Diffusion equation describes the energy density inside a scattering medium such as biological tissues and paint . The solution of the diffusion equation is a sum over a complete set of eigensolutions that shows a characteristic linear decrease with depth in the medium. It is of particular interest if one could launch energy in the fundamental eigensolution, as this opens the opportunity to achieve a much greater internal energy density. For applications in optics, an enhanced energy density is vital for solid-state lighting, light harvesting in solar cells, low-threshold random lasers, and biomedical optics.
Here we demonstrate the first ever selective coupling of optical energy into a diffusion eigensolution of a scattering medium of zinc oxide (ZnO) paint. To this end, we exploit wavefront shaping to selectively couple energy into the fundamental diffusion mode, employing fluorescence of nanoparticles randomly positioned inside the medium as a probe of the energy density. We observe an enhanced fluorescence in case of optimized incident wavefronts, and the enhancement increases with sample thickness, a typical mesoscopic control parameter. We interpret successfully our result by invoking the fundamental eigensolution of the diffusion equation, and we obtain excellent agreement with our observations, even in absence of adjustable parameters .
 R. Pierrat, P. Ambichl, S. Gigan, A. Haber, R. Carminati, and R. Rotter, Proc. Natl. Acad. Sci. U.S.A. 111, 17765 (2014).
 O. S. Ojambati, H. Yilmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, arXiv:1505.08103.
Oluwafemi S. Ojambati, Hasan Yılmaz, Ad Lagendijk, Allard P. Mosk, and Willem L. Vos, "Coupling of light into the fundamental diffusion mode of a scattering medium
(Conference Presentation)," Proc. SPIE 9717, Adaptive Optics and Wavefront Control for Biological Systems II, 971711 (Presented at SPIE BiOS: February 15, 2016; Published: 27 April 2016); https://doi.org/10.1117/12.2212931.4848767682001.
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