Wave scattering in random layered media
The scaling and statistics of the transport of waves in random media depend strongly on the dimensionality of the medium. The statistic of transmission in one dimension (1D) and quasi-1D (Q1D) have been calculated and tested. However, the statistic for other dimensions has not been established. Exploring transport in a layered system of stacks of glass cover slips with transverse nonuniformity has allowed us to study a dimensional crossover in transport from 1D towards 3D. The crossover occurs when the lateral spread of the wave become larger than the transverse coherence length in the transmitted speckle pattern as the number of layers increases.
In thin samples, in which light does not spread beyond a single coherence area of the field on the output surface, the statistics of normalized intensity follow 1D statistics associated with a segment of a log-normal distribution with a sharp drop below the log-normal distribution for low values of intensity. Once the lateral spread is larger than the transverse coherence length, the probability density of intensity becomes a mixture of a mesoscopic distribution and an intensity distribution of a Gaussian field. This distribution was originally found for Q1D. Beyond 1D, the intensity statistics have a same form as Q1D statistics which is a function of a single localization parameter, the "statistical conductance" g'. This transition from 1D to Q1D statistics reflects a topological change in the transmitted field. In 1D, the transmitted intensity never vanishes, while beyond 1D, a speckle pattern built upon a network of phase singularities forms.
Condensed matter physics;
0611: Condensed matter physics