Nonlinear laser lithography for indefinitely large- area nanostructuring with femtosecond pulses Bu ¨lent O ¨ ktem 1† , Ihor Pavlov 2,3† , Serim Ilday 4 , Hamit Kalaycıog ˘lu 2 , Andrey Rybak 2,3 , Seydi Yavas ¸ 1 , Mutlu Erdog ˘an 1 and F. O ¨ mer Ilday 2 * Dynamical systems based on the interplay of nonlinear feed- back 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 techni- cal 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 indefi- nitely large areas with subnanometre uniformity in periodicity. We demonstrate our approach through the fabrication of tita- nium 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, elec- tron-beam lithography, imprint lithography 10 and laser interference lithography 11 , as well as non-conventional approaches such as self- assembly 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 laser- induced 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 15–19 , 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 ident- ified 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 irre- versible, without self-correction, these irregularities become frozen. Our solution to this relies on carefully exploiting feedback mechan- isms 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 inten- sity 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, forming tita- nium dioxide (TiO 2 ). The use of ultrashort pulses is necessary to ensure this process occurs faster than heat diffusion, as this can smear out the nanometre-scale localization of the deposited laser energy. The first two steps constitute a positive feedback loop (Fig. 1a). As the nanostructure grows, so does its scattering power. (3) The growth mechanism also has an imbedded negative feedback loop. As TiO 2 grows on top of the titanium, penetration of O 2 through the oxide layer decreases exponentially, decelerating and eventually halting the growth process (Fig. 1b). The experimental set-up (Fig. 2 and Methods) consists of an ultrafast fibre laser 20 coupled to a microscope system for real-time observation of the nanofabrication process. All experiments were guided by a semi-phenomenological theoretical model developed by us. The main features of the model are summarized in the follow- ing and in the Methods, and the details are discussed in the Supplementary Information. Scattering of the incident laser field from a single point is modelled as dipole radiation 15,16 , with the rela- tive height of the surface point setting the scattering amplitude. This is confirmed experimentally (Fig. 3a) and numerically (Fig. 3b) by the structure formed around an isolated scatterer. The polarization of the laser sets the dipole radiation pattern, which results in regu- larly spaced nanolines parallel to the laser polarization. Circular polarization, which can be visualized as rotating linear polarization, results in an array of nanocircles. The period of the structures ranges between 600 and 900 nm, depending on the film thickness. Because the film is much thinner than the wavelength of light, light experi- ences a sort of a weighted average (effective) index of refraction which depends not only on that of the thin film, but also on those of the air and the substrate above and below the film, respect- ively. The total field at any surface point is the sum of the incident field and the total scattered field, which is given by the integral of the product of the surface height and the incident field over the entire surface. This surface integral is the mathematical origin of the non- local feedback. The amplitude of the dipole radiation decays with distance, which sets a finite range for this nonlocal feedback, such that two distant points on the surface have negligible mutual influ- ence. For this reason, processing a large area at once results in struc- tures with poor long-range order, as seen experimentally (Fig. 3c) and numerically (Fig. 3d). By limiting the size of the laser beam to 10 wavelengths, we ensure that even the most distant points under the beam have contributions to their mutual fields. This way, the problem of independent structure initiation is solved. At points where the total intensity exceeds the ablation threshold (≏1 × 10 12 W cm 22 ), the metal (titanium) disassociates from the solid phase under the non-equilibrium conditions created by the ultrashort pulse and reacts with O 2 from the ambient atmosphere, 1 UNAM—Institute of Materials Science and Nanotechnology, Bilkent University, 06800 Ankara, Turkey, 2 Department of Physics, Bilkent University, 06800 Ankara, Turkey, 3 Institute of Physics, National Academy of Science of Ukraine, Kiev, Ukraine, 4 Department of Micro and Nanotechnology, Middle East Technical University, 06800 Ankara, Turkey; † These authors contributed equally to this work. *e-mail: ilday@bilkent.edu.tr LETTERS PUBLISHED ONLINE: 20 OCTOBER 2013 | DOI: 10.1038/NPHOTON.2013.272 NATURE PHOTONICS | VOL 7 | NOVEMBER 2013 | www.nature.com/naturephotonics 897 © 2013 Macmillan Publishers Limited. All rights reserved.