GE.NKUALIZKD TKLl'XJ KA I'IIIST's EgUATIUN'S 799 



rr rr -l.')\/Z • T I I /I / \2l — 1/'' 



OTT" 



^(12) [10] = .^[111] (12) = .^(21) [111] = •^[01] (21) = 0. 



'llir principiilc^tTet'iol'tlic ji>r()iiuij2;iu'ticnuMliunic)ii theTE|ioi aiidTKioi] 

 modes may be understood by taking into account their mutual coupling 

 hut ignoring thcii- coupling to other modes. The e(iuations of propaga- 

 tion become 



dVm 

 dz 



dI[io] 



—jwnf [10] — Ja;/Xx.v(8/7r")/[ui] 



= - {J^e+ .^— - V 



[10] , 



ds \ jionzzd^ 



= i'^Mi.v(8/7r")/[io] — iw/i7[oi] , 



d\ [01] 



((il) 



dz 



= - ( jwe + ) F[oi] 





dz \ J^iJ-: 



For exponentially propagated waves we have 



l'^[io] = F[io]e ", F[oi] = F[oi]e , 



J [10] — i[10]C , -t [01] — i[01]C 



(02) 



When the mutual permeability is zero, we have two independent modes 

 whose phase constants are 



(2\l/2 / 2\l/2 



wVe - 5 ) , /3oi = ( wVe — — r? ) • (03) 



The phase constants of the pertiu'bed modes may be expressed in terms 

 of the unpertiu'bed constants and the coefficient of coupling. When the 

 losses are neglected, the mutual permeability is a pure imaginary. In 

 this case it is con\-enient to define a real coupling coefficient 



k = ^^ . (64) 



Substituting from (62) in (61) and using (64), we find 



/3F[10] = WM^IlO] — ,/COyu/>"/[01] , (8/[10] = ( COe — )F[10] 



|8F[oi] = jcciJ.J:I[io] + w,u/[oi] , j8/[oii = ( we — r- i v [oi] 



(jiyizzO-/ 



(65) 



