Shaping the branched flow of light through disordered media.

Electronic matter waves traveling through the weak and smoothly varying disorder potential of a semiconductor show a characteristic branching behavior instead of a smooth spreading of flow. By transferring this phenomenon to optics, we demonstrate numerically how the branched flow of light can be controlled to propagate along a single branch rather than along many of them at the same time. Our method is based on shaping the incoming wavefront and only requires partial knowledge of the system's transmission matrix. We show that the light flowing along a single branch has a broadband frequency stability such that one can even steer pulses along selected branches-a prospect with many interesting possibilities for wave control in disordered environments.

Random anti-lasing through coherent perfect absorption in a disordered medium.

Non-Hermitian wave engineering is a recent and fast-moving field that examines both fundamental and application-oriented phenomena1-7. One such phenomenon is coherent perfect absorption8-11-an effect commonly referred to as 'anti-lasing' because it corresponds to the time-reversed process of coherent emission of radiation at the lasing threshold (where all radiation losses are exactly balanced by the optical gain). Coherent perfect absorbers (CPAs) have been experimentally realized in several setups10-18, with the notable exception of a CPA in a disordered medium (a medium without engineered structure). Such a 'random CPA' would be the time-reverse of a 'random laser'19,20, in which light is resonantly enhanced by multiple scattering inside a disorder. Because of the complexity of this scattering process, the light field emitted by a random laser is also spatially complex and not focused like a regular laser beam. Realizing a random CPA (or 'random anti-laser') is therefore challenging because it requires the equivalent of time-reversing such a light field in all its degrees of freedom to create coherent radiation that is perfectly absorbed when impinging on a disordered medium. Here we use microwave technology to build a random anti-laser and demonstrate its ability to absorb suitably engineered incoming radiation fields with near-perfect efficiency. Because our approach to determining these field patterns is based solely on far-field measurements of the scattering properties of a disordered medium, it could be suitable for other applications in which waves need to be perfectly focused, routed or absorbed.

Focusing inside Disordered Media with the Generalized Wigner-Smith Operator.

We introduce a wave front shaping protocol for focusing inside disordered media based on a generalization of the established Wigner-Smith time-delay operator. The key ingredient for our approach is the scattering (or transmission) matrix of the medium and its derivative with respect to the position of the target one aims to focus on. A specific experimental realization in the microwave regime is presented showing that the eigenstates of a corresponding operator are sorted by their focusing strength-ranging from strongly focusing on the designated target to completely bypassing it. Our protocol works without optimization or phase conjugation and we expect it to be particularly attractive for optical imaging in disordered media.

Principal modes in multimode fibers: exploring the crossover from weak to strong mode coupling.

We present experimental and numerical studies on principal modes in a multimode fiber with mode coupling. By applying external stress to the fiber and gradually adjusting the stress, we have realized a transition from weak to strong mode coupling, which corresponds to the transition from single scattering to multiple scattering in mode space. Our experiments show that principal modes have distinct spatial and spectral characteristic in the weak and strong mode coupling regimes. We also investigate the bandwidth of the principal modes, in particular, the dependence of the bandwidth on the delay time, and the effects of the mode-dependent loss. By analyzing the path-length distributions, we discover two distinct mechanisms that are responsible for the bandwidth of principal modes in weak and strong mode coupling regimes. Their interplay leads to a non-monotonic transition of the average principal mode bandwidth from weak to strong mode coupling. Taking into account the mode-dependent loss in the fiber, our numerical results are in qualitative agreement with our experimental observations. Our study paves the way for exploring potential applications of principal modes in communication, imaging and spectroscopy.

Wave propagation through disordered media without backscattering and intensity variations.

A fundamental manifestation of wave scattering in a disordered medium is the highly complex intensity pattern the waves acquire due to multi-path interference. Here we show that these intensity variations can be entirely suppressed by adding disorder-specific gain and loss components to the medium. The resulting constant-intensity waves in such non-Hermitian scattering landscapes are free of any backscattering and feature perfect transmission through the disorder. An experimental demonstration of these unique wave states is envisioned based on spatially modulated pump beams that can flexibly control the gain and loss components in an active medium.

Spatiotemporal Control of Light Transmission through a Multimode Fiber with Strong Mode Coupling.

We experimentally generate and characterize eigenstates of the Wigner-Smith time-delay matrix, called principal modes, in a multimode fiber with strong mode coupling. The unique spectral and temporal properties of principal modes enable global control of temporal dynamics of optical pulses transmitted through the fiber, despite random mode mixing. Our analysis reveals that well-defined delay times of the eigenstates are formed by multipath interference, which can be effectively manipulated by spatial degrees of freedom of input wave fronts. This study is essential to controlling dynamics of wave scattering, paving the way for coherent control of pulse propagation through complex media.

Invariance property of wave scattering through disordered media.

A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed.

Generating particlelike scattering states in wave transport.

We introduce a procedure to generate scattering states which display trajectorylike wave function patterns in wave transport through complex scatterers. These deterministic scattering states feature the dual property of being eigenstates to the Wigner-Smith time-delay matrix Q and to the transmission matrix t(†)t with classical (noiseless) transmission eigenvalues close to 0 or 1. Our procedure to create such beamlike states is based solely on the scattering matrix and successfully tested numerically for regular, chaotic, and disordered cavities. These results pave the way for the experimental realization of highly collimated wave fronts in transport through complex media with possible applications such as secure and low-power communication.