Study of the Eigenmodes of Anoptical Waveguide with a Refractive Index that Varies in the Radial Direction from the Central Axis

Using finite element analysis, the eigenmodes of the optical waveguide whose refractive index vary in the radial direction was obtained. To perform efficient calculations, the cross section of the waveguide was divided into a mesh structure of triangular element. The eigenmatrix equations that describe the characteristics of eigenmode were composed of the edges and nodes of triangular elements. The eigenmodes were established with transverse electric field, and electric potential. These were represented schematically as 2-Dim electric field, 3-Dim electric potential and 2-Dim electric equipotential contour. These representations were arranged sequentially from the lower order eigenmodes. And the unusual ones were randomly organized regardless of ordering index to reveal their characteristics more clearly. From these results, it was found that the refractive index distribution adopted in this study sufficiently performed the function of focusing electromagnetic waves in the central region.