Background: The alignment of liquid crystals by surfaces is crucial for applications. It determines the director configuration in the bulk, its stability against defects and electro-optical switching scenarios. The conventional planar alignment of rubbed polymer layers can be locally flipped to vertical by irradiation with a focused ion beam on a scale of tens of nanometers. Results: We propose a digital method to precisely steer the liquid crystal director tilt at polymer surfaces by combining micrometer-size areas treated with focused ion beam and pristine areas. The liquid crystal tends to average the competing vertical and planar alignment actions and is stabilized with an intermediate pretilt angle determined by the local pattern duty factor. In particular, we create micrometer-sized periodic stripe patterns with this factor gradually varying from 0 to 1. Our optical studies confirm a predictable alignment of a nematic liquid crystal with the pretilt angle continuously changing from 0° to 90°. A one-constant model neglecting the difference between the elastic moduli reproduces the results quantitatively correctly. Conclusion: The possibility of nanofabrication of polymer substrates supporting an arbitrary (from planar to vertical) spatially inhomogeneous liquid crystal alignment opens up prospects of "imprinting" electrically tunable versatile metasurfaces constituting lenses, prisms and q-plates.
Keywords: focused ion beam nanopatterning; nematic liquid crystal; optical retardation; pretilt control; surface anchoring.