Loss and birefringence for arbitrarily bent optical fibres

We present a calculation to determine the radiation losses for arbitrarily bent, weakly guiding optical fibres. Our results are derived for the full set of vector Maxwell's equations, and show that the rate of energy loss due to radiation differs for the various modes. These results are different from that calculated from a scalar theory, where the so-called linearly polarized (LP) modes are used to approximate the electromagnetic field distributions, showing that in this case scalar theories give incorrect loss rates. We also show that different ranges for the size of the curvature and torsion produce quite different effects. In particular, we show that, for smaller amounts of curvature and torsion, the modes retain the basic structure of the modes in the straight fibre while losing energy slowly at differing rates, while, for larger amounts of curvature and torsion, the modes become distorted by the bending.