Nonlinear laser lithography for indefinitely large-area nanostructuring with femtosecond pulses

Dynamical systems based on the interplay of nonlinear feedback mechanisms are ubiquitous in nature(1-5) . 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.