Engineering slow light and mode crossover in a fractal-kagome waveguide network

TL;DR

This paper introduces an exact analytical method to identify and control flat, non-dispersive photonic bands in a fractal-kagome waveguide network, enabling tunable localization of light modes based on fractal geometry.

Contribution

The authors develop a real space renormalization scheme to analyze flat photonic bands in fractal-decorated kagome lattices, overcoming limitations of traditional methods.

Findings

Number of localized modes increases with fractal complexity

Localization length can be tuned by frequency selection

Potential for experimental realization of fractal photonic lattices

Abstract

We present an analytically exact scheme of unraveling a multitude of flat, dispersionless photonic bands in a kagome waveguide strip where each elementary plaquette hosts a deterministic fractal geometry of arbitrary size. The number of non-dispersive eigenmodes grows as higher and higher order fractal geometry is embedded in the kagome motif. Such eigenmodes are found to be localized with finite support in the kagome strip and exhibit a hierarchy of localization areas. The onset of localization can, in principle, be delayed in space by an appropriate choice of frequency of the incident wave. The length scale at which the onset of localization for each mode occurs, can be tuned at will as prescribed here using a real space renormalization method. Conventional methods of extracting the non-dispersive modes in such geometrically frustrated lattices fail as a non-translationally invariant fractal decorates the unit cells in the transverse direction. The scheme presented here circumvents this difficulty, and thus may inspire the experimentalists to design similar fractal incorporated kagome or Lieb class of lattices to observe a multifractal distribution of flat photonic bands.