Using time-resolved transmission measurements, we have found indications of Anderson localization of light in bulk three-dimensional systems. The observed deviation from classical diffusion is in good accord with theoretical predictions of localization and cannot be explained by absorption or experimental artifacts such as stratification, fluorescence, or background illumination. Moreover, we show that in our samples the control parameter is given by the mean free path times the wavenumber as required by the Ioffe-Regel criterion. This is in contrast to quasi-one-dimensional systems that were studied with microwaves. There, the control parameter is related to the number of modes inside a waveguide, and deviations from classical diffusion are possible due to a small number of modes.
Although conservation of energy is fundamental in physics, its principles seem to be violated in the field of wave propagation in turbid media by the energy enhancement of the coherent backscattering cone. In this letter we present experimental data which show that the energy enhancement of the cone is balanced by an energy cutback at all scattering angles. Moreover, we give a complete theoretical description, which is in good agreement with these data. The additional terms needed to enforce energy conservation in this description result from an interference effect between incident and multiply scattered waves, which is reminiscent of the optical theorem in single scattering.
We present an approach to measure the angular dependence of the diffusely scattered intensity of a multiple scattering sample in backscattering geometry. Increasing scattering strength give rise to an increased width of the coherent backscattering and sets higher demands on the angular detection range. This is of particular interest in the search for the transition to Anderson localization of light. To cover a range of −60°to +85°from direct back-reflection, we introduced a new parallel intensity recording technique. This allows one-shot measurements, with fast alignment and short measuring time, which prevents the influence of illumination variations. Configurational average is achieved by rotating the sample and singly scattered light is suppressed with the use of circularly polarized light up to 97%. This implies that backscattering enhancements of almost two can be achieved. In combination with a standard setup for measuring small angles up to ±3°, a full characterization of the coherent backscattering cone can be achieved. With this setup we are able to accurately determine transport mean free paths as low as 235 nm.
The observation of Anderson localization of light has long been hindered by the lack of clear-cut experimental signatures. Static transmission measurements for instance would show an exponential decrease of intensity, which cannot be distinguished from absorption. Here we present time-of-flight measurements of single photons in three-dimensional samples. At long times, localization leads to a less than exponential decrease of transmission, which is observed for very turbid samples. While absorption cannot account for such a non-exponential decay, it is still important to determine the absorption length independently. This can be achieved from reducing the index mismatch of the scatterers and performing similar time-of-flight measurements. Such a decrease of the scattering power of the particles also shows that the only sample property leading to non-classical diffusion is indeed the turbidity 1=kl à as predicted theoretically.
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