Development of the Wavefront Matching Method Based on the 3-D Finite-Element Method and Its Application to Si-wire Mode Converters

A fully three-dimensional wavefront matching method (WFM) based on a finite-element scheme for optical waveguide devices including waveguide discontinuities is newly developed. In contrast to the conventional WFM method based on the beam propagation method, the developed method, in principle, can be applied to optimize any geometry including reflection and structural discontinuities. The procedure for renewing refractive index distribution is described in detail. The application for Si-wire mode converters (TE₀ -TE₁, TE₁ -TE₂, and TE₀ -TE₂) are demonstrated and ultrasmall structure with low loss is obtained. We designed them to confirm the validity of the developed method. A low-loss and compact waveguide structure was obtained by the developed method automatically.