Christian V. Morfonios

Local symmetries and perfect transmission in aperiodic photonic multilayers

We develop a classification of perfectly transmitting resonances occuring in effectively onedimensional 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.

Invariants of broken discrete symmetries.

The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

Local symmetries in one-dimensional quantum scattering

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Local symmetry dynamics in one-dimensional aperiodic lattices: a numerical study

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, determined here numerically for certain lattice types. 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 description 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, revealing the presence of dynamical self-similarity. Our analysis thus provides evidence that the long-range order of aperiodic lattices can be characterized in a compellingly simple way by its local symmetry dynamics.

PT-symmetry breaking in waveguides with competing loss-gain pairs

We consider a periodic waveguide array whose unit cell consists of a

Emitter and absorber assembly for multiple self-dual operation and directional transparency

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Exposing local symmetries in distorted driven lattices via time-averaged invariants.

-symmetric quadrimer with two competing loss/gain parameter pairs which lead to qualitatively different symmetry-broken phases. It is shown that the transitions between the phases are described by a symmetry-adapted nonlocal current which maps the spectral properties to the spatially resolved field, for the lattice as well as for the isolated quadrimer. Its site-average acts like a natural order parameter for the general class of one-dimensional

Current control by resonance decoupling and magnetic focusing in soft-wall billiards.

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Magnetoconductance switching in an array of oval quantum dots

-symmetric Hamiltonians, vanishing in the unbroken phase and being nonzero in the broken phase. We investigate how the beam dynamics in the array is affected by the presence of competing loss/gain rates in the unit cell, showing that the enriched band structure yields the possibility to control the propagation length before divergence when the system resides in the broken

Non-local currents and the structure of eigenstates in planar discrete systems with local symmetries

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