Optical Properties and the Electro-optic and Photoelastic Effects in Crystals Expressed in Tensor Form

T HE electro-optic and photoelastic effects in crystals were first investigated by Pockels,1 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 suggested2 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 1010 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 stroboscope 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.