Em = Dne' 



OPTICAL PROPERTIES IN CRYSTALS 175 



better designation for these effects is the electro-optic effect at constant 

 strain and stress. 



This latter effect can be calculated from equation (47) by setting the 

 stresses Tkt equal to zero and eliminating the Sij strains. After neglecting 

 second order corrections, 



„S lis I fnijmnnoki\ t^O { AC\\ 



?mn + I r„,no + T, ] ^o\- loUj 



Since houdcljkt = gon, the other piezoelectric constant relating the open 

 c ircuit voltage to the stress, the electro-optic effect at constant stress can be 

 written in the form 



T _ .S , mijmn goij /^|N 



• mno ' mno 1^ . • \^' ' / 



47r 

 Tn terms of the two index symbols 



r; = rto + ''-^ (62) 



47r 



since it has been shown^ that goo = gop/2 when i 9^ j, and the tensor in (61) 

 has ij as common symbols which involves the summations of two terms. 



The electro-optic effect is usually measured in terms of an applied field. 

 The change in the impermeability constant (3mn for this case can be de- 

 termined from the first equations (47), setting Tkf equal to zero and neglect- 

 ing second order terms. Multiplying through by the tensor Kop of the di- 

 electric constants 



Dl = ElKl, (63) 



since the product Kopl3op = 1- Introducing this equation into (58) we have 



Em = Dnl^L + rinpKopEl] = Dn[(3L + zLoEl]. (64) 



where the new tensor 2^710 is equal to 



S _ S T^T /z-rx 



^mno 'mnp^op • V"'^/ 



In terms of the two index symbols 



4o = rqpKop . (66) 



in which the repeated index indicates a summation. The difference between 

 the electro-optical constant at constant stress expressed in terms of the field 

 and the electro-optical constant at constant strain is 



T _ S 1^ fftijmngoij j^.T _ ^S , j ( (:ii\ 



■^mno — Zmno I ~, ^op — ■^mno "T ''lijmn '^ pij \^ > J 



47r 

 since the piezoelectric constants dpn are related to the g constants by the 

 equation 



d^,j = S^a^, (68) 



47r 



