An efficient numerical approach, for determining the dispersion characteristics of dual-mode elliptical-core optical fibers

Based on vectorial formulations which combine the surface integral equation method and the finite-element method, a novel numerical approach is proposed for calculating the dispersion coefficients of dual-mode elliptical-core fibers with arbitrary refractive index profiles. By differentiating the original formulations involving the propagation constant β and the guided mode fields H_x and H_y once and twice with respect to the normalized frequency V, the new formulations for {dβ/dV, dH_x/dV, dH_y/dV} and for {d²β/dV², d² H_x/dV², d²H_y/dV² } are obtained respectively. Once {β, H_x, H_y } is solved through the eigenvalue procedure which dominates the computing time, only a few matrix manipulations are required to obtain {dβ/dV, dH_x/dV, dH_y/dV} and {d²β/dV², d²H_x/dV² , d²H_y/dV²}. Some numerical examples are examined to see the influence of different refractive index distributions with dips on the dispersions of the four nondegenerate LP ₁₁ modes for elliptical-core fibers