Two-dimensional model for three-dimensional index-guided multimode plasmonic waveguides and the design of ultrasmall multimode interference splitters

We demonstrate that a three-dimensional (3D) index-guided multimode plasmonic waveguide can be approximated to a two-dimensional (2D) lossy slab waveguide by using an effective-index method. It is found that this 2D approximation is more accurate when the width of the multimode waveguide increases. Such a 2D approximation can be used for a quicker and more efficient design of complicated multimode plasmonic devices. 1 x N ultrasmall multimode interference splitters based on multimode surface plasmon waveguides are designed by using this 2D model and the designs are validated with a 3D finite-difference time-domain method.