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

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**Presentation Overview**

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

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**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

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**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

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**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?

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** 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

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**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

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**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

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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

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**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

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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

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**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

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Thank You

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