Transverse confinement of ultrasound through the Anderson transition in three-dimensional mesoglasses

Abstract

We report an in-depth investigation of the Anderson localization transition for classical waves in three dimensions (3D). Experimentally, we observe clear signatures of Anderson localization by measuring the transverse confinement of transmitted ultrasound through slab-shaped mesoglass samples. We compare our experimental data with predictions of the self-consistent theory of Anderson localization for an open medium with the same geometry as our samples. This model describes the transverse confinement of classical waves as a function of the localization (correlation) length, ξ (ζ), and is fitted to our experimental data to quantify the transverse spreading/confinement of ultrasound all of the way through the transition between diffusion and localization. Hence we are able to precisely identify the location of the mobility edges at which the Anderson transitions occur.

Anisotropy of localized states in an anisotropic disordered medium

“…It allows different types of waves to be studied in a common framework, thus facilitating the identification of the key similarities and differences between light, sound and elastic waves. In particular, the model has provided a plausible explanation for the lack of experimental evidence of localization of light [11,12] while confirming that Anderson localization of elastic waves is very much similar to that of scalar waves, as convincingly demonstrated in experiments [13][14][15]. In addition, it has enabled the calculation of the critical exponent of the localization transition for scalar [16] and elastic [17] waves as well as for light scattered by atoms in a strong magnetic field [18].…”

Localized modes on a metasurface through multi-wave interactions

“…In theory, there is no mobility edge for two-dimensional systems 3 , and to get a clear signature of a localized state, we only need a localization length that is a lot shorter than L of the sample. It might be asked why this appears here in particular, at the flexural resonances inside the bandgap, and not somewhere else.…”

“…In a strongly disordered scattering medium, it is possible to trap waves into energy loops 1 . At the sample size, the trapping induces spatial renormalization of the diffusion coefficient, which highlights the nonconventional transport property of the medium [2][3][4][5] . The diffusion process can then be stopped without the use of absorption, on a length known as the localization length.…”

Transient critical regime for light near the three-dimensional Anderson transition

“…Fit parameters were w 2 (t) (a free parameter for each time t), and A, which was held constant over time. Note that while the shape of I(∆r, t) is only strictly expected to be Gaussian when the diffusion approximation applies, w 2 (t) can still give a good quantification of spatio-temporal energy spreading [5], and that in any case, I(∆r, t) is well-described by a Gaussian for the entire time range under investigation (Fig. 3).…”

“…Strong scattering generally occurs when the wavelength of propagating waves is comparable to the scale of structure variations in the medium, so that the waves are extremely sensitive to the size and arrangement of the scatterers. For strong enough disorder and scattering strength, Anderson localization can occur, wherein wave diffusion is suppressed exponentially or even halted altogether [1][2][3][4][5]. In particular, three-dimensional (3D) materials are expected to exhibit a phase transition [6] from conventional diffusion to localization, occurring as disorder/energy is varied, or alternately, as the time spent by the waves exploring the sample increases.…”