176 BELL SYSTEM TECHNICAL JOURNAL 



In terms of two index symbols 



zlo = 4o + mpqdopip, q = 1 to 6; = 1 to 3) (69) 



where a repeated index means a summation with respect to this index. 



Finally the photoelastic effect is sometimes expressed in terms of the 

 stresses rather than the strains. As can be seen from equation (47), the new 

 set of constants is 



TTpg = niprSrq (70) 



where the Srg are the elastic compliances measured at constant electric dis- 

 placement. 



V. Birefringence Along Any Direction In the Crystal and 



Determination of the Electro-optic and 



Photoelastic Constants 



If we take axes along the Fresnel ellipsoid when no stress or field is ap- 

 plied to the crystal, the result of the electro-optic and photoelastic effects 

 is to change the impermeability constants by the values 



(71) 



^11 = /3i + Ai ; /322 = ^2 + As ; /333 = ^3 + A3 

 /323 = A4 ; |8i3 = As ; I3n = Ag 



where 



Ai = ZnEi + 212^2 + ZnEs -f mnSi + mi252 + Wi3'S'3 + muSi 



A2 = Z21E1 -\- Z22Ei + ZnEz + moiSi + nhiSo + W23'S'3 + m^iSi 



+ ^2555 + nh^i 



A3 = ZziEi -f 232^2 + ZizEz + mziSl + W^32'S'2 + W33^3 + m^^i 



A4 = ZiiEi + 242^2 + Z43-E3 + niiiSi + mioS2 + MizSz + ^44^4 



A5 = Zf,iEi + 252^2 + 253-E3 + m^iSi 4- m52S2 + m^sSs + ni^iSi 



-f- Ws&S's + WbeSe 



Ae = ZuEi. + 262^2 + 263£3 + m^iSi + ^62^2 + m^zSz -f triuSi 



+ nhbSb + nh^Se . 



If we transmit light along the 2' axis which, as shown by Fig. 2, makes an 

 angle of 6 degrees with the 2 axis in a plane making an angle <p with the xz 

 plane, the birefringence can be calculated as follows: Keeping z' fixed and 

 rotating the other two axes about 2' by varying the angle ^, one light vector 



(72) 



