table 1 Parameters levels of silicon nanograins

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Table 2 Parameters levels of erbium ions

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Table 3 Parameters levels of neodymium ions

Equations (13)

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2 P i j t 2 + Δ ω i j P i j t + ω i j 2 P i j = κ i j ( N i N j ) E
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 | nr r KN 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 | nr r + KN Si 1 ( t ) N 0 ( t )
d N 3 ( t ) d t = N 3 ( t ) τ 32 | nr + KN Si 1 ( t ) N 0 ( t ) + C up N 1 2
d N 2 ( t ) d t = + N 3 ( t ) τ 32 | nr N 2 ( t ) τ 21 | nr N 2 ( t ) τ 20 | nr
d N 1 ( t ) d t = + 1 ω 10 E ( t ) d P 10 ( t ) d t + N 2 ( t ) τ 21 | nr N 1 ( t ) τ 10 | nr r 2 C up N 1 2
d N 0 ( t ) d t = 1 ω 10 E ( t ) d P 10 ( t ) d t + N 2 ( t ) τ 20 | nr + N 1 ( t ) τ 10 | nr r KN Si 1 ( t ) N 0 ( t ) + C up N 1 2
d N 4 ( t ) d t = N 4 ( t ) τ 43 | nr + KN 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 | nr N 3 ( t ) τ 30 | nr r N 3 ( t ) τ 31 | nr r N 3 ( t ) τ 32 | nr r
d N 2 ( t ) d t = 1 ω 32 E ( t ) d P 32 ( t ) d t + N 3 ( t ) τ 32 | nr r N 2 ( t ) τ 21 | nr
d N 1 ( t ) d t = 1 ω 31 E ( t ) d P 31 ( t ) d t + N 3 ( t ) τ 31 | nr r N 1 ( t ) τ 10 | nr + N 2 ( t ) τ 21 | nr
d N 0 ( t ) d t = 1 ω 30 E ( t ) d P 30 ( t ) d t + N 3 ( t ) τ 30 | nr r + N 1 ( t ) τ 10 | nr KN Si 1 ( t ) N 0 ( t )
g d B / cm ( x , y , z ) = 10 ln 10 ( σ em N high ( x , y , z ) σ abs N low ( x , y , z ) )

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