GUIDED WAVE PROPAGATION THROUGH GYROMAGNETIC MEDIA. Ill 1150 



and expanding equation (18), we obtain 



where ^ is defined by 



cosh '^ sec^ do — ° sinh ^ 



^0 



1 + cosh2 ^ tan2 ^o 



a =/«/- = e* 



Co 



[This result holds even near do = (n -\- 3^)x where tan do = ^o , as can 

 be seen by expanding the reciprocal of equation (18).] The quantity 

 }4do{8x+ — 8xJ) is the rotation corresponding to a single trip through 

 the sample. The actual rotation is M(5$+ — d^-). Hence we may define 

 a rotation gain as the ratio 



^9o{8x+ — 8x^) 



, ^ 2 ^ tan 00 . , T ^^^^ 



cosh ^ sec 00 — — - — smh ^ 



1 + cosh2 ^ tan2 Bo 



In many cases, 0o » 1, that is, the thickness of the sample is much 

 greater than a reduced wavelength in the specimen. Then the second term 

 in the numerator of gr is always negligible compared with the first, g then 

 simplifies to 



cosh ^ 



gi = 



cos^ do + cosh^ ^ sin^ do 



This expression is plotted in Fig. 6 as a function of d for various a = e*. 



For given ^ it has minima equal to — -. — at do = [ n-\- - I tt, and max- 



cosh ■^ \ 2/ 



ima equal to cosh ^ at 0o = nirin = 0, 1,2, • • •). When a » 1 (a '^ 3 



for many ferrites), cosh ■^ is replaced by }^e = }/2^, and then 



1 

 _ 2 



ylmin — 



a 



It is to be noted that when d = nir, the condition for maximum gi , 

 the unperturbed reflected amplitude is zero, and the elhpticity vam"shes 

 to first order in 8x. 



