Measurement of Absorption Spectra of Active Fibers: Not as Easy as One Might Think!

I was made aware of this issue by the team of Prof. Johan Nilsson at the Optoelectronics Research Centre (ORC) at the University of Southampton (where I had spent a very nice and fruitful time as a post-doc in the 1990s). We then started to put together a model, using my software RP Fiber Power, beginning with the simple case of an ytterbium-doped single-mode fiber. This turned out to be quite simple:

• We use some number of “optical channels” corresponding to the wavelength bins of the optical spectrum analyzer – for example, width a spectral width of 1 nm.
• Each optical channel obtains some small input power according to the white light input.
• The optical channels are defined as “ASE channels”, so that not only the absorption or optical gain is taken into account, but also the fluorescence into the corresponding modes. Although we of course do not have any positive net gain for the typical situation with a very low input power, and consequently no amplified spontaneous emission (ASE), this type of model is fully adequate for analyzing such a situation.
• For each optical channel, the resulting output power is calculated, and from that the apparent absorption of the fiber in dB/m.

For simplicity, the same intensity mode profile has been used for the whole wavelength region; to be more precise, one could use calculated fiber modes, having somewhat larger profiles for longer wavelengths, so that the mode overlap factor becomes wavelength-dependent.

Figure 1 shows the calculated optical spectrum at the fiber output. For comparison, the same spectrum has been calculated with the upper-state lifetime of the ytterbium ions set to zero, so that the fluorescence is totally quenched. One can see that there is a serious discrepancy between these results at the strong absorption peak around 975 nm, whereas the fluorescence effect is negligible at other wavelengths:

Figure 2 shows the absorption spectra calculated from that, of course exhibiting the same discrepancy around 975 nm:

It is clear why the fluorescence is most disturbing at wavelengths where the absorption of the fiber is very high: there, the transmitted optical power to be measured is very low, so that even small amounts of fluorescent light can spoil the results. Well, one might think that as the fluorescence light is also strongly absorbed in the fiber, it should also become very weak towards the fiber end. Note, however, that there is also input light at other wavelengths, which experiences much lower absorption; that light can still be absorbed close to the fiber end and generate fluorescence light there. This is easily calculated with the model (see Figure 3), whereas you could hardly find this out with a measurement.

Additional aspects come into play for multimode fibers. Here, the number of guided modes and their intensity profiles (and thus their overlap with the doped fiber core) can change substantially over the considered wavelength range. This can cause additional features in the apparent absorption spectrum, which would not be seen in the true absorption spectrum. Particularly interesting is the case of double-clad fibers, having a large number of low-loss cladding modes which can capture fluorescent light. For the modeling of such situations, one needs to deal with a large number of modes in the many wavelength bins.

Some first results have been published in a conference paper (Betty Meng Zhang et al., “Fiber absorption measurement errors resulting from re-emission of radiation”, Advanced Solid State Lasers, OSA Technical Digest, paper AM5A.20). More results will probably soon be shown at another conference; a regular journal paper is also planned.

Curiously, I am not aware of any earlier scientific literature addressing this issue. Although the large number of researchers has done such measurements, apparently nobody became aware of this problem, or at least nobody cared to publish about it. In case that we have overlooked something, you are welcome to tell me, and I will update the article accordingly.

An interesting question is of course how to avoid the explained problem.

In principle, one could do such measurements with a bandpass filter applied to the input light, so that each measurement is done only with a quite limited bandwidth. With the described model, one can easily test that approach. Unfortunately, it turns out that even when the spectral range is set to 970–980 nm (only 10 nm wide), the error in the peak absorption is still roughly 10 dB. The problem is essentially that even in that narrow wavelength range there is a strong variation of the absorption. So to be sure one should really measure each wavelength bin separately, which effectively leads to a quite different (and probably less practical) measurement method.

Another approach is just to optimize certain parameters. In the example case above, using half the fiber length (i.e., 1 m instead of 2 m) one would already drastically reduce the error; the measured peak absorption would then be only off by 17% instead of more than a factor of 2. Note, however, that it may not always be sufficient to limit the peak absorption to 30 or 40 dB; the problem can also become more severe for multimode fibers and double-clad fibers. Also, the measurement of the weaker absorption at other wavelengths requires a longer fiber; this means that more measurements are needed.

Obviously, it is difficult to guess how large that measurement error will be in certain situations. A solution could be to take measurements with different fiber lengths; the results for some absorption peak can be considered reliable if the two or three measurements with the shortest fiber lengths lead to the same result. However, it is certainly better to have a computer model with which such effects can be quantified very quickly.

This is really a very general finding: for making fast progress in research and development projects on such matters, one really needs a simulation tool. Once a potential problem of this kind has been recognized, it can easily be studied how exactly things work and what is the dependence on certain parameters. With that, one can much better plan the experiments or avoid certain problems right away by choosing suitable parameters. Some people think that they cannot afford using such a thing; apparently, however, they can afford to waste time and resources by fishing in the dark.

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