Raman scattering from fractals. Simulation on large structures by the method of moments

TL;DR

This study uses spectral moments to analyze vibrational states and Raman coupling in large fractal-like percolators, revealing complex behaviors and discrepancies with existing theories.

Contribution

It introduces a numerical approach employing spectral moments to investigate Raman scattering in large fractal structures, highlighting limitations of current theories.

Findings

Different scattering mechanisms produce varied coupling coefficients.

Existing scaling theories do not fully explain the results.

Coupling coefficients differ significantly above and at threshold.

Abstract

We have employed the method of spectral moments to study the density of vibrational states and the Raman coupling coefficient of large 2- and 3- dimensional percolators at threshold and at higher concentration. We first discuss the over-and under-flow problems of the procedure which arise when -like in the present case- it is necessary to calculate a few thousand moments. Then we report on the numerical results; these show that different scattering mechanisms, all {\it a priori} equally probable in real systems, produce largely different coupling coefficients with different frequency dependence. Our results are compared with existing scaling theories of Raman scattering. The situation that emerges is complex; on the one hand, there is indication that the existing theory is not satisfactory; on the other hand, the simulations above threshold show that in this case the coupling coefficients have very little resemblance, if any, with the same quantities at threshold.