GUIDED WAVE PUOI'AGATIOX TllKOfCIl GYHOMAGXETIC MEDIA. Ill IIC)') 



tions by VVs or ViAs and iiitognitiiig over the cross-section. It i.s then 

 found that the transmitted ampUtude of the ?i*'' mode is 



Tn3 — 2yrnZ„ 



where 

 and 



{Zr + ^«)(cos dn - COS dr) + i(l + Z^Z,) (sjii g„ - sjn Or) 

 (2Z„cos0„ +j{Zl + 1) sin0,.)(2Z,cos0, -\-j{Zj + l)sin0,) ' 





Pn'-rn 



iSn - m 



The perturbation theorj^ just outlined assumed a guide closely fitted 

 A\ith a slug of ferrite of finite length, and slightly magnetized. The per- 

 turbation consisted in the small changes in permeability. Here we treat 

 another kind of perturbation in which the ferrite does not fill the guide 

 completely', and in which the magnetization can be arbitrarily large, 

 but the sample is a thm lamina, mounted normally to the guide axis 

 which only slighth^ perturbes the field pattern. Its shape can then be 

 considered arbitrary; its thickness will be assumed^ uniform and very 

 much smaller than a wavelength in the material. 



Under these conditions, the equations for the perturbed amplitudes 

 of the right-circularly polarized n radial mode are 



— + J/3„6„ = J -r- 



dz An 



dbn I .„ .CO 



I (m - fJio)HtH,n dS -j f KHt*Htn dS 

 + |(e - eo)E,-E.ndS 

 f (e- eo)ErEtnds], 



(30) 



in the usual notation. The terms on the right are assumed different from 

 zero only in the range z, z -\- 8z occupied by the sample, and the integrals 

 are extended over the cross section of the sample only. Eu , Htn are the 

 mode functions for the empty guide. The fields Ht , Ei , E^ are the actual 

 fields inside the sample. For the first-order calculation Et and Ht are 

 identical A\ith the incident field and E^ (by continuity of the normal 



component of Dg) is — times the incident Eg . Now the incident fields may 



e 



