5 - Transmission Matrix Approach to Light Control in Complex Media

Summary

While transmission and scattering matrices have been a convenient way to describe wave propagation in complex media in mesoscopic physics, being able to describe important quantities such as total transmission, intensity statistics, etc. it has mainly been studied in this domain from a statistical point of view, i.e. to extract average quantities. Extracting the exact matrix of a given system was never even considered. In this chapter, we will describe how, leveraging on spatial light modulator technologies and the new possibilities offered by digital holography, it is possible to experimentally measure this quantity in the optical domain, not in a statistical sense, but for a particular realization of disorder, i.e. a given system, which will be for most of the experiments described in this chapter an ideal multiply scattering medium, essentially a layer of white paint, but could in principle be biological tissues. Once this information is known, the problem of recovering an image is not bound to be carried using ballistic photons. Indeed, even in the diffusive regime, the result of the propagation of a field can be deterministically predicted for scattered light. In particular, the optimal wavefront that will generate a focus on one or several output modes can be easily extracted from the matrix. We will discuss the various initial implementations of this concept, and its applications for focusing and imaging. Recent developments have shown different ways of either simplifying the procedure, or expanding its capabilities to new domains, for instance the spectral domain.