Ee 230: Optical Fiber Communication Erbium Doped Fiber Amplifier

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