Wavefront shaping

The propagation of wave can be controlled not only by controlling the medium (correlated disorder), but also by controlling the wave itself. We have been carrying out various studies in this field for many years now. A recent study concerns the control of the length of scattering paths taken by light, or in other words, the residence time of light in a complex medium. Surprisingly, if a medium is illuminated with all the modes available in the surrounding space, the average length takes on a universal value, independent of the level of disorder in the medium [1]. This property was recently verified experimentally in collaboration with a team from the Laboratoire Kastler Brossel (see Fig. 2 (a)) [2]. We have also subsequently shown how to construct a dwell time operator in an arbitrary medium from the scattering matrix [3]. The eigenstates of this operator are the wavefronts that must be sent into the medium to obtain dwell times equal to the corresponding eigenvalues. We have theoretically predicted the complete distribution of dwell times and demonstrated the possibility of modulating these times over several decades. The dwell time operator has also been used to focus a wave on resonators immersed in a complex environment (see Fig. 2(b)) [4].

Figure 2 Examples of light transport engineering induced by wavefront control in disordered media. (a) Invariance of mean path length <s> under Lambertian illumination. Different more or less opaque samples allow the transport mean free path to be modulated over two orders of magnitude, without <s> being affected. (b) Focusing a wave on a resonator (white square) immersed in a medium opaque to plane waves. Focusing is achieved using the dwell time operator, with no prior knowledge of the resonator’s position. (c) Wavefront optimization to increase sensitivity to the presence of absorbers located at depths greater than ten transport mean free paths. The map shows the sensitivity at different depths z.

Overcoming wave scattering to deliver energy in a targeted way, or acquiring information from the depths of opaque media, represent major challenges that wavefront manipulation techniques are now making accessible. In several recent works, an international collaboration involving our team has succeeded in breaking through two important barriers in this field [5] [6]. Firstly, we have succeeded in predicting and measuring the maximum amount of energy that can be delivered by wavefront control at any depth in a scattering medium [7]. Unexpectedly, the deeper the target, the greater the increase in energy. What’s more, this increase is all the greater the more diffusive the medium. These predictions were verified experimentally by Hui Cao’s team at Yale by measuring the deposition matrix, which maps an input wavefront to the field distribution inside the medium.

As part of this collaboration, we have also proposed a protocol to greatly improve the sensitivity of the backscattered signal to local changes in deep layers [8]. Existing protocols took advantage of the separation between source and detector placed on the surface to increase the depth probed. However, these suffered from a very poor signal-to-noise ratio, as the signal collapsed with increasing source/detector distance. By playing with the spatial shaping of the probe wave, we were able to demonstrate theoretically and experimentally a gain that increased with the strength of the disorder and the number of controlled degrees of freedom. This improvement has enabled us to reach depth sensitivity thresholds in excess of ten transport mean free paths (see Fig. 2(c)).