A polar electro-optic response is observed in droplets of an achiral nemati
c liquid crystal in coexistence with the isotropic phase. Between crossed p
olarizers each pancake-shaped droplet shows extinction brushes in the form
of a centred cross aligned with the polarizer axes. An applied electric fie
ld E induces a rotation of the crosses about the field direction, with abou
t half the droplets switching clockwise and the other half anticlockwise. T
he sense of rotation in each droplet changes when E is reversed. We propose
that a twisted bipolar director structure is stabilized in the droplets by
a relatively large splay elastic constant and tangential boundary conditio
ns. The molecules twist along the diameter of the droplets, perpendicular t
o the applied field, which results in a linear rotation of the director by
the inverse flexoelectric effect. Since the molecules are achiral, the hand
edness of the twist, and hence the sense of the switching, in any droplet i
s arbitrary.