MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 51 



By means of the identity 



/ -1 -K -1/ s -1 



{u — V ) = —u {u — V)V 

 since 



the idemfactor can be multiplied into an adjacent matrix giving 



=0-0=0 

 so that/ andy" are mutually perpendicular. 



SECTION 17 



The Electro-Optic Effect 



The velocity of light in a crystalline medium is a single valued function 

 of the unit current vector j 



-J =Jck J (16.11) 



where c is the velocity of light in vacuo and k is the dielectric matrix, also 



j = b where Z) is -r . 



We developed the induction as a linear function of the electric field, 

 deriving the relation: 



47rD = kE (6.1) 



If the induction is not a linear function of the electric field we can improve 

 on eq. (6.1) by adding second order terms: 



AirDi = kiiEi + ki2E2 + kizEz + kiiE\ + ki2El + k^El 



+ I hi^EiEz + I hiiEzEi + . . . ^ hi^xE^ 

 or 

 AirDi = {ka + //a£i + \ Ih.E. + ^ hi^s) Ei 



+ (^,2 + I /^,6£i + h,2E2 + \ hi^z) £2 



+ (^,3 + \ h,^i + i hiiE2 + hisEs) £3 (17.1) 



