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

## Case Study: Double-clad Fiber Amplifier

### Design Goal

We want to design a high-power fiber amplifier based on an ytterbium-doped double-clad fiber. It should amplify a weak input signal (10 mW, Gaussian spectrum with 10 nm bandwidth) at 1080 nm, where the ytterbium gain is well below its maximum. The signal output power should be 50 W. We will see whether we can achieve that goal with a single amplifier stage.

We conveniently use the Power Form for continuous-wave fiber amplifiers.

### Initial Attempt

We try with the commercial fiber Liekki Yb700-20-125DC, pumped with 60 W at 975 nm. Initially, we take the fiber length to be 2 m, which is found to be fully sufficient for efficient pump absorption:

Unfortunately, we see that we don't get nearly enough signal output power, since amplified spontaneous emission (ASE), both in forward and backward direction, extracts far too much power. As one can verify with an additional diagram, the ASE is mostly present around 1030 nm wavelength:

The problem is that the ytterbium gain has its maximum at 1030 nm and is substantially lower at our signal wavelength of 1080 nm. Therefore, the signal has difficulties competing with the ASE.

One may improve this with a dual-stage amplifier design, distributing the gain over two stages with ASE filtering between those. However, it turns out there is a simpler solution:

### Work with Longer Fiber

If we use a substantially longer fiber, e.g. with 10 m length instead of only 2 m, the performance gets far better:

Now, most of the pump power is converted to signal power, while ASE is now much weaker. This may be a rather surprising result; for example, how can it be that forward ASE gets much weaker although it can now develop in a longer fiber?

Let us first look at the same diagram with a logarithmic power scale:

Here is the explanation for what happens:

• Backward ASE first grows to a power of about 30 dBm (1 W) within the first 3 meters, but is then partially reabsorbed in the other 7 meters.
• That reabsorbed ASE leads to a significant Yb excitation, even in a region where the pump power is already negligibly small.
• As a consequence of that, we now get significant preamplification of the weak input signal in that region. Note that due to its longer wavelength, that is possible because we have very little reabsorption there.
• That in turn leads to a higher amplified signal power in the right part, which pushes the Yb excitation down (gain saturation). For that reason, forward ASE is also minimized.

That's cute, isn't it? This trick works well for long-wavelength signals, normally having less gain than ASE, thus often having difficulties competing with that.

We may have found this operation regime with trial & error in the lab, but then probably not understanding why and how it works. Only after simulating it, you understand what happens.

With 60 W pump power, we get 46.6 W signal output power. For obtaining the requested 50 W, we simply increase the pump power to 64 W.

We can also use a variation diagram for the fiber length how the signal output power depends on that:

We see that only for a fiber length beyond 13 m, the signal output power starts to slowly drop, as signal reabsorption is weak.

One may be concerned about the noise figure being increased when using a rather long fiber, where the signal input end is operated with a rather lower degree of ytterbium excitation. However, it turns out that a rather good noise figure of only 3.08 dB is achieved. This is again because Yb reabsorption is weak in that spectral region, where we are close to four-level behavior of ytterbium.

## Conclusions

You can learn various things from this demonstration:

• The modeling of a 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!