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.

The power transfer characteristics of a symmetric nonlinear directional coupler (NLDC) are analyzed rigorously using the beam propagation method based on the finite difference scheme. The NLDC consists of two linear waveguides separated by a Kerr-like nonlinear gap layer. The change of nonlinear refractive index along the coupler is precisely evaluated by making use of the second-order iteration procedure with respect to a small propagation length. For the incidence of TE0 mode of the isolated linear waveguide, the highly accurate numerical results are obtained for the behavior of power transfer, and the coupling length and critical power for optical switching. The dependencies of the coupling length and critical power on the width of the gap layer and the input power levels are discussed, compared with those predicted by the coupled-mode approximations.

The beam propagation method (BPM) is a powerful and manageable method for the analysis of wave propagation along weakly guiding optical waveguides. However, the effects of reflected waves are not considered in the original BPM. In this paper, we propose two simple modifications of the BPM to make it relevant in characterizing abrupt discontinuities in weakly guiding waveguides at which a significant amount of reflection is expected to be observed. Validity of the present modifications is confirmed by the numerical results for abrupt discontinuities in step-index slab waveguides and butt-joints between different slab waveguides.

The beam propagation method (BPM) is a powerful and manageable method for the analysis of wave propagation along weakly guiding optical waveguides. However, the effects of reflected waves are not considered in the original BPM. In this paper, we propose two simple modifications of the BPM to make it relevant in characterizing waveguide discontinuities at which a significant amount of reflection is expected to be observed. Validity of the present modifications is confirmed by the numerical results for the slab waveguide discontinuities and the butt-joints between different slab waveguides which either support the dominant mode or higher order modes.

Power transmission properties are investigated for a butt-joint which contains an air gap between an isotropic planar waveguide and an anisotropic one whose optical axis is lying in the plane defined by the propagation axis and the normal of the waveguide surface. New transmission coefficients are introduced for estimating the optical-power which is launched out into the gap from the incoming waveguide. Wave propagation through the gap is analyzed on the basis of the BPM concept. And the power transmitted across the interface between the gap and the outgoing waveguide is evaluated by means of the overlap integral of the field profiles. The effects of the air gap and the refractive index of filling liquid as well as axial displacement and angular misalignment are discussed on the basis of numerical results.