Enhanced wave localization in multifractal scattering media

TL;DR

This study demonstrates that multifractal arrays of electric dipoles exhibit enhanced wave localization and unique spectral properties, offering new insights for designing advanced nanophotonic systems with strong light-matter interactions.

Contribution

It introduces the role of multifractal structural correlations in wave localization, showing enhanced effects compared to monofractals and homogeneous fractals.

Findings

Enhanced localization in multifractals versus monofractals

Absence of level repulsion in strong scattering regime

Power-law statistics of level spacings

Abstract

In this paper we study the structural, scattering, and wave localization properties of multifractal arrays of electric point dipoles generated from multiplicative random fields with different degrees of multiscale correlations. Specifically, using the rigorous Green's matrix method, we investigate the scattering resonances and wave localization behavior of systems with $N=10^{4}$ dipoles and demonstrate an enhanced localization behavior in highly inhomogeneous multifractal structures compared to homogeneous fractals, or monofractals. We show distinctive spectral properties, such as the absence of level repulsion in the strong multiple scattering regime and power-law statistics of level spacings, which indicate a clear localization transition enhanced in non-homogeneous multifractals. Our findings unveil the importance of multifractal structural correlations in the multiple scattering regime of electric dipole arrays and provide an efficient model for the design of multiscale nanophotonic systems with enhanced light-matter coupling and localization phenomena beyond what is possible with traditional fractal systems.