Erbium Doped Fiber Amplifier
Erbium Atom Energy Levels
Lifetime and pump power Boltzmann factor gives relative populations in energy levels Transition probability W inversely proportional to excited state lifetime At threshold, pump intensity in core gives W:
If =0.4, cross section for pumping is 4.2x10-22 cm2, core radius is 2 μm, pump wavelength is 1.48 μm, and Boltzmann factor is 0.38, what is the lifetime of the excited state? Pump intensity is power divided by area Lifetime is 8.1 ms
Erbium Doped Fiber
Splicing an erbium doped fiber
Maximum possible gain
Saturation Characteristics
Gain and Noise in an EDFA
Passive Components for EDFAs
Typical EDFA
Required length of Er-doped fiber Gain coefficient per length g depends on population inversion and cross section for stimulated emission Overall gain depends on g and length L Expressed in decibels:
Example of doped fiber length N1=1.8x1017 cm-3 N2=4.8x1017 cm-3 σs=7.0x10-21 cm2 g=2.1x10-3 cm-1 How long does the fiber need to be for G to be equal to 35 dB? L=38.4 meters!
How to mitigate long doped fiber length Use a material that can hold many more erbium ions—namely, a polymer. If gain regions can be reduced to centimeters from tens of meters, polymer loss becomes insignificant Short amplifiers might be integratable
Two Stage Amplifier Design
High power Booster Amplifier
Alternate Pumping Schemes
Pumping Choices for EDFAs Backward pumping generates higher gain 980 nm pumping generates both higher gain and less noise 1480 nm pumping generates higher saturated power and tolerates a broader range of pump wavelengths
ASE power and Spontaneous Emission Coefficient
Power and noise outputs Power out where mt=number of transverse modes, Δf=optical filter bandwidth, and nspon=population inversion factor First term is amplified power; second is Amplified Spontaneous Emission (ASE) noise
Example, continued nspon=1.6 G=35 dB=multiplication by 3162 ASE noise=65 μW
EDFA for Repeater Applications
Optical Amplifier Spacing
Optimum number of amplifiers Noise figure for a chain of k amplifiers (ratio of S/N in to that of output) where since
Example PIN diode responsitivity =1 Number of transverse modes mt=1 Population inversion factor nspon=2 =1.55 μm Pmax=10 mW Loss coefficient l=0.2 dB/km Preamp bandwidth B=optical filter bandwidth Δf=100 GHz Distance D=1000 km
Example continued We want dF/dk to be zero. Have to do it by trial and error. What value of k makes this the smallest? a=4 c=20 b=2.57x10-6
Answers Derivative closest to zero when k=5 Gain of each amplifier is thus lD/k=40 dB Noise figure at k=5 is 20.64. At k=4 or k=6 it is higher.
Erbium amplifier advantages High gain per mW of pump power Low crosstalk Happen to operate in most transparent region of the spectrum for glass fiber Extremely long excited state lifetime (on the order of 10 ms)
Erbium amplifier disadvantages Can only work at wavelengths where Er+3 fluoresces Three-level system, so gain medium is opaque at signal wavelengths until pumped Requires long path length of gain medium (tens of meters in glass) Gain very wavelength-dependent and must be flattened Gain limited by cooperative quenching
Raman amplifiers Use stimulated Raman effect and pump laser whose frequency is equal to signal frequency plus frequency of chemical bond in the material Because it is a nonlinear process, requires very high pump powers (watts)
Raman amplifier advantages Can use existing fiber as gain medium (distributed amplification) Can operate in any region of the spectrum
Raman amplifier disadvantages Require very high pump powers Can be used only over long distances, since Raman effect is weak
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