Broadband-Enhanced Transmission through Symmetric Diffusive Slabs

We report on a significant and broadband enhancement of the transmission through an opaque barrier, when placed between symmetric diffusive disordered slabs. The transmission enhancement is accompanied by a bimodal distribution of the transmission eigenvalues, and, for a given transmittance of the barrier, it finds an optimal value for a particular length of the disordered slabs. A simple model allows us to quantify the scalings between the parameters that show that the stronger the barrier, the stronger the maximum possible enhancement. The sensitivity to symmetry defects is also explored, displaying potential interest for wave based sensing.

Figure 1

Sketches of the studied scattering systems. (a) Opaque barrier in an otherwise homogeneous Q1D waveguide. (b) Same as (a), with randomly distributed scatterers on both sides of the barrier. (c) Same as (b), but with a left-right symmetry of the scatterers position. (d) Typical open eigenchannel in the symmetrical case, as sketched in (c).

Figure 2

Enhanced transmission through an opaque barrier, when surrounded by a left-right symmetric disordered medium. The conductance is plotted over the frequency range $(N-1)\pi <k<N\pi$, with $N=300$ and $k$ the wave number. Three configurations are considered. Black: the barrier alone, with a “strength” parameter $\alpha =0.133$ (see Supplemental Material [36]). Red: the barrier, in the middle of a disordered slab with length $L=5$ and mean free path $\ell =0.140$. Blue: the barrier, in the middle of a left-right symmetric disorder slab (same $L$ and $\ell$). In the last two cases, the conductance is not averaged and comes from a single realization of the disorder.

Figure 3

Transmission eigenvalues distributions. Blue colored data correspond to a symmetric disorder and red ones to ordinary disorder. Filled circles: without barrier. Open circles: with barrier. The frequency is such that $N=300$, and the length of the disordered region is $L=5$.

Figure 4

Average conductance of the symmetric configuration, as a function of the length of the diffusive medium (in mean free path unit: $s=L/\ell$), for various values of the barrier transmittance. Colored dots: full wave numerics, averaged over 100 iterations of the disorder; squares: random matrix theory; solid lines: empirical formula (4). The black symbols correspond to the configuration without barrier. In this case, the conductance follows the Ohmic behavior (3) predicted by the Dorokhov-Mello-Pereyra-Kumar theory [4, 5, 6] (solid black line). Dividing this result by two gives the dashed line, which passes by the maxima the different curves, as predicted by Eq. (6). The configuration used to gets Fig. 2 is shown by the red cross.

Figure 5

Variations of the maximum conductance enhancement as the inverse square root of the reduced barrier transmittance $\tau$, for different number $N$ of propagating modes in the leads. There is an enhancement when the barrier is set such that $\tau <{\tau }_{\mathrm{c}}\simeq 0.4$.

Figure 6

Decrease of the averaged conductance when shifting a increasing number of scatterers from the initially symmetric configuration. The black horizontal line shows the barrier transmittance $N\tau$. The frequency is such that $N=300$, and the diffusive slab has a length $L=5$ and a mean free path $\ell =0.140$.