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...

Silicon is an excellent material for microelectronics and integrated photonics1–3 with untapped potential for mid-IR optics4. Despite broad recognition of the importance of the third dimension5,6, current lithography methods do not allow fabrication of photonic devices and functional microelements directly inside silicon chips. Even relatively simple curved geometries cannot be realised with techniques like reactive ion etching. Embedded optical elements, like in glass7, electronic devices, and better electronic-photonic integration are lacking8. Here, we demonstrate laser-based fabrication of complex 3D structures deep inside silicon using 1 µm-sized dots and rod-like structures of adjustable length as basic building blocks. The laser-modified Si has a different optical index than unmodified parts, which enables numerous photonic devices. Optionally, these parts are chemically etched to produce desired 3D shapes. We exemplify a plethora of subsurface, i.e., “in-chip” microstructures for microfluidic cooling of chips, vias, MEMS, photovoltaic applications and photonic devices that match or surpass the corresponding state-of-the-art device performances.

Holography is the most promising route to true-to-life 3D projections, but the incorporation of complex images with full depth control remains elusive. Digitally synthesised holograms 1 – 7 , which do not require real objects to create a hologram, offer the possibility of dynamic projection of 3D video 8 , 9 . Extensive efforts aimed 3D holographic projection 10 – 17 , however available methods remain limited to creating images on a few planes 10 – 12 , over a narrow depth-of-field 13 , 14 or with low resolution 15 – 17 . Truly 3D holography also requires full depth control and dynamic projection capabilities, which are hampered by high crosstalk 9 , 18 . The fundamental difficulty is in storing all the information necessary to depict a complex 3D image in the 2D form of a hologram without letting projections at different depths contaminate each other. Here, we solve this problem by preshaping the wavefronts to locally reduce Fresnel diffraction to Fourier holography, which allows inclusion of random phase for each depth without altering image projection at that particular depth, but eliminates crosstalk due to near-orthogonality of large-dimensional random vectors. We demonstrate Fresnel holograms that form on-axis with full depth control without any crosstalk, producing large-volume, high-density, dynamic 3D projections with 1000 image planes simultaneously, improving the state-of-the-art 12 , 17 for number of simultaneously created planes by two orders of magnitude. While our proof-of-principle experiments use spatial light modulators, our solution is applicable to all types of holographic media.

A profoundly fundamental question at the interface between physics and biology remains open: what are the minimum requirements for emergence of complex behaviour from nonliving systems? Here, we address this question and report complex behaviour of tens to thousands of colloidal nanoparticles in a system designed to be as plain as possible: the system is driven far from equilibrium by ultrafast laser pulses that create spatiotemporal temperature gradients, inducing Marangoni flow that drags particles towards aggregation; strong Brownian motion, used as source of fluctuations, opposes aggregation. Nonlinear feedback mechanisms naturally arise between flow, aggregate and Brownian motion, allowing fast external control with minimal intervention. Consequently, complex behaviour, analogous to those seen in living organisms, emerges, whereby aggregates can self-sustain, self-regulate, self-replicate, self-heal and can be transferred from one location to another, all within seconds. Aggregates can comprise only one pattern or bifurcated patterns can coexist, compete, endure or perish.

An important goal of self-assembly research is to develop a general methodology applicable to almost any material, from the smallest to the largest scales, whereby qualitatively identical results are obtained independently of initial conditions, size, shape and function of the constituents. Here, we introduce a dissipative self-assembly methodology demonstrated on a diverse spectrum of materials, from simple, passive, identical quantum dots (a few hundred atoms) that experience extreme Brownian motion, to complex, active, non-identical human cells (~10 17 atoms) with sophisticated internal dynamics. Autocatalytic growth curves of the self-assembled aggregates are shown to scale identically, and interface fluctuations of growing aggregates obey the universal Tracy-Widom law. Example applications for nanoscience and biotechnology are further provided.