The response of a source in the presence of the N-region, vertically stratified media is an unsolved problem. The finite element method is not appropriate for this problem because of the infinite size of the scatterer. In this paper, the numerical mode-matching method is used to solve this problem. By treating the fields propagating in the direction parallel to the subboundaries of the stratified media in terms of the propagators, and by introducing the concept of reflection operators, transmission operators, and generalized reflection operators, we reduce this twodimensional problem into several one-dimensional problems which are solved by the one-dimensional finite element method (FEM). The one-dimensional finite element method saves computer storage and computation time compared to the twodimensional finite element method. A formulation valid for a general N-region vertically stratified medium is derived. When there are only three regions, the comparison of the results with those in the literature is very good. Some typical numerical results for N > 3 are also shown. This solution can be applied to many areas including geophysical prospecting, integrated optics, nondestructive testing, and biological sensing.
ASJC Scopus subject areas
- Electrical and Electronic Engineering