946 THE BELL SYSTEM TECHNICAL JOUKNAL, JULY 1954 



When the condition, d/(dij) = 0, is put into Maxwell's equations the 

 latter are found to be separable into two sets: 



-^-^^jo^eE., (2a) 



oz 



^' = >e£., (2b) 



dx 

 dz dx 



— jc^noHy , (2c) 



and 



- — -^ = - jco[/x//x - jkH,] , (3a) 



dz 



^^= -jc.[>//.+ m//J, (3b) 



dx 



dHx dHz J-, frf\ 



dz dx 



It is to be stressed that such a separability is possible only when the rf 

 fields do not vary along the dc magnetic field. The sets of equations (2) 

 and (3) correspond to the separate equations for H, and E, which arise 

 from (13) of Part I when /3 is there set equal to zero. The first set de- 

 scribes a TM field of the familiar type, whose propagation through the 

 medium is unaffected by the magnetic field. The second set describes 

 a TE field whose components, because of the presence of k, are con- 

 nected by different relations from those which exist in an unmagnetized 

 medium. The separability of the two fields is equivalent to saying that 

 they are not coupled by the medium itself, but they may, of course, be 

 coupled at the boundaries. 



We may write (3a) and (3b) in the form 



• / 2 •2\TT ■ ^-^y ^-^y f 1 N 



- ja)()U - K )Hx = JK—- - ^x—- , (4a) 



dx dz 



- JC0(m - K )Hz = /X-— + JK—- , (4b) 



dx dz 



and upon eliminating H^ and H^, , the wave equation for Ey is found to be: 



d'Ey d Ey 2 f^' — K' „ ,.. 



-V^ + -^^ + ^ t Ey = 0, (o) 



dx- dZ' ju 



where Ey (and also the H's) are evidently propagated in the ferrite as 



