The Jones matrix calculus is applied to an electro-optic crystal with uniaxial symmetry when the light beam is incident nearly normally on the crystal face. The approach allows one to treat refracted waves and rays that diverge in the crystal and are modulated by an external low-frequency field. The effect of partial interference of overlapping refracted beams is allowed for and calculated for the case of uniform intensity of the beam over its cross section. The method is employed to analyze optical systems containing an imprecisely cut and aligned electro-optic crystal plate.

Taking KDP as an example of a uniaxial crystal, we analyze contributions to its quadratic electro-optic response with a view to explaining differences in published values of certain quadratic coefficients. In an eigenvalue theory of light propagation we show that the linear electro-optic coefficient contributes to the quadratic response, even under ideal laboratory conditions. In addition, the effect of imperfect crystal cutting and alignment is investigated by means of computer calculations based on the Jones calculus. It is found that, for relatively small inaccuracies, the calculated values of the quadratic coefficient $g_{\mathit{xyxy}}$ are approximately two orders of magnitude greater when measured with a static field than with a dynamic one. This finding could explain the observed spread in some results for KDP-type crystals.

Certain optical properties can be described in terms of two linear birefringences existing in separate Jones platelets of a medium. One of these, known as Jones birefringence, although occurring naturally in some crystals is too small to be measurable. However, the two birefringences can be induced by an electric field in $\overline{4}$ and $\overline{6}$ crystals for propagation along the optic axis. For an even slightly divergent light beam, natural birefringence may affect accuracy of measurement. Calculations show that in an experiment with a static field the error depends critically on beam divergence, whereas with a modulated field this is not so.

Electro-optic coefficients can be defined in terms of the changes, which result from an applied electric field, to components of either the impermeability or electric susceptibility tensors. In this paper exact relationships are derived between electro-optic coefficients defined in these two ways for powers of the field up to four. Previously known approximate relationships are also discussed.

In this paper we investigate the dielectric response of cured epoxy resins based on biphenyl group. We chose two monomers, which were earlier synthesised, containing the same mesogen but with long and short symmetric tails. They were cured with standard amines (DDM, DMAP). Firstly we optimised conditions of the curing process by dielectric and optical observation in situ. Small differences in the dynamics of the curing process were observed in different mixtures. For the four selected products we made dielectric measurements in a wide range of frequency and temperature. Although, generally, dielectric response is similar in all the cured materials, differences can be seen in the details. At lower temperatures, quite strong relaxation process is seen in all products, its low activation energy points towards a β-process, which appears in many polymers. The Havriliak-Negami formula was fitted to the data and characteristic parameters of the observed relaxation processes were compared in detail. In some cases the α-process also appears. We conclude how the longer spacer and the type of curing process influence the electrical properties of the resin.