1. EDFA Simulink Model for Analyzing Gain Spectrum and ASE by Stephen Pinter

2. Presentation Overview
Project objectives
Gain characteristics of EDFA
wavelength dependant gain
Gain flattening
non-uniform gain over the spectrum
implications

3. Project Objectives Determine the optimum length for simulations
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
Why Simulink?
optimum length was determined without considering the impact of ASE, with ASE the optimum length is shorter
important to know the gain in this range because in WDM systems we need to see the gain at different input signal wavelengths
it will be shown that this gain is non-uniform over the spectrum
basic implementation of forward ASE

4. Why use Simulink when an EDFA can be simulated using simulation tools such as OASIX or PTDS?
static model
input pump power is a static input internal to the EDFA module
Simulink
dynamic model
input pump power as well as other EDFA parameters can be easily modified
one reason why the input pump power is modified is in order to study cross-coupling between the pump and signal

5. EDFA Gain characteristics
Significant equations governing EDFA dynamics
Output pump and signal power:
Quantities B and C characterize the physical EDFA and are given by:
To handle multiple signal wavelengths, Bs and Cs as well as the input signal must be multidimensional
Why?

6.  and  are wavelength dependant as shown in the figure
 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
different absorption and emission patterns will give a different gain characteristic
O. Mermer, “EDFA Gain Flattening By Using Optical Fiber Grating Techniques,” [Online Adobe Acrobat Document], Available at

7. Note on Aspects of Simulation
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

8. Optimum Length gain varies significantly over wavelength
two distinct peaks
12m and 30m
first peak nm
choose Lopt = 12m
the wavelengths that reach maximum at around 12m on this graph correspond to the wavelengths on the emission and absorption spectra where the peak occurs
so, since we are interested in the effect that the emission/absorption peak has on the gain, we use an optimum length of 12m

9. Simulink Models
implementation of the ordinary nonlinear differential equation used for studying EDFA gain dynamics
rate equation
input/output
EDFA Module
input and output powers are in photons/second
multiple signal wavelengths are clearly represented, 26 signal wavelengths ranging from 1520nm to 1570nm + 1 pump wavelength at 980nm
excited state population in the N2 energy level
EDFA gain output
Full Model
Input signal power is -30dBm because a large signal would drive the EDFA into saturation
Input pump power is 17dBm
length is 12m as shown earlier
output gain – for multiple wavelengths and the pump
ASE block

10. EDFA Gain significant gain variation is visible
about 11dB gain difference in the range 1530nm-1560nm
How do we flatten the gain?
the importance of having a relatively flat gain in WDM systems is obvious
because of this non-uniform gain different channels in a WDM system would experience different signal to noise ratios
gain flattening can be done using notch filters or fiber Bragg grating, I considered how it can be done using the pump signal
if the gain can be flattened by changing the pump signal, then there is no need for external filters and such
why flatten the gain? – large gain difference in cascaded systems, noise, SNR

11. Gain Flattening
using the equations shown earlier, I derived an equation relating the pump gain (GP) to the signal gain (GS)
the resultant equation is:
BP and CP are fixed, and BS and CS vary with wavelength
now GS can be fixed and GP for gain flatness can be obtained

12. for a GS of 30dB, GP 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
pump gain is negative because the pump’s energy gets transferred to the signal resulting in the amplification
the location of the large peak on the output gain (around 1530nm) is where the pump gain should be slightly larger than for the rest of the wavelengths
this relationship is something to be further researched
the resulting model accurately represents EDFA gain dynamics and forward ASE and an interesting approach to gain flattening was presented

13. Thank You