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# RP Fiber Power – Simulation and Design Software for Fiber Optics, Amplifiers and Fiber Lasers

## Case Study: Erbium-doped Fiber Amplifier for a Long-Wavelength Signal

### Design Goal

We want to design an erbium-doped fiber amplifier which can amplify a weak input signal (100 μW, super-Gaussian spectrum with 5 nm bandwidth) at a relatively long wavelength of 1580 nm, where the erbium gain is well below its maximum. The signal output power should be around 100 mW.

### Initial Attempt

We first try with a single amplifier stage. In the Power FormFiber amplifier for continuous-wave signals”, we easily enter the parameters of signal input and amplifier:

We choose the commercial fiber “Liekki Er40-4-125” (as one of many dozens for which we have data) and have to decide on a fiber length and the pump power at 980 nm. We find that a length around 2.5 m is sufficient to absorb most of the pump power.

We then soon encounter a serious problem: We get only a quite low signal power out. For example, for 100 mW pump power in backward direction we get only 5.46 mW signal out, while producing 90.8 mW amplified spontaneous emission (ASE) in forward direction and 47.7 mW ASE in backward direction:

Essentially, the problem is that the amplifier gain is highest around 1530–1560 nm, while at 1580 nm (central wavelength of our signal) we have substantially less gain (see Figure 3). So we produce a lot of ASE at these shorter wavelengths before we reach a sufficiently high signal gain.

The first attempt to solve this problem could be changing the fiber length and pump power. We use one of the helpful variation diagrams in the Power Form, where we can, for example, vary the fiber length in some range for a given pump power. That way, we quickly find that we can indeed achieve our goal of 100 mW signal output power, but with a fiber length of 8 m and a pump power as high as 1 W! This is highly inefficient, with more than half of the pump power converted to ASE rather than to signal power. Changing the pumping direction and fiber type also do not result in significant improvements.

Further, it may be rather surprising that a fiber length of 8 m is better, as we already got most of the pump light absorbed in 2.5 m. So we inspect that situation (8 m fiber length, 1 W pump power):

Although the pump power is largely exhausted already in the middle of the fiber, there is still substantial erbium excitation and signal amplification in the left half – but why? This is because backward ASE is reabsorbed there, now acting as pump light for the still longer-wavelength signal! (For the long signal wavelength, there is still some positive gain despite the moderate erbium excitation level, while shorter-wavelength ASE is reabsorbed.)

So we have a solution for our design goal, but one which works in a somewhat strange and not fully satisfactory way. However, there is a better solution:

### Using a Second Amplifier Stage

We now realize the amplifier with two consecutive stages. That gives us the opportunity to suppress ASE with a bandpass filter between the stages: we prevent most of the ASE light generated in the first stage from entering the second stage, where it would be amplified further.

This is easy to try with the Power Form:

• Enable the second stage and set its parameters (same fiber type, same length (now back to 2.5 m).
• For the first stage, we can now turn the pump power down to 30 mW, as this mainly means less ASE output while not much reducing the signal power.
• At the end of the first stage, we insert a bandpass filter with a Gaussian transmission curve. See the `Losses at output` input of the first stage, where we define a wavelength-dependent loss function (variable `l` for wavelength):
• For the second stage, a pump power of 190 mW turns out to be sufficient, as now we don't have serious gain saturation by ASE.

This results in the wanted signal output power of 104 mW, with a total fiber length of 5 m and a combined pump power of only 220 mW (rather than the 8 m, 1 W pumped single stage amplifier). Further, only 3.6 mW of forward ASE and 2.1 mW of backward ASE are generated in the second stage (in the first stage: 5.5 mW and 2.1 mW).

We can also inspect the evolution of signal power on a logarithmic scale:

See also the ASE output spectra of the first stage, with and without the bandpass filter:

Although the bandpass filter does not remove a very high ASE power, it suppresses the further strong amplification of the short-wavelength ASE while causing only a 0.37-dB loss for the signal.

## Conclusions

You can learn various things from this demonstration:

• The modeling of an erbium-doped fiber amplifier is quite straightforward with the RP Fiber Power software: simply enter its parameters and inspect the resulting numerical and graphical outputs. You can rapidly explore parameters and configurations. The Power Form gives you plenty of freedom, e.g. for using multiple stages, multiple signals and pump sources, filters between the stages, etc., besides offering many useful diagrams.
• Even in seemingly simple cases, fiber amplifiers can exhibit quite unexpected behavior, which can have drastic effects on the amplifier performance. With a simulation model, you identify such effects quickly and have the best chances to find out how things really work. (If you have difficulties, we will help you within our diligent support!)
• With such a model, you can quickly solve the problem by optimizing your design. If you would instead order the parts, build the amplifier, test it and try to analyze and solve the issues there, this would be far more tedious, costly and time-consuming!