  Optical fibres are essential for many types of highly-multiplexed and
precision spectroscopy. The success of the new generation of multifibre
instruments under construction to investigate fundamental problems in
cosmology, such as the nature of dark energy, requires accurate modellisation
of the fibre system to achieve their signal-to-noise goals. Despite their
simple construction, fibres exhibit unexpected behaviour including
non-conservation of Etendue (Focal Ratio Degradation; FRD) and modal noise.
Furthermore, new fibre geometries (non-circular or tapered) have become
available to improve the scrambling properties that, together with modal noise,
limit the achievable SNR in precision spectroscopy. These issues have often
been addressed by extensive tests on candidate fibres and their terminations
but these are difficult and time-consuming. Modelling by ray-tracing and wave
analysis is possible with commercial software packages but these do not address
the more complex features, in particular FRD. We use a phase-tracking
ray-tracing method to provide a practical description of FRD derived from our
previous experimental work on circular fibres and apply it to non-standard
fibres. This allows the relationship between scrambling and FRD to be
quantified for the first time. We find that scrambling primarily affects the
shape of the near-field pattern but has negligible effect on the barycentre.
FRD helps to homogenise the nearfield pattern but does not make it completely
uniform. Fibres with polygonal cross-section improve scrambling without
amplifying the FRD. Elliptical fibres, in conjunction with tapering, may offer
an efficient means of image slicing to improve the product of resolving power
and throughput but the result is sensitive to the details of illumination.
