Looking inside a 3D scattering medium to observe the 3D spatially-resolved optical energy density that is enhanced by wavefront shaping

It is well known that a thick scattering medium (e.g. a slab of paint) is opaque since incident waves are thoroughly scrambled [1, 2]. In the diffusive transport regime, the scattered light has an (ensemble-averaged) energy density that linearly increases with depth from the front surface to about one mean free path 1, and then decreases linearly with depth to the back surface. Two main questions arise: (A) Can one increase (or decrease) the energy density? (B) What is the new position-dependence? Answers to these questions are crucial for light-matter interactions with applications to white LEDs, random lasers, solar cells, and biomedical optics.Therefore, we report here on a wavefront shaping experiment on ZnO samples ((=580 nm [2]). Dilute single fluorescent nanospheres probe the local energy density. The depth z of each single sphere is obtained by modelling the observed intensity pattern with diffusion theory for a point source. The wavefront is shaped to yield a bright spot at the back surface, which closely corresponds to the excitation of a so-called open transmission channel [5]. The resulting energy density enhancement is obtained from the ratio of the emitted fluorescence power measured with shaped incident wavefronts to that measured with reference wavefronts. Fig. 1 shows that results on a 3D sample with thickness L/l = 28 provide affirmative answers to both questions above: (A) the internal energy density is strongly redistributed by wavefront shaping. (B) The redistribution is strongly depth dependent. The energy density is enhanced compared to the diffusive case, and increases when approaching the back surface, contrary to 1D theory. In contrast, our newly developed 3D theory successfully models the data without adjustable parameters.