Enhanced wave transmission in random media with mirror symmetry

Abstract

We present an analysis of enhanced wave transmission through random media with mirror symmetry about a reflecting barrier. The mathematical model is the acoustic wave equation and we consider two setups, where the wave propagation is along a preferred direction: in a randomly layered medium and in a randomly perturbed waveguide. We use the asymptotic stochastic theory of wave propagation in random media to characterize the statistical moments of the frequency dependent random transmission and reflection coefficients, which are scalar valued in layered media and matrix valued in waveguides. With these moments, we can quantify explicitly the enhancement of the net mean transmitted intensity, induced by wave interference near the barrier.

Figures (9)

• Figure 2.1: Schematic of transmission and reflection in the random medium with mirror symmetry about the thin barrier located at $z \in (-d/2,d/2)$.
• Figure 2.2: Mean transmitted intensity $\mathbb{E}[ |\mathcal{T}|^2 ]$ of the system as a function of the strength $L/L_{\rm loc}$ of the randomly scattering medium in the absence of the barrier. Left: The black solid line is the result \ref{['eq:mean3']} for symmetric media and the red dashed line is the result \ref{['eq:mean5']} for independent media. Right: Ratio of the mean transmission of independent media and the mean transmission of symmetric media.
• Figure 2.3: Left: Mean transmission $\mathbb{E}[|{\@fontswitch{}{\mathcal{}} T}|^2]$ of the system as a function of the strength $L/L_{\rm loc}$ of the randomly scattering medium; the black solid line corresponds to the symmetric media and the red dashed line corresponds to the independent media. Right: the mean transmission $\mathbb{E}[|T|^2]$ of one random section (dashed) and the transmission $|T_1|^2$ of the barrier (dot-dashed). Here $|T_1|^2=0.4$.
• Figure 2.4: Same as in Figure \ref{['fig:comp2']} but but for a more reflecting barrier with $|T_1|^2=0.1$.
• Figure 3.1: Waveguide occupying the domain $\Omega = (-X/2,X/2) \times \mathbb{R}$ filled at $|z| \in (d/2,L)$ with a random medium with mirror symmetry about the thin barrier located at $|z| < d/2$.

Theorems & Definitions (8)

• Lemma 2.1
• Lemma 2.2
• Theorem 1
• Lemma 1
• Theorem 2
• Theorem 3
• Proposition 1
• Lemma 2