Unusual modes and photonic gaps in a Vicsek waveguide network

TL;DR

This paper introduces a Vicsek fractal waveguide network model that exhibits unusual extended electromagnetic modes with power law decay, suggesting a new form of light localization and photonic band gap behavior in fractal structures.

Contribution

It presents a novel waveguide network design based on Vicsek fractals and analyzes its electromagnetic modes and photonic gaps using the RSRG method.

Findings

Unusual extended electromagnetic modes identified.

Power law decay observed in light transmission.

Photonic band gaps vary with system parameters.

Abstract

We propose a simple model of a waveguide network designed following the growth rule of a Vicsek fractal. We show, within the framework of real space renormalization group (RSRG) method, that such a design may lead to the appearance of unusual electromagnetic modes. Such modes exhibit an extended character in RSRG sense. However, they lead to a power law decay in the end-to-end transmission of light across such a network model as the size of the network increases. This, to our mind, may lead to an observation of power law localization of light in a fractal waveguide network. The general occurence of photonic band gaps and their change as a function of the parameters of the system are also discussed.