GUIDED-WAVE PKOI'AGATIO.X TIIUOUGII GYKOMAGNETIC MEDIA G39 



sum of right and left circular components which travel with different 

 propagation constants. If these are l3+ and 0^ (measured in units of ,^0) 

 the plane of polarization of the resultant will appear to rotate by 



(/3+ — |S_)/2 radians per reduced wavelength r- = — - . 



27r Po 



In the filled waveguide, on the other hand, it is no longer true that right 

 and left circularh- polarized modes add up to a plane polarized mode, 

 as is readily seen by reference to the field components gi^•en in Appendix 

 IV. To define Faraday rotation in a simple way it is therefore necessary 

 to neglect changes in the field pattern due to the magnetization and 

 consider only the changes in the propagation constants. Then the rota- 

 tion of a mode with azimuthal mode number n will be ~ (^+ — ^-). 



In the present case n ^ 1, and the jS+ , fi- are found from the curves of 

 /3' versus a, Figs. 13(a) to (i), for positive {a, p) and negative {<t, p) re- 

 spectively. 



The merit figure is defined as the ratio — radians rotation per neper 

 loss — and is independent of path-length. For small losses, (neglecting 

 terms 0(a~)), this ratio is 



/?/(/?+ - /3_) _ 1 /3+' - /?_' 



d \(t\ d \ a \ 

 in the notation of the present Section. 



4.10. Formulae for the jer rite. 



I. Cut-off points 



Cut-off points will be classified into three types, 1, 2 and 3, according 

 to the nature of the intersecting curves which generate them. All points 

 of a given tj^pe may be assigned an index which further identifies the 

 generating curve. This will be written as a subscript. 

 Type 1. Intersections of 7„ — {Ia')t , <r > 0, written as 1„ and of 

 In — (Ia)t , a < 0, written as 1/ 

 /3^ = 

 There is a parametric representation: 



(46) 



