Analysis of the propagation of circularly symmetric fields is made using the finite-difference beam-propagation method. After testing the accuracy of this method, we analyze the guided-mode transmission of connected fibers whose core radii are different. The propagation behavior of the unguided-mode field generated at the junction is revealed using a transparent boundary condition.

The finite-difference beam-propagation method is applied to the analysis of hollow slab waveguides (HSWs). The attenuation constants for the TE0 and TE1 modes are evaluated and compared with those obtained by the perturbation theory. The propagating field and differential power loss in the transition from a straight HSW to a bent HSW are revealed and discussed.

Pure bend loss of a fiber with a trench section is calculated by the alternating-direction implicit finite-difference method. The dependence of the loss on the trench location is evaluated. The mechanism of the oscillatory behavior of the loss is discussed in terms of a modal approach in a dielectric slab waveguide.