GUIDED WAA'K PROPAGATION THROT7GII GYK( )MA(;\1:T1C iMlODIA. lit I 1 17 



Within the dielectric, since all fields are hounded at r = 0, both E, and 

 If, are proportional to ./i(air) and, e\identl3', 



in the notation of Part I. (E^)o and {H^)q , similarly, Avill be those two 

 Hnear combinations of Ji(aor) and Yi{aor), which, respectively, vanish 

 and have zero normal deri^'ative at r = ro , in order to ensure the van- 

 ishing of the tangential fields there. The functions 



r d(H.), , r d{E.)o 



and 



(^.-)o dr '" iE,)o dr 



Avill be called //(aor) and G(aor) respectively. 



Eliminating E~{ri) and H,(ri) from equations (15) we obtain the char- 

 acteristic equation of the problem in the form 



an- ar/ \ a^- ao /\ «r "o" 



The perturbation in the present problem is that due to a mild mag- 

 netization of the rod and referring again to equation (9) we have (in 

 unsealed units) 



5/3 = 



5^ = -K^ f [(m - f^o)HfHt - JKH,*-ff,] dS, 



•'rod 



A„ = f E*-IJtdS. 



"guide 



;m, 

 t Jo L\Mo / Mo 



2A 

 ^^•ith 



'guide 



Thus, in the scaled system, 



t*-Htrdr 



'0 



JO 



(16) 



The evaluation of the normalizing integral in the denominator is an ex- 

 ceedingly tedious business and it seems advisable to avoid it. This may 

 be done in the following manner. The characteristic equation has been 

 solved for numerous values of Vi and ^ may be considered to be a reliably 



dB 

 known function of Vi . In particular the slope -p- is knoAvn. But we may 



dri 



dB 

 also deduce -y- , by a perturbation calculation in ^\•hich we start "with a 

 dri 



