Perturbational solution of the Helmholtz equation in arbitrary inhomogeneous media

The one-dimensional Helmholtz equation for a medium with arbitrary inhomogeneities is solved by a uniformly valid iteration technique. Unlike the Born-Newman series approach, this technique does not depend on the assumption of small inhomogeneities. Here, the Helmholtz equation is first manipulated to yield, in terms of a transformation function, a Volterra integral equation whose series solution still converges when the Born-Newman series breaks down. For the case of small inhomogeneities, it is shown that the series solution, using the present technique, reduces to that obtained by a Born-Newman series-solution. Formulas for the reflection and transmission coefficients are set in terms of the transformation function.