Phase-gradient metasurfaces have the potential to revolutionize photonics by offering ultrathin alternatives to a wide range of common optical elements, including bulky refractive optics, waveplates, and axicons. However, the fabrication of stateof-the-art metasurfaces typically involves several expensive, timeconsuming, and potentially hazardous processing steps. To address this limitation, a facile methodology to construct phase-gradient metasurfaces from an exposed standard electron beam resist is developed. The method dramatically cuts the required processing time and cost as well as reduces safety hazards. The advantages of the method are demonstrated by constructing high-performance flat optics based on the Pancharatnam-Berry phase gradient concept for the entire visible wavelength range. Manufactured devices include macroscopic (1 cm diameter) positive lenses, gratings exhibiting anomalous reflection, and cylindrical metalenses on flexible plastic substrates.

In many dynamical systems and complex networks time delays appear naturally in feedback loops or coupling connections of individual elements. Moreover, in a whole class of systems, these delay times can depend on the state of the system. Nevertheless, so far the understanding of the impact of such state-dependent delays remains poor with a particular lack of systematic experimental studies. Here we fill this gap by introducing a conceptually simple photonic system that exhibits dynamics of self-organised switching between two loops with two different delay times, depending on the state of the system. On the basis of experiments and modelling on semiconductor lasers with frequency-selective feedback mirrors, we characterize the switching between the states defined by the individual delays. Our approach opens new perspectives for the study of this class of dynamical systems and enables applications in which the self-organized switching can be exploited.

Metasurfaces enable us to control the fundamental properties of light with unprecedented flexibility. However, most metasurfaces realized to date aim at modifying plane waves. While the manipulation of nonplanar wavefronts is encountered in a diverse number of applications, their control using metasurfaces is still in its infancy. Here we design a metareflector able to reflect a diverging Gaussian beam back onto itself with efficiency over 90% and focusing at an arbitrary distance. We outline a clear route towards the design of complex metareflectors that can find applications as diverse as optical tweezing, lasing, and quantum optics. IntroductionMetasurfaces are artificially engineered arrays of subwavelength-spaced optical scatterers patterned on a flat surface [1][2][3][4][5][6]. The basic concept was introduced long ago in millimeter and microwave technology to manipulate the wavefronts of light by spatially patterning an interface [7][8][9][10][11]. Through advances in nanofabrication, this concept has nowadays been extended to visible light, as nanopatterning tools allow us to induce local and abrupt phase changes to light at the subwavelength scale. The wavefronts of reflected and transmitted beams can be engineered nearly at will by adjusting material and geometrical parameters such as size, shape, separation, and orientation of the metasurface building blocks.The subwavelength separation of the metamaterial building blocks not only enables the control of the phase, amplitude, and polarization of light at high spatial resolution, but also avoids the formation of spurious diffraction orders, which appear in conventional diffractive optical systems such as gratings. In the past few years, metasurfaces have been used for applications such as cloaking [12][13][14][15], absorbing and antireflection coatings [16-18], high-resolution imaging [19,20], focusing [21-24], slow light [25], polarization control [26-28], energy harvesting [29], and tunable beam steering [30]. The versatility in their design together with their straightforward fabrication, which usually involves a single-step lithographic process, makes metasurfaces good candidates to realize multifunctional flat photonic devices [3,31,32].Despite large efforts, metasurfaces are most often designed to manipulate plane waves [33][34][35]. This is mainly because a plane wave is independent of the position of illumination on the metasurface, which significantly simplifies the computational complexity during the design stage as it allows for the use of periodic boundary conditions. Light beams with more complex wavefronts do not have this translation symmetry, and therefore require the simulation of full device structures of the order of tens of micrometers. This often leads to design problems that are computationally too expensive even for modern powerful computers. Nevertheless, the possibility of modifying beams with strongly shaped wavefronts rather than plane waves is of very high importance, in particular for reflectors, i.e., optical elements able t...

We analyze the response of two delay-coupled optoelectronic oscillators. Each oscillator operates under its own delayed feedback. We show that the system can display square-wave periodic solutions that can be synchronized in phase or out of phase depending on the ratio between self-and cross-delay times. Furthermore, we show that multiple periodic synchronized solutions can coexist for the same values of the fixed parameters. As a consequence, it is possible to generate square-wave oscillations with different periods by just changing the initial conditions.

We consider a model for two delay-coupled optoelectronic oscillators under positive delayed feedback as prototypical to study the conditions for synchronization of asymmetric square-wave oscillations, for which the duty cycle is not half of the period. We show that the scenario arising for positive feedback is much richer than with negative feedback. First, it allows for the coexistence of multiple in-and out-of-phase asymmetric periodic square waves for the same parameter values. Second, it is tunable: The period of all the square-wave periodic pulses can be tuned with the ratio of the delays, and the duty cycle of the asymmetric square waves can be changed with the offset phase while the total period remains constant. Finally, in addition to the multiple inand out-of-phase periodic square waves, low-frequency periodic asymmetric solutions oscillating in phase may coexist for the same values of the parameters. Our analytical results are in agreement with numerical simulations and bifurcation diagrams obtained by using continuation techniques.