OPTICAL PROPERTIES IN CRYSTALS ll9 



urement than a birefringence measurement and requires the use of an ac- 

 curate interferometer. 



If, however, the Z axis is an optic axis as it is in ADP, for example, and 

 I Ai = A2 = 0, a birefringence occurs due to the term ^n . As shown in the 

 next section, the electro-optic constants for ADP (tetragonal 42w) are Zi\ 

 and 063 • 063 occurs in the expression for /3i2 = Ae , as can be seen from equa- 

 tions (72), and hence the birefringence along the Z axis is 



3 

 B^ = yx2/3i2 = nlzesEs. (81) 



The constants ^es and Zn have been measured independently by W. L. Bond, 

 Robert O'B. Carpenter, and Hans Jaffe. Probably the most accurate meas- 

 urements, and the only one published, are those of Carpenter,^ who finds 

 that the indices of refraction and the ^63 and 2:41 constants for ADP and 

 KDP are in cgs imits 



f^a Me ''63x10'' ^4jx10^ 



ADP 1.5254 1.4798 2.54 ± 0.05 6.25 ± 0.1 

 KDP 1.5100 1.4684 3.15 ± 0.07 2.58 ± 0.05 



An even larger constant has been found for heavy hydrogen KDP by Zwicker 

 and Scherrer.® They find at 20°C that res = 6 X 10"'^. Using this constant, a 

 half wave retardation for a X = 5461 A° mercury line occurs for a voltage 

 of 4000 volts. 



For tetragonal crystals of these types the only photoeleastic constant for 

 the z axis is mm , and the birefringence for this case is given by 



Bz = MaWee^e (82) 



When a natural birefringence exists for the crystal, measurements of the 

 other three effects A4 , As and Ae can be made by determining the bire- 

 fringence along other directions than the Fresnel ellipsoid axes. In a direction 

 of Z' lying in the XZ plane <p — 0, 9 — variable and 



J, _ ^'\ /[(/3ii - 1322) cos2 e + (/333 - (822) sin2 6 - /3i3 sin^ d]^ /..n 



"' ~ 2 y + [2i8i2 cos d + 2fe sin d]\ ^^-^^ 



When a natural birefringence exists, this reduces to 

 l'.y = ^ { -2 - -1 + Ai - A., ] cos' 9 



2 L\Ma Mb / 



+ (—-— + A3 - A2 ) sin' ^ - As sin 29 



(--- 



I 2 — 2 



Vc M6 



_ (84) 



5 "The Electro-optic Effect in Uniaxial Crystals of the Type XH!jP04 ," Robert O'B. 

 Carpenter, Jour. Opt. Soc. Am., in course of publication. 



^Zwicker and Scherrer, Helv. Phys. Acta., 17, 346 (1944). 



