Optical gratings formed in thin smectic films frustrated on a single crystalline substrate.

Through the combination of three different, complementary techniques (optical microscopy, x-ray diffraction and atomic force microscopy), we reveal the deformations inside thin smectic films frustrated between two interfaces imposing antagonistic anchorings. We study the model system, 4-n-octyl-4'-cyanobiphenyl (8CB) between MoS2 and air, which is characterized by the competition between homeotropic anchoring at air and planar unidirectional anchoring on the substrate, with thicknesses varying around 0.3 microm. Optical microscopy and x-ray diffraction demonstrate the continuous topology of smectic layers between the interfaces, which are stacked into periodic flattened hemicylinders. These latter are one-dimensional (1D) focal conic domains which form an optical grating in the smectic film, of a period ranging from 1 to 2.5 microm. The interpretation of our results through an energetic model, associated with the atomic force microscopy (AFM) measurements, shows the presence below a critical thickness of a new type of curvature wall between neighboring hemicylinders.