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BELL SYSTEM TECHNICAL JOURNAL 



where Ka are the dielectric constants measured at optical frequencies and 

 /3yt are the impermeability constants determined from the relations 



where 



(15) 



and A^* the determinant obtained by suppressing the/ row and t* column, 

 we can eliminate Ei from equation (12) and obtain 

 2 



Tr^D2 = ^12 Di + ^22 D2 + (32zDz 



(Ej nj)n2 



y^ Dz = pnDi + /323l>2 + 033 Dz - {EjnjW 



This can be put in the form 



{Ejnj)ni = D,\fin - i^l^X + ^12^ + ^izDz 

 (Ejnj)n2 = ^i2A + 0322 - v^/V')D2 + (SizDz 

 {Ejnj)nz = /3i3A + 1823^ + (^33 - v^/V')Ds. 

 Solving for Di , A and Dz 



D, = [(^22 - t;VF2)(^33 - V^/V') - As][Ejnj\n, 

 D2 = [(^u - vyV'){^zz - vyV') - 0U[Eini\n2 

 Dz = [(^n - ^VF2)(^22 - vyV') - ^iME^nz- 

 Now, since D and n are at right angles, 



A«i + D2ih + Dziiz = 0. 

 Hence, 



= [(/322 - t'VF)(/333 - ^VF) - /3L3]«1 



+ [(/3n - ^Vn(/333 - ^VF) - ^i3]"2 



(16) 



(17) 



(18) 



(19) 



(20) 



+ [(|Sn - t'Vn(^22 - vyV'~) - fnWz. 



