The dependence of the properties of optical fibres on length

We investigate the dependence on length of optical fibres used in astronomy, especially the focal ratio degradation (FRD) which places constraints on the performance of fibre-fed spectrographs used for multiplexed spectroscopy. To this end, we present a modified version of the FRD model proposed by Carrasco & Parry to quantify the number of scattering defects within an optical fibre using a single parameter. The model predicts many trends which are seen experimentally, for example, a decrease in FRD as core diameter increases, and also as wavelength increases. However, the model also predicts a strong dependence on FRD with length that is not seen experimentally. By adapting the single fibre model to include a second fibre, we can quantify the amount of FRD due to stress caused by the method of termination. By fitting the model to experimental data, we find that polishing the fibre causes more stress to be induced in the end of the fibre compared to a simple cleave technique. We estimate that the number of scattering defects caused by polishing is approximately double that produced by cleaving. By placing limits on the end effect, the model can be used to estimate the residual-length dependence in very long fibres, such as those required for Extremely Large Telescopes, without having to carry out costly experiments. We also use our data to compare different methods of fibre termination.