GTIDKD WAVK I'HOPAGATIOX THROUGH GYHOMAGXKTIC MKDIA. HI I 1 .")8 



Thus all modes have to be iucliuled in the problem, which conse- 

 quently takes the form of an intinite system of linear equations for the 

 mode amplitudes. This can be solved only to some approximation whose 

 general \alidity it would be hard to establish. The problem could also 

 be stated as an integral equation iiivoh-ing a complicated Green's func- 

 tion, with no greater chance of complete solution. 



AVe are therefore forced to restrict the problem to the ranges of mag- 

 netization, or of sample size, in which perturbation theory is applicable. 

 However, we begin with a discussion of the infinite, plane, loss-free slab, 

 a problem which can be solved completely, and which has some bearing 

 on the perturbation problem for a slug of ferrite whose cross section 

 completely fills the waveguide. 



Let the plane boundaries of the slab be normal to the 2-axis, which is 

 also the direction of magnetization and the propagation direction of a 

 circularlj^ polarized wave incident on the boundary z = (see Fig. 4). 

 In terms of the parameters p and a of Section 2.1, Part I, the effective 

 permeability' for a circularly polarized wave is 



fJL ± K =^l = /Xo(l± 



P 



1 ± (7 



the upper sign referring to right circular polarization. The correspond- 

 ing propagation constants in the slab are then 



/3± 



= coVeMoy 1 ± Y^a 



Fig. 4 — Normally niagnotizod foirite slab. 



