Evaluation of modal distribution of optical branching waveguide by phase space

Optical multimode branching waveguides are very important devices in optical communication systems, but the evaluation method of their characteristics has not been established yet. The design and evaluation of these elements, because of their characteristic dependency on modal distribution, have encountered some problems. This paper proposes a new method to evaluate the characteristics of optical multimode branching waveguides. The discussion covers the two branching waveguides of step‐and graded‐index distributions. First, using the ray‐tracing method, the branching characteristics of multimode branching waveguides are investigated and the condition of equal light intensity is obtained. Then as a new method for evaluating the modal distribution at the output, phase space expression in terms of the ray position and its slope, is proposed. It is shown that the optimum condition for the branching ratio does not necessarily agree with the optimum condition if modal distribution is also considered. Further, a diffused branching waveguide is fabricated and a qualitative discussion is given by comparing theoretical and experimental results.