56 



BELL SYSTEM TECHNICAL JOURNAL 



For isotropic bodices, the tt matrix is formed by setting tu = (xn— 7ri2) 



in the x matrix of the cubic system; the m matrix is similarly formed by 



... nin — mn 

 puttmg mu = . 



Isotropic 

 bodies 



xii TTn TTia 



Xl2 Xu Xl2 



Xl2 Xl2 Xll 



X11-X12 



X11-X12 

 xn-xi2 



The m matrix has 



mn—mn 



mu etc = 



2 



(18.16) 



SECTION 19 

 Application of the Electro and Piezo Optical Effect 



In the equations K = K -\- zE and K 



K 



'^° + mE, etc. the K''^'s 



are to be used in forming k for the equation giving the velocity of the light 

 used namely —— ic^ J- Obviously then A' should be formed from the 



squares of the reciprocals of the refractive indices, the lower three members 

 being zero. After applying the electric field or strain a transformation of 

 coordinates may be necessary to rediagonalize, i.e. make A'7' = Ki^ = 

 KJ = 0. From the rediagonalized K" we may write the new principle 

 refractive indices by taking the reciprocals of the square roots of Ki^ , 

 Ki and KJ . 



It should be noted that if A, — Ki + A, then 



+ A/ii 



HiS 



A.- 



(19.1) 



For a given direction of the wave normal there are two velocities, a wave 

 splitting into two components traveling with different velocities. By defini- 

 tion the refractive indices, Ha and /X5 in a given direction are the normal 

 velocities in that direction divided into the velocity of light in free space. 



Whence in a path length / there are — ^ waves in one component and — - 



A X 



waves in the other, where X is the wave-length in vacuum. Consequently if 



/ is the thickness of the crystal along that path the two components can 



recombine after passing through the medium but they are out of phase by 



7 = - (mc — Mfc) whole waves so that the light which entered as plane polar- 

 X 



ized will leave elliptically or circularly polarized, except when 27 is an integer. 



