TABLE OF CONTENTS The immittance approach was introduced in [1.6] in order to simplify the quite tedious procedure of field matching at the interfaces in multilayer structures. It is easily described by following the approach suggested in [16, 26]. It essentially consists in an eigenfunction expansion plus a suitable choice of coordinate. As such, this is another interesting application of the procedure described in eigenfunction expansion in more dimensions, applied to the case of a multi-layer planar dielectric structure, as shown in Figure 2.37. We have already found in Section 2.5.2 that we can analyse the problem of a multilayer in the y-direction in terms of Hertzian LSE and LSM potentials with z-dependence of the type exp( j ?z). On that occasion, this choice was motivated by the fact that we were considering modes propagating along the dielectric interface in the z-direction. However, by using the previous considerations on the eigenfunction expansion, and by noting that exp( j ?z) is the eigenfunction in the z-direction, we can look at this as the first step in finding a solution, by eigenfunction expansion, of the Helmholtz equation for the structure of Figure 2.37.
Let us thus consider the LSE field, here repeated for convenience
| (2.388) |  |
In a similar manner, we may also consider an eigenfunction expansion in the x-direction. In this case eigenfunctions are of the type exp( j ?x). Upon inserting this dependence in (2.388) one...
