THE FLEXOELECTRO-OPTIC EFFECT IN CHOLESTERICS

The flexoelectro-optic effect in short-pitch cholesterics [1] is analy sed in terms of applied electric field strengths and material paramete rs such as the two flexoelectric coefficients e(s) and e(b) and the th ree elastic constants. Starting from the free energy density of the un iformly lying-helix (ULH) configuration, including the flexoelectric p olarization term, the equation describing the field-induced tilt angle of the bulk optic axis is derived. It is convenient to introduce the flexoelectric 'anisotropy' Delta e as the difference between the splay and bend flexoelectric coefficients, hence defined by Delta e = e(s) - e(b). Our results then show that Delta e is the essential material p arameter controlling the sign and magnitude of the electrically induce d tilt. In the region of linear approximation, the tilt is proportiona l to Delta e and to the electric field E, and inversely proportional t o the helical wave vector It, as well as the effective elastic constan t (K-11 + K-33). The individual values of the elastic constants K-11, K-22 and K-33 do have an influence on the magnitude of the effect, but not on its linearity. The Delta e dependence conforms in the simplest way to the physical requirement that the flexoelectro-optic effect mu st be particularly pronounced in the case that e(s) and e(b) are of op posite sign.