1162 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1954 



which, again to first order, equals 



mn 



^l - &i 



Pmm . (24) 



One of the quantities pmm , qmm , is still arbitrary. If it is required that 

 the perturbed field is, to zero order in 7^„ , normalized to the same value 

 as the unperturbed field, it is readily found that one can take 



_ 1 _ i3m 



Pm 



We are now in a position to consider the problem of a right circular 

 mode, say the r*^, incident upon the end plane, 2 = 0, of the ferrite cylin- 

 der extending to z = d. One simplifying feature of this problem is that 

 the unperturbed modes inside, and the modes outside, the sample have 

 the same dependence on radius since the sample fills the whole guide- 

 cross-section. However the modes inside and outside may have different 

 numerical coefficients. Thus, if we distinguish quantities outside the 

 sample by primes, the TE^r mode can be represented outside and inside 

 the sample by 



/ Pr Sgn iS'r ^ , 



coMo 

 /3r Sgn I3r ^ 



Here sgn /S means: sign of the propagation direction, +1 and —1 for 

 forward and reverse respectively. The function \{/sr is given by 



where <p is the azimuthal angle, tq the guide radius, and iir the / zero of 

 J/(x). Tor TM modes we have similarly 



H,^^ = -^°(A*V..)sgn^., 



Pr 



H,^^ = -^^ ( VV«.) sgn ^r , 



Pr 



