The beam-propagation method (BPM) is applied to the evaluation of the loss of S-shaped step-index waveguides. It is demonstrated that the BPM enables us to analyze S-shaped bends which have an offset core and a trench section in the cladding at the outer side of the bend.

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.

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.