Ee 230: Optical Fiber Communication Erbium Doped Fiber Amplifier



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EE 230: Optical Fiber Communication


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:



Lifetime example, continued

  • 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



Gain Flattening for Multi-channel Systems



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

  • Forward pumping generates less noise

  • 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, Δf=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)

  • Can be rewritten as

  • 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 Δf=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

  • Requires specially doped fiber as gain medium

  • 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)



Multi-laser Raman Pumping



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

  • Rayleigh scattering dominates, causing loss of pump power




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