Enhancement of Localization in One-Dimensional Random Potentials with Long-Range Correlations

We experimentally study the effect of enhancement of localization in weak one-dimensional random potentials. Our experimental setup is a single-mode waveguide with 100 tunable scatterers periodically inserted into the waveguide. By measuring the amplitudes of transmitted and reflected waves in the spacing between each pair of scatterers, we observe a strong decrease of the localization length when white-noise scatterers are replaced by a correlated arrangement of scatterers.

Figure 1

Schematic view of the waveguide with 100 scatterers. The waveguide is closed by microwave absorbers at both ends. The lower antenna can be placed anywhere within the scattering arrangement.

Figure 2

Profile of intrusion of all $100$ micrometer screws into the waveguide for uncorrelated and correlated random sequence $U_n$. The insets show the corresponding correlation function calculated from the micrometer screw depths [Eq. (7)].

Figure 3

Transmission spectrum $|S_{12}(k)|$ versus position $n$ (vertical scale) of the moving antenna is shown for uncorrelated (a) and correlated (b) disorder. The transmission spectrum $|S_{12}|$ through the whole waveguide is shown by black solid line at the top of each panel. For comparison, the transmission through uncorrelated disorder is added on the top of panel (b) by a yellow dotted line.

Figure 4

The same as in Fig. 3b but for the reflection pattern $|S_{22}(k)|$. The value $|S_{22}|$ is shown for the antenna located between the 41st and 42nd scatterer.

Figure 5

Details of Fig. 4 for wave numbers between 0.50 and 0.80. In this range of wave numbers one can see several enhanced-localized states. Sharp drop of $|S_{22}|$ at $kd/\pi \approx 0.691$ is due to localized states centered at $n\approx 40$.

Figure 6

Profiles of two enhanced-localized states at $kd/\pi \approx 0.63$ (a) and 0.69 (b) for the correlated sequence (marked by vertical dotted lines in Figs. 4, 5. Graph (b) is the state responsible for a sharp decrease of $|S_{22}|$ shown at the top of Fig. 5. Crosses show an exponential decay with a localization length of 10 scatterer spacings.