Solving the nonlinear circular equation by the HOMOTOPY analysis method for TE polarized wave

In this work, we study TE-polarized electromagnetic waves propagating in an inhomogeneous dielectric waveguide of circular cross section filled with a nonlinear medium; most perturbation methods assume a small parameter exists, but most nonlinear problems have no small parameter at all. Homotopy Analysis Method (HAM) was proposed to obtain series solutions for nonlinear differential equations. The main benefit of the HAM method is that it does not depend on a small parameters.