1176 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1954 



ponents were given there, and it is of some interest to examine numeri- 

 cally or graphically the distribution of E and H. Since all field compo- 

 nents vary (in complex notation) as g^("^+"'^^ with ?i = 1 in the present 

 case, it is clear that the field patterns are stationary in a system rotating 

 with angular velocity, — w. Writing $ for the angular variable, 6 + o^t, 

 in this system, one finds the following formulas : 



where 



E^ = -^_sin2$, 



Ey = £■_ COS 2$ + £■+ , 



Ez = Eo cos $, 



H, = H- cos 2$ + //+ , 



Hy = //_ sin 2$, 



Hz = Ho sin $, 



Er = (E+ - E_) sin $. 

 Ee = {E+ + ^_) cos <!>, 



Hr = {H+ -f //_) cos $, 

 Hg = (H_ - H+) sin $, 



(46) 



^_(r) = 



(h 



2xi«/i(Xi^o) 



1 

 Xi 



J2{xir) 



Ml- 



2xiJi{xin) 



1 + 



H-{r) = -- 



1 — Xi 

 Xi 



2xi/i(xiro) 



J2(xir) 



(47) 



1 + 



1 — Xi 



^o(r) = 



2xi^i(xiro) 

 Uxir) 



^ /o(xir) - 



^i(xiro) 



Hoir) = -y^^^^'^ 



Xi JKxi^o) 



The terms in square brackets are in each case the same as the cor- 

 responding unbracketed terms, X2 and X2 replacing Xi and xi • The ciuan- 

 tities £"+ and E^ are the amplitudes of the left-handed and right-handed 

 components of circular polarization into which the transverse £'-field 

 may be resolved at each point. i/+ and i/_ have a similar significance 



