Localization or classical diffusion of light?

Abstract

Wiersma et al. reply — Scheffold et al. have compared different data sets from our group and suggest that our evidence for localization is not conclusive and that the role of absorption should be characterized further. We believe that their analysis is misleading, and that our conclusions about localization are still valid.

Main

Scheffold et al. compared our data on coherent backscattering from GaAs powders¹ with our previously published data² on coherent backscattering from TiO₂. From a comparison of the widths of the cones, they estimate the inverse of the scattering strength, kl *, of our GaAs samples, where k is the wavevector of the light and l * is the mean free path. However, the GaAs data were recorded using linearly polarized light, whereas the TiO₂data were recorded with circularly polarized light². This difference is fundamental, as linearly polarized light inherently gives a smaller enhancement factor (the top of the cone is lower) than circularly polarized light. To overlay our two data sets, Scheffold et al. scaled the y -axis of one of the data sets and shifted the zero of its y -axis. The results are misleading, however, because shifting the zero also changes the full width at half maximum of the cone, and so gives the wrong value of kl *, because the width is inversely proportional to kl *.

To illustrate the inconsistency of this approach, we repeated the procedure used by Scheffold et al., but keeping the TiO₂instead of the GaAs data fixed, and scaling and shifting the y -axis of the GaAs data. The result indicated that the backscattering cone from GaAs is three times wider than that from TiO₂, which corresponds to a scattering strength of the GaAs samples of kl * = 1.7, instead of 5.0. This shows that manipulating the y -axis leads to strongly varying and thereby inconsistent conclusions about the same experiment.

A strong argument against absorption, for example from surface states, is that the shape of the bandgap does not change upon grinding (see the temperature measurements in Fig.1 in ref. 1). Additional evidence that excludes absorption is the observation that the top of the backscattering cone remains triangular while the surrounding region becomes round. This is exactly the behaviour expected at the localization transition, whereas in the case of absorption, the top of the cone would never be triangular. However, Scheffold et al. have replotted our data in Fig. 1ain such a way that this triangular shape is obscured by the use of larger symbols.

Scheffold et al. use classical diffusion theory with absorption to fit our transmission data (Fig. 1b). An absorption fit yields a χ² of 0.033, whereas our fit with scaling theory (that is, with the desired L ^-2 behaviour instead of exponential decay) yields a better value of 0.0053. Our independent, new transmission measurements using GaAs powders (Fig. 2) show L ^-2 behaviour over two orders of magnitude, confirming again the scaling behaviour at the localization transition and the absence of absorption.

Figure 2: Comparison of scaling theory and classical diffusion using transmission coefficients of a GaAs sample.

Scaling theory, solid line; classical diffusion with absorption, broken line. Average particle diameter is 1 μm, mean free path l * is 0.59 μm, and absorption length L _ais 9.6 μm. Data show the L ^-2 behaviour characteristic of the localization transition, and cannot be fitted as classical diffusion with absorption.

See also - Scheffold et al. ¹