Modeling of single mode optical fiber having a complicated refractive index profile by using modified scalar finite element method

A numerical method based on modified scalar finite element method (SC-FEM) is presented and programmed on MATLAB platform for optical fiber modeling purpose. We have estimated the dispersion graph, mode cut off condition, and group delay and waveguide dispersion for highly complicated chirped type refractive index profile fiber. The convergence study of our FEM formulation is carried out with respect to the number of division in core. It has been found that the numerical error becomes less than 2 % when the number of divisions in the core is more then 30. To predict the accurate waveguide dispersion characteristics, we need to compute expression \(\frac{{{\text{d}}^{2} \left( {\text{vb}} \right)}}{{{\text{dv}}^{2} }}\) numerically by the FEM method. For that the normalized propagation constant b (in terms of \(\beta\)) should be an accurate enough up to around 6 decimal points. To achieve this target, we have used 1 million sampling points in our FEM simulations. Further to validate our results we have derived the higher order polynomial expression for each case. Comparison with other methods in calculation of normalized propagation constant is found to be satisfactory. In traditional FEM analysis a spurious solution is generated because the functional does not satisfy the boundary conditions in the original waveguide problem, However in our analysis a new term that compensate the missing boundary condition has been added in the functional to eliminate the spurious solutions. Our study will be useful for the analysis of optical fiber having varying refractive index profile.