by Stephen Pinter

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Project objectives
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Gain characteristics of EDFA
• wavelength dependant gain
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Gain flattening
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• non-uniform gain over the spectrum implications

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Determine the optimum length for simulations
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ASE not considered – optimum length is shorter when ASE taken into account
Expand the current EDFA Simulink model to show the gain over the entire 1550nm window
• important to know gain in range 1530nm – 1560nm
Consider gain flattening, and
Integrate forward ASE into the EDFA model
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Why Simulink?

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Why use Simulink when an EDFA can be simulated using simulation tools such as OASIX or PTDS?
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OASIX or PTDS
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• static model input pump power is a static input internal to the EDFA module
Simulink
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• dynamic model input pump power as well as other EDFA parameters can be easily modified

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Significant equations governing EDFA dynamics
Output pump and signal power:
P p
( L , t )

P p
( 0 , t ) e
B p N 2

C p
P s
( L , t )

P s
( 0 , t ) e
B s N 2

C s
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Quantities B and C characterize the physical EDFA and are given by:
[ B
P
, B
S
]

 

A

, [ C
P
, C
S
]
 
L
To handle multiple signal wavelengths, B s the input signal must be multidimensional and C s
Why?
as well as

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 and  are wavelength dependant as shown in the figure
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 and  are the absorption and emission coefficients, respectively so, the quantities B and C are wavelength dependant this relationship is how the wavelength dependency of the gain arises
EDFA gain  ratio between the absorption and emission at a particular wavelength is critical in determining the gain
O. Mermer, “EDFA Gain Flattening By Using Optical Fiber Grating Techniques,” [Online Adobe Acrobat Document],
Available at http://bornova.ege.edu.tr/~wwweee/docs/seminer.pdf

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• when performing simulations on the EDFA model it is important to simulate all the wavelengths simultaneously instead of one at a time
EDFAs work in the nonlinear regime, so properties like linear superposition don’t hold true when there are several channels in an EDFA there is an effect called gain stealing
• the energy that each of the channels takes from the pump depends on the details of the emission and absorption spectra
• before simulating the gain, the optimum length was determined

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• gain varies significantly over wavelength two distinct peaks
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12m and 30m first peak
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1520-1536nm choose L opt
= 12m

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• implementation of the ordinary nonlinear differential equation used for studying
EDFA gain dynamics rate equation
• input/output

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• significant gain variation is visible about 11dB gain difference in the range
1530nm-1560nm
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How do we flatten the gain?

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• using the equations shown earlier, I derived an equation relating the pump gain (G
P
) to the signal gain (G
S
) the resultant equation is: ln( G
P
)


 ln( G
S
)

C
S

B
S
C
P
B
P




B
P
B
S


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B
P and C
P are fixed, and B
S now G
S obtained can be fixed and G
P and C
S vary with wavelength for gain flatness can be

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• for a G
S of 30dB, G
P should follow the curve shown in the figure theoretical view of what the pump should be practically, in order to get a different power at each wavelength might be difficult
• something to be further analyzed