Computer calculations of refractive indices in orthoconic SmCA *. Is it possible to obtain “isotropic” antiferroelectric liquid crystal (IAFLC)?

Orthoconic antiferroelectric liquid crystals (OAFLC) are promising materials for applications. The saturated value of the tilt angle for such materials is 45°, while for “classical” antiferroelectric liquid crystals (AFLC) it reaches typically 30°. Homogeneously oriented slab of OAFLC, unwound by surface action of cell walls is apparently optically isotropic for the light beam at normal incidence. Such unwound structure of OAFLC one can call isotropic OAFLC (IOAFLC). Optical indicatrix of OAFLC is represented by an oblate sphere (ellipsoid of revolution) with its short axis perpendicular to cell walls. Here the question arises: “Is it possible to create isotropic AFLC (IAFLC)? An effective refractive index of IAFLC should have the same value for the light beam propagating at each direction, hence the optical indicatrix should be a sphere. In the way of theoretical considerations we found that IAFLC can exist for twisted structure of AFLC characterized by the tilt angle as high as 54.3°. Unfortunately, such a big tilt angle is still not achievable in practice. Calculations show that AFLC can be optically isotropic when the helix is not suppressed by cell walls action.