A new method for investigating wave propagation in optical waveguides of longitudinally invariant structures without using beam propagation algorithm

In this paper, we propose a new method to study wave propagation in longitudinally invariant waveguides with arbitrary index profile. We keep, in the wave equation, the second order derivative of transverse wave field with respect to the propagation direction. An explicit expression for the wave field at any longitudinal position along an optical waveguide is derived. This study has demonstrated that our approach yields the same results as those by using a commercial software in which a beam propagation method with Pade´ approximation is used.