Green´s function formulation for multilayer normally biased ferrite structures using the transmission matrix approach

Normally biased ferrite substrates have been used extensively in antenna applications to control antenna and scattering characteristics. The case of a normally magnetized ferrite slab is considered the most difficult one compared with the case of a transversely or longitudinally magnetized ferrite slab. One can observe this difficulty from the comparison of the permeability tensor for each case. The most popular technique for the analysis of planar structures is the spectral domain approach, which can be adopted for a wide variety of structures. However, the formulation of a Green´s function represents a major complexity in that approach. Determining the Green´s function as a boundary value problem is quite difficult for magnetic substrates and becomes even more complicated for multilayer structures. In addition, Green´s functions developed in such a procedure are useful only for the specific structures for which they are derived. A more flexible approach is to find the transmission matrix of the medium and then use this matrix to obtain the Green´s function numerically. Since the transmission matrix does not depend on the geometry of the total structure, it is possible to form a software library of transmission matrices for several media types and use this library for the analysis of a variety of multilayer structures. Our technique based on the exact derivation of the transmission matrix and no approximation is made in the Green´s function formulation. In addition, the Green´s function is formulated in a way to increase the numerical efficiency in MoM applications.