Fractal waveguide arrays induce maximal localization

TL;DR

This paper demonstrates that fractal potentials in waveguide arrays can induce maximal light localization, revealing a phase transition between localized and delocalized states in 1D and 2D structures, with implications for optical transmission.

Contribution

It introduces fractal potentials as a novel method to achieve maximal localization in waveguide arrays, surpassing disorder-based approaches.

Findings

Fractal potentials induce maximal localization in waveguide arrays.

A localization-delocalization phase transition exists in 1D and 2D structures.

Optimal localization is achieved with strongly detuned waveguides using fractal patterns.

Abstract

The ability to transmit light through an array of closely packed waveguides while minimizing interwaveguide coupling has important implications for fields such as discrete imaging and telecommunications. Proposals for achieving these effects have leveraged phenomena ranging from Floquet-induced flat bands to Anderson localization. Here we demonstrate that, for strongly detuned waveguides, optimal localization is achieved not by disorder but by fractal potentials. We further show that, in both 1D and 2D, these structures possess a localization-delocalization phase transition.