Geometric frustration, the inability of an ordered system to find a unique ground state plays a key role in a wide range of systems. We present a new experimental approach to observe large-scale geometric frustration with 1500 negatively coupled lasers arranged in a kagome lattice. We show how dissipation drives the lasers into a phase-locked state that directly maps to the classical XY spin Hamiltonian ground state. In our system, frustration is manifested by the lack of long range phase ordering. Finally, we show how next-nearest-neighbor coupling removes frustration and restores order.

An efficient method to tune the spatial coherence of a degenerate laser over a broad range with minimum variation in the total output power is presented. It is based on varying the diameter of a spatial filter inside the laser cavity. The number of lasing modes supported by the degenerate laser can be controlled from 1 to 320,000, with less than a 50% change in the total output power. We show that a degenerate laser designed for low spatial coherence can be used as an illumination source for speckle-free microscopy that is 9 orders of magnitude brighter than conventional thermal light.One of the important characteristics of lasers is their spatial coherence. With high spatial coherence the light that emerges from the lasers can be focused to a diffraction limited spot or propagate over long distances with minimal divergence. Unfortunately, high spatial coherence also results in deleterious effects such as speckles, so the lasers cannot be exploited in many fullfield imaging applications 1 .Traditional light sources usually operate at the two extremes, with lasers and super luminescent diodes exhibiting very high spatial coherence and thermal sources or light emitting diodes (LEDs) having very low spatial coherence. Yet, for many applications, a light source with partial or even tunable spatial coherence is needed. Often, sources with an intermediate degree of spatial coherence can be exploited before significant speckles are formed, depending on the scattering properties of the sample and the illumination and collection optics 2-4 . Such sources could provide some of the advantages of laser sources, such as improved photon degeneracy, directionality, spectral control, and efficiency, as compared to thermal sources or LEDs with low spatial coherence. Sources with partial spatial coherence are also able to mitigate noise due to coherent artifacts in digital holographic microscopes 5,6 . Recently, new imaging modalities, such as HiLo microscopy, combine information collected with both high and low spatial coherence sources to obtain images that are superior to those obtained with either source alone 7 . Thus, there is a considerable need for light sources offering intermediate spatial coherence and, in particular, sources in which the spatial coherence can be tailored to the application.While the spatial coherence of LEDs or thermal sources can be increased through spatial filtering, their corresponding output energies are significantly reduced. A more efficient approach could be to reduce the spatial coherence of laser sources by placing a time varying optical diffuser in the output light path. Unfortunately, this involves moving parts and long acquisition times [8][9][10] . Recently, random lasers were shown to exhibit tunable spatial coherence 11 and the ones engineered for low spatial coherence were incorporated in full-field imaging applications to obtain images whose quality is similar to those obtained with traditional low spatial coherence sources such as LEDs 12 . Unfortunately, random lasers have relative...

Focusing light through dynamically varying heterogeneous media is a sought-after goal with important applications ranging from free-space communication to nano-surgery. The underlying challenge is to control the optical wavefront with a large number of degrees-of-freedom (DOF) at timescales shorter than the medium dynamics. Recently, many advancements have been reported 1-15 , following the demonstration of focusing through turbid samples by wavefrontshaping, using spatial light modulators (SLMs) having >1000 DOF 2 . Unfortunately, SLM-based wavefront-shaping requires feedback from a detector/camera and is limited to slowly-varying samples 13. Here, we demonstrate a novel approach for wavefront-shaping using all-optical feedback. We show that the complex wavefront required to focus through highly scattering samples, including thin biological tissues, can be generated at sub-microsecond timescales by the process of field self-organization inside a multimode laser cavity, without requiring electronic feedback or SLMs. This wavefront-shaping mechanism is more than 10 5 faster than state-of-the-art 13 , reaching the timescales required in many applications.

Synchronization in large laser networks with both homogeneous and heterogeneous coupling delay times is examined. The number of synchronized clusters of lasers is established to equal the greatest common divisor of network loops. We experimentally demonstrate up to 16 multicluster phase synchronization scenarios within unidirectional coupled laser networks, whereby synchronization in heterogeneous networks is deduced by mapping to an equivalent homogeneous network. The synchronization in large laser networks is controlled by means of tunable coupling and self-coupling.

We experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish the fundamental rules that govern their state of synchronization. We identified a specific substructure that imposes its synchronization state on the entire network and show that for any coupling configuration the network forms at most two synchronized clusters. Our results indicate that the synchronization state of the network is a nonlocal phenomenon and cannot be deduced by decomposing the network into smaller substructures, each with its individual synchronization state.