Modal Analysis and Dispersion Characteristics of a D-Shaped Dielectric Optical Waveguide

Abstract: A theoretical and numerical investigation of a D-shaped dielectric optical waveguide is presented. The proposed waveguide is obtained by truncating a circular dielectric core with a planar surface, thereby introducing a controlled departure from circular symmetry. The analysis follows the weak-guidance scalar formulation used in the supplied reference work, in which the modal propagation constant is obtained from the transverse eigenvalue problem. A dimensionless truncation parameter, η=d/a, is introduced to quantify the degree of truncation. Numerical calculations were performed for n1=1.50, n2=1.48 and λ=1.55 μm. The normalized propagation constant b was evaluated for the fundamental mode over V=2–5 for several truncation levels. The calculated results demonstrate a clear dependence of modal confinement on the D-shaped geometry. At V=4 and η=0.5, the calculated normalized propagation constant is 0.7218 and the corresponding effective refractive index is 1.49446. The results establish a numerical basis for a more detailed Goell point-matching treatment of the D-shaped boundary.

Keywords: D-shaped waveguide; optical waveguide; weak guidance; modal analysis; dispersion; propagation constant; truncation parameter.