Skip to Main Content
In this paper, we propose an efficient method to find the modal fields and the corresponding propagation constants for a single mode step index optical fiber. The simple effective index method (SEIM-x) and the variational method (VM) are mixed. The Gaussian optical field distribution as a trial function is used. Thereby the circular waveguide converts into two slab waveguides, the first slab has constant refractive index with x-dependent thickness and the second slab has constant thickness with variable core refractive index which is the effective refractive index of the first slab which is as a function of their thickness. The variational parameters of the two slab waveguides are the same to make the field distribution depends upon the radial distance. The application to fiber directional coupler is done by using the coupled mode theory. The numerical results show that our analytical solution presents a good agreement with the published data.