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Flat bands in lattices with non-Hermitian coupling
Leykam, Daniel,Flach, Sergej,Chong, Y. D. American Physical Society 2017 Physical Review B Vol.96 No.6
<P>We study non-Hermitian photonic lattices that exhibit competition between conservative and non-Hermitian (gain/loss) couplings. A bipartite sublattice symmetry enforces the existence of non-Hermitian flat bands, which are typically embedded in an auxiliary dispersive band and give rise to nondiffracting 'compact localized states'. Band crossings take the form of non-Hermitian degeneracies known as exceptional points. Excitations of the lattice can produce either diffracting or amplifying behaviors. If the non-Hermitian coupling is fine-tuned to generate an effective pi flux, the lattice spectrum becomes completely flat, a non-Hermitian analog of Aharonov-Bohm caging in which the magnetic field is replaced by balanced gain and loss. When the effective flux is zero, the non-Hermitian band crossing points give rise to asymmetric diffraction and anomalous linear amplification.</P>
Localization of weakly disordered flat band states
Leykam, Daniel,Bodyfelt, Joshua D.,Desyatnikov, Anton S.,Flach, Sergej Springer-Verlag 2017 The European physical journal. B Vol.90 No.1
<P>Certain tight binding lattices host macroscopically degenerate flat spectral bands. Their origin is rooted in local symmetries of the lattice, with destructive interference leading to the existence of compact localized eigenstates. We study the robustness of this localization to disorder in different classes of flat band lattices in one and two dimensions. Depending on the flat band class, the flat band states can either be robust, preserving their strong localization for weak disorder W, or they are destroyed and acquire large localization lengths xi that diverge with a variety of unconventional exponents v, xi similar to 1/W-v.</P>
Nonreciprocity in synthetic photonic materials with nonlinearity
Chen, Weijian,Leykam, Daniel,Chong, Y.D.,Yang, Lan Cambridge University Press (Materials Research Soc 2018 MRS bulletin Vol.43 No.6
<▼1><B>Abstract</B><P/></▼1><▼2><P>Synthetic photonic materials created by engineering the profile of refractive index or gain/loss distribution, such as negative-index metamaterials or parity-time-symmetric structures, can exhibit electric and magnetic properties that cannot be found in natural materials, allowing for photonic devices with unprecedented functionalities. In this article, we discuss two directions along this line-non-Hermitian photonics and topological photonics-and their applications in nonreciprocal light transport when nonlinearities are introduced. Both types of synthetic structures have been demonstrated in systems involving judicious arrangement of optical elements, such as optical waveguides and resonators. They can exhibit a transition between different phases by adjusting certain parameters, such as the distribution of refractive index, loss, or gain. The unique features of such synthetic structures help realize nonreciprocal optical devices with high contrast, low operation threshold, and broad bandwidth. They provide promising opportunities to realize nonreciprocal structures for wave transport.</P></▼2>