An analysis of the modal field in absorbing optical waveguides and some useful approximations

The authors present a mathematically exact formation of the initial field striking the aperture of an absorbing optical waveguide, via an integral equation description. An analysis of the residual scattering by the waveguide is presented. Because of the presence of the non-negligible absorption coefficient, the solution for the fraction of the confined power is obtained by performing non-trivial integrations of Bessel and Hankel functions with complex arguments. In order to carry out a numerical analysis a specific computational method is applied by using an approximated polynomial expansion whose validity is also discussed.