GUIDED WAVK PROPAGATION' TIlHorCII (!YHOM AGXKTIC MKDIA. Ill 11 11 



where r = (.r, y), a is a constant vector and the coorchnate system has 

 its origin at the centre of the rod. Continuity of tangonlial // at Iho sur- 

 face of the rod requues 



H, 



H i,n + 



n' 



and then 



$out = Htm-r + 4 (^'"'O - Htm)-r. 

 r- 



The normal derivative at the surface of the rod is 



or, externally, 



n 



1 3$ , a$ 



- .(• — -r y — 

 fi [_ dx dy_ 



[Htm-r — {Htmo - Htm)-r]. 



^Matching the normal B's at the surface then gives 



jUo[2 Htm — Htmo] = tJiHtmO — j nH t. 



or 



n tmQ — 



2mo[(/X + lJLf^)Him + JKHtm*] 

 (n + Mo)- — K^ 



(10a) 



In a similar manner, one would find if the dielectric constant of the rod 

 were e. 



EtmO — 



2eoEtm 



e + Co 



(10b) 



The longitudinal fields E^m and H^m are unchanged wdthin the rod. 

 Turning now to the expression (9) for 5/3, Ave have in the present-case. 



80 = --^ [ dS 



■^Za»« •'pencil 



'260(6 - 6o) 



e -\- €o 



1 Etm I' + (6 - €o) I E, 



+ 2mo 



M 



Mo 



Ht,n \' - JK 



4iU0 



HtJHt 



(m + Mo)- — K- ' ^"" ' ■' (m + Mo)^ — K^ 



where we have anticipated that Am is real, which we A'erify below. 

 Since the integrand is constant the integral may be replaced by tt/'i 

 times the value of the integrand at r = 0. We consider now a TE-mode 



