Tensor and complex anchoring in liquid crystals

We propose a tensor description of surface anchoring of liquid crystals (LCs). The model allows one to consider both the homogeneous and inhomogeneous parts of LC anchoring and to calculate the cumulative effect of different treatments as a sum of corresponding tensors. For the planar alignment the tensor representation is reduced to the complex azimuthal anchoring coefficient, whose amplitude and phase determine, respectively, the strength of azimuthal anchoring and the azimuthal angle of the easy axis. We predict and experimentally confirm that two consecutive photoalignment treatments with beams of perpendicular polarizations can compensate each other and restore the initial anchoring.