Pump Absorption in Amplifier Fibers
One of the most basic questions when making a fiber amplifier or laser is what length of rare-earth-doped fiber to use. A simple answer would be: just enough length to get most of the pump light (maybe 80% to 90%) absorbed. That may look simple at a first glance, at least for cases where the fiber manufacturer specifies the pump absorption in dB/m for the intended pump wavelength. For example, if you get 5 dB/m, you may expect to get 10 dB within 2 m of that fiber, which would seem to be sufficient.
Unfortunately, you would often be completely misled by such a simple calculation. The reason is that the pump absorption usually exhibits strong saturation at the typically applied power levels, while the absorption specifications are meant to be low-intensity values, i.e., without saturation effects (also called ground state absorption). So in reality you may get far weaker pump absorption than you would naïvely expect, and you will need a correspondingly longer piece of fiber for an amplifier or laser.
This is a classical example for how computer simulations can help you to make your R & D work efficient.
Example: Yb-doped Single-mode Amplifier
Let me show you some simple example simulations done with our RP Fiber Power software. Here, I assume an ytterbium-doped silica-based single-mode fiber with a ground state absorption (low-intensity absorption) of 5 dB/m at the assumed pump wavelength of 940 nm. The core radius is 5 um.
Let us first see what happens for a quite moderate pump power of 300 mW, injected into a 2 m long fiber, for which one might expect 10 dB pump absorption:
Instead of the strong exponential decay of pump power by 10 dB, we get an approximately linear decay, and we get only about 1.7 dB absorption. The diagram also shows the strong excitation of the ytterbium: roughly 70% of the ions are in their excited state all along the fiber. These can obviously no longer absorb pump radiation, and there is even some amount of stimulated emission at that wavelength.
In order to fix this, we cannot try to use a 3 times longer fiber:
Now, we get a reasonable amount of pump absorption overall, but encounter another potentially surprising detail: the Yb excitation does not monotonously fall from left to right; it is also reduced on the left side as a result of amplified spontaneous emission (ASE). (I have assumed zero reflections of the fiber ends, leading to the minimum amount of ASE.)
Now we may also inject a 10-mW signal at 1060 nm at the left end:
We see that not only we get the signal substantially amplified, but also the pump absorption is substantially improved. This is because stimulated emission reduces the upper-state population in the ytterbium, thus reducing pump saturation. By the way, to some small extent the ASE in the previous example (which is much depressed in cases with a strong enough input signal) also had such an effect.
So you see that in general you need to consider all involved light waves in your model, since all of them may affect the ytterbium excitation. Only that way you can decide on the right fiber length.
Note that the chosen example is in no way particularly extreme. For example, you get even much stronger saturation effects for the also common pump wavelength of 975 nm, where absorption and emission cross-sections of ytterbium are quite high:
Here, the pump absorption is initially weaker, despite the much larger absorption cross-section at that wavelength. Also, the ytterbium excitation is only around 50% because there is also strong stimulated emission at that pump wavelength. Later on, the pump absorption gets much stronger, where the now high enough signal intensity can pull the excitation level down.
The example shows you that even in a rather simple situation with moderate pump power you get substantial saturation effects. As an experienced person in the field, you can anticipate that you will have them, but it is not easy to estimate quantitatively what will happen. Therefore, a proper preparation for such experiments requires that you simulate the expected behavior in order to properly understand it. With a trial-and-error approach in the lab, you would be fishing in the dark, wasting time and other resources, and find it hard to get to the optimal amplifier design.
By the way, you may wonder whether such problems also occur in the area of solid-state bulk lasers. The answer is that it depends on the particular case:
- Many bulk lasers are based on four-level laser gain media like Nd:YAG at 1064 nm, which are often operated with rather low pump intensities and therefore do not exhibit strong pump saturation effects.
- Some of them, however, have quasi-three-level transitions, where relatively high pump intensities need to apply it, and pump saturation effects often become significant.
- Most active fiber devices exploit quasi-three-level transitions, and that is technically also not that difficult because of the small fiber mode areas. It is not even rare that we operate fiber devices far above their saturation intensities.
So we see that while many bulk lasers can be designed without such complications in mind, the situation for fiber devices is usually more complicated. Note that I mentioned only one type of complication; additional effects come into play due to strong ASE, for example. In various other articles of the RP Photonics Software News, I have demonstrated such things.
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