Transmission of Magnetic Fields in Three-Dimensional Multilayered Structures

We have extended an earlier two-dimensional (2-D) analysis to provide a relatively simple approach to calculating the transmission of magnetic fields in three-dimensional (3-D) multilayered structures. The approach accommodates complex structures composed of an arbitrary number of layers, each of which may have an arbitrary magnetization direction and anisotropic permeability. The procedure relies on an initial transformation into the 2-D spatial frequency domain and then the use of transmission matrices to relate the fields in the different layers. The approach is general in that it provides a method for finding the field configuration for any set of 3-D magnetic sources embedded in a layered magnetic structure with a linear B-H relationship. In this paper, we concentrate on the analytical formulation and we illustrate the method by using it to determine both the external and internal fields of some relatively simple finite 3-D geometric shapes. We also derive new 3-D expressions for the flux density at the surface of a multilayered magnetic recording medium. In a companion paper, the procedure is applied to examine readback responses for a variety of 3-D magnetic recording configurations.