  An adaptive algorithm for computing eigenmodes and propagation constants of
optical fibers is proposed. The algorithm is built using a dual-weighted
residual error estimator. The residuals are based on the eigensystem for leaky
hybrid modes obtained from Maxwell equations truncated to a finite domain after
a transformation by a perfectly matched layer. The adaptive algorithm is then
applied to compute practically interesting modes for multiple fiber
microstructures. Emerging microstructured optical fibers are characterized by
complex geometrical features in their transverse cross-section. Their leaky
modes, useful for confining and propagating light in their cores, often exhibit
fine scale features. The adaptive algorithm automatically captures these
features without any expert input. The results also show that confinement
losses of these modes are captured accurately on the adaptively found meshes.
