Scattering in complex environments: Theory, wavefront shaping and system design

Abstract

The scattering of waves is a central feature of many physical systems. Its often very complicated nature has negative ramifications on the capability to achieve certain tasks and therefore on applications due to the perceived destruction of information. Prominent examples of this adverse effect include the reduced line of sight on a foggy day, the limited reception of cell phones and degrading image quality in biomedical imaging. The most important piece of the puzzle to counter this is the precise control over incoming waves and the accurate measurement of the scattered waves. Recent technological advances and their continued development indeed enable us to precisely control not only acoustic, water and microwaves, but also electromagnetic waves in the optical domain and also to measure the associated outgoing fields.In this thesis, we try to provide important insights into this emerging field of wave control in disordered media. Based on the most important tool in scattering theory – the scattering matrix, that takes care of the bookkeeping in scattering processes – we introduce a new capability for the study of scattering problems, which is not restricted to the investigation of a specific subclass of problems but is applicable to all manners of scattering problems with any type of wave. This novel tool, dubbed the generalized Wigner-Smith (GWS) operator, leverages not only information stored in the scattering matrix, but also the response of the scattering matrix to (small) changes in the system.Based on our recent work we put forth a new invariant quantity of wave scattering in disordered systems. Specifically, we exploit the GWS operator and its connection to the Fisher information operator to analytically prove and demonstrate numerically that the scattering strength of the surrounding medium does not have any influence on the mean quantum Fisher information associated with measurements on a point-like particle. This has the counterintuitive consequence, that the average precision associated with estimations of the particle’s properties is the same for systems where ballistic and diffusive wave transport occurs, independently of the particles location. This invariance law only breaks down when the scattering strength enters the regime of Anderson localization. We also present in this thesis a practical application of the GWS operator as a wavefront shaping tool. Our numerical and experimental demonstration shows that the GWS operator provides a simple eigenvalue problem whose solution tells us how to design a wavefront. These wavefronts are judiciously designed such that they are the optimal wave states to deliver the strongest possible force, pressure or torque toa target as well as to achieve the most efficient focus inside the target. This perfect level of efficiency is even reached when the target is hidden inside a (strongly)scattering medium and when its shape is unknown and may be very complicated.Furthermore, we recognize the broad applicability of the GWS operator to all kindsof micromanipulation scenarios and demonstrate that it also serves as a way tocompute the optimal wavefronts for tractor beams. These are wave states that pulltargets closer to their source in the opposite direction of the wave’s momentumflow. From the GWS operator, we also derive an operator that provides us withwavefronts that interact with a target in such way that the target is trapped insidethe wavefield with the optimal trapping stiffness. Our investigation paves the wayto unleash the full potential of shaped waves for manipulating and trapping particlesat the optimal level of efficiency even inside disordered media.One of the hallmarks of the field of wavefront shaping is the creation of wavestates that, when impinging on a disordered medium are fully transmitted without any reflection. These states, however, come in pairs with fully reflecting states andthus we ask ourselves the question if there is an operating procedure such that a disordered medium can be made fully transmitting to all incoming wavefronts. Inthis thesis, we positively answer this proposition and demonstrate numerically andexperimentally that a precisely designed complementary structure put in front ofa disordered medium results in a composite system that is fully transmitting to allincoming wavefronts. Additionally, we propose a new method for the inverse designof scattering structures.