Light Localization in Multifractal Dielectric Environments

Multifractals are heterogeneous structures with multi-scale properties described by a continuous spectrum of fractal dimensions, i.e., the so-called multifractal singularity spectrum. In contrast to traditional fractals, or monofractals, which possess only one global scaling exponent corresponding to the fractal dimension, multifractals have a broad distribution of generalized fractal dimensions and their structural properties exhibit extreme (heavy-tailed) non-Gaussian fluctuations. While the optical properties of fractal structures are well-understood, multiple scattering, light localization and emission phenomena in multifractal dielectric environments remain to be explored. Using rigorous Green’s matrix and multi-particle Mie scattering theory, in this talk we systematically investigate light-matter interactions in engineered photonic multifractal media. Specifically, we generate multifractal point patterns from random multiplicative processes with different correlation properties that interpolate in a tunable fashion between random structures, monofractals, and strongly inhomogeneous multifractals. We study photonic structures with different values of dielectric constants and analyze their spectral statistics, optical Thouless conductance, and local density of states. Our findings demonstrate that tailored multifractal dielectrics support scattering resonances with a stronger localization (i.e., smaller localization length) compared to both uniform random and monofractal systems across a broad spectrum extending from visible to infrared wavelengths. Device applications of multifractal media for the demonstration of ultracompact spectrometers and novel broadband lasers will also be presented.