GUIDED WAVE PKOPAGATIOX THROUGH GYKUMA(;\ETK' M1:DI A. 11 957 



where 



and 



5 = - 



€o V^2 _ ^^'. 



6Mo 



Wo shall assume that we are dealing with slow waves (/3 large), 'i'liis 

 is the case of greatest practical interest and is usually ensured by making 

 cot yp large. Assuming that the waves are slow we simplify the equation 

 (12) and find certain values for ^3. We may then ascertain in what ranges 

 of a and p the simplifying assumptions and the results are consistent. 



In equation (17), then, we replace all square roots by | |8 | and /3 — /3o 

 by /3', obtaining 



.2 .2 , A + tanh \^\xo 1 - B 



00 cot xf/ - 



with 



and 



A -\- 1 1 - B tanh | ^ | rco ^ 



Meff/Mo M + '^ sgn /3 



1 — Ph sgn /3 Mo 



B= -el 



fo 



where sgn /3 = 1 for jS > and sgn ,3 = — 1 for jS < 0. Taking first the 

 simplest case of no separation (.ro = 0), this becomes 



2 ^ |8o"(l + e/eo) cot' ^ ^ i3o'(l + e/ep) cot" i/ ' 

 1 _(_ 1 - Pg Sgl^ /3 -^ _j Mo 



Meff/Mo M + '^' Sgn /3 



Substituting the expressions (G) and (1) for Meff/Mo and pn we arc led to* 



^+ = /3o cot v^. /^l (1 + e/eo) //^^pyq=^ ' ^^^^^ 



^_ = -/3o cot ^. /^\ (1 + .Ao) // /_~//^^^ (18b) 



* Since reversal of the magnetization is equivalent to inlerchanji;e of the 

 propagation directions, we are at liberty to consider a and p always i)ositive, and 

 to deal with the two cases /3 >0 and jS < separately. 



