1 Numerical and Numerical and Analytical Analytical models for various models for various effects in effects in EDFAs EDFAs Inna Nusinsky- Shmuilov Supervisor:Prof. Amos Hardy TelA viv U niversity TEL AVIV UNIVERSITY THE IBY AND ALADAR FLEISCHMAN FACULTY OF ENGINEERING Department of Electrical Engineering – Physical Engineering
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1 Numerical and Analytical models for various effects in models for various effects inEDFAs Inna Nusinsky-Shmuilov Supervisor:Prof. Amos Hardy TEL AVIV.
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Numerical and AnalyticalNumerical and Analytical
models for various effects inmodels for various effects in
EDFAsEDFAs
Inna Nusinsky-Shmuilov
Supervisor:Prof. Amos Hardy
Tel Aviv University
TEL AVIV UNIVERSITYTHE IBY AND ALADAR FLEISCHMAN FACULTY OF ENGINEERING
Department of Electrical Engineering – Physical Engineering
• Spontaneous emission and ASE are negligible compared to the pump and signal powers
• Strong pumping (in order to neglect 1/τ)
• Loss due to upconversion is not too high
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Homogeneous upconversion:Homogeneous upconversion:Homogeneous upconversion:Homogeneous upconversion:Signal and pump powers vs. position along the fiber:
Injected pump power 80mW Input signal power 1mW
Solid lines-exact solution
Circles-analytical formula
Dashed lines-exact solution without upconversion
Approximate analytical formula is quite accurate
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Homogeneous upconversion:Homogeneous upconversion:Homogeneous upconversion:Homogeneous upconversion:Dependence of upconversion on erbium concentration:
Good agreement between approximate
analytical formula and exact numerical
solution
X Analytical formula is no longer valid
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Homogeneous upconversion:Homogeneous upconversion:Homogeneous upconversion:Homogeneous upconversion:Upconversion vs. pump power:
Strong pump decreases the influence of homogeneous upconversion
If there is no upconversion (or other losses in the system), the maximum output signal does not depend on erbium concentration
Approximate analytical formula’s accuracy improves with increasing the pump power
Input signal power 1mW
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Upconversion vs. signal power:Homogeneous upconversion:Homogeneous upconversion:Homogeneous upconversion:Homogeneous upconversion:
Increasing the input signal power decreases the influence of homogeneous upconversion
Approximate analytical formula’s accuracy improves with increasing the input signal power power
The approximate solution is accurate for strong enough input signals and strong injected power.
If input signal is too weak or injected pump is too strong, the ASE can’t be neglected.
Output signal vs. signal and pump powers:
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Multichannel transmission:Multichannel transmission:Multichannel transmission:Multichannel transmission: The analytical model is used to optimize the parameters of a fiber amplifier.
Approximate results are less accurate for small signal powers and smaller number of channels.
Optimum length is getting shorter when the input signal power increases and the number of channels increases.
Optimization of fiber length:
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Inhomogeneous gain broadening:Inhomogeneous gain broadening:Energy band diagram:
is the shift in resonance frequency
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Inhomogeneous gain broadening:Inhomogeneous gain broadening:The model:
• is the number of molecules, per unit volume, whose resonant frequency has been shifted by a frequency that lies between and . ˆˆ d
• The function is the normalized distribution function of molecules, such that . Usually a Gaussian is used.
f
• A photon of wavelength , interacts with molecules with shifted cross-sections and , due to the frequency shift of .
• The width of determines the relative effect of the inhomogeneous broadening.
I f
• All energy levels are shifted manifold is shifted by the same amount from the ground ( ).
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Inhomogeneous gain broadening:Inhomogeneous gain broadening:Single channel amplification:
The inhomogeneous broadening is significant for germanosilicate fiber whereas aluminosilicate fiber is mainly homogeneous
nm5.11hom nmI 5.11 nm4hom nmI 8
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Inhomogeneous gain broadening:Inhomogeneous gain broadening:Multichannel amplification:Aluminosilicate 232 SiOOAl Germanosilicate 22 SiOGeO
There is significant difference between inhomogeneous broadening (solid lines) and homogeneous one (dashed lines) for both fibers.
The channels separation is 10nm, which is larger than the inhomogeneous linewidth of the germanosilicate fiber and smaller than the inhomogeneous linewidth of the aluminosilicate fiber.
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Inhomogeneous gain broadening:Inhomogeneous gain broadening:Multichannel amplification:Germanosilicate 22 SiOGeO
If we decrease the channel distance in germanosilicate fiber to 6nm (less than ), we expect the effect of the inhomogeneous broadening to be stronger.
nmI 8
Here the inhomogeneous broadening mixes the two signal channels and not only ASE channels, thus its influence on signal amplification is more significant.
nm4hom nmI 8
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Inhomogeneous gain broadening:Inhomogeneous gain broadening:Experimental verification of the model:
Circles-experimental results
Solid lines-numerical solution using inhomogeneous model
Dashed lines- numerical solution using homogeneous model
Germanosilicate fiber:
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Conclusions:Conclusions:Numerical models have been presented, for the study of erbium doped fiber amplifiers.
Simple analytical expressions were also developed for several cases.
Numerical solutions were used to validate the approximate expressions.
Analytical expressions agree with the exact numerical solutions in a wide range of conditions.
A good agreement between experiment and numerical model.
The effect of homogeneous upconversion, signal amplification in multi-channel fibers and inhomogeneous gain broadening were investigated, using numerical and approximate analytical models
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Suggestions for future work :Suggestions for future work :
• Time dependent solution
• Modeling for clustering of erbium ions
• Considering additional pumping configurations and pump wavelengths
• Experimental analysis of inhomogeneous broadening
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Publications :Publications :
1. Inna Nusinsky and Amos A. Hardy, “Analysis of the effect of upconversion on signal amplification in EDFAs”, IEEE J. Quantum Electron.,vol.39, no.4 ,pp.548-554 Apr.2003
2. Inna Nusinsky and Amos A. Hardy, ““Multichannel amplification in strongly pumped EDFAs”, IEEE J.Lightwave Technol., vol.22, no.8, pp.1946-1952, Aug.2004
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Acknowledgements :Acknowledgements :
• Prof. Amos Hardy
• Eldad Yahel
• Irena Mozjerin
• Igor Shmuilov
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Appendix :Appendix :
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Homogeneous upconversion:Homogeneous upconversion:Assumptions for analytical solution:
as
es
ppapp P
hcA
0
apepppapp
BP
hcA
110 2
Strong pumping:
where
0
~0
~
2
p
s
epappp
esasss
P
PB
Appendix:Appendix:Appendix:Appendix:
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Homogeneous upconversion:Homogeneous upconversion:Assumptions for analytical solution:
Homogeneous upconversion not too strong:
where
Appendix:Appendix:Appendix:Appendix:
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0042
2
P
PQPQNCC sasppeff
zPQQzPQzP sesaspp
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Appendix:Appendix:Appendix:Appendix:Homogeneous upconversion:Homogeneous upconversion:Derivation of approximate solution: