optical Properties and the Electro-optic and Photoelastic 

 Effects in Crystals Expressed in Tensor Form 



By W. p. MASON 



I. Introduction 



THE electro-optic and photoelastic effects in crystals were first investi- 

 gated by Pockels,^ who developed a phenomenological theory for these 

 effects and measured the constants for a number of crystals. Since then not 

 much work has been done on the subject till the very large electro-optic 

 effects were discovered in two tetragonal crystals ammonium dihydrogen 

 phosphate (ADP) and potassium dihydrogen phosphate (KDP). With these 

 crystals light modulators can be obtained which work on voltages of 2000 

 volts or less. Their use has been suggested^ in such equipment as light valves 

 for sound on film recording and in television systems. Furthermore, since 

 the electro-optic effect depends on a change in the dielectric constant with 

 voltage, and the dielectric constant is known to follow the field up to 10^" 

 cycles, it is obvious that this effect can be used to produce very short light 

 pulses which may be of interest for physical investigations and for strobo- 

 scopic instruments of very high resolution. Hence these crystals renew an 

 interest in the electro-optic effect. 



In looking over the literature on the electro-optic effect and photoelastic 

 effect in crystals, there do not seem to be any derivations that give them 

 in terms of thermodynamic potentials, which allow one to investigate the 

 condition under which equalities occur between the various electro-optic 

 and photoelastic constants. Hence it is the purpose of this paper to give such 

 a derivation. Another object is to give a derivation of Maxwell's equations 

 in tensor form, and to apply them to the derivation of the Fresnel ellipsoid. 



The first sections deal with the optics of crystals, and derive the Fresnel 

 cHipsoid from Maxwell's equations. Other sections give a derivation of the 

 two effects, discuss methods for measuring them by determining the bi- 

 refrigence in various directions and give the constants for the two effects in 

 terms of crystal symmetries. The final section discusses the application of 

 the photoelastic effect for measuring strains in isotropic media. 



' F. Pockels, Lehrbuck Der Kristalloptic, B. Teubner, Leipzig, 1906. 



- See Patent 2,467,325 issued to the writer; "Light Modulation by P type Crystals," 

 (ieorge D. Gotschall, Jour. Soc. Motion Picture Engineers, July, 1948, pp. 13-20; B. H. 

 Hillings, Jour. Opt. Soc. Am., 39, 797, 802 (1949). 



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