Abstract

A time domain analysis of light amplification in an erbium doped silica-titania planar waveguide is reported. The investigation is performed by means of a home-made computer code which exploits the auxiliary differential equation scheme combined with the finite difference time domain technique to solve Maxwell’s equations and the rate equations. The simulation model takes into account the pump and input signal propagation, the secondary transitions pertaining to the ion-ion interactions and exploits the optical, spectroscopic and geometrical parameters measured on the fabricated waveguide.

© 2005 Optical Society of America

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References

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  1. P.G. Kik and A. Polman, “Cooperative Upconversion as the Gain-Limiting Factor in Er Doped Miniature Al2O3 Optical Waveguide Amplifiers,” J. Appl. Phys. 93, 5008–5012 (2003).
    [Crossref]
  2. M. Federighi, I. Massarek, and P.F. Trwoga, “Optical Amplification in Thin Optical Waveguides with High Er Concentration,” IEEE Photon. Technol. Lett. 5, 227–229 (1993).
    [Crossref]
  3. F. Di Pasquale and M. Federighi, “Modelling of Uniform and Pair-Induced Upconversion Mechanism in High-Concentration Erbium-Doped Silica Waveguides,” J. Lightwave Technol. 13, 1858–1864 (1995).
    [Crossref]
  4. W.J. Miniscalco and R.S. Quimby, “General Procedure for Analysis of Er3+ Cross Section,” Opt. Lett. 16, 258–260 (1991).
    [Crossref] [PubMed]
  5. A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
    [Crossref]
  6. A. Taflove and S.C. Hagness, “Computational Electrodynamics: the Finite-Difference Time-Domain Method,” (Artech House Boston-London, 2000)
  7. A. D’Orazio, V. De Palo, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Finite Difference Time Domain Modeling of Light Amplification in Active Photonic Band Gap Structures,” Progress in Electromagnetics Research PIER 39, 299–339 (2003).
    [Crossref]
  8. A.S. Nagra and R.A. York, “FDTD Analysis of Wave Propagation in Nonlinear Absorbing and Gain Media,” IEEE Trans. Antennas Prop. 46, 334–340 (1998).
    [Crossref]
  9. X. Jiang and C. M. Soukoulis, “Time Dependent Theory for Random Lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
    [Crossref] [PubMed]
  10. 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]
  11. K. Jinguji, M. Horiguchi, S. Shibata, T. Kanamori, S. Mitachi, and T. Manabe, “Material Dispersion in Fluoride Glasses,” Electron. Lett. 18, 164–165 (1982).
    [Crossref]
  12. C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
    [Crossref]
  13. A.E. Siegman, “Lasers” (University Science Book1986)

2004 (1)

2003 (3)

P.G. Kik and A. Polman, “Cooperative Upconversion as the Gain-Limiting Factor in Er Doped Miniature Al2O3 Optical Waveguide Amplifiers,” J. Appl. Phys. 93, 5008–5012 (2003).
[Crossref]

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

A. D’Orazio, V. De Palo, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Finite Difference Time Domain Modeling of Light Amplification in Active Photonic Band Gap Structures,” Progress in Electromagnetics Research PIER 39, 299–339 (2003).
[Crossref]

2001 (1)

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

2000 (1)

X. Jiang and C. M. Soukoulis, “Time Dependent Theory for Random Lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
[Crossref] [PubMed]

1998 (1)

A.S. Nagra and R.A. York, “FDTD Analysis of Wave Propagation in Nonlinear Absorbing and Gain Media,” IEEE Trans. Antennas Prop. 46, 334–340 (1998).
[Crossref]

1995 (1)

F. Di Pasquale and M. Federighi, “Modelling of Uniform and Pair-Induced Upconversion Mechanism in High-Concentration Erbium-Doped Silica Waveguides,” J. Lightwave Technol. 13, 1858–1864 (1995).
[Crossref]

1993 (1)

M. Federighi, I. Massarek, and P.F. Trwoga, “Optical Amplification in Thin Optical Waveguides with High Er Concentration,” IEEE Photon. Technol. Lett. 5, 227–229 (1993).
[Crossref]

1991 (1)

1982 (1)

K. Jinguji, M. Horiguchi, S. Shibata, T. Kanamori, S. Mitachi, and T. Manabe, “Material Dispersion in Fluoride Glasses,” Electron. Lett. 18, 164–165 (1982).
[Crossref]

Chang, S.

Chiappini, A.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Chiasera, A.

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

D’Orazio, A.

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

A. D’Orazio, V. De Palo, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Finite Difference Time Domain Modeling of Light Amplification in Active Photonic Band Gap Structures,” Progress in Electromagnetics Research PIER 39, 299–339 (2003).
[Crossref]

De Bernardi, C.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

De Palo, V.

A. D’Orazio, V. De Palo, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Finite Difference Time Domain Modeling of Light Amplification in Active Photonic Band Gap Structures,” Progress in Electromagnetics Research PIER 39, 299–339 (2003).
[Crossref]

De Sario, M.

A. D’Orazio, V. De Palo, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Finite Difference Time Domain Modeling of Light Amplification in Active Photonic Band Gap Structures,” Progress in Electromagnetics Research PIER 39, 299–339 (2003).
[Crossref]

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

Di Pasquale, F.

F. Di Pasquale and M. Federighi, “Modelling of Uniform and Pair-Induced Upconversion Mechanism in High-Concentration Erbium-Doped Silica Waveguides,” J. Lightwave Technol. 13, 1858–1864 (1995).
[Crossref]

Duverger, C.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Federighi, M.

F. Di Pasquale and M. Federighi, “Modelling of Uniform and Pair-Induced Upconversion Mechanism in High-Concentration Erbium-Doped Silica Waveguides,” J. Lightwave Technol. 13, 1858–1864 (1995).
[Crossref]

M. Federighi, I. Massarek, and P.F. Trwoga, “Optical Amplification in Thin Optical Waveguides with High Er Concentration,” IEEE Photon. Technol. Lett. 5, 227–229 (1993).
[Crossref]

Ferrari, M.

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Fossi, M.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Hagness, S.C.

A. Taflove and S.C. Hagness, “Computational Electrodynamics: the Finite-Difference Time-Domain Method,” (Artech House Boston-London, 2000)

Horiguchi, M.

K. Jinguji, M. Horiguchi, S. Shibata, T. Kanamori, S. Mitachi, and T. Manabe, “Material Dispersion in Fluoride Glasses,” Electron. Lett. 18, 164–165 (1982).
[Crossref]

Jiang, X.

X. Jiang and C. M. Soukoulis, “Time Dependent Theory for Random Lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
[Crossref] [PubMed]

Jinguji, K.

K. Jinguji, M. Horiguchi, S. Shibata, T. Kanamori, S. Mitachi, and T. Manabe, “Material Dispersion in Fluoride Glasses,” Electron. Lett. 18, 164–165 (1982).
[Crossref]

Kanamori, T.

K. Jinguji, M. Horiguchi, S. Shibata, T. Kanamori, S. Mitachi, and T. Manabe, “Material Dispersion in Fluoride Glasses,” Electron. Lett. 18, 164–165 (1982).
[Crossref]

Kik, P.G.

P.G. Kik and A. Polman, “Cooperative Upconversion as the Gain-Limiting Factor in Er Doped Miniature Al2O3 Optical Waveguide Amplifiers,” J. Appl. Phys. 93, 5008–5012 (2003).
[Crossref]

Manabe, T.

K. Jinguji, M. Horiguchi, S. Shibata, T. Kanamori, S. Mitachi, and T. Manabe, “Material Dispersion in Fluoride Glasses,” Electron. Lett. 18, 164–165 (1982).
[Crossref]

Massarek, I.

M. Federighi, I. Massarek, and P.F. Trwoga, “Optical Amplification in Thin Optical Waveguides with High Er Concentration,” IEEE Photon. Technol. Lett. 5, 227–229 (1993).
[Crossref]

Mescia, L.

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

Miniscalco, W.J.

Mitachi, S.

K. Jinguji, M. Horiguchi, S. Shibata, T. Kanamori, S. Mitachi, and T. Manabe, “Material Dispersion in Fluoride Glasses,” Electron. Lett. 18, 164–165 (1982).
[Crossref]

Montagna, M.

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Moser, E.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Nagra, A.S.

A.S. Nagra and R.A. York, “FDTD Analysis of Wave Propagation in Nonlinear Absorbing and Gain Media,” IEEE Trans. Antennas Prop. 46, 334–340 (1998).
[Crossref]

Pelli, S.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Petruzzelli, V.

A. D’Orazio, V. De Palo, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Finite Difference Time Domain Modeling of Light Amplification in Active Photonic Band Gap Structures,” Progress in Electromagnetics Research PIER 39, 299–339 (2003).
[Crossref]

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

Polman, A.

P.G. Kik and A. Polman, “Cooperative Upconversion as the Gain-Limiting Factor in Er Doped Miniature Al2O3 Optical Waveguide Amplifiers,” J. Appl. Phys. 93, 5008–5012 (2003).
[Crossref]

Pozzi, F.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Prudenzano, F.

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

A. D’Orazio, V. De Palo, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Finite Difference Time Domain Modeling of Light Amplification in Active Photonic Band Gap Structures,” Progress in Electromagnetics Research PIER 39, 299–339 (2003).
[Crossref]

Quimby, R.S.

Righini, G.C.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Rolli, R.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Ronchin, S.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Rossi, F.

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Shibata, S.

K. Jinguji, M. Horiguchi, S. Shibata, T. Kanamori, S. Mitachi, and T. Manabe, “Material Dispersion in Fluoride Glasses,” Electron. Lett. 18, 164–165 (1982).
[Crossref]

Siegman, A.E.

A.E. Siegman, “Lasers” (University Science Book1986)

Soukoulis, C. M.

X. Jiang and C. M. Soukoulis, “Time Dependent Theory for Random Lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
[Crossref] [PubMed]

Taflove, A.

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]

A. Taflove and S.C. Hagness, “Computational Electrodynamics: the Finite-Difference Time-Domain Method,” (Artech House Boston-London, 2000)

Tosello, C.

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Trwoga, P.F.

M. Federighi, I. Massarek, and P.F. Trwoga, “Optical Amplification in Thin Optical Waveguides with High Er Concentration,” IEEE Photon. Technol. Lett. 5, 227–229 (1993).
[Crossref]

York, R.A.

A.S. Nagra and R.A. York, “FDTD Analysis of Wave Propagation in Nonlinear Absorbing and Gain Media,” IEEE Trans. Antennas Prop. 46, 334–340 (1998).
[Crossref]

Electron. Lett. (1)

K. Jinguji, M. Horiguchi, S. Shibata, T. Kanamori, S. Mitachi, and T. Manabe, “Material Dispersion in Fluoride Glasses,” Electron. Lett. 18, 164–165 (1982).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. Federighi, I. Massarek, and P.F. Trwoga, “Optical Amplification in Thin Optical Waveguides with High Er Concentration,” IEEE Photon. Technol. Lett. 5, 227–229 (1993).
[Crossref]

IEEE Trans. Antennas Prop. (1)

A.S. Nagra and R.A. York, “FDTD Analysis of Wave Propagation in Nonlinear Absorbing and Gain Media,” IEEE Trans. Antennas Prop. 46, 334–340 (1998).
[Crossref]

J. Appl. Phys. (1)

P.G. Kik and A. Polman, “Cooperative Upconversion as the Gain-Limiting Factor in Er Doped Miniature Al2O3 Optical Waveguide Amplifiers,” J. Appl. Phys. 93, 5008–5012 (2003).
[Crossref]

J. Lightwave Technol. (1)

F. Di Pasquale and M. Federighi, “Modelling of Uniform and Pair-Induced Upconversion Mechanism in High-Concentration Erbium-Doped Silica Waveguides,” J. Lightwave Technol. 13, 1858–1864 (1995).
[Crossref]

J. Non-Crystalline Solids (2)

A. D’Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, “Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,” J. Non-Crystalline Solids 322, 278–283 (2003).
[Crossref]

C. Tosello, F. Rossi, S. Ronchin, R. Rolli, G.C. Righini, F. Pozzi, S. Pelli, M. Fossi, E. Moser, M. Montagna, M. Ferrari, C. Duverger, A. Chiappini, and C. De Bernardi, “Erbium-Activated Silica-Titania Planar Waveguides on Silica-on-Silicon Substrates Prepared by rf Sputtering,” J. Non-Crystalline Solids 284, 243–248 (2001).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

X. Jiang and C. M. Soukoulis, “Time Dependent Theory for Random Lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
[Crossref] [PubMed]

Progress in Electromagnetics Research PIER (1)

A. D’Orazio, V. De Palo, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Finite Difference Time Domain Modeling of Light Amplification in Active Photonic Band Gap Structures,” Progress in Electromagnetics Research PIER 39, 299–339 (2003).
[Crossref]

Other (2)

A. Taflove and S.C. Hagness, “Computational Electrodynamics: the Finite-Difference Time-Domain Method,” (Artech House Boston-London, 2000)

A.E. Siegman, “Lasers” (University Science Book1986)

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Figures (8)

Fig. 1.
Fig. 1.

Energetic level transitions of an erbium system

Fig. 2.
Fig. 2.

Buried channel waveguide

Fig. 3.
Fig. 3.

Experimentally measured erbium emission and absorbtion cross sections

Fig. 4.
Fig. 4.

Measure derived Δσ curve and reconstructed Δσ profile. Five Lorentzian lineshipe are also shown.

Fig. 5.
Fig. 5.

Temporal evolution of the population densities of the erbium system

Fig. 6.
Fig. 6.

Transmission spectrum of an active waveguide 5 mm long

Fig. 7.
Fig. 7.

EDWA transmission coefficient as a function of pump signal power Pp for a input signal power of 1 µW.

Fig. 8.
Fig. 8.

EDWA transmission coefficient as a function of erbium ion concentration

Tables (3)

Tables Icon

Table 1. Optical properties of SiO2-TiO2:Er waveguide

Tables Icon

Table 2. Fundamental parameters of the Lorentzian functions used in the fitting procedure.

Tables Icon

Table 3. Simulation input data

Equations (16)

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

dN 4 dt = N 4 τ 43 + C up · N 2 2 + C 3 · N 3 2 C 14 · N 1 · N 4
dN 3 dt = W p · N 1 N 3 τ 32 + N 4 τ 43 2 · C 3 · N 3 2
dN 2 dt = N 3 τ 32 + e ( t ) h ν s · d p ( t ) dt N 2 τ 21 + 2 · C 14 · N 1 · N 4 2 · C up · N 2 2
dN 1 dt = W p · N 1 e ( t ) h ν s · d p ( t ) dt + N 2 τ 21 C 14 · N 1 · N 4 + C up · N 2 2 + C 3 · N 3 2
N T = N 1 + N 2 + N 3 + N 4
x h ( t ) = d ( t ) t
x e ( t ) = μ 0 h ( t ) t
d ( t ) = ε 0 e ( t ) + p at ( t ) + p host ( t )
d 2 p at ( t ) dt 2 + Δ ω a d p at ( t ) dt + ω a 2 p at ( t ) = k Δ N 12 ( t ) e ( t )
ω a = E 2 E 1
Δ ω a = γ r + γ nr + 2 T 2
k = 3 F osc ( e 2 m )
D ( ω ) = ε host E ( ω ) + P at ( ω )
χ at ( ω ) = P at ( ω ) ε host E ( ω )
χ at ( ω ) = 3 γ r λ a 3 ω a Δ N 4 π 2 1 ω a 2 ω 2 + j ω Δ ω a
Δ σ = N 1 σ 12 ( ω ) N 2 σ 21 ( ω ) = 2 π λ a χ ( ω )

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