The finite operator model for step index fibres - Kumar, Das Soumitra (2019)
A ray-based dynamical model is developed to propagate light in passive optical fibres. The developed model provides an efficient way to investigate light propagation in the presence of boundary deformations in optical fibre waveguides using concepts of ray billiards and wave-chaos theory. The light propagation is modelled using the phase space transport, where the phase space method is a standard tool of tracing rays in enclosed cross-sectional boundaries. In the developed model, the light propagation is achieved using coarse-grained phase spaces and Ulam's method is adopted for the numerical discretisation. The phase space is divided into rectangular regions or pixels, and a bundle of rays are traced as ensembles from one pixel to the next. The coarse-graining transforms the process of tracing individual light trajectories into a probabilistic way of mapping power from one region of the phase space to another. On this basis, a finite operator model, a form of Frobenius-Perron operator, is developed to propagate light in 3D fibres. The finite operator deterministically distributes power in the pixelated phase space.