Dynamical systems based on the interplay of nonlinear feedback mechanisms are ubiquitous in nature [1][2][3][4][5] . Well-understood examples from photonics include mode locking 6 and a broad class of fractal optics 7 , including self-similarity 8 . In addition to the fundamental interest in such systems, fascinating technical functionalities that are difficult or even impossible to achieve with linear systems can emerge naturally from them 7 if the right control tools can be applied. Here, we demonstrate a method that exploits positive nonlocal feedback to initiate, and negative local feedback to regulate, the growth of ultrafast laser-induced metal-oxide nanostructures with unprecedented uniformity, at high speed, low cost and on non-planar or flexible surfaces. The nonlocal nature of the feedback allows us to stitch the nanostructures seamlessly, enabling coverage of indefinitely large areas with subnanometre uniformity in periodicity. We demonstrate our approach through the fabrication of titanium dioxide and tungsten oxide nanostructures, but it can also be extended to a large variety of other materials.The fabrication of nanostructures on surfaces is of paramount importance in nanotechnology and materials science 9 . There are several established techniques, including photolithography, electron-beam lithography, imprint lithography 10 and laser interference lithography 11 , as well as non-conventional approaches such as selfassembly 12 and direct laser writing 13 . These techniques require either high-cost, complex systems or offer limited flexibility. An alternative flexible and potentially very low-cost method is laserinduced periodic surface structuring (LIPSS). The first observation of LIPSS dates back to 1965 14 . However, after almost 50 years and a large body of published work that has demonstrated LIPSS on various metals, semiconductors and glasses [15][16][17][18][19] , the method has not found widespread use due to the stubborn problem of quality control 18,19 .Despite the evident role of self-assembly in the LIPSS process, uniformity and long-range order remain poor, a problem we identified as originating from the fact that the structures are initiated from multiple seed locations concurrently and independently, thereby producing an irregular pattern. Because the process is irreversible, without self-correction, these irregularities become frozen. Our solution to this relies on carefully exploiting feedback mechanisms to tightly regulate the formation of nanostructures induced by ultrashort pulses. This process can be summarized in three steps.(1) The laser beam, with a peak intensity close to the ablation threshold for titanium, is focused on a titanium surface, where it is scattered by existing nanostructures or any surface defects 15 . The interference of the scattered and incident fields leads to intensity variations in the immediate neighbourhood of the scattering point. (2) At points where the threshold intensity for ablation is exceeded, titanium reacts rapidly with O 2 from the air, form...

It is well known that today two main and well studied methods for alignment of liquid crystals has been used, namely: rubbing and photoalignment technologies, that lead to the change of anisotropic properties of aligning layers and long-range interaction of the liquid crystal molecules in a mesophase. In this manuscript, we use the nonlinear laser lithography technique, which was recently presented as a fast, relatively low-cost method for a large area micro and nanogrooves fabrication based on laser-induced periodic surface structuring, as a new perspective method of the alignment of nematic liquid crystals. 920 nm periodic grooves were formed on a Ti layer processed by means of the nonlinear laser lithography and studied as an aligning layer. Aligning properties of the periodic structures of Ti layers were examined by using a combined twist LC cell. In addition, the layer of the nanostructured Ti was coated with an oxidianiline-polyimide film with annealing of the polymer film followed without any further processing. The dependence of the twist angle of LC cells on a scanning speed and power of laser beam during processing of the Ti layer was studied. The azimuthal anchoring energy of Ti layers with a periodic nanostructure was calculated. The maximum azimuthal anchoring energy for the nanostructured Ti layer was about 4.6 × 10 −6 J/m 2 , which is comparable to the photoalignment technology. It was found that after the deposition of a polyimide film on the periodic nanostructured Ti layer, the gain effect of the azimuthal anchoring energy to~1 × 10 −4 J/m 2 is observed. Also, AFM study of aligning surfaces was carried out.

It is well known that the alignment of liquid crystals (LCs) can be realised by rubbing or photoalignment technologies. Recently, nonlinear laser lithography (NLL) was introduced as a fast, relatively low-cost method for large area nano-grating fabrication based on laser-induced periodic surface structuring. In this letter for the first time, the usage of the NLL as a perspective method of the alignment of nematics was presented. By NLL, nanogrooves with about 0.92 μm period were formed on Ti layer. The nanostructured Ti layer (NSTL) was coated with oxidianilinepolyimide film with annealing of the polymer followed without any further processing. Aligning properties of NSTLs were examined with combined twist LC cell. The dependencies of the twist angle of LC cells and azimuthal anchoring energy (AE) of layers on scanning speed and power of laser beam during processing of the Ti layer were the focus of our studies as well. The maximum azimuthal AE, obtained for pure NSTL, is comparable with photoalignment technology. It was found that the deposition of polyimide film on NSTL leads to the gain effect of the azimuthal AE. Also, atomic force microscopy (AFM) study of aligning surfaces was carried out.

In spite of the fact that there are different techniques in the creation of the highquality liquid crystals (LCs) alignment by means of various surfaces, the azimuthal and polar anchoring energies as well as the pre-tilt angle are important parameters to all of them. Here, the modified by a certain manner aligning layers, previously formed by nonlinear laser lithography (NLL), having high-quality nano-periodic grooves on Ti surfaces, recently proposed for LC alignment was studied. The change of the scanning speed of NLL in the process of nano-structured Ti surfaces and their further modification by means of ITO-coating, and deposition of polyimide film has enabled different aligning layers, whose main characteristics, namely azimuthal and polar anchoring energies, were measured. For the modified aligning layers, the dependencies of the twist and pre-tilt angles for LC cells filled by nematic E7 (Δε > 0) and MLC-6609 (Δε < 0) were obtained. Also the contact angle for droplets of isotropic liquid (glycerol), and nematic LCs was measured for the various values of the scanning speed during the laser processing.