Prof. A. Douglas Stone, Yale University

"The Renaissance of Mesoscopic Transport Physics in Optics"

Abstract: Anderson Localization, Weak Localization and Mesoscopic Fluctuations in electron transport taught us decades ago that coherence effects have a critical influence on the propagation of electron waves in normal metals at low temperatures. In particular interference effects induced by self-crossing paths generate correlations between diffusing waves that are absent for diffusing classical particles. These can lead to localization, enhanced backscattering and anomalously large fluctuations. A further extraordinary implication of these correlations is that there always exist sample-specific input states (“open channels”) that will propagate with unit transmission through a phase coherent diffusive wire of length L, despite its low average transmission, <T> = lt/L <<1 (lt is the transport mean free path). This prediction was impossible to test directly with electron waves due to lack of control of the input states. However, it was appreciated some time ago [1] that similar effects occur in transmission of light through strong scattering and weakly absorbing media (“white paint”), and recent instrumental advances in modern optics have made it possible to synthesize sample-specific input states and hence to exert control over the propagation of light in diffusive media via such interference effects. Not only have the open channels been observed directly for the first time, in addition significant enhancements of focused transmission and total transmission through a wide disordered sample have been demonstrated [2-4]; the latter being relevant for biomedical imaging applications. To describe theoretically the optimal control of diffusing light in an open medium it is essential to go beyond the standard random matrix theory of disordered conductors to take into account the coherence of the input beam and the reduction of control of the output beam due to transverse diffusion [5]. I will briefly review recent experiments that demonstrate control of diffusing light in good agreement with that theory.

[1] “The Question of Classical Localization: A Theory of White Paint?”, P. W. Anderson, Phil. Mag B52, 505 (1985).
[2] “Universal Optimal Transmission of Light Through Disordered Materials”, I. M. Vellekoop and A. P. Mosk, Physical Review Letters, 101, 120601 (2008).
[3] “Coherent control of transmission of light through disordered media”, S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, Physical Review Letters, 112, 133903 (2014).
[4] “Correlation effects in focused transmission through disordered media”, C. W. Hsu, S.-F. Liew, A. Goetschy, H. Cao and A. D. Stone, Nature Physics, 13, 497–502 (2017).
[5] “Filtering random matrices: The effect of imperfect channel control in multiple-scattering”, A. Goetschy and A. D. Stone, Physical Review Letters, 111, 063901 (2013).