Modelling chaos in asymmetric optical fibres

A ray dynamical approach is developed for the study of large-core asymmetric step index fibres (SIF), especially those made from chalcogenide glasses (ChGs) which can exhibit very high refractive index, large numerical aperture, and which are transparent at mid-infrared wavelengths. The model allows for deformations of the SIF away from concentric circular structures, and for the light rays captured by the fibre to behave chaotically within the asymmetric boundaries of the fibre. Chaotic and periodic rays can be classified by the Poincaré surface of sections (SOSs). In the model, the ray dynamics in the SIF are approximated by dividing the SOSs into pixels; the construction of a transfer matrix stores all the mapping probabilities. The light intensity distribution in the SOSs is efficiently propagated using the constructed transfer matrix, providing a viable alternative to propagating all the rays in the SIF by brute force ray tracing. The model enables the rapid calculation of the power accumulated in the fibre core following an arbitrary excitation.