The dependence of the properties of optical fibres on length

TL;DR

This study models how optical fibre properties, especially focal ratio degradation, depend on length and termination methods, revealing stress effects and guiding design for long fibres in astronomy.

Contribution

We adapt and validate a modified FRD model incorporating stress effects from fibre termination methods, enabling predictions for very long fibres without extensive experiments.

Findings

Polishing induces more stress than cleaving, approximately doubling scattering defects.

Fibre length has minimal impact on FRD when stress effects are accounted for.

The model can predict FRD in extremely long fibres used in telescopes.

Abstract

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 and Parry \cite{Carrasco1994} to quantify the 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 (ELTs), without having to carry out costly experiments. We also use our data to compare different methods of fibre termination.