  Radiative emission from a semi-infinite unflanged circular cylindrical
dielectric waveguide or optical fiber is studied for the case of axisymmetric
modes of TM polarization on the basis of an iterative scheme. The first step of
the scheme leads to approximate values for the reflection coefficients and the
electromagnetic fields inside and outside the waveguide. In a numerical example
the reflection back into the waveguide is appreciable. Correspondingly the
radiation pattern of the outgoing radiation differs appreciably from the lowest
order approximation in which reflection is neglected.
