Absorption measurement errors in single-mode fibers resulting from re-emission of radiation

We investigate errors in small-signal absorption spectra that can result from re-emission of absorbed photons in fibers with overlapping absorption and emission spectra. Experiments on Er-doped fibers as well as simulations of Er and Yb-doped single-mode fibers show that the re-emission can severely distort the spectral shape, especially the peak, under common measurement conditions. Errors can reach well over 10% already at 30 dB peak absorption, and 5% at 20 dB, if only the source or the detector is spectrally filtered. Re-emission can then be the dominant source of error. These levels of absorption are well within the dynamic range of commonly-used equipment, so it is easy to make the mistake of measuring too high absorption and thus introduce re-emission errors. The error increases for higher fiber-NA, and for sufficiently high NA, a significant error remains also in low-absorbing fibers, even in the limit of zero absorption. The error can then reach 5% at the peak of a 0.46-NA Yb-doped fiber. Furthermore, in contrast to the case of high absorption levels, the error is larger for longer wavelengths than it is at the peak. On the other hand, if both source and detector are spectrally filtered with 0.1 nm bandwidth then the re-emission error becomes as low as around 1% even for as much as 90 dB absorption. At such high absorption, other sources of error such as receiver noise and saturation effects are likely to be higher, so that re-emission are no longer significant. We also conclude that that standard amplifier models are well suited to simulations of the rich physics of absorption measurements of single-mode fibers.Original spreadsheet updated 2017-05-04 to combine fig 5a and fig 5b into a single fig 5.Funded by AFOSR (FA9550-14-1-0382).