129G THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



\_ 2 Jo dz 



4 Jo dz Jo dz" 



w,iz) = e-"''' [wM - ^ wM £ ^ e""''' dz' 



(6) 



in which 



p{.z) = f T{z') dz'. 

 Jo 



The initial conditions in the normal mode taper are £"1(0) = 1 and 

 £'2(0) = 0. The taper begins with zero curvature, ^(0) = 0. Hence from 

 (3) tUi(O) = 1 and w^2(0) = 0. The wanted local normal mode is Wi while 

 W2 is an unwanted mode. At the end, Zi , of the taper the unwanted mode 



^7 



< >' 



Fig. 1 — Normal mode bend with linear curvature taper. 



