Engineering light localization in a fractal waveguide network

TL;DR

This paper introduces an exact analytical approach to engineer electromagnetic wave localization in a fractal waveguide network, enabling precise control over localization lengths and states within a Vicsek fractal structure.

Contribution

It provides a novel method to precisely engineer and evaluate localized electromagnetic modes in fractal waveguide networks using real space renormalization group techniques.

Findings

Existence of infinitely many localized modes with varying localization lengths.

Ability to control the onset of localization at desired length scales.

Exact calculation of wave vectors for localized states.

Abstract

We present an exact analytical method of engineering the localization of electromagnetic waves in a fractal waveguide network. It is shown that, a countable infinity of localized electromagnetic modes with a multitude of localization lengths can exist in a Vicsek fractal geometry built with diamond shaped monomode waveguides as the 'unit cells'. The family of localized modes form clusters of increasing size. The length scale at which the onset of localization for each mode takes place can be engineered at will, following a well defined prescription developed within the framework of a real space renormalization group. The scheme leads to an exact evaluation of the wave vector for every such localized state, a task that is non-trivial, if not impossible for any random or deterministically disordered waveguide network.