  We present our simulation tool JCMmode for calculating propagating modes of
an optical waveguide. As ansatz functions we use higher order, vectorial
elements (Nedelec elements, edge elements). Further we construct transparent
boundary conditions to deal with leaky modes even for problems with
inhomogeneous exterior domains as for integrated hollow core Arrow waveguides.
We have implemented an error estimator which steers the adaptive mesh
refinement. This allows the precise computation of singularities near the
metal's corner of a Plasmon-Polariton waveguide even for irregular shaped metal
films on a standard personal computer.
