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, 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, 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, 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, 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, M.Ferrari, �??Design of Er3+ Doped SiO2-TiO2 Planar Waveguide Amplifier,�?? J. Non-Crystalline Solids 322, 278-283 (2003).
    [CrossRef]
  6. A.Taflove, 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, 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, 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, C. M. Soukoulis, �??Time Dependent Theory for Random Lasers,�?? Phys. Rev. Lett. 85, 70-73 (2000).
    [CrossRef] [PubMed]
  10. S. Chang, 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, 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, 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 Book 1986)

Electron. Lett. (1)

K. Jinguji, M. Horiguchi, S. Shibata, T. Kanamori, S. Mitachi, T. Manabe, �??Material Dispersion in Fluoride Glasses,�?? Electron. Lett. 18, 164-165 (1982).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M.Federighi, I.Massarek, 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, 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, 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, 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, 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, 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, C. M. Soukoulis, �??Time Dependent Theory for Random Lasers,�?? Phys. Rev. Lett. 85, 70-73 (2000).
[CrossRef] [PubMed]

Progress in Electromagnetics Research (1)

A. D�??Orazio, V. De Palo, M. De Sario, V. Petruzzelli, 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, S.C.Hagness, �??Computational Electrodynamics: the Finite-Difference Time-Domain Method,�?? (Artech House Boston-London, 2000)

A. E. Siegman, �??Lasers�?? (University Science Book 1986)

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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)

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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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