34 research outputs found
Local symmetry dynamics in one-dimensional aperiodic lattices
A unifying description of lattice potentials generated by aperiodic
one-dimensional sequences is proposed in terms of their local reflection or
parity symmetry properties. We demonstrate that the ranges and axes of local
reflection symmetry possess characteristic distributional and dynamical
properties which can be determined for every aperiodic binary lattice. A
striking aspect of such a property is given by the return maps of sequential
spacings of local symmetry axes, which typically traverse few-point symmetry
orbits. This local symmetry dynamics allows for a classification of inherently
different aperiodic lattices according to fundamental symmetry principles.
Illustrating the local symmetry distributional and dynamical properties for
several representative binary lattices, we further show that the renormalized
axis spacing sequences follow precisely the particular type of underlying
aperiodic order. Our analysis thus reveals that the long-range order of
aperiodic lattices is characterized in a compellingly simple way by its local
symmetry dynamics.Comment: 15 pages, 12 figure
Local symmetries and perfect transmission in aperiodic photonic multilayers
We develop a classification of perfectly transmitting resonances occuring in
effectively one-dimensional optical media which are decomposable into locally
reflection symmetric parts. The local symmetries of the medium are shown to
yield piecewise translation-invariant quantities, which are used to distinguish
resonances with arbitrary field profile from resonances following the medium
symmetries. Focusing on light scattering in aperiodic multilayer structures, we
demonstrate this classification for representative setups, providing insight
into the origin of perfect transmission. We further show how local symmetries
can be utilized for the design of optical devices with perfect transmission at
prescribed energies. Providing a link between resonant scattering and local
symmetries of the underlying medium, the proposed approach may contribute to
the understanding of optical response in complex systems.Comment: 8 pages, 4 figure