Propagating beam analysis by alternating‐direction implicit finite‐difference method

Abstract The three‐dimensional beam propagation problem expressed by the Fresnel equation is analyzed by the beam‐propagation method using an alternating‐direction implicit finite‐difference method (ADI‐BPM). First, following the formulation of the finite‐difference method, the equations to be analyzed are rearranged. The fundamental and higher‐order mode propagation problems in a step index fiber are treated, and the accuracy and advantages of the ADI‐BPM are investigated. It is found that the computing time is shorter and the step length in the propagation direction can be made larger in the ADI‐BPM than in the beam‐propagation method based on the fast Fourier transform (FFT‐BPM). As another advantage in the ADI‐BPM, the usefulness of the transparent boundary condition is described. It is shown that the spreading problem of a Gaussian beam can be analyzed without setting up the absorbing functions needed in the FFT‐BPM. Further, as an example to prove the effectiveness of the ADI‐BPM for the analysis of the problem in which the guided mode and the radiation mode are mixed, the transmission efficiency is evaluated in the case where an axial offset exists in the fiber junctions. The effect of the coherent coupling is studied.