Focusing inside Disordered Media with the Generalized Wigner-Smith Operator

Full transmission of vectorial waves through 3D multiple-scattering media

A striking prediction from the random matrix theory (RMT) in mesoscopic physics is the existence of "open channels": waves that use multipath interference to achieve perfect transmission across an opaque disordered medium even in the multiple-scattering regime. Realization of such open channels requires a coherent control of the complete incident wavefront and has only been achieved for scalar waves in two dimensions (2D) so far. Here, we utilize a recently proposed "augmented partial factorization" full-wave simulation method to compute the polarization-resolved scattering matrix from 3D vectorial Maxwell's equations and demonstrate the existence of open channels in 3D disordered media. We examine the spatial profile of such open channels, demonstrate the existence of a bimodal transmission eigenvalue distribution, and study the effects of incomplete polarization control and finite-area illumination. The simulations provide full access to all spatiotemporal properties of the complex wave transport in 3D disordered systems, filling the gap left by experimental capabilities.

Reaching the precision limit with tensor-based wavefront shaping

Perturbations in complex media, due to their own dynamical evolution or to external effects, are often seen as detrimental. Therefore, a common strategy, especially for telecommunication and imaging applications, is to limit the sensitivity to those perturbations in order to avoid them. Here, instead, we consider enhancing the interaction between light and perturbations to produce the largest change in the output intensity distribution. Our work hinges on the use of tensor-based techniques, presently at the forefront of machine learning explorations, to study intensity-based measurements where its quadratic relationship to the field prevents the use of standard matrix methods. With this tensor-based framework, we can identify the maximum-information intensity channel which maximizes the change in its output intensity distribution and the Fisher information encoded in it about a given perturbation. We further demonstrate experimentally its superiority for robust and precise sensing applications. Additionally, we derive the appropriate strategy to reach the precision limit for intensity-based measurements, leading to an increase in Fisher information by more than four orders of magnitude compared to the mean for random wavefronts when measured with the pixels of a camera.

Photon-efficient optical tweezers via wavefront shaping

Optical tweezers enable noncontact trapping of microscale objects using light. It is not known how tightly it is possible to three-dimensionally (3D) trap microparticles with a given photon budget. Reaching this elusive limit would enable maximally stiff particle trapping for precision measurements on the nanoscale and photon-efficient tweezing of light-sensitive objects. Here, we customize the shape of light fields to suit specific particles, with the aim of optimizing trapping stiffness in 3D. We show, theoretically, that the confinement volume of microspheres held in sculpted optical traps can be reduced by one to two orders of magnitude. Experimentally, we use a wavefront shaping-inspired strategy to passively suppress the Brownian fluctuations of microspheres in every direction concurrently, demonstrating order-of-magnitude reductions in their confinement volumes. Our work paves the way toward the fundamental limits of optical control over the mesoscopic realm.

Wave-momentum shaping for moving objects in heterogeneous and dynamic media

Light and sound waves can move objects through the transfer of linear or angular momentum, which has led to the development of optical and acoustic tweezers, with applications ranging from biomedical engineering to quantum optics. Although impressive manipulation results have been achieved, the stringent requirement for a highly controlled, low-reverberant and static environment still hinders the applicability of these techniques in many scenarios. Here we overcome this challenge and demonstrate the manipulation of objects in disordered and dynamic media by optimally tailoring the momentum of sound waves iteratively in the far field. The method does not require information about the object's physical properties or the spatial structure of the surrounding medium but relies only on a real-time scattering matrix measurement and a positional guide-star. Our experiment demonstrates the possibility of optimally moving and rotating objects to extend the reach of wave-based object manipulation to complex and dynamic scattering media. We envision new opportunities for biomedical applications, sensing and manufacturing.

Non-Invasive Self-Adaptive Information States' Acquisition inside Dynamic Scattering Spaces

Pushing the information states' acquisition efficiency has been a long-held goal to reach the measurement precision limit inside scattering spaces. Recent studies have indicated that maximal information states can be attained through engineered modes; however, partial intrusion is generally required. While non-invasive designs have been substantially explored across diverse physical scenarios, the non-invasive acquisition of information states inside dynamic scattering spaces remains challenging due to the intractable non-unique mapping problem, particularly in the context of multi-target scenarios. Here, we establish the feasibility of non-invasive information states' acquisition experimentally for the first time by introducing a tandem-generated adversarial network framework inside dynamic scattering spaces. To illustrate the framework's efficacy, we demonstrate that efficient information states' acquisition for multi-target scenarios can achieve the Fisher information limit solely through the utilization of the external scattering matrix of the system. Our work provides insightful perspectives for precise measurements inside dynamic complex systems.

Wigner-Smith time delay matrix for acoustic scattering: Theory and phenomenology

The Wigner-Smith (WS) time delay matrix relates a lossless system's scattering matrix to its frequency derivative. First proposed in the realm of quantum mechanics to characterize time delays experienced by particles during a collision, this article extends the use of WS time delay techniques to acoustic scattering problems governed by the Helmholtz equation. Expression for the entries of the WS time delay matrix involving renormalized volume integrals of energy densities are derived, and shown to hold true, independent of the scatterer's geometry, boundary condition (sound-soft or sound-hard), and excitation. Numerical examples show that the eigenmodes of the WS time delay matrix describe distinct scattering phenomena characterized by well-defined time delays.

Anti-reflection structure for perfect transmission through complex media

The scattering of waves when they propagate through disordered media is an important limitation for a range of applications, including telecommunications¹, biomedical imaging², seismology³ and material engineering^4,5. Wavefront shaping techniques can reduce the effect of wave scattering, even in opaque media, by engineering specific modes-termed open transmission eigenchannels-through which waves are funnelled across a disordered medium without any back reflection^6-9. However, with such channels being very scarce, one cannot use them to render an opaque sample perfectly transmitting for any incident light field. Here we show that a randomly disordered medium becomes translucent to all incoming light waves when placing a tailored complementary medium in front of it. To this end, the reflection matrices of the two media surfaces facing each other need to satisfy a matrix generalization of the condition for critical coupling. We implement this protocol both numerically and experimentally for the design of electromagnetic waveguides with several dozen scattering elements placed inside them. The translucent scattering media we introduce here also have the promising property of being able to store incident radiation in their interior for remarkably long times.

Optimal Control of Coherent Light Scattering for Binary Decision Problems

Because of quantum noise fluctuations, the rate of error achievable in decision problems involving several possible configurations of a scattering system is subject to a fundamental limit known as the Helstrom bound. Here, we present a general framework to calculate and minimize this bound using coherent probe fields with tailored spatial distributions. As an example, we experimentally study a target located in between two disordered scattering media. We first show that the optimal field distribution can be directly identified using a general approach based on scattering matrix measurements. We then demonstrate that this optimal light field successfully probes the presence of the target with a number of photons that is reduced by more than 2 orders of magnitude as compared to unoptimized fields.

Invariance Property of the Fisher Information in Scattering Media

Determining the ultimate precision limit for measurements on a subwavelength particle with coherent laser light is a goal with applications in areas as diverse as biophysics and nanotechnology. Here, we demonstrate that surrounding such a particle with a complex scattering environment does, on average, not have any influence on the mean quantum Fisher information associated with measurements on the particle. As a remarkable consequence, the average precision that can be achieved when estimating the particle's properties is the same in the ballistic and in the diffusive scattering regime, independently of the particle's position within its nonabsorbing environment. This invariance law breaks down only in the regime of Anderson localization, due to increased C_{0}-speckle correlations. Finally, we show how these results connect to the mean quantum Fisher information achievable with spatially optimized input fields.

Generalization of Wigner time delay to subunitary scattering systems

We introduce a complex generalization of the Wigner time delay τ for subunitary scattering systems. Theoretical expressions for complex time delays as a function of excitation energy, uniform and nonuniform loss, and coupling are given. We find very good agreement between theory and experimental data taken on microwave graphs containing an electronically variable lumped-loss element. We find that the time delay and the determinant of the scattering matrix share a common feature in that the resonant behavior in Re[τ] and Im[τ] serves as a reliable indicator of the condition for coherent perfect absorption (CPA). By reinforcing the concept of time delays in lossy systems this work provides a means to identify the poles and zeros of the scattering matrix from experimental data. The results also enable an approach to achieving CPA at an arbitrary frequency in complex scattering systems.

Coherent Wave Control in Complex Media with Arbitrary Wavefronts

Wavefront shaping (WFS) has emerged as a powerful tool to control the propagation of diverse wave phenomena (light, sound, microwaves, etc.) in disordered matter for applications including imaging, communication, energy transfer, micromanipulation, and scattering anomalies. Nonetheless, in practice the necessary coherent control of multiple input channels remains a vexing problem. Here, we overcome this difficulty by doping the disordered medium with programmable meta-atoms in order to adapt it to an imposed arbitrary incoming wavefront. Besides lifting the need for carefully shaped incident wavefronts, our approach also unlocks new opportunities such as sequentially achieving different functionalities with the same arbitrary wavefront. We demonstrate our concept experimentally for electromagnetic waves using programmable metasurfaces in a chaotic cavity, with applications to focusing with the generalized Wigner-Smith operator as well as coherent perfect absorption. We expect our fundamentally new perspective on coherent wave control to facilitate the transition of intricate WFS protocols into real applications for various wave phenomena.

Compressively sampling the optical transmission matrix of a multimode fibre

The measurement of the optical transmission matrix (TM) of an opaque material is an advanced form of space-variant aberration correction. Beyond imaging, TM-based methods are emerging in a range of fields, including optical communications, micro-manipulation, and computing. In many cases, the TM is very sensitive to perturbations in the configuration of the scattering medium it represents. Therefore, applications often require an up-to-the-minute characterisation of the fragile TM, typically entailing hundreds to thousands of probe measurements. Here, we explore how these measurement requirements can be relaxed using the framework of compressive sensing, in which the incorporation of prior information enables accurate estimation from fewer measurements than the dimensionality of the TM we aim to reconstruct. Examples of such priors include knowledge of a memory effect linking the input and output fields, an approximate model of the optical system, or a recent but degraded TM measurement. We demonstrate this concept by reconstructing the full-size TM of a multimode fibre supporting 754 modes at compression ratios down to ∼5% with good fidelity. We show that in this case, imaging is still possible using TMs reconstructed at compression ratios down to ∼1% (eight probe measurements). This compressive TM sampling strategy is quite general and may be applied to a variety of other scattering samples, including diffusers, thin layers of tissue, fibre optics of any refractive profile, and reflections from opaque walls. These approaches offer a route towards the measurement of high-dimensional TMs either quickly or with access to limited numbers of measurements.

Chaotic scattering with localized losses: S-matrix zeros and reflection time difference for systems with broken time-reversal invariance

Motivated by recent studies of the phenomenon of coherent perfect absorption, we develop the random matrix theory framework for understanding statistics of the zeros of the (subunitary) scattering matrices in the complex energy plane, as well as of the recently introduced reflection time difference (RTD). The latter plays the same role for S-matrix zeros as the Wigner time delay does for its poles. For systems with broken time-reversal invariance, we derive the n-point correlation functions of the zeros in a closed determinantal form, and we study various asymptotics and special cases of the associated kernel. The time-correlation function of the RTD is then evaluated and compared with numerical simulations. This allows us to identify a cubic tail in the distribution of RTD, which we conjecture to be a superuniversal characteristic valid for all symmetry classes. We also discuss two methods for possible extraction of S-matrix zeros from scattering data by harmonic inversion.

Influence of the Local Scattering Environment on the Localization Precision of Single Particles

We study the fundamental limit on the localization precision for a subwavelength scatterer embedded in a strongly scattering environment, using the external degrees of freedom provided by wavefront shaping. For a weakly scattering target, the localization precision improves with the value of the local density of states at the target position. For a strongly scattering target, the localization precision depends on the dressed polarizability that includes the backaction of the environment. This numerical study provides new insights for the control of the information content of scattered light by wavefront shaping, with potential applications in sensing, imaging, and nanoscale engineering.

Optimizing Light Storage in Scattering Media with the Dwell-Time Operator

We prove that optimal control of light energy storage in disordered media can be reached by wave front shaping. For this purpose, we build an operator for dwell times from the scattering matrix and characterize its full eigenvalue distribution both numerically and analytically in the diffusive regime, where the thickness L of the medium is much larger than the mean free path ℓ. We show that the distribution has a finite support with a maximal dwell time larger than the most likely value by a factor (L/ℓ)^{2}≫1. This reveals that the highest dwell-time eigenstates deposit more energy than the open channels of the medium. Finally, we show that the dwell-time operator can be used to store energy in resonant targets buried in complex media, without any need for guide stars.

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.

Controlling light in complex media beyond the acoustic diffraction-limit using the acousto-optic transmission matrix

Studying the internal structure of complex samples with light is an important task but a difficult challenge due to light scattering. While the complex optical distortions induced by scattering can be effectively undone if the medium’s scattering-matrix is known, this matrix generally cannot be retrieved without the presence of an invasive detector or guide-star at the target points of interest. To overcome this limitation, the current state-of-the-art approaches utilize focused ultrasound for generating acousto-optic guide-stars, in a variety of different techniques. Here, we introduce the acousto-optic transmission matrix (AOTM), which is an ultrasonically-encoded, spatially-resolved, optical scattering-matrix. The AOTM provides both a generalized framework to describe any acousto-optic based technique, and a tool for light control and focusing beyond the acoustic diffraction-limit inside complex samples. We experimentally demonstrate complex light control using the AOTM singular vectors, and utilize the AOTM framework to analyze the resolution limitation of acousto-optic guided focusing approaches.

Various techniques combine light and ultrasound to study the inside of strongly scattering samples, beyond the reach of purely optical imaging. Here, Katz et al. introduce the acousto-optic transmission matrix framework that allows to control and focus light beyond the acoustic diffraction limit.