A beam adaptive frame for finite-element beam-propagation analysis is proposed. The width of the frame can be adapted itself to either the guiding structure or the propagating beam in optical circuits, so the size of the computational window can be reduced.

We propose a beam tracing frame which shifts together with either the guiding structure or the beam propagation in optical circuits. This frame is adaptive to the beam propagation analysis based on the finite-element method and can reduce the computational window size.

An improved finite-element formulation using quadratic shape functions is presented. The improvement in accuracy of the method is investigated in comparative to the case of using linear shape functions. As an example of using the quadratic shape functions, an accurate analysis of a microstrip waveguide has been carried out. Good agreement between the finite-element solutions and the other numerical solutions is confirmed. This agreement shows the validity and usefulness of the method.

A simple method is developed to analyze a bent waveguide, which is described in the cylindrical coordinate system. By means of this method based on the Galerkin method, the sampling spacing can be chosen arbitrarily and it is possible to treat narrow beams. In addition we introduce the absorber using the graded lossy material. As this lossy absorber can remove the radiation wave from the bend, so we can use the finite computational window. The lightwaves propagating in the uniform bend of the slab waveguide and of the nonlinear slab waveguide are demonstrated.