Engineering light localization in a fractal waveguide network

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.

8 pages, 4 figures. arXiv admin note: text overlap with arXiv:1204.4986

References in corpus (4)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Adiabaticity and localization in one-dimensional incommensurate lattices
• Staggered and extreme localization of electron states in fractal space