Tunable phononic transparency and opacity with isotopic defects

Abstract

In an isotopically disordered harmonic chain, phonon transmission attenuates exponentially with distance because of multiple scattering by the isotopic defects. We propose a simple method, which is based on the static structure factor, for arranging the isotopic defects to suppress or enhance phonon scattering within a targeted frequency window, resulting in maximization or minimization of phonon transmission. The phononic transparency and opacity effects are demonstrated numerically from the frequency dependence of the transmission coefficient. We briefly discuss how the underlying concept can be extended to the design of aperiodic superlattices to improve or block phononic transmission.

Figures (2)

• Figure 1: (a) Schematic of AGF simulation of the disordered chain sandwiched between two leads. For structured disorder associated with (b) Type I and (c) Type II disorder, we compare their log-averaged transmission spectra $T_{\text{tr}}(\omega)$ (solid line labeled "Suppressed") with $T_{\text{tr}}(\omega)$ for random disorder (dashed line labeled "Random"). The targeted frequency window with suppressed scattering is shaded in yellow. We also compare the transmission-implied structure factor $S_{\text{tr}}(\omega)$ for random (dashed line labeled "Random") and structured disorder (solid line labeled "Suppressed") for (d) Type I and (e) Type II disorder. In addition, we plot the corresponding $\langle S_{\text{id}}(2k(\omega))\rangle$ for structured disorder (dot-dash line labeled "ID spectrum").
• Figure 2: For structured disorder associated with (a) Type III and (b) Type IV disorder, we compare their log-averaged transmission spectra $T_{\text{tr}}(\omega)$ (solid line labeled "Enhanced") with $T_{\text{tr}}(\omega)$ for random disorder (dashed line labeled "Random"). The targeted frequency window with enhanced scattering is shaded in yellow. We also compare the transmission-implied structure factor $S_{\text{tr}}(\omega)$ for random (dashed line labeled "Random") and structured disorder (solid line labeled "Enhanced") for (c) Type III and (d) Type IV disorder. In addition, we plot the corresponding $\langle S_{\text{id}}(2k(\omega))\rangle$ for structured disorder (dot-dash line labeled "ID spectrum").