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 (18)

• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• A Bose-Einstein condensate in a random potential
• Matterwave localization in disordered cold atom lattices
• Multifractal finite-size-scaling and universality at the Anderson transition
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Transmission eigenvalues and the bare conductance in the crossover to Anderson localization
• Adiabaticity and localization in one-dimensional incommensurate lattices
• Nonreciprocal Anderson Localization in Magneto-Optical Random Structures
• Staggered and extreme localization of electron states in fractal space
• A proposed signature of Anderson localization and correlation-induced delocalization in an N-leg optical lattice
• Extended electron states and magneto-transport in a 3-simplex fractal
• On the spatial structure of anomalously localised states in disordered conductors
• Wave propagation in a quasi-periodic waveguide network
• Spin freezing by Anderson localization in one-dimensional semiconductors
• Decoherence-induced conductivity in the discrete 1D Anderson model: A novel approach to even-order generalized Lyapunov exponents
• Anomalous Transmission in a Hierarchical Lattice
• Unusual modes and photonic gaps in a Vicsek waveguide network

Cited by in corpus (7)

• Topology in the Sierpiński-Hofstadter problem
• Engineering slow light and mode crossover in a fractal-kagome waveguide network
• Level-spectra Statistics in Planar Fractal Tight-Binding Models
• Linearized spectral decimation in fractals
• Analytical study of quasi-one dimensional flat band networks and slow light analogue
• Aharonov-Bohm caging of an electron in a quantum fractal
• A fractal geometry immersed in a hierarchical magnetic flux distribution