Bending loss of modes in optical fibers - Pivotal aspects of a computational scheme

To compute the bending losses of modes in optical fibers, a full-vectorial analysis of the bent fiber is performed. For this analysis, we distinguish between field solutions inside and outside the fiber. For the interior region, a coupled system of ordinary differential equations is integrated numerically from the known regular solutions at the center to the boundary. For the exterior region, modified Bessel functions with large, complex order and argument play an important role. They are the key to an accurate solution and have to be computed to high relative precision (10^-13). A program to compute a scaled version of these functions has been written and tested extensively in the parameter range of interest.