Inelastic scattering puts in question recent claims of Anderson localization of light

To the Editor

In a recent Letter in Nature Photonics, Sperling et al.¹ reported the observation of Anderson localization of light in three dimensions. In contrast to previous studies, the authors designed their experiment to be insensitive to absorption. To this end, they measured the time-dependent broadening of a high-intensity, short laser pulse transmitted through a highly scattering medium made from compressed TiO₂ powder. In analogy with the case of disordered optical fibres², localized light is expected to be laterally confined to roughly the localization length ξ. Using an ultrafast imaging system, Sperling et al. experimentally observed the saturation of the time-dependent transverse width of the total transmitted light intensity, and from this, they derived the claim for the first unequivocal observation of the three-dimensional localization of light.

In this correspondence, we would like to point out that the Letter of Sperling et al. does not report on the observation of elastic scattering of light waves, which is considered to be a necessary condition for the occurrence of Anderson localization. In his recent PhD thesis³, Wolfgang Bührer (who was supervised by Maret and Aegerter) reported that highly nonlinear contributions exceed the linear (elastic) scattering signal by at least one order of magnitude in the most relevant regime, namely the long-time regime (τ/τ_max ≈ 3 in Fig. 2 of ref. 1). Although such incoherent light makes an extremely small contribution to the total transmission, it becomes the dominant contribution to the late arriving signal once the elastically scattered light has leaked out of the sample. Wavelength-resolved experiments reported in this thesis on samples similar or identical to the ones studied in ref. 1, show that the non-exponential tail of the transmitted pulse disappears when the spectrally shifted contributions are blocked by a band-pass filter.

We believe that the dominant contribution of incoherent light puts in question not only the recent claims by Sperling et al. but also similar claims of localization by the same group in 2006 based on time-resolved measurements alone⁴. The long-time regime lies at the heart of both claims of localization, as this is the regime in which the saturation of the transverse width was observed in ref. 1 and in which the deviation from non-exponential decay was observed in ref. 4. Although Bührer extensively studied this incoherent contribution previously³, it was not mentioned in ref. 1.

We note that it is relatively easy to confuse nonlinear effects with localization in this type of experiment using pulsed laser sources. For example, photons generated by nonlinear processes (such as radiative decay after two-photon absorption) are emitted with a distribution of time delays Δt, which contribute to a narrower transmission profile T(ρ, t) = T_elastic(ρ, t) + T_inelastic(ρ, t − Δt) at the output. The transition from elastic to inelastic scattering in the long-time regime can thus result in an 'apparent' saturation of the transverse width, resembling that of localization. Also, the different particle sizes and the different pressures used to produce samples of varying packing fractions can lead to differences in nonlinear optical coefficients, which can be easily misinterpreted as a localization effect that depends on the scattering strength (kl^*), whereas it is actually a nonlinear optical effect.